3D acoustic modelling and waveform inversion in the Laplace domain for an irregular sea floor using the Gaussian quadrature integration method

This paper explores the concept of 3D acoustic modelling and inversion in the Laplace domain. We used the Gaussian quadrature integration method to assemble the element mass matrix of a coarse regular rectangular element containing both water and subsurface parts, approximating the properties of these two parts without refining the element into smaller components. The purpose of this investigation was to model an irregular sea floor using 3D Laplace-domain modelling and inversion without increasing the computational cost incurred when using a small grid interval to precisely delineate the sea floor. The algorithm was verified by comparing the analytical solution to the modelled wavefield obtained using the conventional Laplace-domain modelling method and the modelled wavefield obtained using the Gaussian quadrature integration in a two-layer model (with 50-m, 100-m, and 200-m grid spacing and 5, 10, 20, and 40 Gaussian quadrature integration points) where an oblique water–subsurface interface is given. The results show that, under certain conditions, the Gaussian quadrature integration method can generate relatively accurate and consistent wavefields compared to the conventional modelling method. Moreover, we performed 3D Laplace-domain inversion with this Gaussian quadrature modelling technique to obtain synthetic data with a flat and irregular interface using a 100-m and 200-m grid. The results obtained under the conditions herein show that 3D Laplace-domain waveform inversion with Gaussian quadrature integration can generate a more accurate and cost-efficient velocity model compared to that obtained using conventional Laplace-domain waveform inversion.

► We use large meshes to reduce the computation in 3D Laplace-domain inversions.
► We applied the Gaussian-quadrature method to meshes at the water bottom.
► This method reduces the error originated from incorrect water bottom meshes.