基于纵横波保幅分离的粘弹介质弹性波正演模拟

地下介质往往表现为粘弹特性,研究基于粘弹假设的数值模拟方法对于正确认识地震波的传播规律和提高地震勘探精度具有重要意义。波动方程正演过程中纵横波的保幅解耦是研究准确的粘弹介质中地震波传播机理的前提,基于散度和旋度算子的纵横波解耦方法会使波场的相位和振幅产生畸变,且解耦后的波场在极性反转位置上无法与分离前混合波场各分量对应。在散度和旋度算子上再做一次梯度和旋度运算的波场分离方法虽然能够克服上述缺陷,但存在保幅性差等问题。本文从粘弹介质中的一阶速度-应力方程出发,推导了矢量纵横波分离的波数域表达式,结合有限差分思路给出了其在空间域的求解方法。本文方法利用纵横波的传播速度对现有的矢量波场分离方法进行振幅校正,并将校正结果分别作为纵波与横波对时间的二阶偏导,实现了粘弹介质中的纵横波分离。模型试算结果表明,本文方法能够克服现有方法的缺陷,获得更具保幅性的波场分离结果。

Forward Modeling of Elastic Waves in Viscoelastic Media Based on Amplitude-Preserving Separation of P and S Waves

Due to the viscoelastic properties of underground rocks,it is important to study the numerical simulation method based on viscoelastic assumption for correctly understanding the propagation mechanism of seismic waves and improving seismic exploration accuracy.Amplitude-preserving decoupling of P-wave and S-wave is the prerequisite for accurately understand propagation mechanism of seismic wave in viscoelastic medium.The divergence and curl operators may cause the phase and amplitude distortion of P-wave and S-wave,moreover the physical meaning and polarity inversion position of decoupled wave field is not inconsistent with the original mixed wave field.Another wave field separation method which separate the P-wave and S-wave with gradient and curl operations on divergence and curl operators can overcome the above shortcomings,but the algorithm has the disadvantage of poor amplitude preservation.In this paper,a wavenumber domain expression of vectorial P-and S-wave separation formulas is derived which was based on one-order velocity-stress viscoelastic equations,and its solution method in spatial domain is also according to the finite difference method.In our method,the velocity of P-and S-waves are used to correct the amplitude of the existing wave field separation method,and the correction results are used as the second-order partial derivatives of P-wave and S-wave for time,respectively.Based on above methods,the P-and S-wave separation in viscoelastic media is realized.The experimental results show that the proposed method can overcome the shortcomings of the existing methods and obtain more amplitude-preserving wave field separation results.