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Time high-order precision staggered mesh finite difference method for variable density acoustic wave equations

An acoustic wave equation and staggered grid technology, applied in the field of geophysics, can solve the problems of imaging and inversion quality influence, insufficient time accuracy, serious numerical dispersion, etc.

Inactive Publication Date: 2018-07-13
CHINA UNIV OF PETROLEUM (EAST CHINA)
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Problems solved by technology

[0004] So far, there are relatively few time high-order staggered grid finite difference methods for variable density acoustic wave equations, and the time accuracy is still not enough
When the time step is large or the simulation distance is long, the numerical dispersion is serious, which has a great impact on the quality of subsequent imaging and inversion

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  • Time high-order precision staggered mesh finite difference method for variable density acoustic wave equations
  • Time high-order precision staggered mesh finite difference method for variable density acoustic wave equations
  • Time high-order precision staggered mesh finite difference method for variable density acoustic wave equations

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Embodiment Construction

[0106] The present invention will be described in detail below in combination with specific embodiments.

[0107] Such as figure 1 As shown, it is a flow chart of the present invention to implement the high-precision finite difference numerical simulation of the variable density acoustic wave equation, specifically including:

[0108] (1) Design a new differential template.

[0109] Based on the existing regular grid finite difference template, combined with the "cross" and "diamond" templates, a new staggered grid finite difference template is designed.

[0110] (2) Using a new difference template to numerically discretize the variable density acoustic wave equation.

[0111] The staggered grid finite-difference numerical discretization of the variable-density acoustic wave equation is carried out using a new difference template.

[0112] (3) Deduce the dispersion relation of the variable density acoustic wave equation under the new difference template.

[0113] Based on ...

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Abstract

The invention discloses a time high-order precision staggered mesh finite difference method for variable density acoustic wave equations, comprising: designing a new difference template; using the newdifference template to perform staggered mesh finite difference numerical dispersing on the variable density acoustic wave equations; deducing a frequency dispersion relationship of the variable density acoustic wave equations under the new difference template; using Taylor series expansion or an optimal method to solve a new finite difference coefficient; introducing the new difference coefficient into corresponding discrete equations so as to perform numerical simulation on the variable density acoustic wave equations; analyzing precision and stability of the novel difference method. The time high-order precision staggered mesh finite difference method for variable density acoustic wave equations has the advantages that precise temporal (2M) order and time 10-order simulation precisionare provided, calculating efficiency can be improved by extending time step length; zero distortion of waveform in remote simulation can be better guaranteed.

Description

technical field [0001] The invention belongs to the technical field of geophysics, and relates to a new wave equation numerical simulation method, which can be applied to geophysical problems such as seismic wave forward modeling, reverse time migration and full waveform inversion. Background technique [0002] Numerical simulation of the wave equation is an effective means to understand the propagation of seismic waves in the subsurface and help interpret observation data, and it is also the basic unit of reverse time migration imaging and full waveform inversion. So far, wave equation numerical simulation has been widely used in various links in the field of geophysical exploration. The commonly used numerical solutions of partial differential equations include finite element method, finite difference method, pseudospectral method and so on. The finite difference method is easy to implement and has high computational efficiency, and is the most commonly used wave equation...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G01V1/30G01V1/36
CPCG01V1/30G01V1/36G01V2210/51G01V2210/673
Inventor 任志明李振春孙史磊
Owner CHINA UNIV OF PETROLEUM (EAST CHINA)
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