seismic tomographyhestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2011-11-09 · seismic...

Seismic Tomography FS11S. Husen

Seismic TomographyFall semester 2011

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3 4 5 6 7 8 9P-Wellengeschwindigkeit [km/s]

N

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Ivrea Körper

Europäische Moho

Adriatische Moho

NE

Zentralalpen

Apennin

Westalpen

Ostalpen

Stephan Husen: [email protected]

09.11.2011- Minimum 1D model

mailto:[email protected]

mailto:[email protected]


Minimum 1D model

We solve the non-linear coupled hypocenter velocity problem by linearization of Ti with first order Taylor Series:

€

Ti = f (hnest ,mk

est )

+∂f (h,m)∂h1

Δh1 + .....

+∂f (h,m)∂m1

Δm1 + ...

How to find hestn and mestk ?

Minimum 1D model

needs to be close to true values


Minimum 1D model

The best initial reference model and hypocenter locations are those that represent a 1D least square solution to the coupled velocity-hypocenter problem (Kissling et al., 1994).

Advantages:

Non-linearity is less severe in 1D.

Solution to the 1D problem is computationally less intensive, thus the full set of linear diagnostics can be computed.

Shareware VELEST


Minimum 1D model

Shareware VELEST:

Solving the coupled hypocenter velocity problem by simultaneous inversion of hypocenter locations, 1D velocities, and station corrections.

ideal situation “realistic” situationProbing the solution space:

Trail and error process with varying 1D velocity models. Each inversion consists of several iterations to solve the coupled hypocenter velocity problem.

We should start our 3D inversion in the vicinity of the global minimum!


Minimum 1D modelCharacteristics of a good minimum 1D model:

• Hypocentral parameters are estimated with equal precision for all earthquakes.

• Velocity within each layer reflects average velocity at this depth range (weighted by the ray distribution).

• Station delays reflect near-surface geology and large-scale deviations from 1D structure (f.e. subducting slabs).

How to compute minimum 1D model?

Very suitable model for earthquake location!

Velocities may not be geologically meaningful!


Minimum 1D modelRecipe to calculate minimum 1D model:

1. Select ~500 of the best events (i.e. small GAP, high number of observations).

2. Establish geometry and intervals of potential 1D models using all available a priori data (i.e. refraction, reflection data).

3. Invert a series of varying initial velocity models using the same earthquake data and inversion parameters.

4. Select the most appropriate (data misfit, geological meaningful) 1D model and test stability of the minimum.


Minimum 1D model1. Data selection

Resolution matrix for well constrained event (GAP<1800):

ot 0.9994 -0.0025 0.0022 0.0040

x -0.0025 0.9595 0.0192 0.0165

y 0.0022 0.0192 0.9536 -0.0437

z 0.0040 0.0165 -0.0437 0.8670

All diagonal elements are close to 1.0, except for focal depth -> focal depth less well constrained!


Minimum 1D model1. Data selection

Resolution matrix for poorly constrained event (GAP>1800):

ot 0.9975 -0.0184 -0.0013 0.0027

x -0.0184 0.8247 -0.0087 0.0020

y -0.0013 -0.0087 0.9093 -0.0981

z 0.0027 0.0020 -0.0981 0.7879

Strong decrease in diagonal element for x and z -> coupling between x and z coordinate!

Only earthquakes with GAP < 1800 should be selected!


Minimum 1D model1. Data selection (example from Switzerland)

544 events GAP < 1800

nobs > 8

Selected events need to be representative for data used in tomographic study!


