刚度弱化边界条件在TI拟声波方程模拟中的应用

Application of the stiffness reduction method for modeling the acoustic TI wave equations

由于地震波数值模拟在有限区域内进行,因此减少边界反射波的影响十分重要。完美匹配层(PML)方法被广泛应用于边界反射的吸收。但在各向异性介质模拟中,PML存在稳定性问题。为此,尝试将一种刚度弱化方法(SRM)应用到拟声波各向异性方程的模拟中。首先,给出了TI介质拟声波方程模拟中SRM和PML边界条件的加载方法和差分格式。模拟结果显示,SRM在内存要求和运算速度上优于PML方法。之后,通过对均匀VTI和TTI介质、层状介质以及BP模型进行数值模拟,对比分析两种方法的吸收衰减效果。对VTI介质的模拟结果显示,在本研究的实验条件下,使用同样的吸收层厚度SRM内存需求仅为使用PML方法的50%,运算耗时减少约25%。虽然在VTI条件下SRM吸收效果略逊于PML方法,但在TTI介质、层状介质以及BP模型模拟中显示出了更高的稳定性。模拟结果表明,SRM在TI介质拟声波方程模拟中具有较好的实用性和可靠性。

Underground rocks are generally anisotropic,which affects the velocities,amplitude and phase of seismic waves.The acoustic anisotropic wave equation is a simplification of the anisotropic elastic wave equation.It is widely used in Full Waveform Inversion(FWI)and Reverse Time Migration(RTM).Minimizing boundary reflections is a fundamental aspect of seismic wave numerical modeling.The perfectly matched layer(PML)method is commonly employed to absorb such reflections,but it encounters stability issues in anisotropic media modeling.To address this,in this study,we attempt to apply the stiffness reduction method(SRM)for modeling the acoustic anisotropy wave equations.SRM achieves the reflection absorption by introducing the damping terms into the equations and gradually reducing the stiffness.Firstly,the SRM and PML loading methods and difference schemes in the modeling of acoustic TI wave equations are determined.It is found that SRM is superior to PML in computational storage efficiency and speed.Then,numerical modeling was performed on vertical transversely isotropic(VTI)media,tilted transversely isotropic(TTI)media,layered media and BP model to compare SRM and PML in adsorption attenuation performance.The simulation using VTI media indicates that SRM requires a memory only as a half of PML and reduces the computation time by 25%compared to PML for the same absorbing layer thickness under the given experimental conditions.While SRM demonstrates a slightly lower absorption efficiency than PML in VTI media,it exhibits superior stability in TTI media,layered media,and BP model simulations.These findings prove the practicality and reliability of SRM in modeling the acoustic TI wave equations.