Suppress numerical dispersion in reverse-time migration of acoustic wave equation using optimal nearly analytic discrete method

Abstract

Using staggered-grid finite difference method to solve seismic wave equation, large spatial grid and high dominant frequency of source cause numerical dispersion, staggered-grid finite difference method, which can reduce the step spatial size and increase the order of difference, will multiply the calculation amount and reduce the efficiency of solving wave equationThe optimal nearly analytic discrete (ONAD) method can accurately solve the wave equation by using the combination of displacement and gradient of spatial nodes to approach the spatial partial derivative under rough grid and high-frequency condition. In this study, the ONAD method is introduced into the field of reverse-time migration (RTM) for performing forward- and reverse-time extrapolation of a two-dimensional acoustic equation, and the RTM based on ONAD method is realized via normalized cross-correlation imaging condition, effectively suppressed the numerical dispersion and improved the imaging accuracy. Using ONAD method to image the groove model and SEG/EAGE salt dome model by RTM, and comparing with the migration sections obtained by staggered-grid finite difference method with the same time order 2nd and space order 4th, results show that the RTM based on ONAD method can effectively suppress numerical dispersion caused by the high frequency components in source and shot records, and archive accurate imaging of complex geological structures especially the fine structure, and the migration sections of the measured data show that ONAD method has practical application value.