Synthetic tests of reliability of back-projection images of earthquake ruptures

SUMMARY Back-projection inversions of teleseismic waveforms for the images of rupture progression in great earthquakes have become a popular tool in earthquake studies. However, verifying the trustworthiness of the obtained images in synthetic tests, in which forward-problem data from known propagating ruptures on finite faults are inverted and compared with the true images, have been disproportionally lacking. Such validations for known rupture geometries in a homogeneous medium provide the best-scenario probe into the theoretical ability of the method to resolve the true faulting kinematics. Unambiguous identification of the true source of radiation is possible if alternative trial subfaults, not representing the real emitter, shift the wave-arrival time by different amounts at different stations, resulting in no significant stack achieved for them. This condition is quantitatively expressed in the value of the dimensionless uniqueness coefficient q, which must exceed unity for the inversion to become unique. The criterion is not satisfied for the faults of finite dimensions, precluding reliable determination of rupture progression and speed for them, no matter how wide the coverage of the azimuths from the fault to the stations and how many stations in the network. Unambiguous determination of the exact location is possible for point-source radiators with widening of the azimuthal coverage: the reduction in ambiguity is seen in the progressive improvement in the correctness of the images as the uniqueness coefficient increases to the values greater than one. Fictitious moving, linearly aligned sources appear, increasing in number, as the value of the coefficient gradually drops.