Optimised staggered grid finite difference operators based on the combined window function

Abstract

ABSTRACT The staggered grid finite difference (SGFD) method has been widely utilised in seismic forward modelling. The accuracy of forward modelling results has a great influence on the results of subsequent seismic imaging and seismic inversion. Numerical dispersion is one of the inherent problems in the SGFD method. To suppress dispersion, we here introduce the truncated window function method, which can get optimised finite difference operators after truncating spatial convolution series of the pseudo-spectral method. The empirical criteria of window functions are the main lobe width that should be as narrow as possible and the side lobe attenuation should be as large as possible. According to these criteria, we propose the combined window function method based on the Gaussian window and Hanning window. The result of the amplitude spectrum response shows that the new combined window has narrower main lobe and greater side lobe attenuation, which results in higher accuracy in numerical simulations with SGFD operators. Numerical tests also illustrate the effectiveness of this new method.