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TRANSCRIPT
A PERFORMANCE EVALUATION OF A SINGLE-STATION EARTHQUAKE
LOCATION ALGORITHM (LESSLA) IMPLEMENTED AT WDD SEISMIC
STATION, UNIVERSITY OF MALTA
By
Dane Zammit
UNDER THE SUPERVISION OF
Dr. P. Galea
Department of Physics
University of Malta
May 2009
A dissertation presented to the Faculty of Science in part fulfillment of the requirements for the
degree of Bachelor of Science (Hons.) at the University of Malta
Statement of Authenticity
The undersigned declare that this dissertation is based on work carried out under the auspices
of the Department of Physics by the candidate as part fulfillment of the requirements of the
degree of B.Sc. (Hons.)
(name)
Candidate
(name)
Supervisor
1
Abstract
The standard method of analyzing earthquake locations uses large seismic networks consisting
of many seismic stations. As more seismic stations are added the distribution of the networks
are improved, resulting in better solutions.
However there is poor network coverage around the Sicily Channel because established inter-
national networks lack seismic stations in North Africa. Therefore many earthquakes in the
region, particularly those south of Malta are not detected by these networks. An automated
single-station earthquake location algorithm was designed by Agius (2007) to locate local and
regional earthquakes to address the problem of insufficient network coverage. The system was
nicknamed LESSLA (Local Earthquake Single-Station Location Analyzer) and uses the three
components from three different sampling streams of seismic signals to identify and pick major
arrival times and determine the epicentral azimuth from P wave polarization analysis.
In order to make the data more accessible, a website was designed where registered users can
access and modify all seismic data. LESSLA has been successfully implemented and has been
analyzing seismic data for the past three years, so that a good database of events at station
WDD (Wied Dalam, Malta) is now available. It was required to investigate the performance of
LESSLA with regard to several parameters. In this dissertation, the database for 2006-2008 has
been used for this purpose.
During this period, LESSLA detected and located 135 earthquakes, mostly south of Malta, that
were not found in international bulletins. For the whole dataset, an analysis of the automatic
solution was carried out, particularly the weighting scheme used to classify events, and the P-
and S-picking algorithm. The results indicate that the weighted schemes and phase picking
times functioned very well. Less than 10% of earthquakes (40 from 462) and less than 5% of
quarry blasts (24 from 505) were missed. The P- and S- picking algorithm was very accurate,
the histogram of changes made in the picks had very sharp peaks about 0, meaning that many
adjustments made were less than a second.
A comparison of the manually verified LESSLA epicenter solutions was made with solutions from
EMSC/INGV bulletins when available. Both the origin time and final epicentre location of each
earthquake were compared. The error in the origin time was found to be normally distributed
about 0.358s with a standard deviation of 2.45s. The results of the final epicentre location
was also very good with 47% of LESSLA epicentres were within 100 km of the EMSC/INGV
locations. By contrast, only 19% of LESSLA epicentres were more than 300km away from the
published international locations and many of these errors were traced to be because of missing
phases and noise.
The error in the location could be because of errors in the distance calcuation, or errors in the
azimuth. It was found that the azimuth calculation was more unstable and prone to error because
of its dependance on the P-pick and clear strong seismic signals. For short range earthquakes up
to Greece, the distance formula used was accurate but broke down for more distant earthquakes.
The distance formula was recalibrated using the P and S arrival times of LESSLA and the
published locations of the international bulletins.
When the locations of LESSLA epicentres were plotted on a map, several features of the Central
Mediterranean are evident. LESSLA seems to have a longer detectable range to the east from
Greece than to the north from Italy. In fact, while Italy is one of the most seismically active
regions in the Mediterranean, very few earthquakes from the area are detected by WDD. The
seismic signals are being attenuated before they reach Malta, probably due to subduction zones.
On the other hand, the subduction zones in the Greece area do not attenuate the signal, but
seem to be deflecting them, particularly for earthquakes originating from the Hellenic subduction
zone.
I dedicate this dissertation to my parents, Anthony and Francine, who have given me all the
support I needed.
1
Acknowledgments
I would like to show my appreciation to my supervisor Dr. Pauline Galea for her dedication and
guidance throughout the year.
2
Contents
1 Introduction 12
1.1 Medina Wrench Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2 The Situation in Malta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3 Aim of the Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Locating Earthquakes using Multiple Seismic Stations 15
2.1 Wadati Diagrams and the Method of Circles . . . . . . . . . . . . . . . . . . . . 16
2.2 Locating Earthquakes by Forward Modeling . . . . . . . . . . . . . . . . . . . . 17
2.3 The Inverse Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Single Station Epicentre Location and LESSLA 24
3.1 Single Station Locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 The Wied Dalam Observatory and Data Acquisition . . . . . . . . . . . . . . . . 25
3.2.1 Data Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Manual Data Analysis and Computer Automation . . . . . . . . . . . . . . . . . 27
3.4 LESSLA sequence of execution . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3
3.5 Data Processing and Epicentre Location . . . . . . . . . . . . . . . . . . . . . . 29
3.5.1 Event Detection using the STA/LTA algorithm . . . . . . . . . . . . . . 29
3.5.2 Signal to noise ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.3 Creating an Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.4 Voting Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5.5 Phase Picks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.6 Event Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.7 Azimuth and Coherence Estimation . . . . . . . . . . . . . . . . . . . . . 36
3.5.8 Distance Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.5.9 Origin Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.5.10 Latitude and Longitude Location . . . . . . . . . . . . . . . . . . . . . . 40
3.5.11 Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5.12 Generating a Day Report . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 Analyst Procedure 44
4.1 General Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.1.1 Website Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2 Automatic Analysis and E-mail Notification . . . . . . . . . . . . . . . . . . . . 48
4.2.1 E-mail notification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3 The Online Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.4 Analyzing a Single Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4.1 LESSLA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4
4.4.2 Adding Network Information and Visual Comparison . . . . . . . . . . . 58
4.5 Manual Analysis of an event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5.1 Using Seisgram2k to select the P- and S-picks . . . . . . . . . . . . . . . 62
4.5.2 Manually choosing the azimuth . . . . . . . . . . . . . . . . . . . . . . . 66
4.5.3 Obtaining the Final Coordinates and Plotting . . . . . . . . . . . . . . . 67
4.6 Multi-station plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5 Performance Evaluation of LESSLA Epicentre Location 73
5.1 Seismicity of the Region and the Range of LESSLA . . . . . . . . . . . . . . . . 74
5.2 Analysis of the Voting Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3 Evaluation of the Automatic Solution . . . . . . . . . . . . . . . . . . . . . . . . 81
5.3.1 P- and S-Pick Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.4 LESSLA versus EMSC/INGV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.4.1 Origin Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.4.2 Epicentre Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.4.3 Distance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.4.4 Azimuth Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6 Conclusions and Recommendations 104
6.1 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.2 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5
List of Tables
3.1 Event classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.1 Table showing the classification of the triggers for every possible combination of weight. . . . 79
5.2 Preliminary analysis of modifications that were made on the automated analysis . . . . . . . 82
5.3 Table of equations derived using trigonometry and Figure 5.18 . . . . . . . . . . . . . . . 90
6.1 The updated table of coordinate ranges of various regions in the Mediterranean . . . . . . . 108
6
List of Figures
2.1 The Wadati diagram method for determining the origin time of a local earthquake. The best
straight line is drawn through the points, which is extrapolated to the P arrival time axis. The
value at this intercept is the origin time of the earthquake. . . . . . . . . . . . . . . . . . 16
2.2 Circle method for triangulation of an epicentre . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Adjustments of ’epicentral guesses’ are made by plotting the difference between predicted and
observed travel times and epicentral distances. . . . . . . . . . . . . . . . . . . . . . . . 20
4.1 Screenshot of the main page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 The real-time plot of 30 December 2008. There is clearly an earthquake at around 06:20, which
was confirmed later on when the data was processed. . . . . . . . . . . . . . . . . . . . . 47
4.3 An extracted plot of all 9 channels from 6th January 2008 from 04:00 to 08:00, which shows
that there was an earthquake at around 05:00 from the extracted plot. . . . . . . . . . . . 49
4.4 The position of the three seismic station using LESSLA on a Google map. . . . . . . . . . . 50
4.5 Email notification for 6th January 2008. . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.6 The events database page. In this example a query was made to display the 50 most recent
triggers in the time frame specified for all three stations. The search can be refined further to
display events from a certain region, to display only earthquakes, quarry blasts or verified events
and so on. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
7
4.7 The main page of the January 6 earthquake in Greece. This page displays all the available
details of this event, including initial classifications, maps, pdf attachments of all streams (it is
possible to view each stream independently) and comments. By clicking on ’View Analysis’, the
seismologist can look at the azimuth and coherence calculations for the L, B and H streams. . 56
4.8 The all earthquake locations map view for the 6 January 2008 earthquake. This map plots the
LESSLA solution and the external network solution on the same map for visual comparison. In
this case the two solutions are almost exactly the same; this is because the signal was clear with
virtually no noise and the magnitude of the earthquake was high. . . . . . . . . . . . . . . 60
4.9 Main page of the 24 December 2008 earthquake. This earthquake was not processed by LESSLA
because the total weight of the triggered channels was less than the threshold. However, it is
clear from the signal on the seismogram that this is an earthquake. . . . . . . . . . . . . . 61
4.10 Pdf file of all nine streams before manual picking . . . . . . . . . . . . . . . . . . . . . 63
4.11 Viewing the HH components using Seisgram2k . . . . . . . . . . . . . . . . . . . . . . . 64
4.12 Seisgram2k has interactive zooming and scaling of the seismogram to help select the best pick.
In this case the P-pick is selected for the 24 December 2008 earthquake. . . . . . . . . . . . 65
4.13 Pdf file of all nine streams and azimuth and coherence calculations after manual picking. . . . 68
4.14 Updating the record of the 24 December earthquake. . . . . . . . . . . . . . . . . . . . . 69
4.15 Final manually verified solution and Google maps. . . . . . . . . . . . . . . . . . . . . . 70
4.16 The multi-station plot (blue) is typically much closer to the EMSC/INGV location (yellow)
than the single-station location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.1 The seismicity of the region within the detectable range of LESSLA. Many earthquakes in Italy
are attenuated and are not detected by LESSLA. LESSLA’s range extends as far east as Greece,
but few events are detected from Crete and further. Many earthquakes south of Malta that
were detected by LESSLA are not on either the EMSC or INGV bulletins. . . . . . . . . . 76
8
5.2 This map shows the locations of earthquakes predicted by LESSLA but not found on the
EMSC/INGV bulletins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.3 80% of all triggers were false triggers, while the rest were either earthquakes or quarry blasts. 78
5.4 It is clear from the pie charts that events above the threshold are far more likely to be earthquakes
or quarry blasts. Events below the threshold are almost always false triggers. . . . . . . . . 80
5.5 Difference between automatic P-picks and manually corrected P-picks. The vast majority of the
picks were accurate and were shifted within 0.1 seconds of the automatic pick. . . . . . . . . 83
5.6 Difference between automatic S-picks and manually corrected S-picks. Over 250 of the 310
analyzed earthquakes S-picks were shifted by only 0.1 second or less. . . . . . . . . . . . . 83
5.7 Difference between LESSLA origin times and EMSC/INGV origin times. Most differences were
less than a second. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.8 The distance d between LESSLA and EMSC/INGV locations were calculated using Pythagoras
theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.9 The histogram of the distance between the epicentres calculated by LESSLA and those posted
by EMSC/INGV bulletins indicates that a large proportion of the LESSLA epicentres were
within 100km of the European bulletins. . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.10 The pie chart shows that 47% of all comparable LESSLA earthquakes were within 100 km of the
location posted by EMSC/INGV. A 100km discrepancy is considered to be a good calculation for
single station location algorithms. By contrast, only 19% of the compared LESSLA earthquakes
were more than 300km away from the posted EMSC/INGV location. . . . . . . . . . . . . 91
5.11 The histogram of the distance between the epicentres calculated by LESSLA and those posted
by EMSC/INGV bulletins for earthquakes close to Malta. . . . . . . . . . . . . . . . . . 92
5.12 The histogram of the distance between the epicentres calculated by LESSLA and those posted
by EMSC/INGV bulletins for earthquakes in Sicily and Italy. . . . . . . . . . . . . . . . . 92
9
5.13 The histogram of the distance between the epicentres calculated by LESSLA and those posted
by EMSC/INGV bulletins for earthquakes Greece, Crete and the Eastern Ionian Sea. . . . . 92
5.14 A few examples of good earthquake location for high magnitude, high signal-to-noise ratio
earthquakes from the Greece area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.15 XY scatter graph showing the relationship between the distance calculation of LESSLA and
EMSC/INGV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.16 Histogram of distance discrepancy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.17 New calibration graph showing the relationship of the S-P time with the distance. The polyno-
mial trend line shows a better R2 value than the linear trend line and hence was chosen for the
recommended distance formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.18 This diagram explains the azimuth calculation procedure. The origin of the axes is the WDD
seismic station. The solid blue line joins WDD to an EMSC/INGV location in the first quadrant
while the solid red line joins WDD to a LESSLA location in the first quadrant. The right
triangles are completed and the angles are calculated using trigonometry. The azimuth difference
of LESSLA’s location with respect to the EMSC/INGV location is represented by the green
area. The coloured dotted lines represent possible events in the other three quadrants. By using
trigonometry and the angles φ, φ′, θ, θ′ the azimuth discrepancy ψ can be calculated for any
combination of quadrants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.19 The azimuth shift in the clockwise direction can be seen clearly which shows a peak at +10 degrees 98
5.20 76% of LESSLA locations were less than 30 degrees in either direction from the EMSC/INGV
location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.21 The azimuth shift in the Maltese region has a peak at -10 degrees, but the data set of comparable
earthquakes in this region is too small to draw definite conclusions. . . . . . . . . . . . . . 99
5.22 The azimuth shift for earthquakes in Sicily and Italy peaks at 0 degrees and errors in the azimuth
seem to evenly distributed about 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
10
5.23 The azimuth shift for earthquakes in Greece, Sicily and the Eastern Ionian Sea has a peak at
+10 degrees. In this case, there is a substantial amount of earthquakes to draw conclusions from.
