The common-reflection-surface (CRS) method offers a stack with higher signal-to-noise ratio at the cost of a timeconsuming semblance search to obtain the stacking parameters. We have developed a fast method for extracting the CRS parameters using local slope and curvature. We estimate the slope and curvature with the gradient structure tensor and quadratic structure tensor on stacked data. This is done under the assumption that a stacking velocity is already available. Our method was compared with an existing slopebased method, in which the slope is extracted from prestack data. An experiment on synthetic data shows that our method has increased robustness against noise compared with the existing method. When applied to two real data sets, our method achieves accuracy comparable with the pragmatic and full semblance searches. Our method has the advantage of being approximately two and four orders of magnitude faster than the semblance searches.
It is well known that the quality of stacking results (e.g., noise reduction, event enhancement, and continuity) can be greatly influenced not only by the traveltime operator chosen but also by the apertures used. We have considered two so-called diffraction-stack traveltimes, together with the corresponding apertures, designed to enhance reflections and diffractions, respectively. The first one is the common-reflection-surface (CRS) diffraction traveltime that is obtained from the general CRS traveltime upon the condition that the target reflector reduced to a point, which we refer to as the diffraction CRS (DCRS) traveltime. The second one is the double-square-root (DSR) traveltime, well established in time migration. We have observed that the DCRS and DSR traveltimes depend on fewer parameters (two in 2D and five in 3D) than the full CRS traveltime (three in 2D and eight in 3D). For the DCRS and DSR traveltimes, we have proposed specific apertures based on the projected Fresnel zone, which are able to produce high-quality stacked sections using less parameters to be estimated. The key factor in that approach lies in the choice of traveltime operators together with careful selection of stacking apertures. In particular, suitable choices of operators and apertures lead to stacking volumes in which reflections are enhanced (and the diffractions are attenuated) or the corresponding ones in which diffractions are enhanced (and reflections are attenuated). Synthetic and field data confirm the proposed approach has good potential for image-quality improvement.
The extraction of kinematic parameters from wave propagation through traveltimes is one of the great challenges in seismic data processing. In this context, we modify the common-reflection-surface (CRS) traveltime to improve its accuracy and also interpret its parameters via paraxial ray theory in an anisotropic medium obtaining information about the wavefront curvatures measured at surface. The proposed method consists of searching for the best stacking parameters that fit the data set followed by the extraction of kinematic information from the measured waves. Numerical tests show the effectiveness of our assumptions and that the results obtained in the fitting and parameter extraction in anisotropic media achieve better accuracy than conventional CRS.
Exploration of redundancy contained in the seismic data set assures enhancement of images that are based on stacking results. This enhancement is the goal of developing multiparametric traveltime equations that are able to approximate reflection and diffraction events in general source-receiver configurations. The main challenge of using these equations is to estimate a large number of parameters in a computationally feasible, reliable, and fast way. To obtain a better fit for diffraction traveltime events than the ones in the literature, we have derived a finite-offset (FO) double-square-root (DSR) diffraction traveltime equation (which depends on 10 parameters in three dimensions and four parameters in two dimensions). Moreover, to reduce the number of parameters, we have developed another version called simplified FO-DSR diffraction traveltime equation (which depends on five parameters in three dimensions and two parameters in two dimensions), which delivers a similar performance. We have developed operators that make use of the simplified FO-DSR traveltime equation to construct the so-called diffraction-only data set volumes (or, more simply, D-volumes) assuring enhancement in the diffraction extraction process. The D-volume construction has two steps: first, a stacking procedure to separate the diffraction events from the input data set and second, a spreading procedure to enhance the quality of these diffractions. As proof of concept, our approach has been tested on 2D/3D synthetic and 2D field data sets with successful results.
The effective application of normal moveout correction processes mainly depends on four factors: the chosen traveltime approximation, the stretching associated with the given traveltime, crossing events and phase changes, the last two being inherent to the seismic data. In this context, we conduct a quantitative analysis on stretching considering a general traveltime expression depending on half‐offset and midpoint coordinates. Through this analysis, we propose a mathematically proven procedure to eliminate stretching, which can be applied to any traveltime approximation. The proposed method is applied to synthetic and real data sets, considering different traveltime approximations and achieved complete elimination of stretching.
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