CN104123449A - Subregion local variable-density non-equidistant dual mesh division method for complex mountainous region - Google Patents

Abstract

The invention relates to a subregion local variable-density non-equidistant dual mesh division method for a complex mountainous region. The method comprises the steps that an overall model framework of the complex mountainous region is established according to the earth surface elevation and the calculated region range, the whole model framework is divided through square coarse meshes in sequence, a complex earth surface nearby region is divided through variable-density densified non-equidistant meshes, a seismic origin nearby region is divided through variable-density densified meshes, and other regions are divided through dual uniformly-multiplied densified meshes. By means of the meshes, the complex earth surface morphology and the distribution conditions of complex media nearby the earth surface can be depicted accurately and subtly, the boundary conditions nearby the complex earth surface can be achieved accurately and stably, the problem of a large error nearby a source point can be solved on the premise of not substantially increasing the calculated amount, the calculating efficiency can be improved substantially on the premise of guaranteeing the calculating accuracy, and spending of too much mesh generation cost, an extra storage space and extra calculated amount are not needed.

Description

Partition local densification and unequal distance dual grid generation method in complex mountainous area

technical field

The invention relates to a grid subdivision method for complex medium models in technologies such as seismic wave numerical simulation and data processing in the field of geophysics, especially a fine grid subdivision method for complex mountain models.

Background technique

Complex mountainous geological conditions often bring many thorny problems to technologies such as seismic wave numerical simulation and data processing in complex mountainous areas. The meshing technology for complex mountain models is a basic and key technology that affects the accuracy, efficiency, and stability of seismic wave numerical simulation and data processing technologies under complex mountain conditions.

At present, for the grid division of complex mountain models, uniform and single stepped grids, unequal grids, and curved grids are usually used. In the important technical links such as the accurate description of the complex surface shape of the complex mountain model and the distribution of the complex medium near the surface, the complex surface boundary conditions of the numerical calculation, and the treatment of the problem of large errors near the source, the above-mentioned uniform and single grid is very good. Difficult to achieve good results. First of all, the step grid is actually a kind of step-like approximation to the surface shape. In addition to the inaccurate description of the surface shape, this approximation will also cause problems such as local boundary diffraction and corner scattering of the seismic wave field; Secondly, although the uniform and single non-equidistant grid can accurately locate the surface elevation position, it is also easy to realize the surface boundary conditions, but compared with the densified processing grid near the surface, it cannot accurately determine the shape of the surface and the complex medium near the surface. More detailed description; Finally, although the curved grid is proposed for the easy realization of the boundary conditions on the complex surface, it is also unable to perform a finer description of the surface morphology and the complex medium near the surface, and the curved grid Generation usually requires a large amount of additional grid generation costs. In addition, seismic wave numerical simulation technology usually encounters numerical instability problems in this grid, especially when the surface shape is very complex and the local surface elevation changes sharply. Curvilinear mesh generation technology is not easy to obtain good mesh generation quality and the stability of numerical realization is more difficult to guarantee.

"Journal of Geophysics" 2005 Issue 05 published Zhao Aihua et al. "Double grid method for simulation of travel time of wide-angle reflection seismic waves". The minimum travel time tree method of wide-angle reflection seismic wave travel time and ray path, the double grid method only calculates large grid nodes in the homogeneous medium, and calculates small grid nodes at the same time in the velocity change point, source point and receiver point area; at the interface The boundary points use a larger wavelet propagation area than the internal nodes of the medium. The calculation results of the model show that for a large-scale layered block uniform medium model, under the condition of ensuring accuracy, the dual grid ray tracing method proposed in this paper can achieve Computational efficiency is significantly improved over single-grid methods.

"Advances in Geophysics" 2006 Issue 04 published Lu Yuzeng's "Three-dimensional Finite Element Numerical Simulation of Tetrahedral Subdivision Resistivity under Complex Terrain Conditions". It has been receiving a lot of attention. This paper proposes a tetrahedral grid cross-subdivision method. The subdivided grids are interlaced with each other, so that the subdivided grids are diverse and can better simulate geoelectricity in complex terrain conditions. Model. At the same time, starting from the equation satisfied by the point power field, this paper deduces the finite element numerical simulation algorithm under the condition of three-dimensional complex terrain, and compiles the calculation program. The example shows that this method is effective and the calculation accuracy is high.

"China Coalfield Geology" published No. 02, 2006, Li Xiaobin et al. "Exploration of Static Correction Method of Subdivision Refraction Method under Complex Surface Conditions". The subdivision method is used to perform static correction on seismic data. Firstly, a near-surface refraction wave subdivision model is established, and the refraction wave is divided into several units by vertical grids with equal or unequal spacing. The refraction wave velocity of each unit is approximately a constant. , while the variation of velocity between different units reflects the lateral variation of the velocity of the entire near-surface layer. In practical application, multiple single-shot records can be used to solve the velocity correlation orthogonally.

