时间域黏滞波动方程及其数值模拟新方法

A novel time-domain viscoacoustic wave equation and its numerical simulation

基于常Q模型的应力—应变关系,推导了分数阶拉普拉斯算子黏滞波动方程的一阶速度—压力形式,与现有的一阶速度—压力—应变形式相比,新推导的方程形式更简单,数值模拟时耗费内存更少。针对新推导的一阶速度—压力黏滞波动方程,采用交错网格伪谱法进行数值模拟,并利用卷积型完美匹配层(CPML)作为吸收边界,压制截断边界的反射。数值模拟实验证实,新推导的黏滞波动方程能很好地描述地震波在黏滞介质中的衰减和频散,交错网格伪谱法和CPML的组合是一种高效的数值模拟方法。

We develop a fractional Laplacian viscoacoustic wave equation based on the dispersion relation of the constant-Q model, and formulate the wave equation into the first-order velocity-pressure system. Compared with the existing velocity-pressure-strain formulation, our formulation is more compact, and saves memory storage after discretization. The staggered-grid pseudo-spectral (SGPS) method is adopted to numerically solve our viscoacoustic wave equation. The convolutional perfectly matched layer (CPML) is applied to suppress artificial edge reflections in numerical simulation. Test results demonstrate that numerical simulation of our viscoacoustic wave can correctly describe seismic wave attenuation and dispersion. The SGPS approach combined with the CPML is verified to be an efficient numerical simulation scheme. © 2016, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.