Optimal measurement of relative and absolute delay times by simulated annealing

Conventional approaches to determine relative arrival times of body waves recorded by a local or a regional array rely on cross-correlations between pairs of traces. This problem is better posed as a non-linear inverse problem, which involves the minimization of a cost function that measures the difference between a reference unknown waveform that can be time delayed, and the observed data. The unknown parameters that are solved for, are the amplitude values at each time sample of the optimal waveform and its time delay defined for each trace. The problem, which has a large number of unknown parameters, is solved with simulated annealing. The algorithm is very efficient and can be used for a routine analysis of seismic data. The application of this method to several earthquakes recorded during different PASSCAL experiments demonstrates that it provides accurate and robust differential traveltime measurements even with very noisy data.