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坐标变换法通过将物理空间的曲网格映射为计算空间的矩形网格,将起伏地表转化为水平地表,同时将物理空间的波动方程转化为计算空间的波动方程,在计算空间完成数值模拟,坐标变换的方法对处理起伏自由边界具有较好的适应性和应用效果。本文在传统坐标变换方法的基础上,根据计算区域速度差异采用不同的网格大小和采样时间步长,提出了一种基于时空双变网格的起伏地表坐标变换正演模拟方法。在编程实现算法的基础上,通过典型模型波场模拟试算结果分析可知:(1)变网格方法与常规方法波场模拟误差在0.5%左右;(2)变网格方法计算效率视不同的变网格区域面积及变网格大小可提高几倍量级,在本文模型和计算参数下提高约5倍。(3)在满足模拟精度及频散条件要求下,变网格方法较全局细网格算法能显著节约计算内存。为此,针对起伏地表数值模拟,本文方法具有较高的模拟计算精度和一定的适应性。
The coordinate transformation method transforms the undulating surface into a horizontal surface by mapping the curved mesh of the physical space into a rectangular grid of the computing space, and transforms the wave equation of the physical space into the wave equation of the computing space, completing the numerical simulation in the computing space, The method of coordinate transformation has good adaptability and application effect for handling undulating free boundary. In this paper, based on the traditional coordinate transformation method, a different grid size and sampling time step are calculated according to the speed difference in the calculation area. A forward modeling method based on time-space dual-change grid is proposed. Based on the programming algorithm, we can see from the simulation results of typical model wave field simulation that: (1) the error of the wavefield simulation is about 0.5% for the variable mesh method and the conventional method; (2) the efficiency of the variable mesh method is different The mesh area and mesh size can be increased several orders of magnitude, which is about 5 times higher than the model and calculation parameters in this paper. (3) Under the condition of satisfying the simulation precision and dispersion conditions, the variable mesh method can save memory significantly compared with the global fine mesh algorithm. To this end, for the numerical simulation of undulating surface, this method has a high simulation accuracy and a certain degree of adaptability.