A Frequency-Domain Method for Time-Shift Estimation and Alignment of Seismic Signals

Alignment of seismic signals using time shifts obtained from first breaks or through cross-correlation techniques in the time domain without interpolation can only be done to within an integer multiple of the sampling period. In most seismic applications, the accuracy of such techniques is not sufficient. On the other hand, alignment between only two signals can be achieved to within a fraction of the sampling period by fitting a parabola to the cross-correlation peak. In this paper, we present a new alignment procedure in which the time shifts necessary to align simultaneously an ensemble of signals are determined through a parameter-optimization problem in the discretefrequency omain. A comparison of this procedure with the parabolic fit procedure is performed on synthetic data with various levels of signal-to-noise ratios. The effectiveness of this technique is also demonstrated on a real vertical seismic data set.