Teleseismic Location

• find direction of signals based on Array algorithms• backtrace ray paths through the earth• simplifications: flat earth, plane waves• usually high or reasonable waveform similarity

Epicentre Location using Arrays

estimated ray path

EstimatedSource

ReceiverArray

Angle of Incidence, Slowness

P

global velocity model

Problem: inaccuracy due to deviations from velocity model at the receiverSolution: array calibration (empirical corrections to direction)

Principle of Array Analysis

incomingplane wave

S1 S2S3 earth’ssurface

recording stations

time

S1

S2

S3

resulting seismograms

t2 t1 t3

for a given station geometry: t1, t

2, t

3 (observed) → plane wave (azimuth and slowness) → t

1', t

2', t

3' (theo)

Validate result

time

S1

S2

S3

resulting seismograms

t2 t1 t3

applynegative(t

1',t

2',t

3')

In real life ...

Select Picks and measure tn

Check Accuracy (apply -tn')

Larger aperture

Again, select picks and measure tn

Beamforming not satisfying

for appropriate configuration

incomingplane wave

S1 S2S3 earth’ssurface

recording stations

t1, t

2,..., t

n (observed) → plane wave → t

1', t

2',..., t

n' (theo)

(t1, t

2, ... , t

n) ≈ (t

1', t

2', ... , t

n' )

aperture too large / frequencies too high

incomingplane wave

S1 S2S3 earth’ssurface

recording stations

t1, t

2,..., t

n (observed) → plane wave → t

1', t

2',..., t

n' (theo)

(t1, t

2, ... , t

n) ≠ (t

1', t

2', ... , t

n' )

highveloc.

lowveloc.

problem with small arrays

incomingplane wave

S1 S2S3 earth’ssurface

recording stations

estimated ray path

EstimatedSource

ReceiverArray

Angle of Incidence, Slowness

P

global velocity model

Calibration of arrays

Closer look

FK Algorithm

Plane wave determination without picking

Two ways of determining the plane wave

time

S1

S2

S3

resulting seismograms

t2 t1 t3

a) measure t1,t2,t

3 directly and invert for slowness,azimuth

b) try many plane waves systematically,inversely apply (t

1',t

2',t

3') delays and sum:

assume plane wave with slowness and azimuth,compute theoretical delays (t

1',t

2',t

3') and apply,

in most cases it looks like this:

if you come close the true values of slownessand azimuth you will get aligen signalsand constructive summation:

comparesummationamplitudes

FK diagram

30°

60°

120°

150°210°

240°

300°

330°

4

8

12

slo

wn

ess azimuth

constructive summation(correct t

1', t

2', t

3')

destructive summation(wrong t

1', t

2', t

3')

Example: FK analysis, GRF arrayEvent S. XinJiang, 25-Jul-2007, mb 4.6

30°

60°

120°

150°210°

240°

300°

330°

4

8

12

slo

wn

ess azimuth

Tradeoff: location accuracy and coherency

Frequency

Array aperture

no coherency

no array features

lowresolution

good array features

location possible,

low coherency

Arrays in Germany4°

6°

6°

8°

8°

10°

10°

12°

12°

14°

14° 16°

46°

48° 48°

50° 50°

52° 52°

54° 54°

4km

100km

1000km

GERES: aperture ~4kmfrequencies: 1 - 50 Hz

GRF: aperture ~100kmfrequencies: 0.1 – 5 Hz

GRSN: aperture ~1000kmfrequencies: 0.01 – 0.5 Hz

Array aperture

no coherency

no array features

lowresolution

good array features

location possible,

low coherency

0.05 501

GRSN

GRF

GERES

10°

10°

12°

4km

100km

1000km

Frequency (Hz)

Resolution of German Arrays

Benefits of Array Data Processing

• Improvement of signal/noise ratio• Determination of slowness and azimuth• Phase identification• Location of remote events• Rupture tracking

XinJiang event, time domainImprovement of signal/noise ratio

Phase Identification

P wave

PP wave Source

Earth’s SurfaceReceiver

Angle of Incidence -> Slowness

P

PP

Phase Map, Antofagasta 17-Nov-2007, Chile

Phase Map, Antofagasta 17-Nov-2007, Chile