JP2022109134A - program - Google Patents

Abstract

To provide a technique for meshing a stratum model for reflecting terrain.SOLUTION: In a program for allowing a computer to execute a meshing method for meshing a stratum model, the stratum model has an undulated surface, a side face as a vertical surface, and a bottom face as a horizontal surface, and the meshing method includes the steps of generating a shape model in a rectangular parallelepiped shape by deformation of the stratum model in a vertical direction by a predetermined deformation rule, dividing the shape model into plural blocks in a rectangular parallelepiped shape, meshing respective blocks of the plural blocks such that nodes and connection match in a boundary surface between adjacent blocks and generating meshes for the respective blocks, and deforming the meshes in a vertical direction by adopting the predetermined deformation rule contrarily.SELECTED DRAWING: Figure 2

Description

TECHNICAL FIELD The present invention relates to a technology for creating a mesh for a stratum model.

Techniques have been proposed for analyzing seismic wave propagation by meshing a stratum model. Patent Documents 1 to 3 disclose techniques for dividing a stratum model into a plurality of blocks and generating a mesh for each block. In these documents, meshes are generated such that the nodes and connections on the boundary surfaces between adjacent blocks are coincident. By generating meshes in units of blocks, it is possible to reduce the computational load on the computer and parallel processing is also possible. By generating a mesh so that the nodes and connections on the boundary surface between adjacent blocks match, there is also the advantage that the mesh of the stratum model combining arbitrary blocks can be easily obtained.

Japanese Patent No. 5637956 Japanese Patent No. 5755480 Japanese Patent No. 5762094

However, in the techniques of Patent Documents 1 to 3, a rectangular parallelepiped model is targeted as a stratum model. There is room for improvement in the analysis of strata models that reflect topography (land and seafloor topography).

SUMMARY OF THE INVENTION An object of the present invention is to provide a technique for meshing a stratum model reflecting topography.

According to the invention,
A program for causing a computer to execute a meshing method for meshing a stratum model,
The stratum model has an undulating surface, a side surface that is a vertical surface, and a bottom surface that is a horizontal surface,
The meshing method includes:
a generation procedure for generating a rectangular parallelepiped shape model by deforming the stratum model in the vertical direction according to a predetermined deformation rule;
a procedure in which the shape model is divided into a plurality of rectangular parallelepiped blocks;
a procedure in which each block of the plurality of blocks is meshed so that the nodes and connections on the boundary surface between adjacent blocks match to generate a mesh for each block;
a deformation procedure in which the mesh is deformed in the vertical direction by inversely adopting the predetermined deformation rule;
There is provided a program characterized by:

ADVANTAGE OF THE INVENTION According to this invention, the technique which meshes the stratum model which reflected the topography can be provided.

1 is a block diagram showing the configuration of an information processing system; FIG. 4 is a flowchart showing an example of processing executed by an arithmetic device; Explanatory drawing which shows the flow of a process. Explanatory drawing which shows the example of a meshing procedure. (A) is a diagram showing a stratum model before deformation, (B) and (C) are diagrams showing a stratum model after deformation. 4 is a flowchart showing an example of processing executed by an arithmetic device; FIG. 10 is a diagram showing a display example of calculation results;

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings. It should be noted that the following embodiments do not limit the invention according to the claims, and not all combinations of features described in the embodiments are essential to the invention. Two or more of the features described in the embodiments may be combined arbitrarily. Also, the same or similar configurations are denoted by the same reference numerals, and redundant explanations are omitted.

<Information processing system>
FIG. 1 is a block diagram showing an example of an information processing system capable of executing the program of the present invention. The information processing system 1 includes an arithmetic device 2 , a storage device 5 , a drive device 6 , a LAN interface (I/F) 7 , a user interface (I/F) 8 and a display device 9 . The computing device 2 includes a CPU 3 that executes various programs and a RAM 4 that is used as a work area for the CPU 3 . The storage device 5 is, for example, a hard disk device, and stores various programs executed by the CPU 2 and various data used when the programs are executed. A program for causing the CPU 2 to execute a meshing method for meshing a stratum model can be stored in the storage device 5 .