China University of Petroleum's 2012 master's thesis published Xie Jinping's "variable grid forward simulation under undulating surface conditions". The first is to deal with the free boundary under the condition of undulating surface. This paper studies the method of combining the vacuum method and the generalized virtual image method to deal with the boundary. In the undulating surface, the shear stress is not directly processed, but the shear stress is directly sampled to make it more efficient. It has been improved to a certain extent; secondly, elastic wave staggered grid finite difference is used to discretize the elastic wave equation, and variable grid is introduced to improve the efficiency of forward modeling of undulating surface. The length is small, and at the same time, the efficiency is significantly improved compared with the global fine grid difference, and the calculation memory is saved. A high-order staggered grid differential simulation is used, and a step-by-step reduction process is used when approaching the boundary, and free boundary conditions are realized at the boundary.

In fact, the following core problems need to be solved when meshing complex mountain models: ①How to accurately and finely describe the complex surface morphology and the distribution of complex media near the surface; ②How to accurately and stably realize the numerical simulation of seismic waves, data Processing and other technologies on the complex surface boundary conditions; ③How to deal with the problem of large errors in numerical simulation, data processing and other technologies near the source; ④How to solve the problem of huge calculations in numerical simulation, data processing and other technologies.

Contents of the invention

The purpose of the present invention is to provide a dual grid with variable local density and unequal distance for complex mountainous areas to address the defects of the above-mentioned existing uniform and single ladder grid, unequal grid, and curved grid. splitting method.

The present invention is realized through the following technical solutions and steps:

a. Construct the overall model framework of the complex mountain area according to the surface elevation and the calculation area;

b. Subdividing the above-mentioned model frame by using a square coarse grid with a relatively large grid spacing;

c. Remove the part above the surface of the grid in step b, but keep the accurate position of the surface on the grid line, and then form an unequal grid near the surface;

d. Starting from the surface, from near to far, the above coarse grids are densified locally according to the densification degree of (2 ⁿ ,2 ^n-1 ,2 ^n-2 ,…,2) exponential attenuation, and then form A locally densified grid near the surface;

e. Starting from the designated source point, the grid in the above step d is locally changed according to the encryption method of (2 ⁿ ,2 ^n-1 ,2 ^n-2 ,…,2) exponential attenuation from near to far. Density-densification, thereby forming a local densification grid near the source point;

f. Carry out uniform 2 ⁿ times encryption to the grids other than the encrypted part of steps d and e. The grid of this encrypted part forms a double grid with the grid before this step. In numerical calculation, the double grid is the whole model The subdivision grid of step e is the calculation grid, and the calculation results on the dense grid nodes in this step are obtained by interpolating the calculation results on the local adjacent calculation grids.

In the 2 ⁿ times encryption, n is an encryption index. The encryption index n is comprehensively determined by calculation accuracy, calculation efficiency and storage capacity.

Beneficial effects: ①The variable-densification unequal-distance grid near the surface can precisely and accurately describe the complex surface morphology and the distribution of complex media near the surface; ②It is conducive to accurate and stable realization of boundary conditions near the surface for numerical simulation and data processing;③ The denser grid near the source point is conducive to solving the problem of large errors in numerical simulation, data processing and other technologies near the source point without greatly increasing the amount of calculation; Under the premise of accuracy, the calculation efficiency of numerical simulation and data processing can be greatly improved, and at the same time, the deep sampling rate of some data processing technologies can be greatly improved; At the same time, there is no need to spend too much extra storage space and calculation cost during numerical calculation.

Description of drawings

Accompanying drawing 1 is the process and schematic diagram of establishment of unequal-distance dual grids with local densification and localization;

Accompanying drawing 2 adopts the Marmousi model after the undulating land surface correction of grid division of the present invention;

Accompanying drawing 3 adopts grid division SEG undulating surface Foothill model of the present invention.

Detailed ways

The specific implementation manner of the present invention will be further described below in conjunction with the accompanying drawings and implementation examples. As shown in the schematic diagram of the flow chart in Figure 1, the specific implementation method of the dual grid subdivision technology with localized densification and unequal distance for complex mountainous areas is as follows:

a. As shown in step a of Figure 1, construct the overall model framework of the complex mountain area according to the surface elevation and the calculation area;

b. As shown in Figure 1 step b, the above-mentioned model frame is divided by using a square coarse grid with a relatively large grid spacing;

c, as shown in Figure 1 step c, remove the part above the surface of the grid in step b, but keep the accurate position of the surface on the grid line, and then form an unequal grid near the surface;

d. As shown in step d of Figure 1, starting from the surface, grid the above coarse grid according to (2 ⁿ ,2 ^n-1 ,2 ^n-2 ,…,2) exponentially attenuated densification degree from near to far The local densification and densification of , thus forming a local densification grid near the surface;

e. As shown in step e of Figure 1, starting from the designated source point, the grid in the above step d is decayed exponentially according to (2 ⁿ ,2 ^n-1 ,2 ^n-2 ,…,2) from near to far The encryption method performs local variable density encryption of the grid, and then forms a local variable density grid near the source point;

f. Carry out uniform 2 ⁿ times encryption to the grids other than the encrypted part of steps d and e. The grid of this encrypted part forms a double grid with the grid before this step. In numerical calculation, the double grid is the whole model The subdivision grid of step e is the calculation grid, and the calculation results on the dense grid nodes in this step are obtained by interpolating the calculation results on the local adjacent calculation grids.

