【摘要】 地震波场数值模拟是理论地球物理学和勘探地球物理学的重要研究手段.在众多数值模拟方法中边界元法和有限差分法是两种典型的地震波传播模拟计算方法.边界元法是一种半解析-半数值的边界型方法,它显式地利用边界连续条件,沿着地层边界进行离散,具有降维、高精度和自动满足远场辐射条件的优点;有限差分法是一种典型的基于微分的区域型方法,它隐式地使用边界连续条件,以空间网格形式进行离散和数值逼近,具有高效、实用和容易数值实现的优点.本文以一个半圆形均匀Valley模型和两个非均匀断裂/断层模型为例,从计算精度、计算效率、频散特性以及适用性等方面对这两种方法进行了比较研究.数值计算结果表明:边界元法可以精确地几何描述有内部断点、断面的复杂构造,能够精确地模拟内部不规则界面之间波的反射/传播;有限差分法不能以足够的精度描述几何断点和内部不规则边界.边界元法在高频时计算量大于有限差分法,有限差分法则需要更小的网格间距以压制数值频散.因此,在处理内部非均质和高频计算时,有限差分法更有效;在处理内部不规则边界、断点、大尺度等问题时,边界元法比有限差分法更有优势.更多还原

【Abstract】 Numerical modeling of seismic wave-field plays an important role in both theoretical geophysics and exploration geophysics.With the development of geophysics and numerical simulation technology,boundary element method(BEM) and finite-difference method(FDM) have been two basic methods in the study of seismic wave propagation.BEM is a semi-analytical and semi-numerical boundary type method,which explicitly uses the boundary continuity conditions for displacement and traction across interfaces,discretizes model along stratigraphic boundaries,and has advantages of spatial dimensionality reduction,high accuracy and easy fulfillment of radiation conditions at infinity.FDM is a typical domain type method,which is characteristic of the implicit use of boundary continuity conditions,discretizes model in the form of space grids,and has advantages of high efficiency and easy numerical implementation.To take full advantage of BEM and FDM,the numerical accuracy,computational efficiency,dispersion effect and applicability of the two methods are comprehensively compared in this paper.A homogeneous Valley model and two heterogeneous complex fault models are applied.Comparisons are implemented in frequency domain as well as in time domain.The results show that each method has specific merits and drawbacks.BEM is more accurate in the simulation of reflection/transmission across internal irregular interfaces,FDM cannot geometrically describe internal boundaries with enough accuracy.At high frequencies,BEM is computationally intensive since a considerable amount of matrix must be inverted,FDM is more efficient but it needs a much larger number of discretization grid points to decrease numerical dispersion.Therefore,FDM is a better choice when dealing with the problems of heterogeneity and high frequency computations,while BEM has potential advantages for solving fault point,internal irregular boundaries and large-scale problems.更多还原