The drive device 6 is a device capable of reading data written in a storage medium such as a magnetic disk or an optical disk and writing data to the storage medium. The LAN interface 7 is an interface capable of communicating with nodes connected to the LAN. A terrain model to be meshed is acquired via the drive device 6 or via the LAN interface 7 . The program executed by the CPU 2 may be stored in a storage medium and installed in the system via the drive device 6 .

The user interface 8 is composed of a keyboard, a pointing device, etc., and accepts input of user's instructions. The display device 9 is, for example, a liquid crystal display device, and presents information to the user.

<Mesh formation of stratum model>
FIG. 2 is a flow chart showing an example of a program executed by the CPU 3. This program causes the CPU 3 to execute a meshing method for meshing a stratum model. FIG. 3 is an explanatory diagram showing the flow of processing, and the stratum model M is an example of a model to be meshed. Arrows X and Y indicate horizontal directions orthogonal to each other, and arrow Z indicates a vertical direction.

In S1 of FIG. 2, analysis condition setting processing is performed. Details will be described later. In S2, a shape model S2 is generated from the stratum model M. As shown in FIG. The stratum model M has an undulating surface TS, four vertical rectangular cylindrical side surfaces SS, and a horizontal bottom surface BS. The undulations of the surface TS represent the land topography or the bottom topography. The illustrated stratum model M has three strata L1 to L3. The number of strata is not limited to three. A stratum boundary GB1 indicates the interface between the stratum L1 and the stratum L2, and a stratum boundary GB2 indicates the interface between the stratum L2 and the stratum L3. The stratum model M is defined, for example, by information representing the outer shape of the stratum model M and the position coordinates of each point on each stratum boundary. In the example of FIG. 3, as an example, a stratum boundary GB1 is defined by a large number of constituent points having grid-like X coordinates, Y coordinates, and Z coordinates. Thus, the stratum model M can be defined by data describing the outer diameter of the model and the shape of each stratum.

Since the stratum model M has an undulating surface TS, the block division and meshing disclosed in Patent Documents 1 to 3 cannot be applied as is. Therefore, in the present embodiment, the undulations of the surface TS are once flattened, and after mesh generation, the mesh is deformed so that the undulations are restored.

In the process of S2 in FIG. 2, the surface TS of the stratum model M is made a flat horizontal surface, and the stratum model M is deformed into a rectangular parallelepiped shape model M'. An example of the deformation rule will be described later, but the Z coordinates of all or part of the stratum model M are transformed so that the surface TS' is aligned with the depth D of the geometric model M' set in S1. For example, a coefficient kn is set for each (xn, yn), and the constituent point (x1, y1, z1)→(x1, y1, z1′), z1′=k1·z1. As a result, as illustrated in FIG. 3, the peak portions of the surface TS are lowered and the valley portions are raised to form a rectangular parallelepiped shape model M' having a surface TS', four side surfaces SS' and a bottom surface BS. is generated. The shape model M' has layers L1' to L3' corresponding to the layers L1 to L3, and layer boundaries GB1' and GB2' corresponding to the layer boundaries GB1 and GB2.

In S3 of FIG. 2, the geometric model M' is divided into a plurality of blocks. In FIG. 3, as an example, it is divided into eight blocks B1' to B8' having the same rectangular parallelepiped shape. The division of the geometric model M' is performed by dividing it by vertical planes. The division direction (at least one of X and Y), block size, etc. are set in S1. Positional information of each block and positional information of boundaries between blocks are stored.

In S4 of FIG. 2, each block is meshed to generate a mesh for each block. The order of blocks to be processed follows a predetermined rule. For example, block B1' is the first to be processed, and each block is meshed sequentially. Block meshing is performed under the conditions set in S1 (size of mesh element for each layer, etc.). A tetrahedral element, a hexahedral element, or the like can be used as the mesh element. That is, each layer can be meshed with tetrahedral elements or hexahedral elements. Mesh data for each block (information indicating the arrangement of mesh nodes and connections, mesh physical property information (S wave velocity, P wave velocity, density, S wave Q value and P wave Q value, etc.) is the position information of the block is registered (stored) in the storage device 5 in association with the .