Minimum 1D model2. Establishing geometry

6 7t• Kissling: Tomography

STATION

V2

V3

V 4

V 5

STATION

.,

VB 2

AZ

HYPOCENTER

VELOCITY OF LAYER (K)

A Z CHANGE IN DEPTH OF HYPOCENTER

Fig. 12. One-dimensional model and hypocenter location. A change in the calculated depth of a hypocenter will cause a larger change in the calculated travel time for a 1D model with fewer layers (model B).Considering the likelihood of velocity gradients, a 1D model with several layers (model A) allows the tracing of a more realistic ray path. Using model B for hypocenter location calculations, the observed arrivals at the stations may be interpreted as belonging to many fewer phases as compared to the use of model A, which accounts better for lateral variations of the apparent velocity by introducing more phases. The dependence of the hypocenter depth on the velocity model is smaller for model A. Thus for routine earthquake location in an area of known lateral velocity variations, model A (assuming the same average velocity over the full depth range and assuming enough a priori information to establish such a multilayered model) is preferable.

arrivals from various travel time branches, the 1D velocity model should consist of a fair number of seismic layers. The use of a 1D model with too few layers for an earthquake location procedure will often result in poor depth control of the events and might produce large mislocations for some events (Figure 12).

In areas with crustal blocks with large differences in the near-surface velocity field it is advisable to separate the data into subsets with all travel paths fully within one such crustal block. In Long Valley, California, and in Yellowstone, Wyoming, the sedimentary fill of the calderas and the alteration of the rocks by hydrothermal activities on the rocks

-4_[ SEA

LEVEL

10-

I STATION

••L•. --•,,,•.,• --STATION • --7-- ,r- -

5.5 C5.a-5.731 5.4. 5.7 5.8 (5.8-5.85) 5.8 5.9

I

1D-MODEL FOR 1D-MODEL FOR

LONG VALLEY AREA WITH BASEMENT

CALDERA OUTCROPPING CID-MODEL

WITH VELOCITY GRADIENTS}

5.4

CALDERA BOUNDARY FAULTS

REFRACTING/REFLECTING HORIZONS DEFINED BY

REFRACTION SEISMIC PROFILING

P-VELOCITY IN KM/SEC

Fig. 13. Connecting two 1D models, e.g., in the area of Long Valley, California. The combined 1D model is shown in the column at left.

(Kissling, 1988)

fewer phases; poor approximation of velocity gradients -> less realistic

more phases; better approximation of velocity gradients -> more realistic

There is a trade-off between number of earthquakes and number of velocity layers!


Minimum 1D model

(Husen et. al, 1999)

3. Inversion with varying initial models

output models

Poor convergence

Good convergence

All models converge to more or less the same velocity model with similar data fit, except for shallow layers (< 10 km) which contain no earthquakes.

initial models

S. Husen et al.

© 1999 RAS, GJI 1 3 81 3 81 3 81 3 81 3 8, 687-701

700

clustering of the events appears in space and time, itis likely that the observed crustal activity is triggeredby the main shock, but special studies are needed toconfirm a possible relation to the Atacama Fault Sy-stem. No events have been detected at shallow crustallevels, which may be due to the high noise levelgenerated by the aftershock activity. On the otherhand, no shallow seismicity has been reported byprevious workers (Comte et al. 1994; Delouis et al.1996) contrasting with fault activity observed at thesurface (Armijo & Thiele 1990; Delouis et al. 1998).

MAXIMUM AND MINIMUM DEPTHMAXIMUM AND MINIMUM DEPTHMAXIMUM AND MINIMUM DEPTHMAXIMUM AND MINIMUM DEPTHMAXIMUM AND MINIMUM DEPTHOF THE COUPLED SEISMOGENICOF THE COUPLED SEISMOGENICOF THE COUPLED SEISMOGENICOF THE COUPLED SEISMOGENICOF THE COUPLED SEISMOGENICZONEZONEZONEZONEZONE

