The finite-frequency sensitivity kernel for migration residual moveout and its applications in migration velocity analysis

Abstract

We have derived a broadband sensitivity kernel that relates the residual moveout ͑RMO͒ in prestack depth migration ͑PSDM͒ to velocity perturbations in the migration-velocity model. We have compared the kernel with the RMO directly measured from the migration image. The consistency between the sensitivity kernel and the measured sensitivity map validates the theory and the numerical implementation. Based on this broadband sensitivity kernel, we propose a new tomography method for migration-velocity analysis and updating -specifically, for the shot-record PSDM and shot-index common-image gather. As a result, time-consuming angle-domain analysis is not required. We use a fast one-way propagator and multiple forward scattering and single backscattering approximations to calculate the sensitivity kernel. Using synthetic data sets, we can successfully invert velocity perturbations from the migration RMO. This wave-equationbased method naturally incorporates the wave phenomena and is best teamed with the wave-equation migration method for velocity analysis. In addition, the new method maintains the simplicity of the ray-based velocity analysis method, with the more accurate sensitivity kernels replacing the rays.

Acoustic inverse scattering via Helmholtz operator factorization and optimization

“…Let d/(x 0 , x;x s0 ) = RedU(x 0 , x;x s0 ). We follow Xie and Yang [22] and apply the Rytov approximation, when…”

“…Under certain conditions, another class of annihilators can be constructed reflecting data redundancy in the source coordinates, following an approach known as ''reverse time migration". As in Xie and Yang [22], we use this redundancy in combination with the notion of image continuation [23] to arrive at a misfit criterion and optimization scheme for wave-equation reflection tomography.…”

Removing smearing-effect artifacts in angle-domain common-image gathers from reverse time migration

“…Reflection events in ADCIGs are flat when a correct velocity model is used for migration, curved up when the migration velocity model is slower, or curved down when the migration velocity model is faster than the correct model ( Figure 1). Velocity updates are related to the curvature of the events, as defined by picking residual depth moveouts (Xie and Yang, 2008b;Zhang and McMechan, 2013), or by differential semblance optimization (Shen and Symes, 2008).…”

Nonlinear Fréchet derivative and its De Wolf approximation

“…The derivation of the kernels is usually calculated by the first order Born approximation based on the formulation of linearized Fréchet derivative. Similar sensitivity kernel formulation has been used in reflection seismics (de Hoop et al, 2006;Xie and Yang, 2008). For the full waveform inversion, the Fréchet derivative is also used to relate model parameter perturbations to changes in seismic waveforms (Tarantola, 1984;Tarantola, 1986;Tarantola, 2005).…”