中文摘要：

本文研究了满足衡Q模型的黏弹性介质中声波模拟的时间域数值解法.通过采用有理式基函数描述频率相关的体积模量,使模型满足地震波黏性吸收的衡Q要求.结合弹性波模拟的非规则、非结构网格方法——格子法,本文提出了一种非均匀黏弹性介质中声波模拟的非规则网格方法.非规则、非结构网格的使用,可以精细地刻画地下介质中复杂速度、Q值的变化,及界面的形状.通过和解析解的比较及复杂模型算例分析,验证了该方法的精度及有效性.

英文摘要：

Absorption and dispersion in earth media is an issue we should consider for wavefield simulation.In this paper,we present a time-domain numerical modeling algorithm for acoustic wave in inhomogeneous viscoelastic medium.On one hand,to describe the attenuation effect we use the constant-Q model,which can be frequency-independent.On the other hand for the wavefield modeling engine,we utilize the grid method,which uses irregular,unstructured grid to simulate acoustic wave propagation in non-uniform viscoelatsic media.Specifically to resolve the convolution problem between strain and stress in the time-domain,we approximate the bulk modulus in the frequency domain with a set of rational functions,which meets the constant-Qrequirement.To confirm the model parameters for constant-Q,we apply the L-∞ Norm to reconstruct the objective function,and choose the simulated annealing（SA）method to finish the searching.As a result,we find the optimum solution with low order,like n=2or 3,which simultaneously meets the constant-Qrequirement very well,and reduces the memory demand obviously.In addition,the irregular,unstructured grid,which is used to discretize the velocity model and corresponding Q model,can give detailed descriptions and differentiations when complex interfaces are present,without sacrificing the accuracy and efficiency.As for the numerical examples,we first validate the scheme proposed using simple model and compare the results with analytic solutions.Result with good consistency is obtained regarding the attenuation effect. Moreover the Marmousi model validation proves that the proposed irregular,unstructured gird based simulation method together with the constant-Q model is effective and efficient to describe the acoustic wave propagation in inhomogeneous viscoelastic medium.