When the meshing of one block is completed, the meshing of the next block is performed. If a block to be processed is adjacent to a block that has already been meshed, it is meshed so that the nodes and connections on the boundary surface between these adjacent blocks match. That is, the boundary surface of the block to be processed becomes a constraint surface on which the placement of nodes and connections is constrained. FIG. 4 shows an example of this. The meshed block Bn and the next block to be processed Bn+1 have boundary surfaces Sn and Sn+1, and the nodes and connections on the boundary surface Sn are diverted to the boundary surface Sn+1. The methods of Patent Documents 1 to 3 can be applied to the meshing method of a block to be processed having a constraint surface. In this way, all blocks B1' to B8' are meshed.

In S5 of FIG. 2, the deformation rule adopted (applied) in S2 is reversely adopted (applied), so that the mesh for each block created in S4 is vertically deformed to reflect the shape of the original stratum model M. get a mesh for each block. FIG. 3 schematically shows that the meshes of blocks B1' and B2' created in S4 are converted into meshes of blocks B1 and B2 reflecting the shape of the original stratum model M. FIG. For the conversion, for example, the Z coordinate of each node of the mesh is multiplied by the reciprocal of the coefficient k to convert (xn, yn, zn) to (xn, yn, 1/kn·zn), and the final mesh node Obtain information indicating the coordinates of and the arrangement of connections. This information is registered in the storage device 5 .

Through the above procedure, a block-by-block mesh expressing the undulations of the surface TS of the stratum model M can be obtained. Since the mesh of the stratum model M is registered in units of blocks, it is possible to easily obtain meshes of partial models of the stratum model M by combining a plurality of blocks necessary for analysis. That is, in each block to be combined, nodes and connections with the same arrangement are arranged on the boundary surface with the adjacent block. Therefore, when combining the meshes of each block, it is possible to obtain the mesh of the partial model simply by combining each of the overlapping nodes and connections as one piece of node or connection information. If a wide-area geological model is adopted as the stratum model M and meshes of each block are stored in a database in advance, meshes of stratum models in various regions can be easily obtained. Therefore, seismic wave motion analysis of various seismic sources can be handled, and seismic wave motion analysis can be facilitated.

<Transformation rules>
In the above mesh generation example, a procedure is adopted in which the stratum model M is once deformed into a rectangular parallelepiped shape model M' to create a mesh, and the mesh is deformed so that the model shape returns to the original stratum model. . Although the mesh is deformed only in the Z direction, the mesh deformation may degrade the quality of the mesh, such as increasing the aspect ratio after deformation.

For example, in wave propagation analysis of seismic motion, the length of the wavelength changes according to the wave propagation speed in the ground of each layer. Therefore, the required mesh size may differ depending on each layer. In general, it is preferable to reserve a mesh of 10 elements in one wavelength. When meshing is performed with the shape model M' as a reference, if the size of the mesh after deformation is too large, it may not be possible to secure the number of elements corresponding to the length of the wavelength. Also, when using the explicit method for wave propagation analysis, it is necessary to set the calculation time step below a certain value determined from the size of the mesh and the hardness of the ground in order to guarantee the stability of the solution (Courant condition: calculation time step < mesh size/propagation velocity). When the geometric model M' is meshed as a reference, it is preferable to prevent such conditions from being unsatisfied due to deformation of the mesh.

Therefore, in the present embodiment, the deformation rule applied in the generation of the shape model in S2 can be selectively adopted from two types of deformation rules. From two types of deformation rules, a deformation rule that allows mesh deformation to fall within an allowable range can be selected. 5A to 5C are explanatory diagrams thereof. FIG. 5A shows the vertical cross-sectional shape of the stratum model M before deformation. Thicknesses H1, H2, and H3 indicate layer thicknesses at the same position (hereinafter referred to as reference position) on the horizontal plane of each layer L1, L2, and L3. Depth D is the depth of the shape model M' (see FIG. 3).

