Suppress numerical dispersion in reverse-time migration of acoustic wave equation using optimal nearly analytic discrete
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Suppress numerical dispersion in reversetime migration of acoustic wave equation using optimal nearly analytic discrete method* Liu Ming-Zhu1,2 and He Bing-Shoug1,2 Abstract: Using staggered-grid finite difference method to solve seismic wave equation, large spatial grid and high dominant frequency of source cause numerical dispersion, staggeredgrid 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 equation.The 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. Keywords: Acoustic wave equation, RTM, ONAD method, numerical dispersion suppression
Introduction Reverse-time migration (RTM) is an effective tool to solve the seismic imaging problem of complex geological structures, the forward- and reverse-time
extrapolation is an important part of RTM, and the accurate solution of wave equation is the core step to realize the forward- and reverse-time extrapolation. Staggered-grid finite difference method is one of the most commonly methods to solve wave equation because of its high efficiency and the simple algorithm,
Manuscript received by the Editor August 13, 2018; revised manuscript received October 6, 2019. *This work was financially supported by the National Key R&D Program of China (No. 2018YFC1405900), the National Natural Science Foundation of China (No. 41674118), the Fundamental Research Funds for the Central Universities (No. 201822011) and the National Science and Technology Major Project (No. 2016ZX05027-002). 1. Key Lab of Submarine Geosciences and Prospecting Techniques, Ministry of Education, Ocean University of China, Qingdao 266100, China. 2. Evaluation and Detection Technology Laboratory of Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266071, China. ♦Corresponding author: He Bing-Shou (Email: hebinshou@ou
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