基于有限差分法和伪谱法的井孔声场数值模拟

Modeling of the Wave Propagation in Borehole with the Hybrid Method Based on FDM and PSM

为模拟径向分层的井孔声场,对有限差分法和伪谱法混合算法的原理和特点进行研究,用混合算法重写质点速度和应力的一阶偏微分方程组。通过实例计算,验证该方法的可靠性,在对具有分层界面的地质模型进行声场模拟时具有相当的计算精度。用混合算法对轴对称井孔声场进行了模拟,讨论井径变化和井外地层岩性变化对井孔声场的影响,计算结果可为声波测井仪器研制和数据分析提供理论指导。

In order to simulate the wave propagation in borehole,the theory of hybrid method（HYD）based on the finite difference method（FDM）and pseudo-spectral method（PSM）is studied in this paper.Meanwhile,the first-order partial differential equations of particle velocity and stress are rewrite.The result of example calculation shows that HYD is reliable and has high precision for modeling of acoustic field propagation in layered media.So HYD is used to model the wave propagation in an axial symmetric borehole to analyze the effects of caliper and lithology on acoustic field,the conclusion of which can be used for the design of acoustic logging tool and data analysis.