Article,
Source array scaling for wavelet deconvolution
Geophysical Prospecting, 28 (6): 902--918 (December 1980)
DOI: 10.1111/j.1365-2478.1980.tb01267.x
Abstract
A seismic source array is normally composed of elements spaced at
distances less than a wavelength while the overall dimensions of
the array are normally of the order of a wavelength. Consequently,
unpredictable interaction effects occur between element and the shape
of the far field wavelet, which is azimuth-dependent, can only be
determined by measurements in the far field. Since such measurements
are very often impossible to make, the shape of the wavelet - particularly
its phase spectrum - is unknown. A theoretical design method for
overcoming this problem is presented using two scaled arrays. The
far field source wavelets from the source arrays have the same azimuth
dependence at scaled frequencies, and the far field wavelets along
any azimuth are related by a simple scaling law. Two independent
seismograms are generated by the two scaled arrays for each pair
of source-receiver locations, the source wavelets being related by
the scaling law. The technique thus permits the far field waveform
of an array to be determined in situations where it is impossible
to measure it. Furthermore it permits the array design criteria to
be changed: instead of sacrificing useful signal energy for the sake
of the phase spectrum, the array may be designed to produce a wavelet
with desired amplitude characteristics, without much regard for phase.
