The effect of topography on the wavelet response of seismic arrays

Analyzing seismic arrays using their responses to wavelets provides a more convenient and direct method of analysis than using their conventional time-harmonic responses. In this study, the effect of topography on the wavelet response of seismic arrays is investigated using an approach similar to that of Gangi and Benson (1989). Variations in the positions of the array elements (geophones) and in their weights cause degradations in array response for incident time-harmonic signals (Newman and Mahoney, 1973) as well as for incident wavelets (Gangi and Benson, 1989; Benson, 1989). In the following, these variations are called "errors" and these errors cause degradation relative to the error-free (ideal) array response. For incident wavelets, the degradation in the root-mean-square (RMS) amplitude response of an array generally increases as error magintude and number of elements increase. The degradation with wavelet type (Klauder versus Ricker) is relatively small when the wavelets are similar (in the time and/or frequency domain); therefore, only the results for the Ricker wavelet are presented. The degradation due to elevation "errors" decreases as the wavefront incidence angle increases while the degradation due horizontal position "errors" incraeses. Hence, the array response for seismic signals (which arrive at low incidence angles) is more severely degraded by errors in the element elevations than by errors in the element horizontal positions.