基于贴体全交错网格的起伏地表正演模拟影响因素

贴体网格有限差分正演模拟算法不仅能够精确模拟任意起伏地形下的波场特征，且计算效率较高，是一种很有应用前景的处理西部复杂地表问题的方法；然而，目前求解波动方程时常用的同位网格和标准交错网格，在处理贴体网格起伏地表正演模拟时存在诸多问题。为此，将全交错网格引入到曲线坐标系下，避免了标准交错网格的插值误差和同位网格中奇偶失联引起的高频振荡现象，提高了模拟精度，减小了算法实现的复杂度。在自由边界条件实施时，采用牵引力镜像法计算速度分量，速度自由边界条件配合紧致交错差分格式更新应力分量，得到了较好的效果。随后，重点研究了贴体全交错网格正演模拟算法的影响因素，考虑了网格正交性、网格间距和网格拼接等的影响，并取得了如下认识：算法对网格的正交性没有过分要求；网格间距的突变会引起虚假反射的产生；不同类型的网格拼接对模拟结果不会造成明显的影响。

Factor Analysis of Seismic Modeling with Topography Based on a Fully Staggered Body-Fitted Grids

Finite-difference forward modeling method with body-fitted can accurately simulate wavefields in presence of topography, meanwhile, the computational efficiency is relatively high. Therefore, it is a prospecting method for dealing with the western complex surface. The collocated-grid and standard staggered grid are often used to solve wave equation. However, they show many problems when the above two grids are extend to body-fitted grids. By introducing the fully-staggered grid to curvilinear coordinates, the proposed method can avoid not only the interpolation error when standard staggered grid are used, but also the high-frequency oscillations with the collocated-grid. Thus, it can improve the simulation accuracy and reduce the complexity of the algorithm degrees. To satisfy the free surface boundary condition, we use the traction image method to calculate the velocity components, the method also uses the velocity of free boundary conditions with compact staggered difference format to update the stress components. Model tests show that the proposed method can obtain the good results. And then, we mainly study the influence factors of forward modeling algorithm by a fully staggered body-fitted grids, such as, the orthogonality of grids, the grid spacing change, and the skewness of meshes.Finally, we obtain some conclusions as follows:the algorithm is not sensitive to the orthogonality of grids;the grid spacing changing can lead to false reflection;the result of simulation is not affected by the skewness of different types of grids.