Optimal combining of seismic data with different spectral characteristics

Abstract

When it comes to sharing overlapping seismic surveys and testing various energy sources, geophysicists have to deal with data having different spectral characteristics. It is very important to note that such data share the same information on the reflectivity of the medium, which is of interest to us. In order to combine such redundant data optimally and estimate the reflectivity of the medium more effectively, this article proposes using multichannel reverse Wiener filtering. To avoid the problems associated with a possible difference in the data acquisition systems of overlapping surveys, it is proposed to reduce the amount of information processed and to combine the final seismic images obtained from each of the independent surveys or from different sources. The theory of the optimal method is presented and the structure of the solution obtained is analyzed. It is shown that the method can be represented as a combination of the optimal frequency-dependent weighted summation of images with the subsequent single-channel inverse Wiener filtering (deconvolution) of the summation result. A theoretical comparison of the optimal method with simplified analogues wherein the first step is a simple unweighted summation without and with elimination of the wavelet phase spectra of images is performed. It is shown that the greater the difference between the spectra of the signal components of images at a given frequency, the greater the advantage of the optimal method of combining them over the simplified variants. The article stresses that since seismic exploration capabilities basically allow only signal parameters to be changed, the greatest effect from the optimal method can be achieved due to maximum mutual displacement (minimum mutual overlap) along the frequency axis of the spectra of the wavelets of combined images. This is theoretically confirmed by the calculation of the spectrum of the optimal complementary signal the addition of which to the existing set to participate in optimally combining ensures maximum efficiency of this procedure. The rationale is given that the optimal procedure should be performed only within the frequency interval where the signal averaged over the number of images prevails over the averaged noise. The method is tested on synthetic data. It is shown that its efficiency monotonously increases with increasing the input signal-to-noise ratio, the number of images involved in processing, and the mutual frequency shift of their spectra, i.e. as the degree of overlap of these spectra decreases. Moreover, the effectiveness of the method is confirmed on a field line from the Dnieper-Donets depression, which was independently worked out with dynamite and vibratory sources. It is shown that the optimal method provides the most regular and resolved reflections across the entire image, which significantly exceeds the results of independent single-channel deconvolutions of the images obtained with both types of sources and of their simplified combination.