基于Biot方程的纵波波场高阶有限差分法模拟及波场分析

P WAVE FIELD ANALYSIS AND SIMULATION BY HIGH ORDER FINITE DIFFERENCE METHOD BASED ON Biot THEORY

地球物理勘探中的含油气储层通常被认为是一种典型的双相介质,这种介质模型能更精确的描述含气性储层的特征,开展双相介质波场传播特性的研究具有十分重要意义。研究以Biot理论为基础,从双相介质中的纵波方程出发,导出求解双相各向同性介质中纵波方程的高阶差分格式,在此基础上实现双相各向同性介质中纵波方程的高阶有限差分法正演模拟,数值模拟结果表明:这种算法能在少量增加计算量的前提下大大提高精度,同时波场模拟结果与理论相吻合,波场快照快慢纵波的波场反映出不同速度、相位相反等特征差异,对将该理论应用于实际有重要的指导意义。

In geophysical exploration,oil and gas reservoir can usually be considered as a typical two-phase medium and the characters of reservoir can be described more accurately by two-phase medium model. So it is necessary to make research on rule of wave field propagating in two-phase medium. On the basis of Blot theory, this paper deduced a high-order finite difference expression from the P-wave equation of two-phase isotropy medium. Then author forwarded the wave field characters in two-phase medium by deduced expression above. The calculated result revealed that the algorithm,given by this paper,can greatly improve the precision and efficiency at a litter cost of time and all of simulation wave field characters, such as fast wave, slow wave velocity and phase etc are matched well with the theoretic result. The research result is very significant in making the two-phase medium theory more practical.