CN118587306A - A regularized cross-pore imaging method, system, computer device and storage medium - Google Patents

Abstract

The present invention provides a regularized cross-hole imaging method, system, computer equipment and storage medium, which belongs to the field of imaging technology, including dividing the geological area to be detected into a number of grid points and obtaining observation data; constructing a regularized iterative inversion formula through observation data, slowness matrix, ray tracing matrix, and ray tracing operator, according to the initial value of the slowness matrix, the initial value of the ray tracing matrix and the numerical value of the observation data, using the inversion formula, alternately iterating the ray tracing matrix and the slowness matrix in the formula, respectively, and obtaining the estimated values of the slowness matrix and the ray tracing matrix according to the iteration end condition; obtaining an image of the structure of the area to be observed according to the estimated value and the grid structure of the area to be detected. This solution solves the problem in the prior art that a large number of forward calculations are required for each iteration in the numerical calculation process of solving the observation equation, resulting in the final reconstructed image of the structure of the area to be observed not being timely enough and the structure of the area to be observed cannot be accurately estimated.

Description

A regularized cross-pore imaging method, system, computer device and storage medium

Technical Field

The present invention belongs to the field of imaging technology and relates to a regularized cross-pore imaging method, system, computer equipment and storage medium.

Background Art

Inversion imaging can collect relevant signal data after various waveform signals (or other observation media) penetrate/refract/reflect underground/structures (such as human bodies, bridges, industrial machinery, etc.), and combine relevant models and algorithms to reversely solve the stratum structure or internal information of the structure.

Typical applications of this type of method include medical CT, industrial CT, and exploration of underground structures in energy geology (geological inversion, seismic tomography, etc.). As shown in Figure 1, cross-hole imaging refers to the vertical distribution of signal transmission points and receiving points in two wells A and B. The transmission point sends a signal through the area to be observed (generally, the information m in this area cannot be directly observed, such as the inside of the structure), and then collects data d at the receiving point, and then uses relevant models and algorithms to solve the internal information of the area. The signals involved in the observation technology in medical CT are often high-frequency and have extremely short wavelengths. It can be considered that G is only related to the signal transmission and receiving devices and is not affected by m; the observation technology in geological inversion involves signals with longer wavelengths, and G often needs to be calculated through m. To be more precise, the observation equation is G(m)m=d.

Given an observation system Gm=d, G is the observation matrix/operator, m is the observation object, and d is the observed data. Forward calculation generally refers to calculating d through G and m; inverse calculation refers to calculating m through d and G.

In some specific scenarios (such as geological exploration), the observation equation is G(m)m=d. When traditional methods solve m by inverting d, they generally introduce a regularization term about m (that is, using prior information about m) to solve the problem's ill-posed nature. During the numerical calculation process, each iteration requires a costly and time-consuming forward calculation (ray tracing/shortest path calculation) based on the estimated value of m to determine G(m), which results in the final reconstructed image of the structure of the area to be observed not being timely enough and making it impossible to accurately estimate the structure of the area to be observed.

Summary of the invention

In order to solve the problem that a large amount of forward calculations are required for each iteration in the numerical calculation process of solving the observation equation in the prior art, resulting in the reconstructed image of the structure of the area to be observed not being timely enough and the structure of the area to be observed not being accurately estimated, the present invention provides a regularized cross-hole imaging method, system, computer device and storage medium.

In order to achieve the above object, the present invention provides the following technical solutions:

A regularized cross-pore imaging method, characterized in that it comprises the following steps:

According to the positions of the signal transmitting points and receiving points in the geological detection area, the detection area is evenly discretized into a number of grid points, and the observation data of the receiving points are obtained;

A regularized iterative inversion formula is constructed through the relationship between the observation data, the slowness matrix, the ray tracing matrix, and the ray tracing operator, wherein the ray tracing matrix is a projection matrix of the ray tracing operator on the slowness matrix;

According to the given initial value of the slowness matrix of the area to be observed, the initial value of the ray tracing matrix and the observed data value, the regularized iterative inversion formula is used to alternately iteratively update the ray tracing matrix and the slowness matrix in the regularized iterative inversion formula, and the estimated value of the slowness matrix and the estimated value of the ray tracing matrix of the area to be observed are obtained according to the iteration end condition;

The final reconstructed image of the structure of the area to be observed is obtained according to the estimated value of the slowness matrix, the estimated value of the ray tracing matrix and the grid structure of the area to be detected.

Furthermore, the iteration termination condition includes: the norm of the difference between the slowness matrix of the current iteration and the slowness matrix of the previous iteration is less than the set slowness matrix iteration error, and the norm of the difference between the ray tracing matrix of the current iteration and the ray tracing matrix of the previous iteration is less than the set ray tracing matrix iteration error.

