The offset-continuation operation (OCO) is a seismic configuration transform designed to simulate a seismic section, as if obtained with a certain source-receiver offset using the data measured with another offset. Based on this operation, we have introduced the OCO stack, which is a multiparameter stacking technique that transforms 2D/2.5D prestack multicoverage data into a stacked common-offset (CO) section. Similarly to common-midpoint and common-reflection-surface stacks, the OCO stack does not rely on an a priori velocity model but provided velocity information itself. Because OCO is dependent on the velocity model used in the process, the method can be combined with trial-stacking techniques for a set of models, thus allowing for the extraction of velocity information. The algorithm consists of data stacking along so-called OCO trajectories, which approximate the common-reflection-point trajectory, i.e., the position of a reflection event in the multicoverage data as a function of source-receiver offset in dependence on the medium velocity and the local event slope. These trajectories are the ray-theoretical solutions to the OCO image-wave equation, which describes the continuous transformation of a CO reflection event from one offset to another. Stacking along trial OCO trajectories for different values of average velocity and local event slope allows us to determine horizon-based optimal parameter pairs and a final stacked section at arbitrary offset. Synthetic examples demonstrate that the OCO stack works as predicted, almost completely removing random noise added to the data and successfully recovering the reflection events.
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.
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