FIG. 5(B) shows a shape model M' that adopts the first deformation rule. A dashed line indicates the surface of the stratum model M or the stratum boundary. The first deformation rule is a rule for deforming the stratum model while maintaining the layer thickness of each layer except for the lowest layer (referred to as layer thickness maintenance rule). Layer thicknesses at the reference positions of layers L1′, L2′, and L3′ corresponding to layers L1, L2, and L3 are H1-1 (=H1), H2-1 (=H2), and H3-1. H3-1=D-(H1+H2). If the number of strata is 1 to n, and the original layer thickness H of each layer and the layer thickness H' after deformation are expressed by a general formula,
Hi'(X,Y)=Hi(X,Y)
(i = 1 to n-1)
Hn'(X,Y)=D-(H1(X,Y)+H2(X,Y)+...+Hn-1(X,Y))
is.

The transformation of the Z coordinate in S2 is
Z'(X, Y)=Z(X, Y)-(Hn-Hn')
(Other than bottom layer)
Z′(X, Y)=Z(X, Y)×(Hn′/Hn)
(bottom layer)
becomes.

The transformation of the Z coordinate of the mesh in S5 is
Z(X, Y)=Z'(X, Y)+(Hn-Hn')
(Mesh other than the bottom layer)
Z (X, Y) = Z' (X, Y) x (Hn/Hn')
(bottom layer mesh)
(Z′: coordinates after meshing of S4, Z: coordinates after deformation of S5).

FIG. 5(C) shows a geometric model M' that adopts the second deformation rule. The second deformation rule is a rule for deforming the stratum model while maintaining the layer thickness ratio of each layer (referred to as the layer thickness ratio maintenance rule). The layer thicknesses at the reference positions of the layers L1′, L2′, and L3′ corresponding to the layers L1, L2, and L3 are H1−2 (=H1×D/(H1+H2+H3)), H2−2 (=H2×D/( H1+H2+H3)) and H3-2 (=H3×D/(H1+H2+H3)). If the number of strata is 1 to n, and the original layer thickness H of each layer and the layer thickness H' after deformation are expressed by a general formula,
Hi'(X,Y)=Hi(X,Y)*D/(H1(X,Y)+H2(X,Y)+...+Hn(X,Y))
is.

The transformation of the Z coordinate in S2 is
Z′(X,Y)=Z(X,Y)×D/(H1(X,Y)+H2(X,Y)+...+Hn(X,Y))
becomes.

The transformation of the Z coordinate of the mesh in S5 is
Z(X,Y)=Z′(X,Y)/D×(H1(X,Y)+H2(X,Y)+...+Hn(X,Y))
(Z′: coordinates after meshing of S4, Z: coordinates after deformation of S5).

An index for evaluating which deformation rule is appropriate is required. In the case of this embodiment, the strain in the vertical direction of the mesh before and after deformation is used as an evaluation index. The strain value γ is the mesh size after deformation compared to before deformation, that is, the ratio of layer thickness after deformation to before deformation,
γi(X, Y)=Hi'(X, Y)/Hi(X, Y)
(i = 1 to n)
becomes. Let γimin be the minimum value of the strain value γ for each layer, and γimax be the maximum value thereof. It means that the closer the minimum strain value and the maximum strain value are to 1, the smaller the deformation of the mesh is suppressed. By calculating the strain value and presenting it to the user at the stage of S1 in FIG. 2, the user can select a more desirable deformation rule.

In addition, unlike the analysis of objects such as machines and buildings, the analysis of a stratum model has a clear boundary only on the surface (upper part), and the side and bottom surfaces can be regarded as an infinitely expanding area. Therefore, in this embodiment, the user can set the depth D as a variable in addition to the deformation rule, so that deformation of the mesh can be alleviated. If the depth D is increased, deformation of the mesh tends to be suppressed, but the number of meshes tends to increase, resulting in an increase in computational load during analysis.

