1. 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

2. Epicentre Location using Arrays
Problem: inaccuracy due to deviations from velocity model at the receiver
Solution: array calibration (empirical corrections to direction)

3. Principle of Array Analysis
for a given station geometry:
t1, t2, t3 (observed) → plane wave (azimuth and slowness) → t1', t2', t3' (theo)

4. Validate result
apply
negative
(t1',t2',t3')

5. In real life ...

6. Select Picks and measure tn

7. Check Accuracy (apply -tn')

8. Stations Available

9. Larger aperture

10. Again, select picks and measure tn

11. Beamforming not satisfying

12. for appropriate configuration
t1, t2,..., tn (observed) → plane wave → t1', t2',..., tn' (theo)
(t1, t2, ... , tn) ≈ (t1', t2', ... , tn' )

13. aperture too large / frequencies too high
veloc.
low
veloc.
t1, t2,..., tn (observed) → plane wave → t1', t2',..., tn' (theo)
(t1, t2, ... , tn) ≠ (t1', t2', ... , tn' )

14. problem with small arrays

15. Calibration of arrays

16. Closer look

17. Plane wave determination without picking
FK Algorithm
Plane wave determination without picking

18. Two ways of determining the plane wave
a) measure t1,t2,t3 directly and invert for slowness,azimuth
b) try many plane waves systematically,
inversely apply (t1',t2',t3') delays and sum:
compare
summation
amplitudes
assume plane wave with slowness and azimuth,
compute theoretical delays (t1',t2',t3') and apply,
in most cases it looks like this:
if you come close the true values of slowness
and azimuth you will get aligen signals
and constructive summation:

19. FK diagram 330° 30° 300° 60° 240° 120° 210° 150° destructive summation
(wrong t1', t2', t3')
330°
30°
azimuth 12
300° 8
60°
slowness
constructive summation
(correct t1', t2', t3') 4
240°
120°
210°
150°

20. Example: FK analysis, GRF array Event S. XinJiang, 25-Jul-2007, mb 4.6
330°
30°
azimuth 12
300° 8
60°
slowness 4
240°
120°
210°
150°

21. Tradeoff: location accuracy and coherency
Array aperture
no plane waves
no array features
no coherency
location possible,
good array features
low coherency
resolution
low
Frequency

22. Arrays in Germany GERES: aperture ~4km frequencies: 1 - 50 Hz
GRF: aperture ~100km
frequencies: 0.1 – 5 Hz
GRSN: aperture ~1000km
frequencies: 0.01 – 0.5 Hz

23. Resolution of German Arrays
Array aperture
GRSN
no plane waves
no array features
no coherency
location possible,
GRF
good array features
GERES
low coherency
resolution
low
0.05 1 50
Frequency (Hz)

24. Benefits of Array Data Processing
Improvement of signal/noise ratio
Determination of slowness and azimuth
Phase identification
Location of remote events
Rupture tracking

25. Event in XinJiang, 53°dist, mb 4.5 Improvement of signal/noise ratio

26. Phase Identification

27. Phase Map, Antofagasta 17-Nov-2007, Chile

28. Phase Map, Antofagasta 17-Nov-2007, Chile

29. Rupture Tracking