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Method for obtaining stable nearly perfectly matched layer absorption boundary condition

A technology of absorbing boundary conditions and optimal matching layer, applied in special data processing applications, instruments, electrical digital data processing, etc., can solve problems such as hindering the application of CFS-NPML, algorithm instability, etc., and achieve stable and good absorbing boundary conditions Effect

Inactive Publication Date: 2018-05-25
CHINA PETROLEUM & CHEM CORP +1
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Problems solved by technology

However, when CFS-NPML is used in combination with the discontinuous Galerkin finite element seismic numerical simulation algorithm, in the case of long-term simulation, the algorithm has obvious instability from the boundary, which hinders the application of CFS-NPML

Method used

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  • Method for obtaining stable nearly perfectly matched layer absorption boundary condition
  • Method for obtaining stable nearly perfectly matched layer absorption boundary condition
  • Method for obtaining stable nearly perfectly matched layer absorption boundary condition

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Embodiment

[0052] attached figure 1 It is a free surface homogeneous model, in which the calculation area of ​​the model is 4000m*4000m, and the thickness of the PML area is 400m. The following absorbing boundary conditions are used in combination with the discontinuous Galerkin finite element method (DGFEM) to carry out seismic wave numerical simulation, and the spatial third-order simulation is adopted. Surface excited blast source. ; attached figure 2 The wave field snapshot results using the near-optimally matched layer absorbing boundary condition (CFS-NPML) based on complex stretching coordinate transformation, the left is the result at 0.4s, and the right is the result at 2s. It can be seen from the figure that the simulation calculation has been obviously unstable at 2s, and this instability mainly comes from the inside of the absorbing boundary layer; image 3 The wave field snapshot results using the stable near-best matching layer absorbing boundary condition (CFS-NPML) bas...

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Abstract

The invention provides a method for obtaining a stable nearly perfectly matched layer absorption boundary condition. The method comprises the following steps of (1) converting an elastic wave first-order speed-stress equation of a time domain to a frequency domain; (2) performing coordinate conversion on the elastic wave first-order speed-stress equation of the frequency domain; (3) setting a parameter of a complex frequency shift stretching function in a CFS-NPML; (4) transferring the stretching function into a derived wave field function; (5) performing conversion on the complex frequency shift stretching function, performing variable substitution, and substituting the function into the stretched elastic wave first-order speed-stress equation of the frequency domain; (6) introducing an auxiliary wave field variable for performing variable substitution on the stretched elastic wave first-order speed-stress equation of the frequency domain, and converting the auxiliary variable to be in the form of a first-order ordinary differential equation; and (7) inversely converting the stretched elastic wave first-order speed-stress equation of the frequency domain and the auxiliary equationto the time domain, thereby obtaining an elastic wave first-order speed-stress equation and an auxiliary ordinary differential equation of the CFS-NPML of the time domain.

Description

technical field [0001] The invention is applied in the field of high-precision seismic propagation numerical simulation in complex areas such as piedmont, and can specifically provide good and stable absorption boundary conditions for seismic wave numerical simulation algorithms such as discontinuous Galerkin finite elements. Background technique [0002] Discontinuous Galerkin finite element method (DGFEM) is a high-order high-precision finite element method, which is especially suitable for numerical simulation of seismic wave propagation in complex geological conditions (especially under severe terrain fluctuations). Seismic wave numerical simulation generally simulates the propagation of seismic waves in a limited area, so it is necessary to introduce artificial absorbing boundary conditions to reduce the reflection from the boundary. When applying the discontinuous Galerkin finite element seismic numerical simulation algorithm, the wave field flow at the cell boundary c...

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Application Information

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IPC IPC(8): G06F17/50G01V1/28
CPCG01V1/28G06F30/23
Inventor 薛昭佘德平杨丽
Owner CHINA PETROLEUM & CHEM CORP
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