The clockwise shift of LESSLA locations to the EMSC/INGV location is evident, although it is
noted that many are within +30 degrees. . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.24 The locations of Greek earthquakes as published by EMSC/INGV bulletins are focused in three
main areas where it is most seismically active. . . . . . . . . . . . . . . . . . . . . . . . 102
5.25 The locations of Greek earthquakes predicted by LESSLA are clearly scattered and not focused
like the EMSC/INGV locations. Several earthquakes, because of the refraction of the P-wave,
were predicted by LESSLA to be coming from the South-East. A few earthquakes were predicted
to be in Malta; this is because the P-wave was attenuated and undetected by WDD seismic station.103
6.1 71% of earthquakes were regional, 18% were local, 5% were near and 5% were teleseismic. 1%
of the earthquakes were verified as earthquakes but were too noisy and discarded. . . . . . . 106
11
Chapter 1
Introduction
The Mediterranean region is seismically active area where many earthquakes take place very
day. The most active countries are Greece, Italy and Sicily which have recorded many major
earthquakes, the effects of these earthquakes have left many destructive marks throughout his-
tory. Over the last century, when seismograms started to be analyzed, a clear picture of the
mechanism behind earthquakes and how tectonic plates in the Mediterranean region move have
been developed.
1.1 Medina Wrench Zone
The Maltese Islands are situated in the centre of the Mediterranean and form part of the Sicilian-
Tunisian Platform. Malta is linked to the southeast of Sicily by a shallow area less than 200
metres deep called the Malta Plateau. In the east there is the Sicily-Malta Escarpment where
sea depths are over 3000 metres deep while to the west of Malta there is a series of troughs;
Malta Trough, Pantelleria Trough and the Linosa Trough, better known as the Sicily Channel
Rift Zone.
Earthquakes are located within the Medina Wrench Zone indicate that the entire area is seis-
mically active. Although the average magnitude of the earthquakes within this region is about
12
3.0ML (Scerri, 2001) a detailed study was needed. In today’s world, real-time seismic data has
become an important issue, where decision makers need to know exactly where an earthquake
can strike. A network of seismic stations can be used to rapidly calculate the hypocentre of fault
plane-plane solutions, while an array network can provide information on apparent velocities
and classification of phases.
1.2 The Situation in Malta
Unfortunately, in the central Mediterranean, especially the Sicily Channel, there has always
been a problem with epicentre location because of poor network station coverage of the region.
Data from North African stations are only included in EMSC/INGV locations for earthquakes
of larger magnitude, but this is not the case for average seismicity, which is quite low.
The Maltese Islands are very small and there is only one station installed at Wied Dalam.
Over the years a large number of seismic events have been recorded by this seismic station and
many of them corresponded with events listed in Italian and international seismic bulletins.
However, there are a good number of earthquakes that are not listed on these bulletins or are
very weakly detected. Agius (2007), designed a automated single station earthquake detection
and localisation algorithm, called LESSLA, so that the WDD station can use its own seismic
data to predict earthquake epicentres.
1.3 Aim of the Project
Agius (2007) did a performance evaluation of the LESSLA locations when compared to published
EMSC/INGV locations for all available seismic data for the years 2004-2006 in the Sicily Channel
and Ionian Sea. Although Agius’ statistical analysis indicated that the LESSLA locations were
fairly accurate, there were too few comparable earthquakes to be certain of the results.
13
A new statistical analysis was required with a larger database of earthquakes to analyze. The seis-
mic data from 2006 was reprocessed and data from 2007 and 2008 was added to SMRU’s database.
The locations predicted by LESSLA were compared in several ways to those of EMSC/INGV.
Again it was noted that a large number of earthquakes predicted by LESSLA around the Sicily
Channel was not listed in the EMSC/INGV bulletins.
14
Chapter 2
Locating Earthquakes using Multiple
Seismic Stations
One of the most important tasks is observational seismology is locating seismic sources. This
involves determining both the hypocentral coordinates and the source origin time. In general,
determining the source location requires identification of seismic phases and measuring their
arrival times, as well as knowing their velocity structure between the hypocenter and the seismic
station. Given the location of a seismic source, the travel time for any phase to any seismic
station can be calculated in an arbitrarily complex velocity model. This type of problem is
known as a forward model, arrival times are calculated based on a parameterized model.
On the other hand, finding the earthquake location is usually posed as an inverse problem,
where we know the data and the arrival times but which we must solve for a source location and
origin time that are consistent with the data. Therefore, we have the concept of a generalized
inverse, which is probably the most critical modern tool for interpreting seismogram as well as
for addressing other geophysical problems.
15
2.1 Wadati Diagrams and the Method of Circles
When several stations are available, an accurate location can be determined by using P and/or S
arrival times alone. If the event is at local distances, the two principal phases on the seismogram
are P and S. The origin time of the earthquake can be determined with a very simple graphical
technique called a Wadati diagram. The time separation of the S and P phase is plotted against
the absolute arrival time of the P wave as shown in the diagram below. Since the time separation
goes to zero at the hypocenter, a straight-line fit on the Wadati diagram gives the approximate
origin time at the intercept with the P arrival axis. Figure 2.1 shows an example of a Wadati
diagram. The slope of the trend is m = (αβ− 1), which can be related to Poisson’s ratio.
Figure 2.1: The Wadati diagram method for determining the origin time of a local earthquake. The best
straight line is drawn through the points, which is extrapolated to the P arrival time axis. The value at this
intercept is the origin time of the earthquake.
α
β=
√1− v12− v→ v =
1− n2
1− n(2.1)
16
where n = (m+ 1)2.
Once the origin time has been estimated, the epicentral distance for the ith station can be
estimated by taking the travel time of the P wave and multiplying it by an estimate for the
average P velocity
Di = (tiP −OT )α (2.2)
The epicenter must lie on a hemisphere of radius Di, centred on the ith station. In the map
view, this corresponds to a circle of radius Di. Figure 2.2 shows an example of this for three
stations. Since a single hypocenter must account for all three P-arrival times, the hemispheres
for all the stations must intersect at a point. The epicenter can be found by drawing the chord
of intersecting sections of the circles. The intersection of the cords will give the epicenter.
The focal depth, d, can be determined by taking the square root of the difference between the
squares of propagation distance, Di, and the distance along the surface to the epicenter, ∆, i.e.,
d = (D2−∆2)12 . Including more observations will give additional intersections that theoretically
should pass through the epicenter. In practice, error is always present, both in the data and in
the assumptions that raypaths are straight and that the velocity is known perfectly, so scatter
in the intersection usually occurs.
This method for determining the hypocenter of an earthquake is called the method of circles.
A homogenous half-space was assumed in the example. The method will still work for an
inhomogenous velocity structure as long as it is flat layered. The method can be extended to a
spherical Earth, but we will consider a slight variation that will help conceptually visualize the
inverse problem.
2.2 Locating Earthquakes by Forward Modeling
Consider several globally distributed seismic stations that have recorded an earthquake. Four
unknowns need to be determined; the three coordinates of the hypocenter and the origin time.
17
Figure 2.2: Circle method for triangulation of an epicentre
If a solution is guessed for these, then the expected P wave arrival times can be calculated. The
predictions are then compared to the observed times at each station, and therefore the error in
the guess can be determined, which can then be corrected. This procedure is repeated until the
differences between the calculated and arrival times become sufficiently small.
In Figure 2.3, 10 seismic stations are shown distributed about a presumed epicenter, E. The
actual epicenter, E0, lies to the northwest. The predicted arrival times of seismic waves at
stations to the northwest of the presumed epicenter will be later than observed, and conversely,
predictions at stations to the southeast will be earlier than observed. Travel times of waves
arriving at seismic stations to the northeast and southwest will not be greatly affected by this
particular source mislocation. These relationships can be used in order to estimate a correction
in the presumed epicenter by using a 5-step process.
• Determine a predicted travel time, ti, and distance Di, for each station based on the
presumed epicenter.
• Determine a distance, D̂i, to each station by taking the difference between the observed
18
P arrival time and the presumed origin time, t̂i, and converting this time difference to
distance by consulting a travel-time table.
• Plot the difference, Di-D̂i, against the calculated azimuth from the presumed azimuth for
each station. If the presumed epicenter is exactly right, then Di-D̂i will be zero. Otherwise,
the variation of Di-D̂i with azimuth will be sinusoidal, with the maximum and minimum of
the sinusoid aligned along the vector that points from the presumed to the true epicenter.
• Shift the origin time by an amount equal to the average value of t̂i-ti, and shift the location
by the amplitude of the sine-curve variations, with the direction of shift being along the
azimuth of the maximum of the sine curve.
• Once a new epicenter is found, it can be used as a new starting model and this procedure
is repeated. In general, a single iteration will give epicentral locations accurate to within
±100km.
This procedure is a series of forward-modeling exercises that generate data that can be compared
to observations. When a forward model the closely approximates the observations is found,
the model is said to sufficiently describe the earthquake location for given model assumptions.
Mathematically, this can be represented as a series of equations:
tipredicted= f(x̃i, v) = tiobserved
(2.3)
where x̃i is the location of the earthquake, v is the velocity structure and f is a function which
calculates the arrival time, tipredicted, given x̃i and v. If there are n stations which have measured
arrival times, then tiobservedcan be considered to be the i th component of a data vector d that has
n components, which is written as d= (t1, t2, . . . , tn). The variable x̃i gives the model parameters,
which can be considered to be a vector m that has m components. In general, m=4 for the
three spatial components and the temporal coordinate of the earthquake. Therefore, (2.3) can
be written as a series of equations of the form
19
Figure 2.3: Adjustments of ’epicentral guesses’ are made by plotting the difference between predicted and
observed travel times and epicentral distances.
F(m)=d (2.4)
2.3 The Inverse Problem
If the terms in (2.4) could be rearranged so that d could be divided by some operator F−1
to give m directly, this is equivalent to solving an inverse problem. In order to develop the
inverse problem, it is assumed that the seismic waves travel through a homogenous material
with velocity v, since the resulting simple straight line raypaths simplify the algebra.
20
Let the Cartesian coordinates of the true hypocenter and the ith seismic station be (x, y, z) and
(xi, yi, zi) respectively, and let t and ti be the origin time of the earthquake and the arrival time
at the ith station, respectively. Then
ti = t+
√(xi − x)2 + (yi − y)2 + (zi − z)2
v(2.5)
It is obvious that ti is an element of the data vector d and x, y, z and t are the elements of the
model vector m that we wish to determine. Ideally, only one unique combination of hypocentral
parameters fits the observed times. Individual data elements, di, are related to the model vector
the the right-hand side of (2.5), which can be written as
F(x, y, z, t) = d (2.6)
The equation for d is nonlinear, which means that a linear least-squares solution is not possible.
The standard method is to linearize the problem and iteratively improve guesses of m. The
first step is to guess a solution m0 for which the predicted times, d0, can be calculated and
investigate the behaviour of d0 in the neighbourhood of m0. Changes in m0 are approximation
with a Taylor series approximation
m1j = m0
j + δm0j (2.7)
where δm0j is an incremental variation of the jth model parameter that moves the model towards
a better fit to the data. This amounts to guessing a solution (x0, y0, z0, t0) and then determining
incremental changes in that guess, therefore
δx0 = x1 − x0
δy0 = y1 − y0
δz0 = z1 − z0
δt0 = t1 − t0
21
The corresponding change in the predicted data vector can be found by expanding (2.7) in a
Taylor series about m0 + δm0
δF
δx0
δx0 +δF
δy0
δy0 +δF
δz0
δz0 +δF
δt0δt0 = di − F 0
i (x0, y0, z0, t0) (2.8)
Examination of (2.8) shows that the difference in the observed and predicted travel times is now
linearly related to changes in the hypocentral coordinates to make the model better predict the
data. Using only the first term of a Taylor series provided the linearization, but this also prevents
the perturbations from immediately converging to the true m. The derivatives are evaluated at
the guessed solution, m0j . Substituting (2.6) into (2.8) and rearranging gives
δdi =δdiδmj
δmj = Gijδmj (2.9)
where Gij = δdi
δmjis a matrix of partial derivatives. Using Gij, a system of equations can be
written that maps changes in model parameters onto improvements in the fit to the data.
∆d = G∆m (2.10)
Applying equation 2.8 to get a system of equations with four unknowns with constant coefficients.
If there are four observed arrival times, four equations can be obtained which can be solved by
Gaussian elimination, giving either no solution or an exact result for δm0j . Errors in the data
leads to an incorrect solutions or inconsistent equations. Once δx, δy, δz and δt are calculated,
the ’correct’ source parameters can be guessed, i.e.
x1 = x0 = δx0 y1 = y0 = δy0
z1 = z0 = δz0 t1 = t0 = δt0(2.11)
The entire procedure, from (2.7) to (2.11), is repeated using the new coordinates (x1, y1, z1, t1)
to estimate a refined model (x2, y2, z2, t2), which is repeated until the parameter ∆d becomes
22
acceptably small. This iterative process is sometimes called Geiger’s method. This method has
its shortcomings, namely, if the starting model is inaccurate, the rate of convergence can be slow,
if it converges at all.