<Condition setting>
An example of condition setting in S1 of FIG. 2 will be described. FIG. 6 is a flow chart thereof. In S11, input of various conditions by the user is accepted. Here, the ground conditions (thickness of each stratum, S-wave velocity, P-wave velocity, etc.), analysis conditions planned for wave propagation analysis (analysis target period T, number of mesh elements in one wavelength), etc. are input. be. Initial values for the depth D and the reference size (smallest size) of the mesh are also input.

In S12, for each of the layer thickness maintenance rule and the layer thickness ratio maintenance rule, the maximum strain value, minimum strain value, mesh size after deformation (mesh standard size x maximum strain value), and calculation time step based on Courant conditions (Mesh standard size x minimum strain value) is calculated. The calculation result of S12 is displayed on the display device 9 in S13. FIG. 7 shows an example thereof. The illustrated display example assumes that the number of strata is three.

Among the display examples, the "maximum mesh size" is calculated by S-wave velocity of stratum×analyzed period/number of mesh elements in one wavelength. "Mesh size" is a multiple of 2 except for strata to which the standard size is applied (assuming the adoption of the octree method, in the example shown in the figure, the second layer is doubled and the third layer is quadrupled). is). The user will examine whether or not to modify the depth D and the reference size of the mesh based on the calculation result. In the example of FIG. 7, the maximum strain value and the minimum strain value in the third layer of the layer thickness maintenance rule exceed the allowable value (0.8 to 1.2 here), so the selection of the layer thickness maintenance rule is disadvantageous. becomes. In addition, the maximum strain value and the minimum strain value are barely permissible in the layer thickness ratio maintenance rule. In such a case, it may be possible to obtain better results by changing the depth D or the reference size and trying again.

In S14 of FIG. 6, it is determined whether or not the user has selected retry. If the user selects retry, the process advances to S16 to receive the user's input to change the conditions. The user changes at least one of the depth D and the reference size. After the change, the process returns to S12 and similar processing is executed.

At S14, if the user does not select retry, proceed to S15. Selection of the transformation rule by the user is accepted, various conditions are determined as the current conditions, and the process ends, and the processes from S2 onward in FIG. 2 are executed.

As described above, in the present embodiment, while maintaining the advantages of large scale and speeding up by applying parallel processing in Patent Documents 1 to 3, by deforming the mesh in the Z direction, a mesh that reflects the undulations of the terrain is generated. becomes possible. In addition, the deformation rule can be selected from two types of rules to provide deformation of the mesh, and by adding the depth D to the adjustment parameter, it is possible to obtain a more desirable mesh.

Although the embodiments of the invention have been described above, the invention is not limited to the above embodiments, and various modifications and changes are possible within the scope of the gist of the invention.

1 Information processing system

Claims (3)

A program for causing a computer to execute a meshing method for meshing a stratum model,
The stratum model has an undulating surface, a side surface that is a vertical surface, and a bottom surface that is a horizontal surface,
The meshing method includes:
a generation procedure for generating a rectangular parallelepiped shape model by deforming the stratum model in the vertical direction according to a predetermined deformation rule;
a procedure in which the shape model is divided into a plurality of rectangular parallelepiped blocks;
a procedure in which each block of the plurality of blocks is meshed so that the nodes and connections on the boundary surface between adjacent blocks match to generate a mesh for each block;
a deformation procedure in which the mesh is deformed in the vertical direction by inversely adopting the predetermined deformation rule;
A program characterized by The program according to claim 1,
As the predetermined deformation rule,
a first deformation rule for deforming the stratum model while maintaining the layer thickness of each layer other than the lowest layer;
a second deformation rule for deforming the stratum model while maintaining the layer thickness ratio of each layer is selectively adopted;
A program characterized by The program according to claim 2,
Before the generation procedure, the vertical strain of the mesh due to the deformation procedure is calculated for the case where the first deformation rule is adopted and the case where the second deformation rule is adopted, respectively, and the calculation is performed. the results are displayed on the display means,
A program characterized by

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