The extent of the seismogenic zone has beenstudied by analysing either the distribution of focalmechanisms of the normal seismicity (e.g. Comte etal. 1994; Delouis et al. 1995) or the aftershockdistribution of a great underthrust event within theseismogenic zone (Tichelaar & Ruff 1993). Both

approaches complement each other and are neededto clearly define the extent of the seismogenic zonewithin a subducting plate. In general, thedetermination of the maximum and minimum depthsof the seismogenic zone has been based on detailedfocal mechanism analysis. Several studies in northernChile aimed at defining the extent of the coupled plateinterface. Comte et al. (1994) used focal mechanismsof locally recorded earthquakes and found amaximum depth of shallow dipping thrust events of47 km in the Antofagasta area. Recently, Delouis etal. (1996) performed a simultaneous determinationof orientation and shape of the local stress tensorand of individual focal mechanisms using locallyrecorded earthquakes within the same region andfound the lower limit of the coupled plate interfaceat a depth of 50 km. Tichelaar & Ruff (1991) usedfocal mechanisms from teleseismically recordedaftershocks of magnitudes greater than 6 for thecentral and northern part of the Chilean subductionzone. Their results of a maximum depth of 46-48 kmfor northern Chile are poorly constrained because

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Figure 13 :F igure 13 :F igure 13 :F igure 13 :F igure 13 : Accurate hypocenters as determined by an independent P+S inversion using a combined on-/offshore network. Vertical depth sections along latitude and longitude are shown at the bottom resp. rightside. The minimum 1D velocity model for P- and S-wave is displayed at the lower right. Area marked by thedashed line denotes the rupure area of the Antofagasta main shock after Delouis et al. (1997).


Minimum 1D model3. Inversion with high/low initial models

prelim. min. 1D model

input models

output models

High and low input models converge to the preliminary minimum 1D model for depths < 50 km.


Minimum 1D model4. Stability tests

Hypocentre determination in the seismogenic zone of the Nazca Plate 695

© 1999 RAS, GJI 1 3 81 3 81 3 81 3 81 3 8, 687-701

a combination of both. When reducing the degree offreedom by fixing the velocities during the inversion,the hypocentres are relocated relatively close to theiroriginal position (Figure 8b) except for a small shiftin a depth of 3.4 km. The hypocentres remain in theirshifted position (Figure 8a) when we use regulardamping in the inversion. In combination with theprevious findings regarding the depth of thehypocentres, the small deviations in latitude andlongitude for both test cases (Figure 8a,b) indicate adecoupling of the epicentre from the velocity problemand a strong coupling of the depth/origin-timeproblem to the velocity for our data set.

Accuracy of Hypocentre LocationsAccuracy of Hypocentre LocationsAccuracy of Hypocentre LocationsAccuracy of Hypocentre LocationsAccuracy of Hypocentre Locations

Relocating mine blasts or shots provides a goodabsolute error estimate for hypocentre locations. Toprovide independent information for such testing thisdata has not been included in the previous inversionprocess. The error expected from this approach willbe higher than that of earthquakes at greater depth,because for events located close to the surface thewaves travel twice through shallow andheterogeneous structures poorly accounted for by themodel (Kissling 1988, his Figure 14). In the CINCAexperiment, near surface velocities are poorlyconstrained, because most rays travel nearlyvertically at shallow depths due to the unfavourableevent-depth distribution. Seven blasts in the Mantos

Blancos copper mine situated inside the network wererelocated using the minimum 1D model for P- and S-wave velocities with corresponding stationcorrections. The mislocation vectors of the relocatedblasts relative to the true mine location are shown inFigure 9. The diameter of the circle represents theuncertainty of the blasts within the mine. The firstrelocations (marked by circles in Figure 9) with theminimum 1D model result in precise epicentrepositions; focal depths, however, show consistentlylarge offset. This unexpected high deviation in depthcould be caused by an inadequate approximation ofthe local near-surface velocities in the vicinity of themine. To overcome this problem, we relocate the mineblasts performing a P- and S-wave inversion with allvelocities fixed except for the first two layers, whichwere regularly damped. The new positions withadjusted near-surface velocities (marked as stars inFigure 9) show identical results for the epicentresand a more realistic focal depth. Hence, we estimatean absolute error of 1 km in epicentre location andof 2 km in focal depth.

