Linearized wave-equation migration velocity analysis by image warping

Abstract

Seismic imaging produces images of contrasts in physical parameters in the subsurface, e.g., velocity or impedance. To build such images, a background model describing the wave kinematics in the earth is necessary. In practice, the structural image and background velocity model are unknown and have to be estimated from the acquired data. Migration velocity analysis deals with estimation of the background model in the framework of seismic migration and relies on two main elements: data redundancy and invariance of the structures with respect to different seismic experiments. Because all the experiments probe the same model, the reflectors must be invariant in suitable domains (e.g., shots or reflection angle); the semblance principle is the tool used to measure the invariance of a set of multiple images. We measure the similarity of the structural features between pairs of single-shot migrated images obtained from adjacent experiments. By using the estimated warping vector field between two migrated images, we construct an image perturbation which describes the difference in reflectivity observed by two shots. We derive an expression for the image perturbation that drives a migration velocity analysis procedure based on a linearization of the wave-equation with respect to the model parameters. Synthetic 2D examples show promising results in retrieving errors in the velocity model. This methodology can be directly applied to 3D.

Wave-equation migration velocity analysis using plane-wave common-image gathers

“…These artifacts in the plane-wave CIGs might bias the extraction of the moveout information. Moreover, for a velocity with strong lateral variations, the plane-wave CIGs will possibly suffer from the multi-pathing or kinematic artifacts, and such problems also exist for surface-offset or shotprofile CIGs (Stolk and Symes, 2004;Perrone et al, 2014 This paper presented here as accepted for publication in Geophysics prior to copyediting and composition. © 201 Society of Exploration Geophysicists.…”

“…To be more general, the local shift between 3D images is a three-component vector, and the objective function in equation 4 can be generalized as the squared summation of the length of the shift vector Perrone et al, 2014Perrone et al, , 2015Perrone and Sava, 2015). In this case, the corresponding gradient with respect to the migration slowness is derived in Appendix B.…”

“…PWEMVA inverts for the migration velocity by minimizing the objective function which is the squared summation of the local shifts between a plane-wave migration image and a reference image. The idea of defining the objective function as the local displacements between different images or data has been proposed to invert for the subsurface velocity model (Ma and Hale, 2013;Perrone et al, 2014Perrone et al, , 2015, or the velocity variations during a 4D time-lapse seismic survey (Perrone and Sava, 2013). However these methods still require a high computational cost because they compute images or data for every shot profile.…”

Image‐warping waveform tomography

“…Perrone et al . () derived an approximation for the image perturbation based on the estimated displacement field and design a linearised wave‐equation MVA algorithm based on the method developed by Sava and Biondi (). The method presented by Perrone et al .…”

“…The method presented by Perrone et al . () relies on several approximations and linearisations: the wave‐equation MVA operator is obtained from the phase‐shift continuation operator. The entire inversion procedure stems from the particular form of the extrapolation operator that allows one to derive a linearized operator that links perturbation in the image space to perturbation in the model parameters.…”