三维地震波场模拟──稳定波束与克希霍夫积分近似
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摘要
稳定波束法，是一种适合于多层复杂介质模型地震波场模拟的快速精确方法，它基于一种稳定快速的射线追踪技术，利用反射／透射和绕射波的迭加来近似波动理论的结果。本文阐明了稳定波束法模拟的结果可视为克希霍夫积分的近似解，并简述了三维稳定波束地震波场模拟方法研究的新进展。
In this paper, the 3D stable beam seismic modeling scheme is introduced. A type of multi-layered (or blocked) model is considered in this method. For convenience of programming, it is supposed that the model can be divided into a series of constant velocity/density layers (or blocks) separated by single-valued (in depth) interfaces. If a nonuniform velocity function is assigned within a single layer, it may be approximated using a number of ‘thin’ constant velocity layers. An interface which does not meet the single-valued condition needs to be divided into a suitable number of branches such that each of them is single-valued. Each interface of the model is then represented by a finite number of planar elements (triangular elements) with different size to meet the condition of Rayleigh's quarter wave criterion. The basis of the method is to model both the geometrical waves from the source and the pseudo-diffractions from the element edges and vertexes, which are considered to be ‘secondary sources’ as in the edge wave theory. Similar to the 2D case, the wave field (ray field) from a source (the original or a secondary one) can be systematically divided into a finite number of stable beams. All rays within each beam pass through (or reflected by) a single element on each interface. This allows very fast and stable two-point ray tracing through the model since there is one and only one ray at any output location within a stable beam. Any ray trajectory within a beam can be accurately determined, and the total number of rays emerging at a receiver equals the total number of the real stable beams illuminating the receiver. The wave field at the receiver is formed by a superposition of the contributions of all the stable beams from both the original and the secondary sources. All the pseudo-diffractions, analogous to first order and multiple edge or tip diffractions, are weakening waves. In practice, an accurate wavefield can be achieved using only lower order pseudo-diffractions. It is demonstrated that the wave field modeled in the stable beam implementation is an approximation of the Kirchhoff integral solution. The new development of 3D stable beam modeling is also briefly outlined in this paper.
In this paper, the 3D stable beam seismic modeling scheme is introduced. A type of multi-layered (or blocked) model is considered in this method. For convenience of programming, it is supposed that the model can be divided into a series of constant velocity/density layers (or blocks) separated by single-valued (in depth) interfaces. If a nonuniform velocity function is assigned within a single layer, it may be approximated using a number of ‘thin’ constant velocity layers. An interface which does not meet the single-valued condition needs to be divided into a suitable number of branches such that each of them is single-valued. Each interface of the model is then represented by a finite number of planar elements (triangular elements) with different size to meet the condition of Rayleigh's quarter wave criterion. The basis of the method is to model both the geometrical waves from the source and the pseudo-diffractions from the element edges and vertexes, which are considered to be ‘secondary sources’ as in the edge wave theory. Similar to the 2D case, the wave field (ray field) from a source (the original or a secondary one) can be systematically divided into a finite number of stable beams. All rays within each beam pass through (or reflected by) a single element on each interface. This allows very fast and stable two-point ray tracing through the model since there is one and only one ray at any output location within a stable beam. Any ray trajectory within a beam can be accurately determined, and the total number of rays emerging at a receiver equals the total number of the real stable beams illuminating the receiver. The wave field at the receiver is formed by a superposition of the contributions of all the stable beams from both the original and the secondary sources. All the pseudo-diffractions, analogous to first order and multiple edge or tip diffractions, are weakening waves. In practice, an accurate wavefield can be achieved using only lower order pseudo-diffractions. It is demonstrated that the wave field modeled in the stable beam implementation is an approximation of the Kirchhoff integral solution. The new development of 3D stable beam modeling is also briefly outlined in this paper.
引文
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