复杂地表条件下地球物理场数值模拟方法评述
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摘要
在将起伏地表、复杂近地表构造以及复杂近地表岩性的任意组合统称为复杂地表的一种广义诠释下,分别对近地表岩层或土层的数学物理模型以及对地震波场、电磁波场、稳定电流场、重力场和磁力场在复杂地表条件下的数值模拟方法进行了分析和评述。结果表明,近地表数学物理模型并不是越复杂越好。实践中,要根据计算量以及所要解决的地质问题综合考虑。目前所用到的诸多数值模拟方法,如有限差分法、有限单元法、广义有限差分法、伪谱法、积分方程法和射线法等各有千秋,只要应用得当都能得到正确的结果。作为非网格法代表的积分方程法在对复杂地表和模型内边界的精确描述方面要优于以有限差分法为代表的网格法,而网格法在对模型的适应程度上要优于非网格法。传统的几何射线法在经过一定的修改和补充后,例如加入自由界面转换系数、采用几何绕射理论和Maslov方法,即可用于解决复杂地表条件下的波场数值模拟问题。对于重力场和磁力场,其在起伏地表条件下的空间换算(转换)问题在实质上也是一种正演问题,可纳入到复杂地表数值模拟的框架内去理解和处理。虽然国内外的研究者在复杂地表数值模拟领域内已经做了大量的工作,但离实际应用还有很大的距离。
Under a generalized understanding of the complex surface that includes any arbitrary combinations of complex surface topography and complex near surface geology,we give an analysis and a critical review on numerical modeling methods for geophysical fields,including seismic wave field,electromagnetic wave filed,direct current field,gravitational field and magnetic field,under complex surface conditions.As a result,we find that a very complicated near surface model is not always an adequate choice for solving some problems appeared in practice.How complex the near surface model should be depends on the purpose of the modeling computation and the computer resource available.Furthermore,many modeling methods used have advantages and disadvantages.They all can give correct results when used properly.Specifically,the integral equation method that is a representative of non-gird methods can implement surface boundary conditions better than the finite difference method that is a representative of the grid methods.However,grid methods can treat complex medium models better than the non-grid methods.Also,traditional ray method can solve complex surface problem as well,provided that the geometrical theory of diffraction and the Maslov method as well as the free surface transform coefficients are used in the modeling scheme.Similarly,transformation of potential fields(gravitational and magnetic field) from a curved surface to a plane can also be understood as a forward numerical modeling problem.Although a large amount of work in relation to the complex surface has been done,it still has a long way to go for practical applications.
Under a generalized understanding of the complex surface that includes any arbitrary combinations of complex surface topography and complex near surface geology,we give an analysis and a critical review on numerical modeling methods for geophysical fields,including seismic wave field,electromagnetic wave filed,direct current field,gravitational field and magnetic field,under complex surface conditions.As a result,we find that a very complicated near surface model is not always an adequate choice for solving some problems appeared in practice.How complex the near surface model should be depends on the purpose of the modeling computation and the computer resource available.Furthermore,many modeling methods used have advantages and disadvantages.They all can give correct results when used properly.Specifically,the integral equation method that is a representative of non-gird methods can implement surface boundary conditions better than the finite difference method that is a representative of the grid methods.However,grid methods can treat complex medium models better than the non-grid methods.Also,traditional ray method can solve complex surface problem as well,provided that the geometrical theory of diffraction and the Maslov method as well as the free surface transform coefficients are used in the modeling scheme.Similarly,transformation of potential fields(gravitational and magnetic field) from a curved surface to a plane can also be understood as a forward numerical modeling problem.Although a large amount of work in relation to the complex surface has been done,it still has a long way to go for practical applications.
引文
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