earthquake.usgs.govU.S. Geological Survey Earthquake Science Center

An Automatic S-phase Arrival Time Picker

Volume - 1 Processing

Earthquake Science CenterU.S. Geological SurveyMenlo Park, California

http://earthquake.usgs.gov/

Erol Kalkan (ekalkan@usgs.gov)

Mathematical model of an idealized �xed-based linear-elastic SDF oscil-lator with viscous damping is:

Volume - 2 Processing

Theory

Take-home Message

S-phase Onset Picking

Manual vs. Automatic S-picks

SPHASEPICKER is a powerful tool for automatically picking S-phase onsets with reasonable precision without requiring multi-components, detection interval or threshold settings.

NC.NMI record of 2014 M6 South Napa earth-quake.

SPHASEPICKER is available at MatLAB FEX. For its source code and demo �le, scan the QR code - ------------->

u

m

k c

mug

ug

mu2

2+ cu du + ku du = mug du = mugu dt

0

t

and its relative energy formulation:

This equation can be expressed in terms of the following energy com-ponents:

Energy components are compared below for short-period-high-damped and long-period-low-damped SDF systems:

In a viscously damped SDF oscillator, the rate of change (power) of damping energy dissipated for a unit mass is computed by di�erentiat-ing with respect to time (t) as

where is the cyclic frequency, de�ned as 2Π/T . T is the natural period of damped vibration related to the natural period of vibration without damping (Tn) by

where EK' is the relative-kinetic energy, Eζ is the damping energy, ES is the elastic-strain energy and EI' is the relative-input energy.

EK' + E + ES = EI

'

dEdt

= 2 Du2

TD = Tn / 1 2

SPHASEPICKER uses a SDF oscillator with a high damping ratio (60% of critical). At this damping level, the frequency response approaches the Butterworth “maximally �at” magnitude �lter, and phase angles are preserved. The relative input energy imparted to the oscillator by the input signal is converted to elastic-strain energy and then dissipated by the damping element as damping energy.

The damping energy yields a smooth envelope over time; it is zero in the beginning of the signal, zero or near zero before the P-phase ar-rival, and builds up rapidly with the S-wave.

Since the damping energy function changes considerably at the onset of the emergent or impulsive S-wave arrival, it is used here as a metric to track and pick the arrival time. The SPHASEPICKER detects S-phase onset using the histogram method.

2014 M6 South Napa Earthquake SPHASEPICKER’s performance is compared with AIC-based picker’s performance and USGS analyst’s picks.

D D D

Abstract- Accurate and automated onset time determination of S-phases are important for real-time location of local, regional and teleseismic events.

- A new method is developed for automatic detection of S-phases in single-component acceleration or broadband velocity records.

- The algorithm “SPHASEPICKER” transforms the signal into a response domain of a single-degree-of-freedom (SDF) oscillator with viscous damping, and then tracks the rate of change of dissipated damping energy in order to pick S-wave phases.

- The proposed algorithm is applied to a data set recorded by a dense regional seismic network in northern California. The picking algorithm is tested against the pciker based on Akaike Information Criterion (AIC) as well as analyst’s S-phase readings, serving as reference picks, with the corresponding automatically derived S-wave arrival times.

Poster Number 65

The SPHASEPICKER ALGORITHMThe algorithm operates on a digital time-series signal, which may be either an acceleration or a broadband velocity record as output from the recorder without �ltering or baseline correction. It’s computa-tional �ow is shown below:

Normalize amplitudesand remove mean

Single componentvelocity or

accelerationrecord

Trim signal frombeginning to itsabsolute peak

Construct a SDFsystem with  T = 0.5 s,

damping = 0.6 

Compute P-phaseonset using:

PphasePicker* (Kalkan, 2016)

Bandpass filtermean-removed signal

Iterate over trial bin sizes using

integrand of dampingenergy via histogram 

method

For each bin, computegradient ratio in dampingenergy before and aftereach trial S-phase onset 

Compute viscousdamping energy and

its integrand

Get S-phaseonset

Identify the bin sizewith the maximum

gradient ratio

P-phaseonset

*asd* Kalkan, E. (2016). “An Automatic P-phase Arrival Time Picker“, Bulletin of Seismological Society of America,106(3): 971-986.

-1

0

1

2

Cou

nts

NCNMI--n.711.HNE.--.V1c

P-phase S-phase

Nor

m. D

amp.

En.

t:0.01s | Bin size:30

9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5Time, s

Pow

er o

f Nor

m. D

amp.

En. Number of bins:30

0 20 40Counts

-200

0

200

Am

plitu

de

P-phase onset:10.08 s | S-phase onset:12.76 s | SNR:26.76 dB

P-phaseS-phase

9 10 11 12 13 14 15Time, s

-200

0

200

Am

plitu

de

0 10 20 30−1

−0.5

0

0.5

1

Record No.

Man

ual −

Aut

omat

ic (S

phas

ePic

ker)

Pic

ks, s

μ = −0.02 s, σ = 0.13 s

0 10 20 30Record No.

Man

ual −

Aut

omat

ic (A

IC) P

icks

, s

μ = 0.10 s, σ = 0.18 s

Impulsive SEmergent S

−40

0

40

0

15

0

3

0

1.5

10s 20s 30s 40s0

15

0

1.5 x 10−3

0

1.5 x 10−7

0

1.5 x 10−3

10s 20s 30s 40s0

1 x 10−4

(cm/s )2

Raw Acceleration

Relative Input Energy

Relative Kinetic Energy

Elastic Strain Energy

Damping Energy

(T = 0.01s, ζ = 0.6) (T = 1s, ζ = 0.1)

10s 20s 30s 40s

n n

(a)

(b)

(c)

(d)

(e)

(kg.cm/s ) 2

0

1.5Raw Acceleration

0

10

0 50s 1m 40s 2m 30s 3m 20s−4

0

6

(cm/s2)

HN1

HN2

UP

Normalized Damping EnergyNormalized

Power of Damping Energy

50s 1m 40s 2m 30s 3m 20s 50s 1m 40s 2m 30s 3m 20s

P0-61.55s

P0-61.80s

P0-61.08s

1

0

1

01

0

1

01

0

1

0

−1.5

-10

S-wave

60 62 64 66−5

0

5

60 62 64 66−0.5

0

0.5

60 62 64 66−3

0

3