地震数值模拟中模型粗化方法研究

地震数值模拟是地震勘探和地震学的重要基础，也是地震勘探、天然地震中不可或缺、非常有效的手段，更是地震波传播理论研究备受关注的前沿热点课题之一。因地球介质的复杂性，其物性的空间分布是非均匀的、具有一定的随机性，传统的针对连续介质的模拟方法受计算资源的限制，已不能有效模拟非均匀介质的局部特性。本项目拟针对地震波场建立相对的非均匀介质尺度的量化，通过将一点的场值展开成为细观尺度的小参数渐近级数，并与谱元法结合，建立一系列控制方程，发展模型的粗化方法，并给出粗化准则。项目通过对单胞问题的求解，把细观尺度上的信息，映射到宏观尺度上，从而可在宏观尺度上求解原问题。该粗化方法针对非周期模型介质，拟从理论和数值实验两方面进行论证说明，使得模拟既可节省计算时间和存储，又能保证计算精度，达到发展非均匀复杂介质中地震波场快速模拟算法之目的，为大尺度地震波传播正演模拟和基于波动方程的反演成像奠定理论和方法基础。

Seismic numerical modeling is an important basis for seismic exploration and seismology. It is also an indispensable and effective tools for seismic exploration and seismology, and thus become a research hotspot in these fields. Because of the complexity of earth medium, its physical space distribution is heterogeneous with a certain randomness, therefore, the traditional modeling methods, which are effective for continuous medium, are out of ability to deal with local characteristics of the earth medium due to limited computational resource. By introducing length scale of inhomogeneous medium, and combining asymptotic expansion method with spectral element method, we'll give so-called upscaling method based on deriving a series of control equations to replace original equations. The method is presented to compute the effective behaviour of the wavefield within similar unit-cell, and the information of the micro scale is mapped on the macro scale, thus, the original heterogeneous problem can be solved. The upscaling method is constructed for non-periodic medium, and would be validated from the aspects of mathematical theory and numerical experiments. In this project we present a upscaling method to build the effective medium and equations allowing to homogenize the small scales of the original medium without losing the accuracy of the wavefield computation, and achieve the fundamental purpose of the development for fast simulation of seismic wave in inhomogeneous medium. The method is also developed to provide theory and methodology basis for large-scale forward modeling of seismic wave propagation and for wave equation inversion and imaging.