含起伏地形的粘弹性波动方程有限差分正演与强地面运动模拟研究

Accuracy, efficiency and adaption to the complex geological structure of seismic wave forward-modeling technique are the actual needs of earthquake disaster reduction and resource exploration. Based on 4-element Generalized Standard Linear Solid viscoelastic model, we approximate a constant Q over a frequency band 0.05-25Hz. By applying the mapping relation between curvilinear and regular grid, we derive the viscoelastic wave equation in curvilinear coordinates. The MacCormack finite-difference (FD) scheme is used to solve the wave equation. The traction image method is used to deal with the free surface and the effective parameters are used to treat the discontinuous interior interfaces. By using these numerical techniques seismograms are synthetized in the viscoelastic model with topography. We propose to perform FD simulation on hybrid-grid system according to the characters of shallow earth materials. The hybrid-grid system is that upper region is discretized using a curvilinear grid, middle region is discretized using a regular fine grid and the bottom region using a regular coarse grid. The transition of regular fine and coarse grid is completed using the discontinuous-grid FD scheme. We parallel the hybrid-grid FD simulation code and verify the code with spectral-element method program SPECFEM3D. Through the simulation of of Lushan earthquake, we obtain the seismic characters of the strong ground motion and the distribution of seismic intensity with surface topography in hypocentral region.

准确、高效并适应复杂地质结构的地震波正演模拟技术是现代防震减灾和资源勘探的实际需要。基于4个标准线性体的粘弹性模型，采用常数Q值(频带范围0.05-25Hz)近似粘弹性参数，利用曲线网格和规则网格的映射关系，推导曲线网格下的3D一阶速度-应力-记忆变量粘弹性波动方程组。波动方程求解采用MacCormack差分格式，自由表面采用牵引力镜像法，内部不连续界面采用有效介质参数，模拟计算含地形起伏的衰减介质中的理论地震图。根据地球浅层介质的特点，提出基于混合网格的粘弹性有限差分模拟方案，即地表采用曲线网格，中间过渡到规则细网格，底部采用规则粗网格，其中规则粗细网格的过渡即为变网格有限差分模拟技术。将基于混合网格的模拟程序并行化，并与谱元法程序SPECFEM3D的模拟结果对比，检验可靠性。通过模拟芦山地震强地面运动，获得地形起伏强烈的芦山地震震源区的强地面运动特征，刻画地震烈度分布。

准确高效并适应复杂地质结构的地震波正演模拟技术是天然地震模拟和资源勘探的实际需要，含起伏地形的粘弹性有限差分正演模拟能进一步贴近真实地震波的传播状态而具有重要研究意义。在本项目中，我们基于4个标准线性体的粘弹性模型，采用常数Q值(频带范围0.05-25Hz)近似粘弹性参数，利用曲线网格和规则网格的映射关系，推导曲线网格下的3D一阶速度-应力-记忆变量粘弹性波动方程组。波动方程求解采用MacCormack差分格式，自由表面采用牵引力镜像法，内部不连续界面采用有效介质参数，模拟计算含地形起伏的衰减介质中的理论地震图。根据地球介质浅层速度小深部速度大的特点，提出基于混合网格的粘弹性有限差分模拟方案，即地表采用曲线网格，中间过渡到规则细网格，底部采用规则粗网格，其中规则粗细网格的过渡即为变网格有限差分模拟技术。将基于混合网格的模拟程序并行化，并与谱元法程序SPECFEM3D的模拟结果对比，验证了此模拟方法的准确性。从而建立一套完整的含起伏地形的粘弹性有限差分正演模拟方法，为强地面运动模拟等提供重要研究手段。