Waveform Tomography by Correlation Optimisation

An important ingredient of any tomography-based velocity inversion method is the determination of traveltime differences. When a ray-based method is used, the modelled traveltimes are directly available and the traveltimes in the observed data need only to be picked once. When using wave-equation-based methods, however, the traveltime difference between two complex waveforms needs to be determined at each iteration. A straight-forward approach automatically picks the onset of relevant arrivals, either directly or via a correlation of the two waveforms. If the waveforms are not very similar, however, this approach is problematic. We propose to measure the traveltime difference via a weighted norm of the correlation of the two waveforms. The weighted norm can be used directly as an optimisation criterion for waveform tomography. We illustrate this with a synthetic and real data example.