介质离散方法对地震波场有限差分数值模拟准确性的影响

地震波场有限差分数值模拟的准确性取决于空间网格大小,而空间网格大小通常仅依据差分格式的色散和耗散误差所要求的每最短波长网格数的选取,没有考虑速度模型的复杂性。对于存在速度间断面的复杂速度模型来说,不同的介质离散方法将导致不同的有限差分离散速度模型,进而导致模拟波形的差异。定量分析了地震波有限差分模拟中不同的介质离散方法(包括直接取值法、格点平均法、体积分平均法与正交各向异性等效介质法)对反射/透射波准确性的影响,探索了界面误差随网格变化的规律。通过数值计算获得了每种介质离散方法对不同类型弹性波满足给定的误差精度所要求的网格大小,为地震波场正演模拟中的网格参数选取提供了参考依据。

The accuracy of finite difference simulations for seismic wave fields strongly depends on the spatial grid size.The spatial grid size is simply determined by the minimum number of grids per wavelength required for dispersion and dissipation errors of the grid scheme,ignoring the complexity of velocity models.For velocity models with strong velocity contrast interfaces,different discretization methods for the velocity model would result in different discrete velocity models in finite difference grids,which will cause different simulated waveforms.Different discretization methods for media used in finite difference simulation are discussed,including the direct value method,grid mean method,volume integral method,and orthorhombic effective media method.Their influence on reflection/transmission waveforms are compared and analyzed quantitatively to explore how the law of interface errors changes with different grid size.Using points per wavelength (PPW) as a constraint,the grid size required by each media discretization method to satisfy a pre-defined error level for different seismic waves is numerically calculated,to provide a reference for the selection of grid size parameters in seismic forward modeling.

国家自然科学基金项目(41374056)资助。