Angle‐domain common‐image gathers by wavefield continuation methods

Abstract

Migration in the angle domain creates seismic images for different reflection angles. We present a method for computing angle-domain common-image gathers from seismic images obtained by depth migration using wavefield continuation. Our method operates on prestack migrated images and produces the output as a function of the reflection angle, not as a function of offset ray parameter as in other alternative approaches. The method amounts to a radial-trace transform in the Fourier domain and is equivalent to a slant stack in the space domain. We obtain the angle gathers using a stretch technique that enables us to impose smoothness through regularization. Several examples show that our method is accurate, fast, robust, and easy to implement. The main anticipated applications of our method are in the areas of migration-velocity analysis and amplitude-versus-angle analysis.

Full waveform inversion using envelope-based global correlation norm

“…The possible reason could be our ignorance of the anisotropic parameters since the Volve area has significant anisotropy above the caprock (Alkhalifah et al, 2016). The angle domain common image gathers (yellow arrows in Figure 12; Sava and Fomel, 2003) are also improved after using the proposed two-stage inversion.…”

Wave-Equation Angle-Domain Hessian

“…The wave-equation angle-domain Hessian can be computed from the subsurface offset waveequation Hessian via an angle-to-offset transformation following the approach presented by Sava and Fomel (2003). This result allow us to implement an angle-domain regularization that stabilizes the the wave equation inversion problem.…”

“…The next sections show how to include the subsurface offset dimension in the Hessian computation and how to go from subsurface offset to reflection and azimuth angle dimensions following the Sava and Fomel (2003) approach. Valenciano et al (2005b) define the zero subsurface-offset Hessian by using the adjoint of the zero subsurface-offset migration as the modeling operator L. Then the zero-offset inverse image can be estimated as the solution of a non-stationary least-squares filtering problem, by means of a conjugate gradient algorithm (Valenciano et al, 2005b,a).…”

“…The next subsection shows how to go from subsurface offset to reflection and azimuth angle dimensions following the Sava and Fomel (2003) approach.…”

“…In this paper, we define the wave-equation angle-domain Hessian from the subsurface offset wave-equation Hessian via an angle-to-offset transformation following the Sava and Fomel (2003) approach. To perform the inversion, the angle-domain Hessian matrix can be used explicitly or, implicitly as a chain of the offset-to-angle operator and the subsurface offset Hessian matrix.…”