Regularized tomographic inversion with geological constraints

Abstract

Reflection tomography is the industry standard tool for velocity model building, but it is also an ill-posed inverse problem as its solution is not unique. The usual way to obtain an acceptable result is to regularize tomography by feeding the inversion with some a priori information. The simplest regularization forces the solution to be smooth, implicitly assuming that seismic velocity exhibits some degree of spatial correlation. However, velocity is a rock property; thus, the geometry and structure of rock formations should drive correlation in velocity depth models. This observation calls for constraints driven by geological models. In this work, we present a set of structural constraints that feed reflection tomography with geometrical information. These constraints impose the desired characteristics (flatness, shape, position, etc.) on imaged reflectors but act on the velocity update. Failure to respect the constraints indicates either velocity inaccuracies or wrong assumptions concerning the constraints. Reflection tomography with structural constraints is a flexible framework that can be specialized in order to achieve different goals: among others, to flatten the base of salt bodies or detachment surfaces, to recover the horizontalness of oil–water contacts, or to impose the co-location of the same imaged horizon between PP and PS images. The straightforward application of structural constraints is that of regularizing tomography through geological information, particularly at the latest stages of the depth imaging workflow, when the depth migration structural setting reached a consistent geological interpretation. Structural constraints are also useful in minimizing the well-to-seismic mis-ties.Moreover, they can be used as a tool to check the consistency of interpreters’ hypothesis with seismic data. Indeed, inversion with structural constraints will preserve image focusing only if the interpreters’ insights are consistent with the data. Results from synthetic and real data demonstrate the effectiveness of reflection tomography with structural constraints.