完全纵波方程有限差分波场模拟

通常情况下，当介质的密度变化相对于其速度变化很小时，可以近似地将密度看作常数，使用声波方程及速度函数来描述波动问题是可行的；如果介质的密度变化与其速度变化相当或更大时，则密度的变化不可忽略，声波方程没有体现密度函数对波场的影响。本文从弹性动力学的基本方程出发，导出了非均匀介质的完全纵波方程及其有限差分格式，完全纵波方程右端含有压力场空问变化项和密度空间变化项，完整地描述了介质的速度和密度两种因素对波动过程所起的作用。数值算例表明，在研究不均匀地质体和地层界面上的反射、透射问题时，完全纵波方程的模拟结果能更准确地描述波场特征。文中还结合反射、透射问题的解析解对相应的模拟结果进行了分析，指出当界面上、下存在明显的密度差异时，考察反射问题时要使用阻抗或阻抗率的概念。

Finite-difference wavefield simulation of full P-wave equation.

Generally, when the variation of density of medium is smaller than that of velocity,it can approximately take the density as constant and using acoustic equations and velocity functions to describe wave is feasible; but when the variation of density of medium is equivalent to or greater than the variation of velocity, the variation of density can't be neglected,the acoustic equations do not reflect the influence of density function on wavefield. Starting from the basic equations of elastic dynamics , the paper deduced full P-wave equations in non-homogeneous medium and its finite-difference format. The right items of full P-wave equations include spatial variation item of pressure field and spatial variation item of density and completely describe the role of two factors--velocity and density during waving. The numeric computation showed that the simulated results by full P-wave e-quations could more accurately describe the feature of wavefield when studying reflection and transmission in non-homogeneous geologic body and on interface of beds. The analyses of relevant simulated results were conducted in combining with analytic solution of reflection and transmission issues in the paper,which pointed out that it should use the conception of impedance or impedance rate in reflection issue when there is distinct difference of density on both sides of interface.