Pre-stack diffraction separation by parameterizing the reflection local slope

Diffracted waves provide the opportunity to detect small-scale subsurface structures because they give wide illumination direction of geological discontinuities such as faults, pinch-outs, and collapsed columns. However, separating diffracted waves is challenging because diffracted waves have greater geometrical amplitude losses and are generally weaker than reflections. To retain more diffracted waves, a pre-stack diffraction separation method is proposed based on the local slope pattern and plane-wave destruction method. Generally, it is difficult to distinguish between the hyperbolic reflections and hyperbolic diffractions using the data-driven local slope estimation in the shot domain. Therefore, we transfer the slope estimation in the shot domain to the velocity analysis in the common midpoint domain and the ray parameter calculation in the stack domain. The connection between the local slope and the normal move-out velocity and the surface-ray parameter is known, which provides a novel approach for estimating the local slope of the hyperbolic reflected waves in the shot domain. The estimated slope can provide an exact slope-based operator for the plane-wave destruction (PWD) method, thus allowing the PWD to separate diffracted waves from reflected waves in the shot domain. Synthetic and field data tests demonstrate the feasibility and effectiveness of the proposed pre-stack diffraction separation method.

Approximations for traveltime, slope, curvature, and geometrical spreading of elastic waves in layered transversely isotropic media

Each seismic body wave, including quasi compressional, shear, and converted wave modes, carries useful subsurface information. For processing, imaging, amplitude analysis, and forward modeling of each wave mode, we need approximate equations of traveltime, slope (ray-parameter), and curvature as a function of offset. Considering the large offset coverage of modern seismic acquisitions, we propose new approximations designed to be accurate at zero and infinitely large offsets over layered transversely isotropic media with vertical symmetry axis (VTI). The proposed approximation for traveltime is a modified version of the extended generalized moveout approximation that comprises six parameters. The proposed direct approximations for ray-parameter and curvature use new, algebraically simple, equations with three parameters. We define these parameters for each wave mode without ray tracing so that we have similar approximate equations for all wave modes that only change based on the parameter definitions. However, our approximations are unable to reproduce S-wave triplications that may occur in some strongly anisotropic models. Using our direct approximation of traveltime derivatives, we also obtain a new expression for the relative geometrical spreading. We demonstrate the high accuracy of our approximations using numerical tests on a set of randomly generated multilayer models. Using synthetic data, we present simple applications of our approximations for normal moveout correction and relative geometrical spreading compensation of different wave modes.

Offset-extended sparse Radon transform: application to multiple suppression in the presence of AVO

The conventional Radon transform suffers from a lack of resolution when data kinematics and amplitudes differ from those of the Radon basis functions. Also, a limited aperture of data, missing traces, aliasing, a finite number of scanned ray parameters, noise, residual statics, and amplitude variations with offset (AVO) reduce the de-correlation power of the Radon basis functions. Posing Radon transform estimation as an inverse problem by searching for a sparse model that fits the data improves the performance of the algorithm. However, due to averaging along the offset axis, the conventional Radon transform cannot preserve AVO. Accordingly, we modify the Radon basis functions by extending the model domain along the offset direction. Extending the model space helps in fitting data; however, computing the offset-extended Radon transform is an under-determined and ill-posed problem. To alleviate this shortcoming, we add model domain sparsity and smoothing constraints to yield a stable solution. We develop an algorithm using offset-extended Radon basis functions with sparsity promoting in offset-stacked Radon images in conjunction with a smoothing restriction along the offset axis. As the inverted model is sparse and fits the data, muting common-offset Radon panels based on ray-parameter/curvature is sufficient for separating primaries from multiples. We successfully apply the algorithm to suppress multiples in the presence of strong AVO on synthetic data and a real data example from the Gulf of Mexico, Mississippi Canyon. The results show that extending the Radon model space is necessary for improving the separation and suppression of the multiples in the presence of strong AVO.