Other methods exist that improve the accuracy of this algorithm. Using the concept of a
generalized inverse, it is possible to solve the matrix G for all the model parameters by finding
the eigenvalues of G. However, in seismology, G is not a square matrix because there are
more seismic stations (n) than model parameters (m=4). In this case the problem is called an
overdetermined problem and the best solution for the model parameters can be found by solving
the following equation,
m = [GTG]−1GTd (2.12)
where [GTG]−1GT = G−g is called the generalized inverse of G. Equation (2.12) provides the best
solution to m in a least-square sense and is one of the most important equations in geophysics
for both linear and nonlinear problems. Equation (2.12) is then solved using the method of
singular value decomposition.
23
Chapter 3
Single Station Epicentre Location and
LESSLA
In this chapter, a brief description is given on how the single-station earthquake location algo-
rithm, LESSLA, designed by Matthew Agius works. A more detailed description is given in his
thesis (Agius, 2007).
3.1 Single Station Locations
Usually the arrival times of various seismic phases at many seismic stations are required to
determine an earthquake hypocenter and origin time accurately. However, it is possible to
obtain a crude estimate using data from a single seismic station. Single stations require three-
component recordings of ground motion. Since P waves are vertically and radially polarized, the
vector P wave motion can be used to infer the azimuth to the epicenter.
If the vertical component of the P-wave is upward, the radial component of the P wave is directed
away from the epicenter. If the vertical component of the P wave is downward, then the radial
component of the P wave is directed back toward the epicenter. Unless the event is at a back
24
azimuth such that the horizontal P wave motion is naturally rotated onto a single component,
both horizontal seismometers will record the radial component of the P wave. The ratio of the
amplitudes on the two horizontal components can then be used to find the vector projection of
the P wave along the azimuth to the seismic source.
The distance to the seismic source is obtained from the difference between the arrival times of
two phases, normally P and S. If the earthquake is at local ranges, then the distance can be
approximated by
D =tS − tP√
3− 1α (3.1)
The equation assumes a Poisson solid. For most crustal events, D = (tS − tP ) × 8.0. At larger
distances time-travel tables are used to estimate the distance. Knowing the distance the P travel
time can be estimated which can be used to determine the origin time of the event. Comparing
differential times between multiple sets of phases with times from the travel-time curves can
improve the distance estimation. If clear depth phases are present, a reasonable estimate of the
source depth can be made. However, this method is not accurate at distances greater than 20
degrees (2222km) because the P wave arrives steeply and its horizontal component is too small
to give a reliable estimate of the azimuth to the source.
3.2 The Wied Dalam Observatory and Data Acquisition
The seismic observatory station at Wied Dalam (WDD) is located at 35.8374N, 14.5245E. The
seismometer at WDD is a Streckeiser Model STS-2 triaxial component connected to a
Quanterra 24-bit integer data acquisition system. It operates several channels
• HH at 80 samples per second
• BH at 20 samples per second
25
• LH at 1 sample per second
• VH at 0.1 samples per second
• UH at 0.01 samples per second
Since seismic waves of local earthquakes are predominant in the higher frequencies and are
attenuated at long distances, the LH, BH and HH channels were used. The channels that trigger
give a good indication about the type of event detected.
Real time data transmission system is maintained by SeisComp, which is a concept for a net-
worked seismographic system and was originally developed for the GEOFON network and ex-
tended within the MEREDIAN project. The software is responsible for data acquisition, data
recording, monitoring, controlling and real-time communication.
The core of SeisComp is the SeedLink data acquisition system. SeedLink clients connect to the
server using a robust TCP/IP application level protocol, SeedLink Protocol. Data is transmitted
via the internet to another computer at the University of Malta, where data backup is kept.
3.2.1 Data Format
SEED (Standard for the Exchange of Earthquake Data) is a standard defined by FDSN and was
needed because of the large amounts of data that needs to be transferred every second, analyzed
and backed up. SEED data format contains a header with the instrument name, sensitivity,
location, etc. and the data section. which contains the waveform data.
RDSEED is used to extract data in SEED format for analysis by other packages. As data is
extracted from the SEED volume, RDSEED uses the dataless file, looks into orientation and
sensitivity of each channel and determines if channel polarity is reversed.
SAC (Seismic Analysis Code) is a general purpose interactive program designed for studying
sequential signals, especially time series data. Originally developed in ForTran and ported to C
(renamed to SAC2000). SAC2000 is the seismologist’s primary tool for the analysis of earthquake
26
signals. SAC2000 has many analysis capabilities including general arithmetic operations, Fourier
transforms, filtering, signal stacking, decimation, interpolation and correlation and seismic phase
picking.
3.3 Manual Data Analysis and Computer Automation
In a completely manual mode, the station operator must go through each day’s seismograms
carefully. In the case of a possible event, the beginning and ending times of the event must be
noted and the data converted to SAC file format. In most cases only the three components:
North, East and vertical of one sample rate, such as the BH (20 samples/sec) are decompressed.
Then the seismograms are plotted using SAC2000. Users can filter, zero adjust, zoom data and
perform mathematical operations such as integration to improve the analysis. If P, S and other
picks are identified, a mark can be placed and a SAC file will be stored.
A close look at the primary wave and a study of the polarization of the first impulsive wavelet
of the three components gives an indication of the origin of the source by calculating the back-
azimuth.
Manual analysis of earthquakes is a sequential routine and can be automated. LESSLA is such
an automated system and processes seismic data in SEED and SAC file formats. LESSLA does
not communicate with the data acquisition system, thus making it independent from specific
configurations and can be installed with different data acquisition protocols.
3.4 LESSLA sequence of execution
RDSEED and SAC2000 are used as a black-box: data files are input, then processed and output
as new files. The list below gives a summary of the sequence of execution of the program. If one
stage fails, then the following stages will have errors and inaccuracies.
27
1. Step 1
(a) RDSEED converts LH, BH and HH streams, 3-C data, day SEED files into SAC files
(b) SAC2000 filters 3-C SAC data using specific low and high cut-off frequencies depend-
ing on the channel.
(c) SAC files are imported into LESSLA memory
2. Step 2 - Create a day’s event list
(a) STA/LTA trigger algorithm along the time series of each component of each channel.
(b) Each trigger and detrigger is considered as a potential event.
(c) Each event begin and end time is compared with the begin and end values of events
in the day’s events list.
(d) Events are graded in relation to the channel the trigger and detrigger belongs.
3. Step 3 - Eligible Events are processed
(a) Event categorized as regional, local or near based on the duration from the begin
mark to the maximum horizontal amplitude between the begin and the end of the
event.
(b) Create the event pick list: STA/LTA, Peak/Valley along the time series of each com-
ponent of all channels.
(c) Set P and S mark
(d) Distance Calculation
(e) Process azimuth estimate of all channels and choose the most stable one after the P
onset.
(f) Event re-categorized as regional, local or near by the S-P time
(g) Location calculation (latitude and longitude)
(h) Magnitude calculation
28
(i) Map event
4. Step 4 - Issue Report
5. Step 5 - Store event’s SAC data
In the next section, these steps are analyzed in more detail.
3.5 Data Processing and Epicentre Location
3.5.1 Event Detection using the STA/LTA algorithm
The Short-Term Average/Long-Term Average (STA/LTA) method is one of the most widely
used algorithms in weak-motion seismology. It continuously calculated the average values of the
absolute amplitude of a seismic signal in two consecutive moving-time windows: the short term
window and the long term window.
The STA measures the ’instant’ amplitude of the seismic signal while LTA represents the current
average seismic noise amplitude. An average of the absolute amplitudes of each data sample
w(t) within both windows is calculated
STA(t) =1
S
S−1∑j=0
|w(t− j)| (3.2)
where S = sampling rate × STA length in seconds. Similarly, the equation for the LTA at time
t is given by
LTA(t) =1
L
L−1∑j=0
|w(t− j)| (3.3)
where L = sampling rate × LTA length in seconds. The sampling rate is determined by the time
interval ∆ between samples, i.e.,
29
Samplingrate =1
∆
The STA and LTA values are calculated for each sample by the ’moving average’. This means
that if the time window contains 100 samples, the next sample would be included by removing
the first entry and adding the next one. This procedure is much more efficient than recalculating
the entire window and saves a lot of processing time
The ratio of STA and LTA is then calculated at each sample. This ratio is continuously compared
to a STA/LTA trigger threshold level. If the ratio exceeds this threshold, a trigger flag is issued.
Similarly, as the signal decays the STA/LTA ratio will decrease. When the ratio falls below
a different, lower threshold, the channel detriggers. The detrigger point is stored as the ’Fini’
identification, ’F’ on the seismograph. This detrigger point indicates the end of the event since
no more signal is being detected by the seismogram.
Power Characteristic
LESSLA does not use the absolute values of the seismic trace as the characteristic function for
the calculation of STA and LTA. Instead it uses the power, or envelope function of the seismic
trace, which was developed by Kanasewich (1981), given by
STA(t) =1
S[(STA(t− 1) ∗ S)− w(t− S)2 + w(t)2]
Where S = STA time window in seconds∆ of seismic trace w(t)
. The equation for the power characteristic of the LTA is
exactly the same, replacing the S with L.
The power characteristic increases the sensitivity of the STA/LTA algorithm and makes trigger-
ing more responsive to spikes. This decreases the chance of missing an event but increases the
chance of false triggers.
30
Pre-Trigger Valley
The main problem when using the STA/LTA algorithm to trigger events is because of the length
of the time window. Since the trigger threshold is higher than 1, the moving averages may take
some time to exceed the threshold. By the time the threshold is breached and there is a trigger,
some of the P-phase may have already passed and data will be lost. The problem was resolved
by recording the minimum point before the sharp increase in the ratio as the beginning of the
event, labeled with an ’A’. LESSLA is also capable of adding seismic data to the event before
triggering and an analogue smoothing algorithm was also implemented to smooth the STA/LTA
plots.
3.5.2 Signal to noise ratio
The signal-to-noise ratio is similar to the STA/LTA and is determined by the power ratio between
the signal and the background noise. The signal-to-noise ratio is measured in decibels, which is
10 times the logarithm of the power ratio. Therefore
signal-to-noise ratio = 10 log10(PsignalPnoise
) = 20 log10(AsignalAnoise
)
Where P is the average power and A is the RMS amplitude. Both signal and noise power/amplitude
must be measured at the same or equivalent points in the system, within the same system band-
width. The highest SNR value is noted for each event.
3.5.3 Creating an Event
As LESSLA processes the nine channel components in sequence, a list of ’events’ is generated,
each corresponding to a triggered/detriggered segment. Events in which all or some of the
components fall within the same time interval are considered to be the same event. The start
31
and end time of the event are taken to be the earliest and the latest time of all the individual
component events.
When an event is detected by the STA/LTA method, a function takes the component name,
begin and end time, maximum amplitude and its time, maximum SNR and the day list of events
as its input and tries to match the new event with other events previously registered from another
component. The new event is inserted in such a way that we have a list that is always sorted in
chronological order.
New events can overlap a number of listed events; this can happen if the new event range matches
the listed event range but the new end-time is beyond the listed event time. Three overlapping
checks are made to determine whether two events overlap,
• If new event end time is less than next listed begin time, there is no overlap.
• If new event end time is between the begin-end range of the next listed event there is a
partial overlap.
• If the new event end time is beyond the end-time of the next listed event there is a complete
overlap.
After processing all the nine components and each triggered event has been put in place, the
linked list of events represents the activity of a whole day.
3.5.4 Voting Mechanism
In order to decide which events in the day list should be further processed as earthquake, a
voting mechanism was introduced which depended on a reasonable combination of STA/LTA
triggers. Events with a valid combination of component triggers are called True Events.
The voting mechanism is weight-based and it measures which components triggered during the
event. A triggered L component has a weight of 1, a triggered B component has a weight of 2
32
and a triggered H component has a weight of 3. The H component has a higher weight because
local earthquakes are more sensitive to the high sampling rate channels. All the weights of the
event are added together and the event is labeled as follows,
• If the cumulative weight of all the triggered components is greater than, or equal to 11,
then the event is labeled as a True Event and will be further processed.
• If the cumulative weight of all the triggered components is less than 11, but greater than
3, then the event is listed as Possible. The event will not be further processed but will be
available to the seismologist for manual review.
• If the cumulative weight of all the triggered components is less than, or equal to 3, then
the event is discarded.
The events labeled True Events are given a preliminary classification (near, local, regional or
teleseismic) based on the time difference between the maximum horizontal amplitude and the
begin time. This classification is used in determining the time windows used while processing
the event.
3.5.5 Phase Picks
Since the primary body and surface seismic waves travel with different velocities through the
earth, they appear at different times in the seismogram. The most important waves are the
P- and S-waves, although there are other waves as well, which are usually reflections of the
primary P- or S-waves at the surface of the Earth or at velocity-density discontinuities inside
the Earth. The primary P- and S- picks are easily recognizable because of their large amplitude,
which decays with time. The energy pulses are evident in the STA/LTA plots of earthquakes.
LESSLA is designed to reprocess the True Events from the A mark to the F mark in order to
detect these picks.
