Wave‐equation migration velocity analysis with extended common‐image‐point gathers
SEG Technical Program Expanded Abstracts 2010
Wave-equation migration velocity analysis (WEMVA) is an image-domain velocity model building technique based on band-limited wave propagation and designed especially for complex subsurface environments. It exploits the coherency of reflection events measured in extended images produced by a cross-correlation imaging condition with non-zero lags. Conventional approaches use either space-lags or time-lag common image gathers, in which only partial information of the extended images is used for
... ages is used for velocity updates. We propose an WEMVA approach using the complete information from both spacelags and time-lags of extended images. With this approach, the velocity model building benefits both from the robustness of using the time-lag information and from the high resolution of using the space-lags information. Such an implementation is facilitated by using extended common-image-point gathers (CIPs) constructed sparsely along reflections and defined jointly for space-and time-lags. These CIPs avoid the bias towards nearly-horizontal reflectors so that steeply dipping events are well preserved in the gathers and the corresponding information related to velocity can be used. Also, the computation of the extended images can be avoided in areas where the velocity is known, e.g., inside salt bodies, or areas where the signal-to-noise ratio is too low, e.g., in shadow zones. This significantly reduces the cost of constructing extended images. A velocity estimation process based on these images requires an objective function based on an operator penalizing the distortion of the images caused by velocity errors. Such an objective function can be designed using the differential semblance principle. The objective function built in this way is uni-modal with respect to the model, thus preventing the inversion from being trapped in local minima. The smoothness of the function around the global minima facilitates the use of gradient-type solvers for achieving convergence towards the true model. The velocity estimation process requires computing the gradient of the objective function which links image errors to velocity model updates. One key component for the construction of the gradient is the adjoint scattering operator which we construct in the framework of frequencydomain downward continuation. Such an operator is formulated by applying the Born linearization to the single square-root equation, and it serves as the foundation for image-domain wavefield tomography algorithms.