Wavefield tomography based on local image correlations

Abstract

The estimation of a velocity model from seismic data is a crucial step for obtaining a high-quality image of the subsurface. Velocity estimation is usually formulated as an optimization problem where an objective function measures the mismatch between synthetic and recorded wavefields and its gradient is used to update the model. The objective function can be defined in the data-space (as in full-waveform inversion) or in the image space (as in migration velocity analysis). In general, the latter leads to smooth objective functions, which are monomodal in a wider basin about the global minimum compared to the objective functions defined in the dataspace. Nonetheless, migration velocity analysis requires construction of commonimage gathers at fixed spatial locations and subsampling of the image in order to assess the consistency between the trial velocity model and the observed data. We present an objective function that extracts the velocity error information directly in the image domain without analysing the information in common-image gathers. In order to include the full complexity of the wavefield in the velocity estimation algorithm, we consider a two-way (as opposed to one-way) wave operator, we do not linearize the imaging operator with respect to the model parameters (as in linearized wave-equation migration velocity analysis) and compute the gradient of the objective function using the adjoint-state method. We illustrate our methodology with a few synthetic examples and test it on a real 2D marine streamer data set.

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

“…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.…”

Acoustic wavefield imaging using the energy norm

“…The second step is to crosscorrelate these extrapolated wavefields in time and form an image as the zero-lag correlation (Claerbout, 1985). This procedure is based on the assumption that, for the single scattering approximation, the reflector is at the location where source and receiver wavefields coexist in time and space (Cohen and Bleistein, 1979;Oristaglio, 1989;Perrone and Sava, 2015). At the source location, the real injected pressure function is often unknown and an estimated source function is used; i.e., the source wavefield is synthetic for the majority of RTM implementations.…”