叠前逆时偏移在理论上是现行偏移方法中最为精确的一种成像方法,其实现过程中的核心步骤之一是波动方程的波场延拓,而波场延拓的本质是求解波动方程,所以精确、快速地求解波动方程对逆时偏移至关重要.本文采用一种基于时空域频散关系的有限差分方法来求解声波方程,分析其频散和稳定性,实现波场数值模拟,并将分析和模拟结果与传统有限差分法进行对比.分析结果和模型数值模拟结果都表明时空域有限差分法模拟精度更高、稳定性更好.将时空域高阶有限差分法应用到叠前逆时偏移波场延拓的方程求解中,然后再利用归一化互相关成像条件成像,理论模型数据偏移处理获得了精度更高的成像.同时,在逆时偏移波场延拓的实现中,采用自适应变长度的空间差分算子求解空间导数的有限差分策略,在不影响数值模拟和成像精度的前提下,有效地提高了计算效率.%Prestack reverse time migration (RTM) is the most accurate method for seismic imaging in theory at present, and one of its key steps is wavefield extrapolation. The essence of wavefield extrapolation is to solve the wave equation. Solving the wave equation accurately and fast is very important. In this paper, we use a time-space domain dispersion-relation-based finite-difference (FD) method to solve the acoustic wave equation, then analyze the dispersion and stability of the numerical solution, perform the numerical modeling, and compare the results with the conventional FD method. Results of numerical analyzing and modeling demonstrate the time-space domain FD method has better accuracy and stability than the conventional method under the same discretization. We adopt the time-space domain high-order FD method to solve the acoustic wave equation in the process of wavefield extrapolation, then use the normalized cross-correlation imaging condition to obtain imaging in RTM. Results of synthetic data processing show that the imaging has been improved. Meanwhile, in the process of wavefield extrapolation, we adopt adaptive variable-length spatial operators to compute spatial derivatives and thus to decrease computing costs significantly without reducing the numerical modeling and imaging accuracy.
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