A new paper is added to the collection of reproducible documents: Full-waveform inversion using seislet regularization

Because of inaccurate, incomplete and inconsistent waveform records, full waveform inversion (FWI) in the framework of local optimization approach may not have a unique solution and thus remains an ill-posed inverse problem. To improve the robustness of FWI, we present a new model regularization approach, which enforces the sparsity of solutions in the seislet domain. The construction of seislet basis functions requires structural information, which can be estimated iteratively from migration images. We implement FWI with seislet regularization using nonlinear shaping regularization, and impose sparseness by applying soft thresholding on the updated model in the seislet domain at each iteration of the data fitting process. The main extra computational cost of the method relative to standard FWI is the cost of applying forward and inverse seislet transforms at each iteration. This cost is almost negligible compared to the cost of solving wave equations. Numerical tests using the synthetic Marmousi model demonstrate that seislet regularization can greatly improve the robustness of FWI by recovering high-resolution velocity models, particularly in the presence of strong crosstalk artifacts from simultaneous sources or strong random noise in the data.

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.