)mk(htpeD pV)s/mk( )s/mk(sV sV/pV

05.0- 12.5 99.2 47.1

05.2 73.5 90.3 47.1

05.4 55.5 91.3 47.1

05.6 27.5 92.3 47.1

05.8 98.5 93.3 47.1

05.01 89.5 44.3 47.1

00.51 08.6 57.3 18.1

00.02 18.6 88.3 67.1

00.52 59.6 49.3 67.1

00.03 89.6 50.4 27.1

00.53 11.7 11.4 37.1

00.04 14.7 81.4 77.1

00.54 96.7 03.4 97.1

00.05 50.8 93.4 38.1

00.06 84.8 37.4 97.1

00.07 84.8 87.4 77.1

T a b l e 1 :T a b l e 1 :T a b l e 1 :T a b l e 1 :T a b l e 1 : P-wave and S-wave velocities andresulting Vp/Vs ratio of the minimum 1Dvelocity model.

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longitude mean [m]: -1035

sigma [m]: 714

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latitude mean [m]: -390

sigma [m]: 483

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shift [m

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depthdepthmean [m]: 794

sigma [m]: 1450

Figure 7:Figure 7:Figure 7:Figure 7:Figure 7: Mislocation of hypocenters randomlyshifted by 10 km to 15 km before introduced inthe 1D P+S inversion using the minimum 1D P+Svelocity model. Grey dots denote the systematicalshift of the hypocenter locations beforeintroducing them in the inversion. Allhypocenters are relocated to their originalpostion indicating that no location bias is present.The relative mislocation error in focal depth isnearly twice that in latitude resp. longitude asexpressed by the larger sigma value.

randomly shifted hypocenter locationsS. Husen et al.

© 1999 RAS, GJI 1 3 81 3 81 3 81 3 81 3 8, 687-701

696

Improvement on hypocentreImprovement on hypocentreImprovement on hypocentreImprovement on hypocentreImprovement on hypocentrelocations using OBH datalocations using OBH datalocations using OBH datalocations using OBH datalocations using OBH data

Apart from the applied velocity model, hypocentrelocations are also sensitive to the azimuthaldistribution of stations observing the event. Since asignificant part of the aftershock series is locatedoffshore, the OBH are of obvious importance to extendthe seismic network over the seismogenic zone andto improve its location capabilities. To investigate theinfluence of the OBH data on hypocentre locationswe also established a second minimum 1D modelusing only stations on land. In both casesunfavourable distribution of selected earthquakesprevented us from resolving the expected strongvariations in the upper crust between the offshoreand onshore part. Hence, the differences betweenthese two minimum 1D velocity models are small.

The changes in the hypocentres discussed below are,therefore, mainly due to alterations in the geometryof the location problem.

Differences in hypocentre locations of up to 9 kmin focal depth and 4 km in epicentre are observedwhen locating the offshore events with and withoutOBH. To demonstrate that these mislocations are dueto an unfavourable azimuthal coverage, we computedfor each case the resolution matrix for one event.Figure 10 shows the azimuthal coverage and Table 2lists the hypocentre locations obtained with andwithout OBH for this event. Analogue to seismictomography and other inversion studies, theresolution matrix for the hypocentre location problemprovides an estimate of the interdependence of theresulting hypocentral parameters. For a perfectsolution the corresponding diagonal element is closeto one. Table 3 summarises the resolution diagonal

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sigma [m]: 274

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sigma [m]: 166

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depth mean [m]: 9421

sigma [m]: 478

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sigma [m]: 781

100 200 300 400 500

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sigma [m]: 604

100 200 300 400 500

event

depth mean [m]: 3438

sigma [m]: 1519

a bdamped velocities fixed velocities

Figure 8 :F igure 8 :F igure 8 :F igure 8 :F igure 8 : a) Mislocation of hypocenters systematically shifted to greater depth before introduced in the1D P+S inversion using the minimum 1D P+S velocity model. Damping of the velocities prevents a relocationof the hypocenter to their original position. b) Same as a) but with fixed velocities. Hypocenters are nowrelocated close to the original position. Note the weak influence of the shift in depth on latitude andlongitude indicating the decoupling of epicenter and depth/origin-time determination. Grey dots denotethe systematical shift of the hypocenter locations before introducing them in the inversion.

systematically shifted hypocenter locations

Coupling between velocities and focal depth!

