Performance of time-delay estimators

Abstract

I analyze the problem of estimating differences in the arrival times of a seismic wavefront recorded by an array of sensors. The two-sensor problem is tackled first, showing that even an approximate knowledge of the wavelet, such as its power spectrum, can substantially increase the accuracy of the time-delay estimate and reduce the signal-to-noise ratio (S/N) threshold for reliable time-delay estimation. The use of the complex trace, although beneficial for time-delay estimates in the presence of frequency-independent phase shifts, reduces the estimation accuracy in poor S/N conditions. I compare the performance of five time-delay estimators for arrays of sensors. Four of five estimators are based on crosscorrelation with a reference signal derived according to one of the following criteria: one trace in the array randomly selected, the stack of all array traces, the stack of all array traces iteratively updated, and (possible only for synthetic data) the noise-free wavelet. Another method, which is referred to as integration of differential delays, is based on the solution of an overdetermined system of linear equations built using the time delays between each pair of sensors. In all the situations considered, the performance of crosscorrelation with a trace of the array randomly selected is significantly worse than the other methods. Integration of differential delays proved to be the best-performing method for a large range of S/N conditions, particularly in the presence of large fluctuations in time delays and large bandwidth. However, for small time delays with respect to the wavelet duration, or if a priori knowledge of the moveout can be used to detrend the original data, crosscorrelation with a stacked trace performs similarly to integration of differential delays.