Towards the shear-wave sonic reverse time migration with the spectral element method

Abstract

This paper evaluates feasibility of three-dimensional sonic reverse-time migration (RTM) based on the spectral element method (SEM). A GPU based algorithm capable of performing both fluid-solid and purely elastic RTM is presented. The key properties of our algorithm is efficient organization of GPU computations, use of optimized unstructured meshes and elements of high order, leveraged with sufficient amount of memory available on newer generations of GPUs. We review the imaging conditions (ICs) for shear-wave imaging, derive four ICs using the Lagrangian formalism and study their merits. We also propose a simple yet powerful approach for automatically constructing unstructured all-hexahedral meshes that respect the borehole geometry. The RTM algorithm's validity and merits are demonstrated through its application on synthetic data as well as a real data set. Overall, our results suggest that the sonic community already possesses the technical capability to perform industrial-scale sonic RTM, at least using GPU clusters employing top-tier chips with large global memory.