The common-reflection surface (CRS) method is a sophisticated alternative to the traditional common-midpoint stacking because its traveltime approximation allows for the use of more traces than the normal moveout. This in turn requires more parameters for the moveout description, thus increasing the computational burden of the parameter estimation. In the literature, a suboptimal strategy is often used, which decreases the complexity but, as we found in this work, compromises the accuracy of the parameters in some cases. To cope with this problem, in this work, we have devised detailed information for efficient estimation of the CRS parameters using the differential evolution (DE) global optimization algorithm. Because we used data sets with low fold and low signal-to-noise ratio, from which no reliable velocity analysis could be easily performed, we applied this algorithm in a fully automatic global search, i.e., without any velocity guide. The results for a 2D real data set from Brazil indicated that the global strategy yielded good results, both in terms of image quality as in the quality of the parameter volumes, especially the stacking velocity estimates, while keeping the computational costs relatively low. We also developed a convergence and a sensitivity analysis of the DE that shows its computational efficiency and the robustness of the optimization method with respect to the choice of the control parameters of the algorithm.
In this paper, we discuss high‐resolution coherence functions for the estimation of the stacking parameters in seismic signal processing. We focus on the Multiple Signal Classification which uses the eigendecomposition of the seismic data to measure the coherence along stacking curves. This algorithm can outperform the traditional semblance in cases of close or interfering reflections, generating a sharper velocity spectrum. Our main contribution is to propose complexity‐reducing strategies for its implementation to make it a feasible alternative to semblance. First, we show how to compute the multiple signal classification spectrum based on the eigendecomposition of the temporal correlation matrix of the seismic data. This matrix has a lower order than the spatial correlation used by other methods, so computing its eigendecomposition is simpler. Then we show how to compute its coherence measure in terms of the signal subspace of seismic data. This further reduces the computational cost as we now have to compute fewer eigenvectors than those required by the noise subspace currently used in the literature. Furthermore, we show how these eigenvectors can be computed with the low‐complexity power method. As a result of these simplifications, we show that the complexity of computing the multiple signal classification velocity spectrum is only about three times greater than semblance. Also, we propose a new normalization function to deal with the high dynamic range of the velocity spectrum. Numerical examples with synthetic and real seismic data indicate that the proposed approach provides stacking parameters with better resolution than conventional semblance, at an affordable computational cost.
Common‐reflection surface is a method to describe the shape of seismic events, typically the slopes (dip) and curvature portions (traveltime). The most systematic approach to estimate the common‐reflection surface traveltime attributes is to employ a sequence of single‐variable search procedures, inheriting the advantage of a low computational cost, but also the disadvantage of a poor estimation quality. A search strategy where the common‐reflection surface attributes are globally estimated in a single stage may yield more accurate estimates. In this paper, we propose to use the bio‐inspired global optimization algorithm differential evolution to estimate all the two‐dimensional common‐offset common‐reflection surface attributes simultaneously. The differential evolution algorithm can provide accurate estimates for the common‐reflection surface traveltime attributes, with the benefit of having a small set of input parameters to be configured. We apply the differential evolution algorithm to estimate the two‐dimensional common‐reflection surface attributes in the synthetic Marmousi data set, contaminated by noise, and in a land field data with a small fold. By analysing the stacked and coherence sections, we could see that the differential evolution based common‐offset common‐reflection surface approach presented significant signal‐to‐noise ratio enhancement.
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