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.

中文翻译：

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使用最佳近解析离散方法抑制声波方程逆时偏移中的数值弥散

用交错网格有限差分法求解地震波方程，较大的空间网格和高震源频率引起数值离散，采用交错网格有限差分法，可以减小步长空间，增加差分阶次，可以乘以计算量并降低求解波动方程的效率最佳的近解析离散（ONAD）方法可以通过使用空间节点的位移和梯度的组合来精确求解波动方程，以在粗糙网格和高频条件下逼近空间偏导数。在这项研究中，ONAD方法被引入到逆时偏移（RTM）领域，以执行二维声学方程的正时和逆时外推，通过归一化互相关成像条件实现了基于ONAD方法的RTM，有效抑制了数值色散，提高了成像精度。利用ONAD方法对RTM的槽形模型和SEG / EAGE盐穹顶模型进行成像，并与交错网格有限差分法在相同的时阶2阶和空阶4阶下获得的偏移截面进行比较，结果表明基于RTM的RTM ONAD方法可以有效地抑制源记录和炮击记录中高频成分引起的数值离散，并可以对复杂的地质构造特别是精细构造的精确成像进行存档，实测数据的偏移剖面表明，ONAD方法具有实际应用价值。有效地抑制了数值色散，提高了成像精度。利用ONAD方法对RTM的槽形模型和SEG / EAGE盐穹顶模型进行成像，并与交错网格有限差分法在相同的时阶2阶和空阶4阶下获得的偏移截面进行比较，结果表明基于RTM的RTM ONAD方法可以有效地抑制源记录和发射记录中高频成分引起的数值离散，并可以对复杂的地质构造特别是精细构造的精确成像进行存档，实测数据的偏移剖面表明，ONAD方法具有实际应用价值。有效地抑制了数值色散，提高了成像精度。利用ONAD方法对RTM的槽形模型和SEG / EAGE盐穹顶模型进行成像，并与交错网格有限差分法在相同的时阶2阶和空阶4阶下获得的偏移截面进行比较，结果表明基于RTM的RTM ONAD方法可以有效地抑制源记录和炮击记录中高频成分引起的数值离散，并可以对复杂的地质构造特别是精细构造的精确成像进行存档，实测数据的偏移剖面表明，ONAD方法具有实际应用价值。