Min. 1D model is sensitive to systematic errors!


Minimum 1D model4. Stability tests

Hypocentre determination in the seismogenic zone of the Nazca Plate 697

© 1999 RAS, GJI 1 3 81 3 81 3 81 3 81 3 8, 687-701

elements for the selected event and for both locations(with/without OBH). A strong decrease for the diago-nal elements corresponding to longitude and focaldepth is clearly visible. The first one is a response tothe lack of stations located to the west of the epicentrewhen neglecting the OBH. The lower resolution infocal depth results from the loss of a station withinthe focal depth distance. Readings within thesedistance provide a higher constraint on thehypocentre location than those with larger offset(Gomberg et al. 1990). Consequently, the poorerresolution in longitude and focal depth for thelocation without OBH is expressed in a large differencein focal depth and longitude between the twolocations.

Computing and analysing the resolution matrix fora large set of earthquakes is obviously unpractical.On the other hand, RMS values are a poor diagnostictool for judging the quality of hypocentre solutions.In the test event we observe a smaller RMS value forthe location without using OBH. This is a consequence

of the smaller number of stations for this event, whichin general results in a lower RMS value estimate. Rat-her than the RMS value or the full resolution matrix,we propose to use the Dirichlet-Spread function(DSPR) and the Average Logarithmic Eigenvalue (ALE),which have been introduced by Kradolfer (1989). TheALE is based on the eigenvalues of the hypocentrelocation problem and qualifies the geometry of anearthquake location problem. For an optimal locationgeometry the ALE is close to zero. The DSPR is basedon the L2 norm of the difference between the

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Figure 9 :F igure 9 :F igure 9 :F igure 9 :F igure 9 : Mislocation in epicenter (top) anddepth (bottom) of relocated Mantos Blancosblasts. The large offset for the events marked bya circle is due to in inadequate approximationof the near surface velocities of the minimum1D model. Adjusting the velocities results in amore realistic depth (marked with stars). Usingthese relocations the location error in depth isestimated to 2 km and to 1 km in epicenter.

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ZIA

Figure 10 :igure 10 :igure 10 :igure 10 :igure 10 : Azimuth distribution of recordedstations for an offshore event located with andwithout OBH. Details about location accuracy canbe found in the text and Table 2 & 3.

HBOhtiw HBOtuohtiw

edutital S°1675.32 S°4075.32

edutignol W°6518.07 W°5587.07

htpedlacof mk46.41 mk41.32

)S+P(sesahpfo.on 43 04

nimP mk31 mk82

nimS mk82 mk82

PAG °77 °532

SMR s42.0 s71.0

ELA 418.1 661.2

RPSD 520.0 012.0

Tab l e 2 :Tab l e 2 :Tab l e 2 :Tab l e 2 :Tab l e 2 : Statistical parameters for selectedevent located with and without OBH.

Relocating blasts with known location to assess accuracy of minimum 1D model.

without adjusted near-surface velocities

with adjusted near-surface velocities


Minimum 1D model5. Station corrections in minimum 1D model

- Station corrections are an integral part of a minimum 1D model.

- They compensate near-surface velocity heterogeneity beneath a station and for large-scale velocity deviations (e.g. subducting slab, dipping Moho).

- Station corrections are computed relative to a reference station (set to zero) and to the velocity of the top layer.

- Negative station corrections: true velocities are faster than model Positive station corrections: true velocities are slower than model.


