A Comparison of Adaptive Processing Techniques with Nth Root Beam Forming Methods

Abstract

Summary Small differences in slowness and azimuth for overlapping phases especially where the branches of the travel-time curve are triplicated must be resolved for a meaningful inversion of array data. A computer program package has been written in FORTRAN IV which enables a user to determine, automatically, the apparent azimuth and slowness of any portion of the seismic wavetrain recorded at various arrays if he has the raw data on digital tape and has access to any modern computer. These programs make use of two methods, (i) adaptive processing, and (ii) Nth root beam forming which have been compared to determine the apparent azimuth and slowness of the seismic wavelets. The former method is performed by cross correlating the signal on each channel with a velocity and azimuth filtered trace in an iterative manner until the convergence takes place. In the latter method the operation is done by delaying the various channels to align a group of arrivals with a particular velocity and azimuth; taking the Nth root of the signal; summing and then raising the result to the Nth power. The value of apparent velocity and azimuth which produces a maximum filtered signal is determined. Experiments with clean and noisy synthetic data have shown that the adaptive processing method is more successful for resolving small differences in apparent velocity and azimuth of overlapping wavelets. It also has an advantage that a set of residuals may easily be obtained from the analysis. The Nth root method is extremely powerful in enhancing the signal to noise ratio at the expense of signal distortion. The computation time for both methods is about the same.