A new paper is added to the collection of reproducible documents: Diffraction imaging and time-migration velocity analysis using oriented velocity continuation

We perform seismic diffraction imaging and time-migration velocity analysis by separating diffractions from specular reflections and decomposing them into slope components. We image slope components using migration velocity extrapolation in time-space-slope coordinates. The extrapolation is described by a convection-type partial differential equation and implemented in a highly parallel manner in the Fourier domain. Synthetic and field data experiments show that the proposed algorithms are able to detect accurate time-migration velocities by measuring the flatness of diffraction events in slope gathers for both single and multiple offset data.

A new paper is added to the collection of reproducible documents: Analytical path-summation imaging of seismic diffractions

Diffraction imaging aims to emphasize small subsurface objects, such as faults, fracture swarms, channels, etc. Similarly to classical reflection imaging, velocity analysis is crucially important for accurate diffraction imaging. Path-summation migration provides an imaging method, which produces an image of the subsurface without picking a velocity model. Previous methods of path-summation imaging involve a discrete summation of the images corresponding to all possible migration velocity distributions within a predefined integration range and thus involve a significant computational cost. We propose a direct analytical formula for path-summation imaging based on the continuous integration of the images along the velocity dimension, which reduces the cost to that of only two fast Fourier transforms. The analytic approach also enables automatic migration velocity extraction from diffractions using double path-summation migration framework. Synthetic and field data examples confirm the efficiency of the proposed techniques.

A new paper is added to the collection of reproducible documents: 3D generalized nonhyperboloidal moveout approximation

Moveout approximations are commonly used in velocity analysis and time-domain seismic imaging. We revisit the previously proposed generalized nonhyperbolic moveout approximation and develop its extension to the 3D multi-azimuth case. The advantages of the generalized approximation are its high accuracy and its ability to reduce to several other known approximations with particular choices of parameters. The proposed 3D functional form involves seventeen independent parameters instead of five as in the 2D case. These parameters can be defined by zero-offset traveltime attributes and four additional far-offset rays. In our tests, the proposed approximation achieves significantly higher accuracy than previously proposed 3D approximations.

A new paper is added to the collection of reproducible documents: Theory of interval traveltime parameter estimation in layered anisotropic media

Moveout approximations for reflection traveltimes are typically based on a truncated Taylor expansion of traveltime squared around zero offset. The fourth-order Taylor expansion involves NMO velocities and quartic coefficients. We derive general expressions for layer-stripping both second- and fourth-order parameters in horizontally-layered anisotropic strata and specify them for two important cases: horizontally stacked aligned orthorhombic layers and azimuthally rotated orthorhombic layers. In the first of these cases, the formula involving the out-of-symmetry-plane quartic coefficients has a simple functional form and possesses some similarity to the previously known formulas corresponding to the 2D in-symmetry-plane counterparts in VTI media. The error of approximating effective parameters by using approximate VTI formulas can be significant in comparison with the exact formulas derived in this paper. We propose a framework for deriving Dix-type inversion formulas for interval parameter estimation from traveltime expansion coefficients both in the general case and in the specific case of aligned orthorhombic layers. The averaging formulas for calculation of effective parameters and the layer-stripping formulas for interval parameter estimation are readily applicable to 3D seismic reflection processing in layered anisotropic media.

A new paper is added to the collection of reproducible documents: Weighted stacking of seismic AVO data using hybrid AB semblance and local similarity

Common-midpoint (CMP) stacking technique plays an important role in enhancing the signal-to-noise ratio (SNR) in seismic data processing and imaging. Weighted stacking is often used to improve the performance of conventional equal-weight stacking in further attenuating random noise and handling the amplitude variations in real seismic data. In this study, we propose to use a hybrid framework of combining AB semblance and local-similarity-weighted stacking scheme. The objective is to achieve an optimal stacking of the CMP gathers with class II amplitude-variation-with-offset (AVO) polarity-reversal anomaly. The selection of high-quality near-offset reference trace is another innovation of this work because of its better preservation of useful energy. Applications to synthetic and field seismic data demonstrate a great improvement using our method to capture the true locations of weak reflections, distinguish thin-bed tuning artifacts, and effectively attenuate random noise.

This paper is the first direct contribution from the University of Houston.

A new paper is added to the collection of reproducible documents: Lowrank one-step wave extrapolation for reverse-time migration

Reverse-time migration (RTM) relies on accurate wave extrapolation engines to image complex subsurface structures. To construct such operators with high efficiency and numerical stability, we propose an approach of one-step wave extrapolation using complex-valued lowrank decomposition to approximate the mixed-domain space-wavenumber wave extrapolation symbol. The lowrank one-step method involves a complex-valued phase function, which is more flexible than a real-valued phase function of two-step schemes, and thus is capable of modeling a wider variety of dispersion relations. Two novel designs of the phase function lead to desired properties in wave extrapolation. First, for wave propagation in inhomogeneous media, we include a velocity gradient term to implement a more accurate phase behavior, particularly when velocity variations are large. Second, we develop an absorbing boundary condition, which is propagation-direction-dependent and can be incorporated into the phase function as an anisotropic attenuation term. This term allows waves to travel parallel to the boundary without absorption, thus reducing artificial reflections at wide-incident angles. Using numerical experiments, we demonstrate the stability improvement of a one-step scheme in comparison with two-step schemes. We observe the lowrank one-step operator to be remarkably stable and capable of propagating waves using large time step sizes, even beyond the Nyquist limit. The stability property can help minimize the computational cost of seismic modeling or reverse-time migration. We also demonstrate that lowrank one-step wave extrapolation handles anisotropic wave propagation accurately and efficiently. When applied to RTM in anisotropic media, the proposed method generates high quality images.