Furthermore, the specific relationship of the regularized iterative inversion formula is as follows:

in, is the slowness matrix estimation matrix of the area to be observed and is the ray tracing matrix estimation matrix, H is the ray tracing matrix, α, λ _m , λ _H are weight coefficients, represents the L ¹ regularization (norm) of H, ||m|| _TV represents the TV regularization of m, m is the slowness matrix, ||·|| ₂ represents the L ² regularization (norm), It is the partial derivative of the vector, and R represents the regularization operation on H.

Furthermore, the steps of performing alternating iterative updates on the ray tracing matrix in the regular iterative inversion formula are as follows:

The iterative update formula of the ray tracing matrix H is:

Use Bregman iteration and Gauss-Seidel iteration to alternately iterate the ray tracing matrix. The specific iteration formula is as follows:

Among them, V, b are auxiliary variables, H is the ray tracing matrix, m is the slowness matrix, ξ is the regularization parameter, α, λ _H are weight coefficients, It is the partial derivative of a vector.

Further, the steps of performing alternating iterative updating on the slowness matrix in the regular iterative inversion formula are as follows:

The iterative update formula of the slowness matrix m is:

Use Bregman iteration and Gauss-Seidel iteration to alternately iterate the slowness matrix m. The specific iteration formula is as follows:

[(H ^k ) ^T H ^k -ξΔ]m ^k+1 = (H ^k ) ^T d+ξΔ·(w ^k+1 -p ^k+1 )

Among them, w, p are auxiliary variables, H is the ray tracing matrix, m is the slowness matrix, ξ is the regularization parameter, α, λ _m are weight coefficients, It is the partial derivative of a vector.

Furthermore, the step of obtaining a final reconstructed image of the structure of the area to be observed according to the estimated value of the slowness matrix, the estimated value of the ray tracing matrix and the grid structure of the area to be detected includes:

The path nodes are determined by the ray tracing matrix estimation value to draw the discrete ray tracing path; the grid structure of the area to be detected is used as the spatial position, and the slowness matrix estimation value is used as the pixel value to draw the inversion imaging result of the structure of the area to be observed.

A regularized cross-well imaging system, comprising:

Region segmentation module: used to discretize the area to be detected into several grid points evenly according to the positions of the signal transmitting points and receiving points in the geological area to be detected, and obtain the observation data of the receiving points;

Model construction module: used to construct a regularized iterative inversion formula through the relationship between observation data, slowness matrix, ray tracing matrix, and ray tracing operator, wherein the ray tracing matrix is a projection matrix of the ray tracing operator on the slowness matrix;

Iteration module: used for performing alternate iterative updates on the ray tracing matrix and the slowness matrix in the regular iterative inversion formula according to the given initial value of the slowness matrix of the area to be observed, the initial value of the ray tracing matrix and the observed data value, and obtaining the estimated value of the slowness matrix and the estimated value of the ray tracing matrix of the area to be observed according to the iteration end condition;

Image generation module: used to obtain a reconstructed image of the structure of the area to be observed based on the estimated value of the slowness matrix, the estimated value of the ray tracing matrix and the grid structure of the area to be detected.

A computer device comprises a memory and a processor, wherein the memory stores computer-executable instructions, and the processor executes the computer-executable instructions stored in the memory to implement the regularized cross-pore imaging method as described above.

A computer-readable storage medium is used to store computer-executable instructions, and when the computer-executable instructions are executed by a processor, they are used to implement the regularized cross-pore imaging method as described above.

The regularized cross-pore imaging method, system, computer device and storage medium provided by the present invention have the following beneficial effects:

This method constructs a regularized iterative inversion formula through the relationship between the observed data, the slowness matrix, the ray tracing matrix, and the ray tracing operator. According to the given initial value of the slowness matrix of the area to be observed, the initial value of the ray tracing matrix and the numerical value of the observed data, the regularized iterative inversion formula is used to alternately iterate and update the ray tracing matrix and the slowness matrix in the regularized iterative inversion formula, respectively, and obtain the estimated value of the slowness matrix and the estimated value of the ray tracing matrix of the area to be observed according to the iteration end condition, and finally obtain the reconstructed image. An approximate ray tracing matrix is introduced to replace the accurate but complex ray tracing operator, and the slowness matrix and the ray tracing matrix are alternately iteratively updated during the iteration process, which reduces the forward calculation cost, improves the inversion calculation efficiency and the stability of the numerical results, so that the reconstructed image of the structure of the area to be observed is real-time, and then the structure of the area to be observed is accurately estimated through the inverted image.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiment of the present invention and its design scheme, the following briefly introduces the drawings required for this embodiment. The drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

FIG1 is a diagram showing the principle of cross-pore imaging in the prior art;

FIG2 is a structural model of the region to be detected in an embodiment of the method of the present invention;

FIG3 is a diagram showing a signal sending point, a receiving point and a discrete ray path in an embodiment of the method of the present invention;

FIG4 is a diagram of simulated observation data in an embodiment of the method of the present invention;

FIG5 is an inversion result in an embodiment of the method of the present invention;

FIG. 6 shows the iteration error in the embodiment of the method of the present invention.

