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波动方程有限差分法是地震数值模拟中的一种重要的方法,对理解和分析地震传播规律、分析地震属性和解释地震资料有着非常重要的意义。但是有限差分法由于其离散化的思想,产生了不稳定性。精细积分法在有限差分法的基础上,在时间域采用解析解的表达形式,在空间域保留任意差分格式,发展成为半解析的数值方法。本文结合并发展了以往学者的成果,推导了任意精细积分法的三维弹性波正演模拟计算公式,并对其稳定性进行了数值分析。在计算实例中,实现了精细积分法二维和三维弹性波模型的地震正演模拟,对计算结果的分析表明,精细积分法反射信号走时准确,稳定性好,弹性波场相较于声波波场,弹性波波场成分更为丰富,包含了更多波型成分(PP-和PS-反射波、透射波和绕射波),这对实际地震资料的解释和储层分析有重要的意义。实践证明,该方法可直接应用到弹性波的地质模型的数值模拟中。
The wave equation finite difference method is an important method in numerical simulation of earthquakes and is of great significance for understanding and analyzing the laws of seismic propagation, analyzing seismic attributes and interpreting seismic data. However, the finite difference method has instability due to its discretization. Based on the finite difference method, the precise integration method adopts the expression of analytical solution in the time domain, preserves any difference format in the space domain, and develops into a semi-analytical numerical method. In this paper, we combine and develop the results of past scholars, deduce the formula of 3D elastic wave forward simulation by any precise integral method, and analyze its stability by numerical analysis. In the calculation example, the seismic forward simulation of two-dimensional and three-dimensional elastic wave models of the precise integration method is realized. The analysis of the calculation results shows that the accurate integral signal reflected by the precise integration method has good stability and stability. Compared with the acoustic wave Field and elastic waves have more abundant wavefield components and contain more wave components (PP- and PS- reflected waves, transmitted waves and diffraction waves), which is of great significance for the interpretation of actual seismic data and reservoir analysis . Practice has proved that this method can be directly applied to the numerical simulation of elastic wave geological model.