33
Since the start of a phase is not at the STA/LTA peak but at the bottom of the previous
minimum, called a valley, the picks are detected using an STA/LTA Peak-Valley ratio. Firstly,
each True Event is reprocessed, one component at a time, using more sensitive time windows
depending on the preliminary classification of the event. Each newly processed STA/LTA sample
is compared to the previously indexed STA/LTA sample. If the value is lower then it is stored
as the new valley. Each new STA/LTA sample is considered to be a peak and is divided by the
valley and compared to a predefined threshold. When the ratio exceeds a predefined threshold,
a new pick is made.
The Peak-to-Valley threshold was set to be 1.1, which makes it sensitive enough to account for
shallow valleys. However to avoid exceeding the threshold where the difference in the peak and
valley is less than the noise, a second condition, Peak−V alley > 1 in order to avoid registering
picks that could just be fluctuations in the noise.
In some cases, the STA/LTA Peak-Valley Threshold can be too high for weak events which could
result in wrong picks. Therefore an amplitude sensitive threshold was implemented to cater for
high and low SNR earthquakes. The function used was
Threshold =log(A0)
f
where A0 is the maximum amplitude and f is a factor determined by trial and error.
Adding Picks
Picks are created and added to the list very similarly to how the events are added in the day
list. Each event has a header pick. When a pick is added this pick is read first while the new
pick time is compared to the pick times of the other picks and inserted in the correct position.
If the time of the new pick is equal to the time of a listed pick, i.e. matched picks, or if the new
pick time is less than the time of the next pick, the new pick is inserted between the two. In
this way if several picks are detected at the same time (resulting from different components due
to a phase) they are all included in the list.
34
However, unlike how matched triggered events from different components are compiled as a single
event, a list of picks will be made up of a long string of picks, some having the same time. This
will result in the picks being in groups that are close to each other. These are called clustered
picks. Each cluster of picks is given a weighting based on how far apart, in the time domain, the
picks in the cluster are. The weighting procedure is as follows
• The algorithm goes through all the linked picks and creates a linked list of clusters, using
a predefined cluster range to determine if a pick fits in the cluster. The range depends on
the preliminary event classification.
• Each pick within a cluster is assigned a weight whose value is associated with the ’parent’
component, similar to the voting mechanism described previously. The weights assigned
are based entirely on the component frequency of the pick; an LH component has a weight
of 1, a BH component has a weight of 3, while an HH component has a weight of 5.
Therefore a seismogram can be represented as a list of clusters rather than a list of picks. Cluster
with a higher grade will represent important seismic phases. In local and regional earthquakes,
the primary P- and S-phases are the dominant picks. Therefore LESSLA chooses the two highest
graded clusters to be the P-and S-phase; the earlier one being the P pick and the cluster closest
the the horizontal maximum amplitude as the S pick.
Other intermediate clusters are hard to interpret using a single station and are not considered
by LESSLA.
3.5.6 Event Classification
Subtracting the S and P pick times classifies the event more effectively than using the Preliminary
Event Classification as given in Table 2.1.
35
Type t = S-P (seconds)
Near t ≤ 4
Local 4 < t ≤ 15
Regional 15 < t ≤ 120
Teleseismic t > 120
Table 3.1: Event classification
3.5.7 Azimuth and Coherence Estimation
Information about the azimuth, angle of incidence and coherence are all calculated from the
P-wave signal. These estimations are based on the paper presented by Christoffersson et al
(1989), who based their mathematics on the auto- and cross-correlations of the three orthogonal
components within a short time window.
Let y = yn(t), ye(t), yz(t) be the vector representing the observed particle motion at a receiver
at time t, where the vector components represent the north, east and vertical contribution
respectively. The three vector components are described individually by the following equations
yn(t) = aP (t) +Q(t) +Nn(t)
ye(t) = bP (t) + cQ(t) +Ne(t)
yz(t) = P (t) +Nz(t)
where P is the P-wave signal arriving at an angle along the vertical, appearing in the horizontal
components, Q is correlated noise on the horizontal components, N is Uncorrelated random noise
on all three channels and a,b,c are constants.
These equations assume the Earth surface is flat and homogenous in the vicinity of the receiver
such that no phase shifts are introduced by local scattering effects.
In the absence of noise, the azimuth would simply be given by tan(azi) = ye(t)yn(t)
, but the equation
above shows that the noise contribution can distort the azimuth. Roberts et al, eliminates
these difficulties by using coherence properties with the vertical component. Calculating the
36
cross powers over a time window of length T eliminates the uncorrelated signal between the
horizontal and the vertical components leaving only a P-wave signal.
Therefore, we get the following equations
E(< ynyz >) = E(a < P 2 >)
E(< yeyz >) = E(a < P 2 >)
E(< yzyz >) = E(< P 2 >) + E(< N2z >)
where <> indicates averaging over the time window T, E denotes the expectation value of the
cross products.
Azimuth Estimation
The back azimuth of an arriving signal is processed by studying the particle motion within
the three-component data. LESSLA produces three different azimuth estimations, one from
each stream. The azimuth from each stream towards the source is obtained from the following
equation
Tan(azi) =− < yeyz >
− < ynyz >=−b−a
The value of azi has 180 degrees ambiguity since both a and b are values obtained from the
cross powers which relate to the vertical component, yz, automatically corrects the signs of the
horizontal component as described in Figure 3.2.
The mathematics is reproduced in an implemented function in LESSLA, which loops through
the samples from start to end of the input range at a predefined time-step. At each time step,
a nested loops calculates the summation of all possible cross powers. The length of the nested
loop is the size of the time window. The time window is ’positioned’ such that the current time
step sample is at the centre.
37
The azimuth was calculated using the standard function atan2f(), which takes two numbers, x
and y, and computes the principal value of the arctangent of yx, using the signs of both arguments
to determine the quadrant of the return value.
The azimuth is estimated at every time-step; to avoid misinterpretation the same azimuth value
is stored between one time-step and another.
Coherence Estimation
An estimate of how well-polarized the incoming P-wave is could be a powerful tool for the seis-
mologist. The vertical component yz(t) of a noise-free linearly polarized wave can be represented
purely by the horizontal components yn(t) and ye(t) by
yz(t) = Ayn(t) +Bye(t)
The noise term can be calculated by
N(t) = Yz(t)− Ayn(t)−Nye(t)
The predicted coherence is defined to be the ratio of the noise power to the signal in the vertical
component, i.e.
C = 1− < NN >
< yzyz >= 1− < (yz − Ayn −Bye)2 >
< yzyz >
If y describes a noise-free linearly polarized signal, then C=1, although this is rarely the case
since noise is always present.
Christofferson et al, suggests that for analysis of real data, the coherence value can be used as
a detection mechanism. If C for a time window is above a set threshold then a signal can be
detected, although this can be unpractical because correlated noise can lead to many incorrect
detections.
38
As done previously, the coherence values for all three channels are stored in three arrays, and
the coherence is estimated at every time step, and to avoid misinterpretation the same coherence
value is stored between one time step and another.
Selection of Azimuth and Coherence
A plot featuring a seismogram with the azimuth and coherence gives a lot of information about
the event. The azimuth right after the P pick is the angle from North to the earthquake source.
Each event will have three azimuth calculations, one for each channel. The average value of the
azimuth is calculated starting off from P until a user set ± range is exceeded. The channel (either
BH or HH) with the longest stable time after the P pick is chosen to be the event azimuth.
Although Christofferson et al, suggested that the coherence estimate can be used to detect events
and even to check the P-picking, the coherence estimates are too unreliable. Therefore, it is used
as a tool for the seismologist during manual earthquake analysis, since a spike in the coherence
can be used to check the correctness of the P- and S-picks.
3.5.8 Distance Calculation
The distance of a local or regional event is calculated using the standard S-P time interval
method using specifically constructed travel time graphs. Several events detected at WDD in
2006 that matched with international bulletins were used as the sample dataset. For each event,
the distance of the listed epicenter from WDD was calculated, and the S-P time was measured
from the seismogram. A graph of distance against S-P time was plotted using Microsoft Excel,
and the best fit trend line was generated. The type of trend line chosen was the one with the
best fit for R2, the square of the correlation coefficient. A value of R = 1 indicates a good
relationship between x and y. This relation should have a zero intercept, which was set. The
equation generated was then used to calculate the distance of an event.
Distance = 0.0426(S − P )2 + 7.5882(S − P )
39
Events classified as near events are treated differently, since shallow rock structures vary from
deeper rocks. The wave propagation velocity in these rocks is slower and therefore the S-P time
is multiplied by a user-defined S-P velocity factor, which was set to 2.5 based on the results of
Agius (2003). It is assumed that all near events are quarry blasts and therefore surface sources.
Distance = 2.5(S − P )
3.5.9 Origin Time
In a similar manner to the distance calculation, another graph of P travel time (P-Origin Time)
against the S-P time was plotted and a trend line with zero intercept was added. The best R2
value achieved was that of a straight-line graph.
P Travel Time = 1.3482(S − P )
The time of origin can be calculated by subtracting the P travel time from the P onset
Origin Time = P − (P travel time)
3.5.10 Latitude and Longitude Location
The location of an earthquake, the latitude and longitude, can be calculated given the station
location, the distance and the azimuth of the event from the station. For local and regional
events, it is a good approximation to assume a flat earth surface, although specific trigonometric
equations exist to help describe the earth’s spherical surface.
The law of cosines and the law of sines for spherical triangles were used to calculate locations,
distances or angles for a spherical model. Consider a triangle with sides labeled a, b and c and
angles A, B and C is defined by two end points and the North Pole. In order to calculate the
40
second end point using a given starting point, distance and azimuth, the unknown parameters
of the triangle need to be calculated.
First b is obtained by calculating the ratio of the earthquake distance with the earth’s radius
b =distance
Earth radius
where b is in radians. a is calculated using using the law of cosines.
a = arccos{[cos(b)× cos(π
2− lat1)] + [sin(
π
2− lat1)× sin(b)× cos(azimuth)]}
Where the station latitude lat1 , earthquake azimuth and a are in radians. The earthquake
latitude lat2, is obtained from a where lat2 = π2− a.
The earthquake longitude is obtained if B is known
B = arcsin( sin(b)×sin(azimuth)sin(a)
)
⇒ lon2 = long1−B
3.5.11 Magnitude
LESSLA calculates the local magnitude and the duration magnitude, which are the most suitable
magnitudes for local and regional events.
The duration magnitude is based on the duration of the earthquake and does not consider the
maximum amplitude or the distance. It is based on the hypothesis that a stronger earthquakes
takes a longer time to decay. The duration time of an event is calculated from the P pick to
the final F mark. The final equation is based on the work of Scerri (2001), who derived a local
duration magnitude regression formula based on Sicily Channel Earthquakes located by INGV.
MD = 2.58× log10(F − P )− 1.86
41
In the 1930s, Charles Richter devised a standard scale to determine the magnitude of an earth-
quake. He defined an earthquake of magnitude 0 to be an earthquake which produced a maximum
amplitude of 1 micron on a standard Wood-Anderson torsion seismograph 100km away from the
source. Then the magnitude of an earthquake at any distance ∆ was given by
ML = log(AMAX(∆))− log(A0(∆))
AMAX(∆) is the maximum trace amplitude at distance ∆ and A0(∆) represents the attenuation
function. Since no attenuation functions are available for the Sicily Channel region, the formula
for Southern California was implemented
− logA0 = 1.110 log(R
100) + 0.00189(R− 100) + 3.0
Where R is the hypocentral distance, R =√
∆2 + h2, where ∆ is the epicentral distance and h
is the hypocentral depth.
This attenuation correction assumes that the maximum amplitude phase of local events (Sg, Lg
or Rg) have roughly the same dominant frequency. It assumes shallow earthquakes of less than
15km; this is also assumed for Malta.
3.5.12 Generating a Day Report
The user running LESSLA can see the progress on screen during processing. A detailed report
is stored on hard disk in HTML format. Several functions were designed to generate the event
SAC files and plots. These functions perform various tasks such as updating the data members
of the SAC structure before the SAC files are written, generation of all the SAC files related to
an event and a SAC macro that generates different formats of a plot.
The true events and possible events are then listed in an HTML document including the station
information, which is stored on disk as well as the PDF files of the plots.
42
LESSLA sends out a daily report in HTML format as an email using all the PDF attachments,
so the data can be accessed from any computer with internet access. The email includes station
information such as station name, network and location which is linked to Google maps for
viewing.
The email report includes a list of true events and possible events in a chronologically ordered
table. True events have all the information available listed, including component triggers, origin
time, P time, etc. PDF files are attached and a map view of the earthquake location is available.
Possible events have only the basic information, since these were not processed fully since the
channel triggers did not have a high enough weight.
43
Chapter 4
Analyst Procedure
In the previous two chapters, both the standard method of epicenter location by the solution
of the over-determined eigenvalue problem and the system designed by Agius (2006), LESSLA
were discussed. This chapter discusses the interface of the web page where the data is available
online and the various tools available for the seismologist to view and modify events.
Agius (2006) gives a brief description of the email notification system and in Chapter 8, section
8.1 he makes several suggestions on how to improve the system. An online database has been
set up, where all the necessary information can be accessed by a seismologist. It is now possible
to edit events and reprocess them to get a more accurate solution in the cases where there are
obvious errors in the picks or azimuth. These will be discussed in further detail later in the
chapter.
4.1 General Overview
All the data recorded at WDD from 2006 to 2008 has been uploaded into an online database.
The main page can be accessed by following the link http://www.phys.um.edu.mt/seismic/,
shown in Figure 4.1.
