Optimal staggered-grid finite-difference schemes based on weighted convolution combination window

Abstract

Staggered-grid finite-difference (SFD) method has higher accuracy and stability than conventional method, so it is widely used in reverse time migration and full waveform inversion. However, due to the high dominant frequency and large grid interval, numerical dispersion is an inevitable problem. To suppress numerical dispersion, we first propose a weighted convolution combination window function for SFD, which is based on traditional binomial window function. Accuracy error analysis shows that the spectral coverage of new method far exceeds that of the Taylor-expansion SFD method, and the new method also has better spectral coverage and stability than the previous optimisation methods. Finally, we perform numerical forward modelling, which denotes that our method is superior than other optimum methods. From an economic point of view, this method will effectively reduce the computation cost and improve efficiency.