基于保角变换法的地震裂缝波场研究

针对实际地层中的裂缝形状，提出了两种裂缝模型，一种是广义四边形裂缝模型，另一种是角形裂缝模型。基于保角变换，对单个裂缝的波场进行了研究。首先，对物理域中的裂缝区域施加保角变换，将其变换为计算域中的上半平面，对物理域中的裂缝边界条件进行保角变换为计算域中的边界条件；其次，在计算域中求出裂缝边界及其附近的波场；最后，通过保角变换的反变换得到物理域中裂缝边界波场变化规律。提出的保角变换法对研究单个和多个任意形状的裂缝波场之间的定量关系以及勘探地球物理中的非均质问题提供了新的思路。

Application Research Based on the Conformal Mapping to theWave Field of Seismic Fracture

In view of the actual shape of fracture formation，two fracture models are presented in this paper. One is generalquadrilateral fracture model，and the other is the horny fracture model. The wave fields of single fracture were studied based onthe conformal mapping method. First of all，the conformal mapping on the fracture area in physical domain was transformed tothe upper half plane in the computational domain and the boundary conditions in physical domain to the boundary conditionsin the computational domain；secondly，the wave fields near the boundary of the fracture in the computational domain werecalculated；fInally，the wave fields variation curve in the boundary of physical domain through the inverse conformal mappingtransformation was obtained. The conformal mapping method are used in our research on the quantitative relationship of thewave fields of a single and several any shape fracture provides some new ideas about the heterogeneity problem in the explorationgeophysical.