44
Figure 4.1: Screenshot of the main page
4.1.1 Website Features
On the left-hand side of the webpage there is a list of links providing useful information including
a notice board describing important events since the website was uploaded at the beginning of
2008. There are also several press releases, where the seismic data and maps of the location
of major earthquakes recorded at WDD were released to the public. There is also an online
questionnaire, where the public are invited to share their experiences of any earthquakes they
may have felt. This feature has proved to be a success generating over 300 responses from
Maltese citizens after the 6 January 2008 earthquake.
The other links give information about the Seismic Monitoring and Research Unit (SMRU),
various projects and research papers that have been done since the early 90s, presentations and
posters and the contact details of the SMRU leader, Dr Pauline Galea, and Matthew Agius, who
designed the LESSLA algorithm and the current website where all the data from 2006 onwards
is available, including map plots of verified events.
Real Time Plots
Underneath these links there is a diagram which shows the real-time plot of the seismic activity
of the current day. The active plot displays all the data that has been recorded during the
current day. Clicking on the diagram links to a page where this diagram is expanded, where it
can be viewed in better detail. The active plot auto-refreshes and gives the seismologist a good
indication of the seismic activity over the current day. At midnight, the data from that way is
stored into the database and a new active plot is started. Figure 4.2 shows the real time plot of
30 December 2008.
Active plots are also available for the IDI and CEL stations. Active plots from previous days
can be extracted by using the search queries on the left-hand side of the web page, filling in the
required information and clicking ’Plot’. An extracted plot of 6th January 2008 from 04:00 to
08:00 is shown in Figure 4.3
46
Figure 4.2: The real-time plot of 30 December 2008. There is clearly an earthquake at around 06:20, which was confirmed later on
when the data was processed.
The active plot of the current day can be viewed in real-time, which is easily accessible from the
main page. The figure below is an active plot of the 30th December 2008. In the active plot, it
is noted that there is an earthquake at around 06:20. Active plots of the other two stations in
the MN network, CEL and IDI, are also available.
It is also possible to extract the plots from previous days. In order to extract a plot, the user
must specify the year, day of year (from 0-365), the time range of the plot and the channels
required to view. Figure 4.3 shows the active plot from the 6th January, where there was a
recorded event at 5am.
4.2 Automatic Analysis and E-mail Notification
Every day at 04:00 AM, LESSLA processes the previous day’s data as described in Chapter 2,
and adds all True Events and Possible Events to the database. The list of events is arranged in
reverse-chronological order, with the latest events being at the top of the list, while the earliest
events, from early 2006, are at the bottom. These events can be viewed individually with all the
parameters of the event including the origin time, P time, S time, distance, azimuth, channel
triggers, etc.
From the beginning of 2008, two other stations were added to the network. One, based on Sicily,
was given the label CEL, while the other is on Crete and was labeled IDI. Figure 4.4 shows the
position of all three stations on a Google map. While these two stations are not of direct interest
in this study, they use the same algorithm as that of WDD and the data gathered is added to
the University database. With the addition of these stations, when an event was detected by
more than one station in the network, the method of circles described in Chapter 1 was applied
to give a multi-station plot. A very brief analysis of the accuracy of these multi-station plots is
given at the end of the chapter.
48
Figure 4.3: An extracted plot of all 9 channels from 6th January 2008 from 04:00 to 08:00, which shows that there was an earthquake
at around 05:00 from the extracted plot.
Figure 4.4: The position of the three seismic station using LESSLA on a Google map.
4.2.1 E-mail notification
To avoid having to connect directly to the computer at university or the WDD station, LESSLA
sends out a daily report in HTML format as an email including all PDF attachments. The email
includes station information such as the station name, network and location which is linked to
Google maps for viewing.
The email report includes a list of true events and possible events in a chronologically sorted ta-
ble as seen in Figure 4.5. True events are displayed in red and have all the information displayed
in one row in the table (component triggers, origin time, P and S times, distance, latitude and
longitude, etc). PDF files are attached and a map view of the earthquake location is available.
Possible events are listed albeit with only the basic information such as the triggered compo-
nents, trigger time, maximum amplitude, SNR and duration. There are no pdf attachments or
map plots for possible events since LESSLA did not process these events sufficiently to have
coordinates for map plots.
A set of links are available to check the INGV and EMSC bulletins for events that match the
LESSLA events as well as online reports of quarry blasts issued by the Maltese Environment
and Planning Authority (MEPA).
Attached to every email notification there is a 24 hour plot of the BHZ channel. In the example
given below, it is evident there was only one major trigger, just after 05:00.
51
Figure 4.5: Email notification for 6th January 2008.
The daily email report, is also accessible from the website.
4.3 The Online Database
The database consists of all possible and true events from 2006 onwards, with the most recent
events being displayed at the top of the list. There is also a Google map plot displaying all the
events that have been manually verified and published by the SMRU depending on the query.
Figure 4.6 is a screenshot showing a typical list of events stored in the database.
Each event is displayed using a single row in the table, where all the essential information about
that trigger is displayed. In the last column of the table there are the ’Manual Attributes’ which
are user-given labels so that by looking at these labels, the seismologist will know what kind of
event it is at a glance. A list of the manual attributes with a brief explanation is given below.
• Red Ink - Manually Verified Earthquake and plotted on the main page Google map.
• Orange Ink - Quarry Blast
• C - Comments were made by a user
• E - Classified as an earthquake
• T - Classified as a teleseismic earthquake
• V - Classified as a verified earthquake and is the label that causes the event to be displayed
in red and plotted on the map.
• M - This indicates that an event was detected by more than one station in the MN network
and a multistation plot and location is available.
• N - Information about the event was found on external network databases (EMSC or
INGV) and a plot is available to compare the LESSLA plot with the external network plot
on a Google map.
53
• sP - This label indicates a manually verified earthquake with no external network or mul-
tistation information available.
• mP - This label indicates a manually verified earthquake with a multistation location and
plot available.
• nP - This label indicates a manually verified earthquake with external network location
and plot available.
• qA - indicates the seismologist reviewing the earthquake is very confidant with the final
solution. This tag is given to events with very clear, noise-free signals with well-defined P
and S phases, where the LESSLA solution is very close to the external network’s solution.
• qB - indicates the seismologist reviewing the earthquake is satisfied with the result, however
some doubts remain whether the solution is fully accurate. This tag is given to events that
agree reasonably well with external network locations but some noise or dubious azimuth
estimations provided some errors.
• qC - indicates the seismologist reviewing the earthquake is not confidant at all about the
final location of the earthquake. These events are clearly earthquakes, but because of
high noise and/or missing phases (especially the P phase) mean that no reliable result is
possible.
4.4 Analyzing a Single Event
A single event can be viewed by clicking on the magnifying glass on the right hand side of the
row where the event is in the online database. This will open that events page in a separate
window/tab for further analysis as shown in Figure 4.7. This earthquake was felt in Malta and
a press release on this event was released by the SMRU, available from the website as described
previously.
54
Figure 4.6: The events database page. In this example a query was made to display the 50 most recent triggers
in the time frame specified for all three stations. The search can be refined further to display events from a
certain region, to display only earthquakes, quarry blasts or verified events and so on.
55
Figure 4.7: The main page of the January 6 earthquake in Greece. This page displays all the available details of this event, including
initial classifications, maps, pdf attachments of all streams (it is possible to view each stream independently) and comments. By clicking
on ’View Analysis’, the seismologist can look at the azimuth and coherence calculations for the L, B and H streams.
The single event page is divided into 4 main sections: ’LESSLA’, ’Multi Station Earthquake
Location Map View’, ’Other Network Information’, and ’All Earthquake Locations Map View’.
4.4.1 LESSLA
This is the main part of the page and thus it gives all the necessary information about the event
in order to calculate the location of the earthquake. On the top left, a Google map showing the
final location calculated is given. The radius of the blue circle has the value in the ’Distance’
space and its centre is about the WDD station. The red line is of length equal to the radius of
the circle starting at the centre and extending to the circumference. The line is drawn in such
a way that it makes an angle equal to the azimuth relative to the geographical North of the
Google map. The point where the red line touches the circumference of the circle is the location
of the earthquake, as calculated by LESSLA.
To the right of the Google map, the seismographs of all nine channels are available. These plots
can be viewed in better detail in either .pdf or .gif format. Moreover, a seismologist can also use
the program Seisgram2k to view the plots. This is a very useful tool which allows a seismologist
to correct missed picks with great accuracy. This earthquake was predicted very accurately by
the automatic solution and so none of these tools were used on this earthquake. The next section
will consider an earthquake that needed these tools to give the best solution.
Below the Google map and the pdf attachment of the seismogram plots, all the important
information defining the earthquake can be found, some of which are,
1. Year, day and date
2. Network and Station
3. Channel Triggers - 1 means that the channel triggered while a 0 means that it did not
4. Maximum Amplitude
5. Signal-to-Noise ratio
57
6. Pretype - the preliminary classification of the earthquake (near, local, regional, or teleseis-
mic)
7. Origin Time, A time, P time, S time and Fini
8. Duration and S-P
9. Distance
10. Back Azimuth
11. Incidence
12. Latitude and Longitude
13. ML and MD
14. Event Type (near, local, regional, or teleseismic)
A user with access to the database can modify most of the data; most importantly, changes in
the P time, S time and azimuth are allowed and it is also possible to recalculate the origin time,
S-P, distance, location and duration magnitude. This procedure will be explained in the next
section when an event that needs to be modified is analyzed.
4.4.2 Adding Network Information and Visual Comparison
In order for the seismologist to be able to visually compare the LESSLA location to the locations
calculated by other European networks, the information must be found on the online databases
of these networks. The two networks of choice are the European-Mediterranean Seismological
Centre (EMSC) and Istituto Nazionale di Geofisica e Vulcanologia (INGV). Many earthquakes
detected by LESSLA are usually found in the EMSC bulletin but some that were not found in
EMSC were found in INGV, particularly in the Sicily Channel.
58
Once the relevant network information is found on EMSC or INGV, the essential information
is added under the ’Other Network Information’ window on the events webpage in the LESSLA
database. After the network information is added, the record is updated and the ’All Earthquake
Location Map View’ can be used.
The ’All Earthquake Location Map View’ is the bottom most window on the single events web
page. This is simply a Google map which plots the LESSLA location, the multi-station location
and the other network location on a single map for visual comparison, if they are available. The
map for 6 January is given in Figure 4.8.
In this case, the LESSLA location and the EMSC location were almost exactly the same. The
reasons for this high accuracy are because of clear noise-free signals on all 9 channels. The P
and S picks are very clear on both the H and B channels and the L channels show a strong
signal. Moreover the magnitude of the earthquake was very high at around 6.1ML which also
contributed to the clear signal.
4.5 Manual Analysis of an event
Every earthquake predicted by LESSLA is manually reviewed by the SMRU to obtain the best
solution of the seismic data. Not every automated solution is as accurate as the example shown
above. For example, the picks might be taken too early or too late or the azimuth calculation
might be unstable leading to an error in the final location. Moreover, several earthquakes were
below the threshold of the weighting voting mechanism and so no solution was available. An
example of such an earthquake occurred on 24 December 2008 and the main page is shown in
Figure 4.9.
59
Figure 4.8: The all earthquake locations map view for the 6 January 2008 earthquake. This map plots the LESSLA solution and the
external network solution on the same map for visual comparison. In this case the two solutions are almost exactly the same; this is
because the signal was clear with virtually no noise and the magnitude of the earthquake was high.
Figure 4.9: Main page of the 24 December 2008 earthquake. This earthquake was not processed by LESSLA because the total weight
of the triggered channels was less than the threshold. However, it is clear from the signal on the seismogram that this is an earthquake.
4.5.1 Using Seisgram2k to select the P- and S-picks
For earthquakes such as the 24 December earthquake, where the automatic P- and/or S-picks
are incorrect or unavailable, tools are available to help the seismologist choose the optimum pick.
It is possible to estimate the pick using the pdf files of the streams as in Figure 4.10, but the
best way to choose the best pick is by using a tool called Seisgram2k.
Seisgram2k is an easy-to-use, platform-independent Java software package developed by Anthony
Lomax for interactive visualization and analysis of earthquake seismograms. Seisgram2k can run
and read data files locally and over the Internet. The Seisgram Viewer displays one or more sets
of single trace or 3-component seismograms and has many features, some of which are
• Direct reading of trace data files over the Internet.
• Internal browser for opening trace data files on a web server.
• Able to read data in multiple data formats including SAC and SEED.
• Interactive zooming, scaling, rotation and transformations of the seismograms.
• Time and amplitude picking
• Frequency domain filtering and processing
The features listed above are the key features used to choose the best picks. Seisgram2k works
with any standard browser such as Internet Explorer and Firefox. The seismic data from a single
channel or all nine can be viewed, zoomed and scaled to improve the accuracy of the manual
pick. Frequency filtering can be done to help reduce the noise level of the signal. When a phase
pick is made, Seisgram2k gives the time of the pick to the nearest millisecond. These values can
be added into the P- and S-pick entries on the event’s main page. Now it is possible to calculate
the origin time, S-P time, distance and duration magnitude given the optimized P- and S-picks.
Screenshots of the HH channel of the 24 December earthquake and a zoomed and amplified view
of the same streams can be seen in Figures 4.11 and 4.12 respectively.
62
Figure 4.10: Pdf file of all nine streams before manual picking
Figure 4.11: Viewing the HH components using Seisgram2k
Figure 4.12: Seisgram2k has interactive zooming and scaling of the seismogram to help select the best pick. In this case the P-pick is
selected for the 24 December 2008 earthquake.
