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

Principle of Array Analysis for a given station geometry: t 1, t 2, t 3 (observed) → plane wave (azimuth and slowness) → t 1 ', t 2 ', t 3 ' (theo)

Validate result apply negative (t 1 ',t 2 ',t 3 ')

In real life...

Select Picks and measure t n

Check Accuracy (apply -t n ')

Larger aperture

Again, select picks and measure t n

Beamforming not satisfying

for appropriate configuration t 1, t 2,..., t n (observed) → plane wave → t 1 ', t 2 ',..., t n ' (theo) (t 1, t 2,..., t n ) ≈ (t 1 ', t 2 ',..., t n ' )

aperture too large / frequencies too high t 1, t 2,..., t n (observed) → plane wave → t 1 ', t 2 ',..., t n ' (theo) (t 1, t 2,..., t n ) ≠ (t 1 ', t 2 ',..., t n ' ) high veloc. low veloc.

problem with small arrays

Calibration of arrays

Closer look

FK Algorithm Plane wave determination without picking

Two ways of determining the plane wave a) measure t 1,t 2,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 slowness and azimuth you will get aligen signals and constructive summation: compare summation amplitudes

FK diagram 30° 60° 120° 150°210° 240° 300° 330° slowness azimuth constructive summation (correct t 1 ', t 2 ', t 3 ') destructive summation (wrong t 1 ', t 2 ', t 3 ')

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

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

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

Array aperture no coherency no array features low resolution good array features location possible, low coherency GRSN GRF GERES 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 domain Improvement of signal/noise ratio

Phase Identification

Phase Map, Antofagasta 17-Nov-2007, Chile

Rupture Tracking