Equivalent source distribution for efficient 3-D acoustic wave equation modelling in the Laplace domain

Abstract

SUMMARY Since the recent introduction of the Laplace-domain full waveform inversion, an efficient and accurate modelling technique for the 3-D Laplace-domain wave equation has been sought. The efficiency and accuracy of the 3-D acoustic wave equation modelling in the Laplace domain strongly depends on how to accurately account for free surface conditions and the actual source and receiver locations. In terms of efficiency, fortunately, the Laplace-domain wave equation can be solved on a coarse grid because the field is not propagating as if it were a potential field. However, it is not possible to accurately compute the Laplace-domain response by assuming that the source and the receivers are located at the grid nodes when we use a coarse grid. To resolve this problem, we propose an equivalent source distribution algorithm that allows us to simulate the free surface condition accurately using a coarse-grid finite-element or finite-difference method. It is shown that the equivalent source vector obtained from a homogeneous half-space model can be used for arbitrarily complex models. The extension of the equivalent source to complex heterogeneous media is explained by the approximation of the Dirac delta function. Numerical tests show that our algorithm is better than the Kaiser windowed sinc function method in the Laplace domain. Our technique for solving the 3-D Laplace-domain wave equation can significantly reduce the computational time required for the 3-D Laplace-domain acoustic full waveform inversion because we can use the coarse grid to accurately simulate conventional marine seismic exploration.