4.5.2 Manually choosing the azimuth
Since the P-pick time has been manually edited (in this case, there was no automatic P-pick) to
be in the optimum position, it remains to choose the best azimuth. This is done by using the
“View Analysis” tool, which replaces the normal seismogram pdf files with a different pdf file
showing the azimuth and coherence calculations, as shown in Figure 4.13.
The first nine streams are the usual seismic data streams of the BH, HH and LH channels
respectively. The remaining six “streams” are the azimuth and coherence estimates for each
channel respectively. LESSLA was designed to choose the azimuth at the P-pick for one of the
three azimuth streams. The system automatically chooses the most stable of the three azimuths
after the P-pick. In this case, the system chose the BH azimuth, which was calculated to be
175.22. For events with good clear signals and high magnitude, the azimuth values of the HH
and BH are usually close.
However there are some problems with selecting this azimuth,
• This azimuth indicates that the earthquake source is directly South of Malta, i.e. North
Africa. This is not a seismologically active region and it is unlikely that the true source is
in this direction.
• Although the BH azimuth was the most stable, it was noted that none of the channel
components, BHE, BHN and BHZ were triggered during this earthquake. This is strong
evidence indicating that the azimuth is incorrect.
• There is zero coherence at the P-pick for the BH stream. A high coherence value at the
P-pick would suggest that the azimuth is correct. However, in this case the coherence is
zero throughout the entire BH stream.
Consider the other two streams, i.e. the HH and LH azimuths. The LH azimuth can immediately
be discarded because there is no change in the azimuth calculation as the signal (P-wave) arrives
at the station. Moreover, there is zero coherence and only 1 of the 3 channels of the stream
triggered.
66
Although the HH azimuth is the least stable of the three azimuths, it is the best choice for this
particular earthquake. Firstly, all three components of the HH were triggered and the azimuth
calculation of 76.77 is towards Greece, one of the most seismologically active regions in the
Mediterranean. Moreover, although the coherence is zero at the P-pick, there are several spikes
in the coherence when the signal is detected by the seismic station. Therefore the HH azimuth
was chosen for this earthquake.
In general, the HH azimuth is the most sensitive at short distances. At longer distances (Crete
and beyond), if there is a good signal and a good coherence peak on the LH stream, the LH az-
imuth is usually the best solution. However, the LH can usually be ignored for close earthquakes
such as the one considered here.
4.5.3 Obtaining the Final Coordinates and Plotting
When the azimuth has been selected and the value inserted in the azimuth field on the event
main page, the “Get Location” is clicked on so that the coordinates of the earthquake epicentre
are calculated from the values given in the distance and azimuth fields. Clicking on the “Update”
button as shown in Figure 4.14 updates the record and plots the new location calculated on a
Google map.
If the earthquake was found on the EMSC/INGV bulletins, the manually verified and optimized
position of the epicentre can be compared to the locations of these bulletins in the “Other
Location” section of the main page, as shown in Figure 4.15. A comparison of these manually
optimized epicentres to the locations published by these bulletins is the main scope of this
project.
67
Figure 4.13: Pdf file of all nine streams and azimuth and coherence calculations after manual picking.
Figure 4.14: Updating the record of the 24 December earthquake.
Figure 4.15: Final manually verified solution and Google maps.
4.6 Multi-station plots
In 2008, two other seismic stations, one based in Crete, the other in Sicily started to use the
LESSLA system to locate earthquakes. For several earthquakes in 2008, two or more of the
stations using LESSLA detected the same earthquake. When this happens, it is possible to use
the method of circles described in Chapter 1 to predict the location of the epicentre, using the
distances calculated and ignoring the azimuth calculation. In general, the epicentre predicted
using this method is usually more accurate than the epicentre predicted using the distance and
azimuth calculations from a single station, as shown in Figure 4.16. Multi-station location by
the method of circles was not part of this performance evaluation.
71
Figure 4.16: The multi-station plot (blue) is typically much closer to the EMSC/INGV location (yellow) than
the single-station location.
72
Chapter 5
Performance Evaluation of LESSLA
Epicentre Location
All data analysis was done using Microsoft Excel spreadsheets. All of the automatically processed
earthquakes were saved on a spreadsheet for future comparisons. Then all the earthquakes were
manually reviewed from 2006-2008 to find the optimum solution of each earthquakes as described
in the previous chapter. After manual review, the data was once again saved on a different
spreadsheet for future comparisons with the automatic data.
The two international bulletins used for comparison with LESSLA earthquakes were EMSC and
INGV. For every manually reviewed earthquake on the LESSLA database, these bulletins were
searched for a possible match. If an earthquake with similar origin time and epicentre was found
on these bulletins, the important details such as origin time, latitude, longitude, magnitude
and depth were saved on a separate spreadsheet. The most important detail that was checked
repeatedly was that the automatic data, the manually reviewed data and the corresponding
bulletin data were inserted in the same row number on the three different spreadsheets to avoid
confusion.
For the analysis of the channel triggers algorithm a separate spreadsheet was required. All
earthquakes, quarry blasts, and false triggers were sorted based on the total accumulated weight
73
of the channels. All triggers with total weight, say 18, were saved onto one spreadsheet; a different
spreadsheet was created for all possible total weights. A count of the number of earthquakes,
quarry blasts and false triggers were done for each channel weight and expressed as a percentage.
In all, all seismic data from 2006-2008 was processed and manually reviewed by the SMRU for
the optimum solution before comparison with the European bulletins. There was a technical
difficulty with one of the sensors in 2006 leading to many events being discarded. Moreover,
a problem with the computer at WDD caused a complete shutdown of the station in March
and April 2008. Nonetheless, LESSLA predicted 462 earthquakes, excluding false triggers and
quarry blasts, 135 of which were not found on any European bulletins. The following analysis is
available on Microsoft Excel files on the attached CD.
5.1 Seismicity of the Region and the Range of LESSLA
The first evaluation of LESSLA was done by plotting on a map the locations as predicted by
LESSLA and the locations published by EMSC/INGV as shown in Figure 5.1, which gives a good
picture of the seismicity of the region, the range of LESSLA and the general accuracy of LESSLA
epicentre location. In Figure 5.2, a map plot of all earthquakes predicted by LESSLA but not
on the EMSC/INGV bulletins is given. Note that a significant number of these earthquakes are
south of Malta. Several conclusions can be drawn from these maps, namely,
1. The overall seismicity of the region appears to be correct, although there is some scattering
of LESSLA earthquakes, especially near Greece. This will be investigated more thoroughly
later in the chapter.
2. Many earthquakes south of Malta were detected by LESSLA but were not published on
the EMSC/INGV bulletins. This is indicative of the poor coverage of the area by their
networks and emphasizes the need of a single station algorithm in Malta to detect these
earthquakes.
74
3. The range of LESSLA goes to about Crete in the East and southern Italy in the North.
The distance from Malta to Italy is far less than the distance to Crete. Theoretically,
Italy is within the detectable range of LESSLA but many of the seismic waves seem to
be attenuated, most likely by inclined surfaces and subduction arcs, for events north of
Sicily. In the East, LESSLA seems to have a detectable range of around 1000 km, although
several earthquakes of high magnitude were detected farther away.
5.2 Analysis of the Voting Mechanism
As described in Chapter 2, a voting mechanism based on a fitting combination of STA/LTA com-
ponent triggers were used to decide which events were True Events. Recall the nine component
triggers were assigned the following weights,
• a triggered H component has a weight of 3.
• a triggered B component has a weight of 2.
• a triggered L component has a weight of 1.
An event with the total weight of its component triggers greater than, or equal to 11 were called
True Events and were fully processed. Events with a total weight less than 11 but greater than
3 were not fully processed but were available on the database for manual review.
In all, LESSLA recorded over 4700 individual triggers. After manual review 462 of these were
classified as earthquakes, while 505 as quarry blasts. The rest were noise/false triggers. A test
of how well the voting mechanism was working to decide which triggers were earthquakes was
required. The list of events was sorted according to the total weight of the trigger and classified
into 3 catagories: earthquake, quarry blast, false trigger. Table 5.1 shows this classification.
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Figure 5.1: The seismicity of the region within the detectable range of LESSLA. Many earthquakes in Italy are attenuated and are
not detected by LESSLA. LESSLA’s range extends as far east as Greece, but few events are detected from Crete and further. Many
earthquakes south of Malta that were detected by LESSLA are not on either the EMSC or INGV bulletins.
Figure 5.2: This map shows the locations of earthquakes predicted by LESSLA but not found on the EMSC/INGV bulletins.
The table clearly shows that the vast majority of earthquakes and quarry blasts predicted by
LESSLA had a weight above the threshold. The most common triggers were 18 (all), 15 (all
except the L channel), 11 and 10 (usually the H components supplemented by one or two B or L
components). Many of the manually verified earthquakes, 127 from 462 (27.5%), had a weight of
18, while most of the quarry blasts, 230 from 505 (45.5%), had a weight of 15. This first result
is a positive one, because it is expected for earthquakes to trigger all 9 channels. On the other
hand, quarry blasts are expected to have full H and B triggers but not the L, since the source
of the blasts are very close to the seismic station.
Figure 5.3 shows that 80% of all triggers recorded by LESSLA were false triggers. 10% were
earthquakes while the remaining 10% were classified as quarry blasts. For a clearer picture
and analysis of the voting mechanism, the database was split into two parts: above threshold
and below threshold. The pie charts for these can be seen in Figure 5.4, where it is clear that
the voting mechanism is effective, discarding over 2000 false triggers, while missing only 40
earthquakes and 24 quarry blasts. The high sensitivity of the sensor means that there are many
false triggers at all weights, but, as a percentage, false triggers are far less likely to appear above
the threshold than below it.
Figure 5.3: 80% of all triggers were false triggers, while the rest were either earthquakes or quarry blasts.
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Weight Earthquake Quarry Blast False Trigger Total
18 127 15 433 575
17 15 19 5 30
16 54 28 104 186
15 86 230 266 582
14 26 13 88 127
13 60 82 178 320
12 18 20 267 305
11 36 83 398 517
10 24 21 698 743
9 6 2 304 312
8 2 0 244 246
7 0 0 22 22
6 5 1 589 595
5 3 0 103 106
4 0 0 0 0
3 0 0 0 0
Table 5.1: Table showing the classification of the triggers for every possible combination of weight.
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Figure 5.4: It is clear from the pie charts that events above the threshold are far more likely to be earthquakes
or quarry blasts. Events below the threshold are almost always false triggers.
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5.3 Evaluation of the Automatic Solution
Although every event was manually reviewed and modified before comparison with EMSC/INGV
bulletins, a performance evaluation of the automatic solution including phase picking and az-
imuth was needed. Earthquakes were studied individually without the influence of the EMSC/INGV
bulletins.
As mentioned above, LESSLA predicted 462 earthquakes after manual modifications. Not all of
these earthquakes could be subject to this analysis for several reasons,
1. Teleseismic earthquakes were ignored because LESSLA was not designed to find the source
of such earthquakes.
2. Several earthquakes were ignored because of a poor signal (low SNR) and it was impossible
to determined phases accurately.
3. Earthquakes that were below the voting mechanism threshold could not be analyzed in
this way because no automatic solution was available.
Therefore this analysis was done for only 413 of the 462 earthquakes. 310, or 75% of these
earthquakes were modified from the initial solution given by LESSLA. The next question con-
sidered was how much modification to the original solutions had to be done to obtain the best
solution. The three important parameters for LESSLA is the P-pick, the S-pick and the azimuth.
The P-pick is the most important of the three since changing the value of the P-pick results in
changes in the distance, origin time and most likely the azimuth. Changes is the S-pick affect
only the distance and origin time calculations while changes in the azimuth do not affect any
other parameter. Table 5.2 summarizes the results.
The table shows clearly that the P-pick, the most critical parameter, is also the one that is mod-
ified the most (53.0% of all the earthquakes, and 70.6% of the earthquakes that were modified).
The dependance of the azimuth calculation on the P-pick is evident; there were only 9 cases
where a modification in the P-pick did not result in changes to the azimuth. The S-pick was
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Parameter Number of Modifications Modifications (% from 413) Modifications (% from 310)
P 219 53.0% 70.6%
S 147 35.6% 47.4%
Azimuth Only 85 20.6% 27.4%
P and Azimuth 210 50.8% 67.7%
P only 9 2.2% 2.9%
Table 5.2: Preliminary analysis of modifications that were made on the automated analysis
modified only around 35% of the time, while the azimuth was modified only 20% of the time
when the P-pick was not modified.
5.3.1 P- and S-Pick Accuracy
The accuracy of the picking algorithm was visually evaluated by examining the picks and using
Seisgram2k to adjust the picks if necessary. Two histograms were plotted to show the manual
corrections made in the P and S picks and are given in Figures 5.5 and 5.6 below.
The histograms clearly show that although the automatic solution was modified 75% of the time,
in most cases the errors in the picking algorithm was very minor, usually less than 0.1 seconds.
A very interesting thing to note is that when modifications were needed, both the P- and the
S-pick were usually shifted backwards in time. This means that the automatic phase picker is
either accurate or it is late in choosing the picks. There could be several reasons for this
1. As explained in Chapter 2, picks are detected using an STA/LTA Peak-Valley ratio, which
depends on a threshold to make picks. If there is a low signal-to-noise ratio at the picks,
it is possible that the Peak-Valley threshold is reached slightly later than expected, which
results in the two clusters defining the P- and S- pick being late. This explains why many
automatic picks were made a few seconds later than the true pick.
2. The explanation given above does not explain why some picks, most notably the P-picks,
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Figure 5.5: Difference between automatic P-picks and manually corrected P-picks. The vast majority of the
picks were accurate and were shifted within 0.1 seconds of the automatic pick.
