迎风型组合紧致差分的二维地震波场数值模拟

Numerical Simulation of 2D Seismic Wave-Field Used Upwind Combination Compact Difference

声波方程方面的数值模拟正是地震正演模拟的一种,而地震正演模拟对于研究地震波传播性质来说有着相当重要的地位。传统的有限差分方法如果要达到一个较高的精度其所需的网格数会较多,而紧致格式的出现刚好弥补了这一缺陷。迎风型组合紧致差分格式是在组合型紧致差分格式的基础上引入了迎风机制,该差分格式不仅具有组合型紧致差分格式的高分辨率、高频散、低网格数的优势,而且在稳定性及粘性分辨率上更吸收了迎风格式的优点。首次将迎风型组合紧致差分格式用于声波方程的数值模拟中。根据泰勒级数展开和声波方程,建立了位移场时间四阶离散格式,并将该差分格式用于位移场空间导数的求取,然后对该差分格式进行了精度分析、误差分析、频散分析和稳定性分析,以及在均匀介质及层状介质中进行正演模拟,效果理想。

The numerical simulation of acoustic equations is a kind of seismic simulation. Seismic simulation is very important for studying the propagation properties of seismic waves. The traditional finite difference method requires more grid number to achieve a higher accuracy,and the compact finite difference scheme makes up for this defect.In this paper,we discuss about the upwind combination compact difference scheme,as is the combination compact difference scheme on the basis of introducing the mechanism of the wind. This scheme has the advantages of high resolution,including high frequency dispersion and low grid number. In addition,the advantages of upwind finite difference scheme are also absorbed. In this paper,a numerical simulation of acoustic equations is presented for the first time. Based on Taylor series expansion and acoustic equation,the displacement field is for fourth order discrete format. And then,the accuracy,including dispersion and stability of the upwind combination compact difference scheme are all analyzed. At last,the numerical simulation and wave field analysis are carried out to be used in uniform and horizontal lamellar models. We think the effect is ideal.