Minimum 1D model5. Geological meaningful interpretation of station corrections

negative station corrections: real velocities are faster than model

negative station corrections: real velocities are slower than model

Shallow Moho

Ivrea body

Bündner Schiefer

minimum 1D model


Minimum 1D model5. Interpretation of min. 1D model

Different data sets based on Moho topography

northern Switzerland

southwest Switzerland

southeast Switzerland


Minimum 1D model5. Interpretation of min. 1D model

normal upper crust

no clear Moho due to mixing of lower crust and upper mantle velocities

clear MohoSeismic velocities in a minimum 1D model are average velocities weighted by the ray distribution!


Minimum 1D model

The computation of a minimum 1D model allows to check each parameter (hypocenter, station delay, velocity) individually since, unlike a 3D model, a 1D model may not absorb most systematic errors with false (3D) structures.

X - 28 MAURER ET AL.: DETECTION OF SYSTEMATIC ERRORS IN TRAVEL TIME DATA

Figure 3. Polar diagram distance/azimuth showing the travel time residuals in seconds at

station PAL: a) using wrong station coordinates, and b) using correct station coordinates.

July 10, 2009, 2:47pm

1. Wrong station coordinates

original coordinates corrected coordinates

unrealistic residual distribution

Detecting systematic errors


Minimum 1D model3 Compilation of teleseismic and local earthquake data sets forCosta Rica region

Figure 3.4: Station delays at crt03, crt04, crt05, crt06, BUS, CDM, LAR, and LCR2, andgeological setting. Yellowish colours represent sediment rocks. Reddish coloursrepresent igneous rocks.(Geological map taken from Tournon and Alvarado (1997))

to arrival times picked at station BUS, situated only 820 meters away. For this

reason BUS and CDM were also added to the unreliable stations list. Figure 3.4

shows the delays observed at several stations situated near crt06, BUS, and CDM

in relation to the delays obtained for the three of them with the above described

procedure. In a region with outcropping high velocity volcanic rocks close to deep

sedimentary basins, stations delays could vary laterally by up to ±1s in a 350 km

wide country like Costa Rica. Furthermore, depending on azimuthal sampling,

a station delay may normally vary up to ±20% for different data sets from the

same region. Stations crt03, crt04 and crt05, together with crt06 form a transect

from the coast to the Talamanca cordillera. Their station delays are respectively

0.11s, 0.02s and −0.20s seconds, and 0.98s for crt06 (see Table 3.3). Except for

crt06, these delays are in good agreement with a reduction in the thickness of a

low-velocity Oligocen-Miocen sedimentary basin and the limits of the region of

high-velocity, volcanic post-intrusive rocks of the Talamanca cordillera along this

50

2.Timing problems

Detecting systematic errors

Station crt06 shows a very large positive station delay (compared to crt05), which can be indicative for a possible clock error.

Stations BUS and CDM show very different stations delays although they are located only 800 m apart.


Minimum 1D modelTesting performance of min. 1D model as initial reference model.

(Kissling et. al, 1994)

Synthetic velocity structure Data set



Starting models


schematic representation

Slower velocities at shallower layers for a priori model but faster velocities at greater depth.



synthetic velocity structure real local earthquake data set

synthetic local earthquake data set (incl. errors)

initial reference model A initial reference model B

3D tomographic results A 3D tomographic results B

identical inversion scheme

Comparison of tomographic results A and B with synthetic velocity structure allows to assess the performance of each initial reference model.



3-D inversion results

True model A priori initial model

min. 1D initial model

strong artifacts


3D tomographic results A

3D tomographic results B

Tomographic results depend on the choice of the initial reference model. The use of a minimum 1D model yields results that are closer to the true model!


Minimum 1D modelHomework assignment

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- Test stability of preliminary min. 1D model for southwest Switzerland.

- Run Velest on three different models.

- Compare final models and discuss station corrections.

- Files and instructions can be found on datconv.ethz.ch. Each group will have its own subdirectory, named group1, 2, 3.

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seismic tomographyhestia.lgs.jussieu.fr/~boschil/tomography/lecture3... · 2011-11-09 · seismic...

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