Figure 5.6: Difference between automatic S-picks and manually corrected S-picks. Over 250 of the 310 analyzed
earthquakes S-picks were shifted by only 0.1 second or less.
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were made far later than the true pick in some cases more than a minute. The reason this
happens is because for many earthquakes coming from Greece, in particular Crete and the
Dodacenese Islands, the P-wave is often attenuated and does not appear on the seismogram.
Therefore the automatic picker often misses the P, but detects the S. Therefore, since the
algorithm is forced to make two phase picks, the P-pick is chosen instead of the S-pick,
while the S-pick is chosen a few seconds later. After manual review and reprocessing
using Seisgram2k, the missing P-wave can often be located and shifted back to its proper
position. Since the distance of the sources of these earthquakes to the seismic station at
WDD is far, the S-P time is almost always over 30 seconds, which accounts for these large
errors in the P. The errors in the S are smaller because it is taken somewhere in the middle
of the S-phase and is only shifted a few seconds to the beginning of the phase.
5.4 LESSLA versus EMSC/INGV
The list of earthquakes predicted by LESSLA was compared with online bulletin information
of EMSC and INGV. Earthquakes were identified with the listed bulletin events based on the
origin time and the location1.
In this study, several important parameters of LESSLA earthquakes were compared to the earth-
quakes on EMSC and INGV bulletins. It is important to note that the Earth’s surface in the
Central Mediterranean region was assumed to be flat to simplify the calculations. Moreover, it is
assumed that the seismic waves travel through homogenous rock structure at constant velocity
and no compensations are made for focal depth.
1This is a check to make sure that the events are really the same. For instance, an earthquake whose source
is at Western Turkey is out of LESSLA’s range and the match in the origin time is purely coincidental.
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5.4.1 Origin Time
The origin time of an earthquake is calculated from the S-P time as explained in Chapter 3.
Figure 5.7 shows the error of the LESSLA origin time when compared to that of EMSC/INGV.
The mean and standard deviation of the origin time discrepancy was calculated from the dataset
with the extremities removed. 15 events (5% of the total dataset) were removed from both the
positive extreme and the negative extreme because these earthquakes were more likely to be
wrong because of poor signals and missed picks rather than the algorithm itself. The average
origin time discrepancy was found to be 0.36 seconds with a standard deviation of 2.45 seconds.
Figure 5.7: Difference between LESSLA origin times and EMSC/INGV origin times. Most differences were
less than a second.
5.4.2 Epicentre Location
The estimated differences in the final location between LESSLA and EMSC/INGV were calcu-
lated for each comparable earthquake. As mentioned previously, the Earth’s surface was assumed
to be flat and Pythagoras theorem was used as in Figure 5.8 below,
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Let the coordinates of the LESSLA epicentre be given by (lat0, long0) and the coordinates of
the EMSC/INGV epicentres be given by (lat1, long1). Using Pythagoras’s theorem
(d0)2 =√
(lat0)2 + (long0)2
(d1)2 =√
(lat1)2 + (long1)2
Now d = d1− d0, and since 1 degree = 111.1 km, therefore
d =√
(lat1− lat0)2 + (long1− long0)2 ∗ 111.1
Results of Final Epicentre Location
The results of the epicentre location comparison is given in Figure 5.9 below, the separations of
LESSLA epicentres and EMSC/INGV epicentres were grouped into bin ranges of 50 km. Figure
5.10 is a pie chart of the analysis which gives a better picture of the overall performance of
LESSLA.
Final Epicentre Location Analysis by Region
A region-by-region analysis of LESSLA’s epicentre location was done isolating the three major
regions of seismicity in LESSLA’s range; Malta, Sicily/Italy, and Greece/Crete/Eastern Ionian
Sea to determined which regions give the more accurate epicentre predictions. The histograms
of this analysis is given in Figures 5.11, 5.12 and 5.13 respectively.
LESSLA’s prediction of earthquakes around Malta was very accurate, with more than half of
comparable earthquakes within 50 km of the EMSC/INGV location. Earthquakes originating
from Sicily and Italy were also very accurate overall, with only around 25% of predicted locations
being more than 200 km from the published EMSC/INGV location. On the other hand, in the
Greece area there was more variability in the accuracy. In general, for larger earthquakes with
a good signal-to-noise ratio, the quality of the LESSLA location was very good as shown in the
example in Chapter 4. A few more examples are given in Figure 5.14. For smaller earthquakes,
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the error in the final location is usually much larger. There are two possible sources of error;
the distance calculation and the azimuth calculation, both of which are investigated in the next
sections.
5.4.3 Distance Analysis
As explained in Chapter 3, a distance-calibration curve of distance against S-P time was plotted
to derive the equation for distance calculation. This was given by
Distance = 0.0426(S − P )2 + 7.5882(S − P )
To evaluate the performance of the distance formula, a graph of LESSLA’s distance calculation
against the distance of the EMSC/INGV location from WDD seismic station was plotted as
shown in Figure 5.15. Events with completely wrong distance calculations because of missing
phases were ignored because this would interfere with the integrity of the analysis2. A histogram
of the distance discrepancy of LESSLA locations with respect to EMSC/INGV locations is given
in Figure 5.16. The results indicate that re-calibration of the distance calculation formula is
required since there are significant errors, particularly for distant earthquakes. It is noted that
the formula derived by by Agius works very well for close earthquakes but breaks down for
earthquakes more than 1000 km for WDD.
A new calibration graph was plotted, using the distances of the published EMSC/INGV locations
from WDD against the S-P times measured from the WDD seismometer. The new calibration
curve is given in Figure 5.17, and the best trend line was generated. The best trend line was
chosen based on the value of R2, the square of the correlation coefficient, where R = 1 indicates
a perfect relationship. The intercept of the trend lines were set to zero, because an S-P time of
zero must give a distance of zero. The best trend line was a polynomial of degree 2, and the
2If the LESSLA distance calculation is less than 100km but the distance of the EMSC/INGV location is
hundreds of km from WDD, this is obviously an error because of a poor signal.
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equation generated from this trend line is recommended as the new distance calculation formula,
given by
Distance = 0.0198(S − P )2 + 10.324(S − P )
5.4.4 Azimuth Analysis
The azimuth estimation is the most critical part of the single-station location procedure and is
also the most prone to errors because it is dependant on the accuracy of the P-pick. Furthermore,
it is assumed that the P-wave is not refracted or reflected while it is traveling from the source
location to the WDD seismic station. However, it has been noted that much of the seismicity
from Italy is not detected by WDD and that several earthquakes originating from Crete and the
Dodecanese Islands had attenuated P-waves. Therefore, it is clear that the seismic waves could
be interfered with which could result in incorrect azimuth estimations.
Azimuth Analysis Procedure
Again, the curvature of the earth was ignored during this analysis and the latitudinal and
longitudinal grids were assumed to be squares. These are reasonably good assumptions because
of the small portion of the surface we are considering. The following list explains step-by-step
how the azimuth calculations were done.
1. Let (X, Y ) = (14.5242, 35.8373) be the coordinates of WDD seismic station.
2. Consider an EMSC/INGV location with coordinates (x1, y1).
3. Shift the entire grid so that the origin is exactly at the WDD seismic station, i.e. subtract
the coordinates of each location by (X, Y ) so that the coordinates of the EMSC/INGV
location with respect to the shifted grid is given by (x′1, y′1) = (x1 −X, y1 − Y ).
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4. Assign to every shifted EMSC/LESSLA location a value (E = 1, 2, 3, or 4) depending on
which quadrant it lies in relative to the WDD seismic station.
5. Use trigonometry, i.e. tanφ =y′1
x′1
to find the angle subtended by the EMSC/INGV location
with respect to the x-axis (longitude). Let φ′ = 90− φ.
6. Repeat steps (2) - (5) using the corresponding LESSLA locations with initial coordinates
(x2, y2), shifted to (x′2, y′2), and the angles θ and θ′, where θ = tan−1 y′
2
x′2
and θ′ = 90 − θ.The quadrant the LESSLA location lies in relative to the WDD seismic station is denoted
by L.
7. Evaluate E-L to find the relative difference in the quadrants the EMSC/INGV and LESSLA
locations lie in relative to WDD. This value is important in defining the formula used to
calculate the azimuth difference between EMSC/INGV and LESSLA locations.
8. The azimuth difference, ψ, is calculated using the formula derived below.
Using Figure 5.18, 16 equations can be derived for which the azimuth difference can be calculated
for every combination. Every equation was derived such that a positive difference means that
the LESSLA location is in the clockwise direction relative to the EMSC/INGV, while a negative
difference means that the LESSLA location is in the anticlockwise direction relative to the
EMSC/INGV location. If ψ turns out to be greater than 180 degrees or less than -180 degrees
for any pair of locations, then if ψ > 180, then ψ = ψ − 360, and if ψ < 180, then ψ = ψ + 360.
This ensures that all azimuth calculations are within ±180 degrees. The formulae derived are
given in Table 5.3 below.
Results of Entire Database
These equations were implemented in a nested loops using a Microsoft Excel sheet which is avail-
able on the CD. Histograms were plotted of the entire database and histograms of the azimuth
calculation performance for each major region (Malta, Sicily/Italy, and Greece/Crete/Eastern
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Figure 5.8: The distance d between LESSLA and EMSC/INGV locations were calculated using Pythagoras
theorem.
E L E-L Equation
1 1 0 ψ = (φ− θ)
1 2 -1 ψ = −(φ′ − θ′)
1 3 -2 ψ = −(φ′ + 90 + θ)
1 4 -3 ψ = (φ+ θ)
2 1 1 ψ = (φ′ − θ′)
2 2 0 ψ = −(φ− θ)
2 3 -1 ψ = −(φ+ θ)
2 4 -2 ψ = (φ′ + 90 + θ)
3 1 2 ψ = (φ+ 90 + θ′)
3 2 1 ψ = −(φ+ θ)
3 3 0 ψ = (φ− θ)
3 4 -1 ψ = −(φ′ + θ′)
4 1 3 ψ = −(φ+ θ)
4 2 2 ψ = (φ′ + 90 + θ)
4 3 1 ψ = (φ′ + θ′)
4 4 0 ψ = −(φ− θ)
Table 5.3: Table of equations derived using trigonometry and Figure 5.18
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Figure 5.9: The histogram of the distance between the epicentres calculated by LESSLA and those posted by
EMSC/INGV bulletins indicates that a large proportion of the LESSLA epicentres were within 100km of the
European bulletins.
Figure 5.10: The pie chart shows that 47% of all comparable LESSLA earthquakes were within 100 km of the
location posted by EMSC/INGV. A 100km discrepancy is considered to be a good calculation for single station
location algorithms. By contrast, only 19% of the compared LESSLA earthquakes were more than 300km away
from the posted EMSC/INGV location.
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Figure 5.11: The histogram of the distance between the epicentres calculated by LESSLA and those posted by
EMSC/INGV bulletins for earthquakes close to Malta.
Figure 5.12: The histogram of the distance between the epicentres calculated by LESSLA and those posted by
EMSC/INGV bulletins for earthquakes in Sicily and Italy.
Figure 5.13: The histogram of the distance between the epicentres calculated by LESSLA and those posted by
EMSC/INGV bulletins for earthquakes Greece, Crete and the Eastern Ionian Sea.
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Figure 5.14: A few examples of good earthquake location for high magnitude, high signal-to-noise ratio earth-
quakes from the Greece area.
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Figure 5.15: XY scatter graph showing the relationship between the distance calculation of LESSLA and
EMSC/INGV.
Figure 5.16: Histogram of distance discrepancy.
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Figure 5.17: New calibration graph showing the relationship of the S-P time with the distance. The polynomial
trend line shows a better R2 value than the linear trend line and hence was chosen for the recommended distance
formula.
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Figure 5.18: This diagram explains the azimuth calculation procedure. The origin of the axes is the WDD
seismic station. The solid blue line joins WDD to an EMSC/INGV location in the first quadrant while the
solid red line joins WDD to a LESSLA location in the first quadrant. The right triangles are completed and
the angles are calculated using trigonometry. The azimuth difference of LESSLA’s location with respect to the
EMSC/INGV location is represented by the green area. The coloured dotted lines represent possible events in
the other three quadrants. By using trigonometry and the angles φ, φ′, θ, θ′ the azimuth discrepancy ψ can be
calculated for any combination of quadrants.
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Ionian Sea) were also included. These histogram of the global performance evaluation of the
azimuth is given in Figure 5.19. While the distribution of azimuth errors is fairly close to 0 (for
single station an azimuth error of 30 degrees is considered to be an acceptable result. Uncon-
trollable factors such as noise and unstable azimuth estimations mean that an exact azimuth
calculation for every earthquake is unexpected.), there seems to be an overall azimuth shift in
the clockwise direction. In fact the peak of the histogram appears in the bin range 0-10 de-
grees. Figure 5.20 is a pie chart showing the percentage of LESSLA earthquakes within a certain
azimuth discrepancy range. 76% of LESSLA locations had less than 30 degrees azimuth error
which indicates that many of LESSLA’s azimuth calculations were acceptable after the optimum
solution was determined. Only around 4% of LESSLA azimuth calculations were more than ±60
degrees from the position of the EMSC/INGV location.
Similarly to the origin time, the mean and standard deviation of the azimuth discrepancy was
calculated and was found to be 2.018 with a standard deviation of 20.85, which indicates a slight
bias in the clockwise direction with a lot of scattering in the azimuth.
