Optimum primary and supplementary signals optimizing the seismic data resolution

Abstract

Often in practice, when generating seismic waves on a line, even with a wide-band source, numerous natural and technical obstacles cause a low resolution of reflection seismograms. In this case, the economy of the survey should be taken into consideration and rather than ignoring preexisting data, generating additional signal to complement the preexisting data should be tried. This paper describes how this can be done to optimize the resolution of the combined data. The new approach requires a fundamental change in the field technique such that records with different spectral characteristics (RDSC) are now generated from each source–receiver pair. These coincident records share a common reflectivity series, but differ from each other in wavelets and noise. A comprehensive theory for optimum processing (deconvolution) of any available suite of the RDSC is developed. The solution for the problem is a particular case of multichannel Wiener filtering. It can be thought of as two successive procedures. The first is optimum frequency-dependent weighted stacking of the RDSC. The second is single-channel zero-phase Wiener deconvolution filtering of the previous output. This representation enables suggested multichannel filtering to be easily implemented. The effectiveness of the method as well as its advantage over straight summing of the RDSC, followed by single-channel Wiener deconvolution filtering, are corroborated theoretically and demonstrated with field data. Furthermore, a solution is suggested for the problem to evaluate the spectrum of an optimum supplementary signal. The signal contributes to the available set of the RDSC and yields either maximum resolution with limited energy expenses or a certain desired resolution with minimum, but unrestricted energy expenses at the output of the optimum procedure. The optimum distribution of the spectral energy of a primary signal along the frequency axis is a particular case of the above problem with no preexisting data.