A new paper is added to the collection of reproducible documents: Simulating propagation of separated wave modes in general anisotropic media, Part II: qS-wave propagators

Shear waves, especially converted modes in multicomponent seismic data, provide significant information that allows better delineation of geological structures and characterization of petroleum reservoirs. Seismic imaging and inversion based upon the elastic wave equation involve high computational cost and many challenges in decoupling the wave modes and estimating so many model parameters. For transversely isotropic media, shear waves can be designated as pure SH and quasi-SV modes. Through two different similarity transformations to the Christoffel equation aiming to project the vector displacement wavefields onto the isotropic references of the polarization directions, we derive simplified second-order systems (i.e., pseudo-pure-mode wave equations) for SH- and qSV-waves, respectively. The first system propagates a vector wavefield with two horizontal components, of which the summation produces pure-mode scalar SH-wave data, while the second propagates a vector wavefield with a summed horizontal component and a vertical component, of which the final summation produces a scalar field dominated by qSV-waves in energy. The simulated SH- or qSV-wave has the same kinematics as its counterpart in the elastic wavefield. As explained in our previous paper (part I), we can obtain completely separated scalar qSV-wave fields after spatial filtering the pseudo-pure-mode qSV-wave fields. Synthetic examples demonstrate that these wave propagators provide efficient and flexible tools for qS-wave extrapolation in general transversely isotropic media.

Another old paper is added to the collection of reproducible documents: Multiple realizations using standard inversion techniques

When solving a missing data problem, geophysicists and geostatisticians have very similar strategies. Each use the known data to characterize the model’s covariance. At SEP we often characterize the covariance through Prediction Error Filters (PEFs) (Claerbout, 1998). Geostatisticians build variograms from the known data to represent the model’s covariance (Issaks and Srivastava, 1989). Once each has some measure of the model covariance they attempt to fill in the missing data. Here their goals slightly diverge. The geophysicist solves a global estimation problem and attempts to create a model whose covariance is equivalent to the covariance of the known data. The geostatistician performs kriging, solving a series of local estimation problem. Each model estimate is the linear combination of nearby data points that best fits their predetermined covariance estimate. Both of these approaches are in some ways exactly what we want: given a problem give me `the answer’…

A new paper is added to the collection of reproducible documents: Double sparsity dictionary for seismic noise attenuation

A key step in sparsifying signals is the choice of a sparsity-promoting dictionary. There are two basic approaches to design such a dictionary: the analytic approach and the learning-based approach. While the analytic approach enjoys the advantage of high efficiency, it lacks adaptivity to various data patterns. On the other hand, the learning-based approach can adaptively sparsify different datasets but has a heavier computational complexity and involves no prior-constraint pattern information for particular data. We propose a double sparsity dictionary (DSD) for seismic data in order to combine the benefits of both approaches. We provide two models to learn the DSD: the synthesis model and the analysis model. The synthesis model learns DSD in the data domain, and the analysis model learns DSD in the model domain. We give an example of the analysis model and propose to use the seislet transform and data-driven tight frame (DDTF) as the base transform and adaptive dictionary respectively in the DSD framework. DDTF obtains an extra structure regularization by learning dictionaries, while the seislet transform obtains a compensation for the transformation error caused by slope dependency. The proposed DSD aims to provide a sparser representation than the individual transform and dictionary and therefore can help achieve better performance in denoising applications. Although for the purpose of compression, the proposed DSD is less sparse than the seislet transform, it outperforms both seislet and DDTF in distinguishing signal and noise. Two simulated synthetic examples and three field data examples confirm a better denoising performance of the proposed approach.

A new paper is added to the collection of reproducible documents: Seismic data interpolation using nonlinear shaping regularization

Seismic data interpolation plays an indispensable role in common seismic data processing workflows. Iterative shrinkage thresholding (IST) and projection onto convex sets (POCS) can both be considered as a specific form of nonlinear shaping regularization. Compared with linear form of shaping regularization, the nonlinear version can be more adaptive because the shaping operator is not limited to be linear. With a linear combination operator, we introduce a faster version of nonlinear shaping regularization. The new shaping operator utilizes the information of previous model to better constrain the current model. Both synthetic and field data examples demonstrate that the nonlinear shaping regularization can be effectively used to interpolate irregular seismic data and the proposed faster version of shaping regularization can indeed get obvious faster convergence.