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Quadratic circle equation travel time interpolation method based on triangular mesh

A technology of triangular mesh and interpolation method, applied in CAD numerical modeling, design optimization/simulation, seismic signal processing, etc., can solve the problems of low accuracy, large calculation error in the near field, low calculation efficiency, etc., to improve the accuracy , the effect of less computational cost and high computational accuracy

Active Publication Date: 2022-05-03
CHENGDU UNIVERSITY OF TECHNOLOGY
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Problems solved by technology

[0015] The purpose of the present invention is to provide a quadratic circle equation travel time interpolation method based on a triangular grid, which is used to replace the existing LTI linear travel time interpolation method, and solve the large near-field calculation error and low accuracy in the LTI algorithm and low computational efficiency

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  • Quadratic circle equation travel time interpolation method based on triangular mesh
  • Quadratic circle equation travel time interpolation method based on triangular mesh
  • Quadratic circle equation travel time interpolation method based on triangular mesh

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Embodiment

[0048] The design idea of ​​this embodiment is to construct an auxiliary circle through the center point between two adjacent nodes, and construct a nonlinear travel time interpolation. The interpolation process of this embodiment is as follows figure 1 Specifically, the process is as follows:

[0049]S1. Set the currently traversed triangular grid containing the source excitation points, wherein the coordinates of any two vertices A and B in the triangular grid are known values, and the coordinates of the third vertex C are to be interpolated. D is any point on side AB, and point M is the midpoint of side AB, such as figure 2 shown;

[0050] S2. Establish a coordinate system with the vertex A in the triangular grid as the coordinate origin, and the vertex A is the vertical axis when traveling, then the coordinates of the vertex A are A'(0,t a ), the coordinates of another vertex B in the triangular mesh are B'(AB,t b );

[0051] S3, according to the coordinates of verti...

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Abstract

The invention discloses a quadratic circle equation travel time interpolation method based on a triangular mesh, and the method comprises the steps: setting a currently traversed triangle (wherein two vertexes A and B are known points, the coordinate of a third vertex C is a to-be-interpolated point, a point D is any point on an AB side, and a point M is the midpoint of the AB side), and calculating the travel time of the points according to the two vertexes A and B, the method comprises the following steps of: firstly, constructing a circle equation function of a current traversal triangle by combining coordinates of two vertexes and a midpoint and travel time, and then solving a quartic equation by adopting a Ferrari method according to a Fermat principle by combining an internal travel time expression of the triangle, so as to obtain the shortest travel time of the vertex C of the current traversal triangle. According to the method, starting from the propagation characteristics of waves, the auxiliary circle is constructed through the center point between the two adjacent nodes, the nonlinear travel time interpolation is constructed, and compared with traditional LTI and other methods, higher numerical precision can be obtained, and the calculation cost is lower.

Description

technical field [0001] The invention relates to the technical field of geophysics, in particular to a triangular grid-based quadratic circle equation travel time interpolation method. Background technique [0002] With the rapid development and progress of computer technology, people have a deeper understanding of the structure of the earth's interior, tomography technology has also become a powerful tool for research, and ray tracing is one of the indispensable methods in geoscience tomography one. The ray tracing method is based on Snell's law and Huygens' principle to simulate the kinematic characteristics of seismic wave propagation, and its essence is a two-point ray tracing problem between a given source excitation point and a receiving point. [0003] With more in-depth research, many improved new algorithms have emerged. Sethian and Popovici (1999) proposed a fast marching method (FMM) to solve the local eikonal equations using the upwind difference scheme. Asakaw...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/20G01V1/28G06F111/10
CPCG06F30/20G01V1/28G06F2111/10
Inventor 邓飞杨中山董秀军余思令
Owner CHENGDU UNIVERSITY OF TECHNOLOGY
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