An efficient 3D traveltime calculation using coarse-grid mesh for shallow-depth source

Abstract

3D Kirchhoff pre-stack depth migration requires an efficient algorithm to compute first-arrival traveltimes. In this paper, we exploited a wave-equation-based traveltime calculation algorithm, which is called the suppressed wave equation estimation of traveltime (SWEET), and the equivalent source distribution (ESD) algorithm. The motivation of using the SWEET algorithm is to solve the Laplace-domain wave equation using coarse grid spacing to calculate first-arrival traveltimes. However, if a real source is located at shallow-depth close to free surface, we cannot accurately calculate the wavefield using coarse grid spacing. So, we need an additional algorithm to correctly simulate the shallow source even for the coarse grid mesh. The ESD algorithm is a method to define a set of distributed nodal sources that approximate a point source at the inter-nodal location in a velocity model with large grid spacing. Thanks to the ESD algorithm, we can efficiently calculate the first-arrival traveltimes of waves emitted from shallow source point even when we solve the Laplace-domain wave equation using a coarse-grid mesh. The proposed algorithm is applied to the SEG/EAGE 3D salt model. From the result, we note that the combination of SWEET and ESD algorithms can be successfully used for the traveltime calculation under the condition of a shallow-depth source. We also confirmed that our algorithm using coarse-grid mesh requires less computational time than the conventional SWEET algorithm using relatively fine-grid mesh.