Investigation of the Azimuth Discrepancy by Region
The same analysis described in the previous section was done on specific regions in LESSLA’s de-
tectable range, namely Malta, Sicily/Italy, and Greece/Crete/Eastern Ionian Sea. The purpose
of focusing the analysis to a specific region was because there are suspicions that the P-waves
of earthquakes originating in Greece are being refracted of an inclined surface, due to the Hel-
lenic and Calabrian subduction arcs in the Ionian Sea. A histogram was drawn for each region,
given in Figures 5.21, 5.22, and 5.23. The results from Malta, Sicily and Italy show a random
scattering about 0 degrees with no clear bias of error in either direction. On the other hand,
earthquakes in the Greece region peaked at +10 degrees and there are clearly more earthquakes
with a positive (clockwise) shift than a negative (anticlockwise shift). This means that many
earthquakes predicted by LESSLA originating from this region will be plotted further South
than the true location.
The mean error in the azimuth for the Greece region was 3.53 degrees with a standard deviation
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Figure 5.19: The azimuth shift in the clockwise direction can be seen clearly which shows a peak at +10 degrees
Figure 5.20: 76% of LESSLA locations were less than 30 degrees in either direction from the EMSC/INGV
location.
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of 14.38. When compared to the mean and deviation of all the data, the mean of the Greece
region indicates that the error is more likely to be in the clockwise direction. Since the standard
deviation is much less than the global deviation, this indicates less scattering of the azimuth in
this region is evidence in favour of refraction of the P-wave because of the Hellenic subduction
zone.
Two conclusions can be drawn from the region-to-region analysis, namely that the azimuth cal-
culation formulae implemented by LESSLA are operating correctly and providing good overall
solutions, especially if the signal has a high signal-to-noise ratio. Conclusions can also be drawn
about the geology of the Mediterranean; the analysis points towards deflection of the P-wave
because of subduction arcs in Greece, leading to southward shifts in the azimuth calculations.
Figures 5.24 and 5.25 shows the map plots of this region for EMSC/INGV and LESSLA respec-
tively, which shows the scattering of the LESSLA predicted epicentres.
Figure 5.21: The azimuth shift in the Maltese region has a peak at -10 degrees, but the data set of comparable
earthquakes in this region is too small to draw definite conclusions.
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Figure 5.22: The azimuth shift for earthquakes in Sicily and Italy peaks at 0 degrees and errors in the azimuth
seem to evenly distributed about 0.
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Figure 5.23: The azimuth shift for earthquakes in Greece, Sicily and the Eastern Ionian Sea has a peak at +10
degrees. In this case, there is a substantial amount of earthquakes to draw conclusions from. The clockwise shift
of LESSLA locations to the EMSC/INGV location is evident, although it is noted that many are within +30
degrees.
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Figure 5.24: The locations of Greek earthquakes as published by EMSC/INGV bulletins are focused in three main areas where it is
most seismically active.
Figure 5.25: The locations of Greek earthquakes predicted by LESSLA are clearly scattered and not focused like the EMSC/INGV
locations. Several earthquakes, because of the refraction of the P-wave, were predicted by LESSLA to be coming from the South-East.
A few earthquakes were predicted to be in Malta; this is because the P-wave was attenuated and undetected by WDD seismic station.
Chapter 6
Conclusions and Recommendations
It is difficult to have an estimate, from the automated solutions, of the error in the location. This
is because there are too many factors involved which may give rise to a wrong location such as
missed P picks, very unstable azimuths, poor signal-to-noise ratios, etc. Moreover, unlike for the
inverse problem, where the error calculation is part of the solution and is reduced upon further
iterations, this is not possible for a single station algorithm, which uses STA/LTA averages of
the signal to select picks.
Overall, the implementation of LESSLA has been a success - we now have a much better picture
of the seismicity of the Sicily Channel as shown in Figure 5.2. This was the reason why LESSLA
was designed and implemented at WDD seismic station. Unfortunately, while it is good that the
seismic station at WDD is able to detect and locate the Sicily Channel earthquakes, since very
few of them are published on international bulletins, it is impossible to compute the accuracy
of the locations of earthquakes from this region. In fact, this performance evaluation depended
mostly on Greek earthquakes, which made up the bulk of all analyzable earthquakes. The
only way to have comparable earthquakes is if these international bulletins extend their seismic
networks to North Africa, which would provide sufficient coverage of the Central Mediterranean
for publication of earthquakes from the Sicily Channel.
Analysis of LESSLA earthquakes can provide a general picture of the geology of the Central
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Mediterranean. The two features which stand out the most are the attenuation of seismic waves
coming from Italy, and the refraction of the P-wave of earthquakes coming from the Hellenic
subduction zone resulting in a clear shift in the azimuth.
This project’s principal aim was to test several important components of the automated earth-
quake detection system LESSLA (Local Earthquake Single-Station Location Analyzer) and try
to improve the system to give more accurate locations. In the previous chapter, the following
were analyzed,
• The voting mechanism based on the channel triggers used to determine which earthquakes
are True Events.
• An evaluation of the automatic P- and S-picking process.
• Comparison of the manually reviewed and verified LESSLA locations to the published
locations of bulletins such as EMSC and INGV.
As an automated system, LESSLA does a very good job on decided which events are earthquakes
by the voting mechanism, missing very few earthquakes over the past three years. However, it
was noted that around 75% of all earthquakes were modified in some way after manual review,
which indicates that a professional seismologist is still needed to give the best solution. In the
case of the P and S picks, many of the changes were very minor, but these could lead to larger
errors in the final location, especially for the P pick. Attenuation of certain phases of the seismic
wave, especially from the Dodacenese Islands, contributed to this error.
After manual review of the earthquakes, it was often possible to optimize the solution so that
many earthquakes were within 100 km of the published EMSC/INGV earthquakes, which is
considered to be the standard for a ’good’ final location in this study. The main source of error
was found to be the azimuth, which had a standard deviation of almost 21 degrees. In the Greece
region, the azimuth error was more likely to be in the clockwise direction indicating refraction of
the P-wave signal. The lower standard deviation of these azimuths add weight to this argument.
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For short range earthquakes, the error in the distance calculation was very small, in many
cases negligible. However, for longer range earthquakes beyond Crete, the distance formula
implemented from the old calibration curve gives larger distance values than the actual distance.
A new calibration curve was plotted and a new formula for the distance derived based on S-P
times.
After manual review, LESSLA predicted 462 individual earthquakes. These earthquakes are
classified based on the S-P time (which is used to calculate the distance) into Near, Local,
Regional or Teleseismic earthquakes. Figure 5.1 is a pie chart showing how the earthquakes
detected by LESSLA were classified.
Figure 6.1: 71% of earthquakes were regional, 18% were local, 5% were near and 5% were teleseismic. 1% of
the earthquakes were verified as earthquakes but were too noisy and discarded.
LESSLA detected 23 teleseismic earthquakes from all over the world from 2006-2008. Although
trying to locate these earthquakes using LESSLA is impossible, time-travel graphs can be used
to verify. It was noted that for many regional earthquakes and all teleseismic earthquakes,
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the L channels were predominant, while for near and local events, the H and B channels were
predominant.
The voting mechanism using the weighted channel triggers is quite efficient and rarely missed
an earthquake from 2006-2008. There was a very large number of false triggers for all weights
although the percentages were lower for events above the threshold. False triggers are easily
spotted manually and the ’Earthquake’ tag can be removed.
6.1 Recommendations
Although LESSLA is fairly accurate at earthquake location, several improvements to the system
can be made,
• Calculate the signal-to-noise ratio at the picks - Currently the signal-to-noise ratio
calculates the ratio of the maximum amplitude of the signal to the noise. By calculating
two SNRs, one at the P-pick and another at the S-pick, it will be easier to analyze the
effects of noise on the picking accuracy.
• Adjusting the distance formula - The distance formula derived by Agius (2007) was
done using only 17 earthquakes and there were no earthquakes farther than 800 km from
WDD seismic station. A new distance calibration curve was plotted using the 300 earth-
quakes, some of which were over 1000 km from WDD. The new distance calculation formula
derived from the calibration curve is given by
Distance = 0.0198(S − P )2 + 10.324(S − P )
and is the recommended distance formula.
• Agius (2007) divided the regions within LESSLA’s seismicity range into various boxes with
the coordinate ranges. Upon closer investigation, it was noted that several of these defined
regions overlapped each other. Therefore, a new series of boxes were defined to represent
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Region Left Latitude Right Latitude Left Longitude Right Longitude
Malta 34.0 36.5 12.0 16.0
Sicily 36.5 38.5 12.0 16.0
Italy 38.5 42.0 14.0 19.0
Tyrrhenian Sea 38.5 42.0 10.0 14.0
Albania 39.5 42.5 19.0 21.0
Greece
39.5 41.0 21.0 24.0
38.0 39.5 19.0 24.0
36.5 38.0 22.0 25.0
Aegean Sea 38.0 41.0 24.0 26.5
Crete 34.0 36.5 22.0 28.0
Dodecanese Islands 36.5 38.0 25.0 28.0
Egypt 25.0 34.0 20.0 32.0
Tunisia 33.0 37.5 8.0 12.0
Libya 25.0 33.0 10.0 20.0
Southern Mediterranean 33.0 35.0 12.0 20.0
Ionian Sea35.0 38.5 16.0 19.0
35.0 38.0 19.0 22.0
Table 6.1: The updated table of coordinate ranges of various regions in the Mediterranean
the regions of the Mediterranean more accurately without overlapping as given in Table
6.1.
• LESSLA automatically selects the most stable azimuth after the P-pick to be the earth-
quake azimuth. It has already been discussed in Chapter 3 that this is not always the
best azimuth to select. The following suggestions may help in a better automatic azimuth
selection.
– For far events, beyond Crete (i.e. at 1000 km from WDD and beyond), if the LH chan-
nels have a good signal and all three components triggered, it may be advantageous
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to have the system choose this azimuth.
– In some cases, there is no change in the azimuth calculate both before and after the
P wave arrives. It is expected that before the P-pick the azimuth changes and then
stabilizes. Therefore, extend the azimuth stability check to some time before the P
wave arrives, say x seconds. If there is no change in the azimuth in this defined time
range before the P-pick, then ignore the azimuth of that channel even if it is the most
stable.
– If the most stable azimuth is from a stream that did not trigger any of the components,
then ignore this stream and select the azimuth from the other two streams.
• Currently, recalculation of the local magnitude after modification of an earthquake is not
available. This should be enable because changes in the earthquake parameters, distance
in particular, will change the value of the local magnitude.
• For multi station plots, the depth of the earthquake could be estimated by using the
’method of spheres’ to find the hypocenter, similar to how the method of circles is currently
being used to determine the epicentre.
6.2 Further Work
While significant work has been done to evaluate and improve several functions of LESSLA in
this project, there is still further work that can be done.
• Evaluation of the magnitude formulae - LESSLA calculates two types of magni-
tude, the duration magnitude and the local magnitude. In particular, the local magnitude
formula uses attenuation functions for Southern California. Although the formula gives
reasonably good agreements with EMSC/INGV magnitude values, it would be better to
find the attenuation functions for the Sicily Channel to use a more appropriate formula.
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• Two other seismic stations, CEL based in Sicily, and IDI located in Crete now use LESSLA
as a single-station earthquake epicentre locater. Similar analysis as described in this dis-
sertation can be done using data from those stations. In particular, seismic data from the
IDI station can be used to investigate further on the geometrical effects of the Hellenic
and Calabrian subduction arcs in the Ionian Sea. Using this station’s data would be more
suitable for this investigation than that of WDD, because of the proximity of IDI from
these subduction arcs.
• It has been shown that when an earthquake was detected by multiple stations, the method
of circles usually gave more accurate locations than the single station. Better network
coverage of the southern Mediterranean, particularly from North Africa, would give a
better picture of the seismicity of the Sicily Channel, particular south of Malta which is a
very active seismic region.
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CD-ROM
Attached with this dissertation is a CD-ROM containing Microsoft Excel spreadsheets containing
all the the data from both LESSLA and EMSC/INGV, and all the analysis and charts used in
this project. There is also a soft copy of this dissertation.
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Internet Links
Seismic Monitoring and Research Unit
www.phys.um.edu.mt/seismic
European-Mediterranean Seismological Centre
http://www.emsc-csem.org
Istituto Nazionale di Geofisica e Vulcanologia
http://www.ingv.it
Malta Environment and Planning Authority
http://www.mepa.org.mt
Seisgram2k Seismogram Viewer
http://alomax.free.fr/seisgram/SeisGram2K.html
SeisComP
http://gfz-potsdam.de/geofon/seiscomp
SAC2000
http://www.llnl.gov/sac
SEED
http://www.iris.edu/manuals/SEEDManual_V2.4.pdf
RDSEED
http://www.iris.edu/manuals/rdseed.htm
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MERIDIAN
www.orfeus-eu.org/Organization/Projects/Meredian/project-summary.html
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References
Agius, M. (2007). Automatic Earthquake Detection and Localisation from a Three-Component
Single-Station. M.Sc. thesis, University of Malta, Malta.
Bolt, B. (1982). Inside the Earth: Evidence from Earthquakes, Thomson Press, India.
Lay, T; Wallace, T. (1995). Modern Global Seismology, Inter. Geophys. Series 58, Academic
Press, America.
Christofferson et al. (1989). Real-time event detection, phase identification and source loca-
tion estimation using single station three-component seismic data, Geophys. J., 97, 471-480.
Scerri, T. (2001). Duration magnitude scale and analysis of seismicity around the Maltese
Islands, B.Sc. thesis, University of Malta, Malta.
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