In the 2 ⁿ times encryption, n is an encryption index. The encryption index n is comprehensively determined by calculation accuracy, calculation efficiency and storage capacity.

Example 1

As shown in Figure 2, a complex surface Marmousi model is introduced to the classic Marmousi model after adding surface correction, and the surface fluctuations of this model are relatively severe. When using the grid subdivision technology of the present invention to subdivide it, set the grid spacing of the larger square coarse grid used in step b as h. When performing exponential encryption on the grid near the surface, the maximum index factor is n=4, that is, the distance between the nearest grid to the surface is h/16, and each exponential encryption factor (respectively n=4, 3, 2) corresponds to The range of the grid densification area starts from the surface and extends downward successively for no more than 1.0h, 1.5h, and 2.0h. When performing exponential refinement on the grid near the seismic source, the maximum exponential factor is n=4, that is, the distance between the grids closest to the seismic source is h/16, and each exponential refinement factor (respectively n=4, 3, 2) is respectively The corresponding grid-densified area range is concentric rings with a width of 2h and a width of 2h with the center of the seismic source as the center. Finally, when the double grid is formed in step f, the multiple of the doubling densification degree of the square coarse grid is 2, that is, the grid spacing of the double grid is h/2. Analysis of the subdivision results in Figure 2 shows that the grid subdivision technology proposed by the present invention can describe the shape of the complex surface relatively finely, and can also describe the complex distribution of the near-surface medium finely, and at the same time, it can also analyze the grid near the seismic source. Perform variable density encryption.

Example 2

As shown in Figure 3, the model is the classic SEG undulating surface Foothill model, and the surface elevation changes in some areas of the model are relatively drastic. Also, when it is subdivided by the grid subdivision technology of the present invention, the grid spacing of the larger square coarse grid used in step b is set to be h. When performing exponential encryption on the grid near the surface, the maximum index factor is n=4, that is, the distance between the nearest grid to the surface is h/16, and each exponential encryption factor (respectively n=4, 3, 2) corresponds to The range of the grid densification area starts from the surface and extends downward successively for no more than 1.0h, 1.5h, and 2.0h. When performing exponential refinement on the grid near the seismic source, the maximum exponential factor is n=4, that is, the distance between the grids closest to the seismic source is h/16, and each exponential refinement factor (respectively n=4, 3, 2) is respectively The corresponding grid-densified area is a concentric ring with a width of 2h and a width of 2h centered on the hypocenter. Finally, when the double grid is formed in step f, the multiple of the doubling density of the square coarse grid is 2, that is, the grid spacing of the double grid is h/2. Analysis of the subdivision results in Figure 3 shows that the grid subdivision technology proposed in the present invention can describe the shape of the complex surface relatively finely, and can also describe the complex distribution of the near-surface medium finely, and at the same time, it can also accurately describe the grid near the seismic source. Perform variable density encryption.

Claims (2)

1. A method for subdivision local variable densification unequal distance double grid subdivision in complex mountain area, is characterized in that, comprises the following steps: a. Construct the overall model framework of the complex mountain area according to the surface elevation and the calculation area; b. The model framework constructed in step a by adopting a square coarse grid with uniform grid spacing; c. Remove the part above the surface of the grid in step b, but keep the exact position of the surface on the grid line, and then form an unequal grid near the surface; d. Starting from the surface, from the near to the far, the above coarse grids are densified locally according to the densification degree of (2 ⁿ ,2 ^n-1 ,2 ^n-2 ,…,2) exponential attenuation, forming a near The local densified grid of the surface; e. Starting from the designated source point, the grid in step d is densified locally according to the (2 ⁿ ,2 ^n-1 ,2 ^n-2 ,…,2) exponential attenuation encryption method from near to far, Form a local densified grid near the source point; f. Carry out uniform 2 ⁿ times encryption to the grids other than the encrypted part of steps d and e. The grid of this encrypted part forms a double grid with the grid before this step. In numerical calculation, the double grid is the whole model The subdivision grid of step e is the calculation grid, and the calculation results on the dense grid nodes in this step are obtained by interpolating the calculation results on the local adjacent calculation grids. 2. according to the subregion of the complex mountainous area described in claim 1, the method for subdivision localized densification and non-equidistant double meshing is characterized in that, the n of 2 ⁿ in the steps c, e and f is the densification index.