DETAILED DESCRIPTION

In order to enable those skilled in the art to better understand the technical solution of the present invention and implement it, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the scope of protection of the present invention.

In some specific scenarios (such as geological exploration), the observation equation is G(m)m=d. When the traditional method solves m by inversion through d, it generally introduces a regularization term about m (that is, using the prior information of m) to solve the problem's ill-conditioned nature. During the numerical calculation process, each iteration requires a costly forward calculation (ray tracing/shortest path calculation) based on the estimated value of m to determine G(m). The method of the present invention proposes to introduce the regularization term of G and the regularization term of m at the same time, and adopts two-stage path ray tracing during the iteration process to reduce the forward calculation cost, improve the inversion calculation efficiency and the stability of the numerical results.

m is the slowness matrix of the area to be observed (that is, the inverse of the speed at which the signal propagates in this area, and obtaining m is equivalent to obtaining the structure of the area to be observed), and H is the approximate ray tracing matrix corresponding to m; the original form of the problem is to solve m through the equation G(m)m=d (known data d, known calculation rules of the ray tracing operator G), but the calculation cost of G(m) is high, especially when m is not accurate enough (in the early stage of iterative inversion), this calculation is particularly wasteful, so this method introduces the approximate ray tracing matrix H instead of the precise but complex G.

Method Example:

The present invention provides a regularized cross-pore imaging method, comprising the following steps:

(1) Signal transmission and reception settings: As shown in Figure 2, it is assumed that K signal transmission points (red) and receiving points (black) are arranged on both sides of the area to be detected (600 meters deep and 320 meters wide); and the area to be detected is evenly discretized into a number of grid points (blue) with a scale of 61×33; two low-speed structures are simulated in the area, and the discrete ray paths are shown in Figure 3.

(2) Data collection: Obtain the observation data d in the observation equation G(m)m=d. As shown in FIG4 , a row of 61 data represents the signal data collected by all 61 receiving points from one transmitting point.

(3) Perform regularized iterative inversion according to the following model.

in, is the slowness matrix estimation matrix of the area to be observed and is the ray tracing matrix estimation matrix, H is the projection matrix of the ray tracing operator G on the slowness matrix m, α, λ _m , λ _H are weight coefficients, represents L ¹ regularization (norm) on H, ||m|| _TV represents TV regularization on m, α, λ _m , λ _H are weight coefficients, and ||·|| ₂ represents L ² regularization (norm).

The meaning of this optimization model: solve m,H so that the function Reach a minimum.

The existence of λ _m ||m|| _TV +λ _H R(H) will impose corresponding requirements (regularization) on the solved m and H when minimizing the function F(m,H), such as making them as smooth as possible (just an example, the regularization here does not completely correspond to this meaning). This will make H as close to the real ray tracing operator G as possible when minimizing the function F(m,J), and Hm as close to the observed data d as possible.

As for the solution of this model, it is completed by the following alternating iterative inversion calculation. The specific calculation steps are as follows:

1) Given initial values m ⁰ , H ⁰ , a regularized iterative inversion formula is constructed using observed data, and the ray tracing matrix H and the slowness matrix m in the regularized iterative inversion formula are updated alternately and iteratively;

The iteration is performed according to the following principles.

2)H iterative update formula:

Introducing auxiliary variables v, b, applying Bregman iteration and Gauss-Seidel iteration, the above formula can be calculated as follows

3) m iterative update formula:

Introducing auxiliary variables w, p, applying Bregman iteration and Gauss-Seidel iteration, the above formula can be calculated as follows

[(H ^k ) ^T H ^k -ξΔ]m ^k+1 = (H ^k ) ^T d+ξΔ·(w ^k+1 -p ^k+1 )

Step 2) of the method has different physical meanings for the first problem and the second problem corresponding to step 3). The first subproblem is regularized ray tracing with ^mk as prior information; the second subproblem is TV (total variation) regularization with ^Hk as prior information to find a structural model with sharp boundaries. Alternating between solving these two problems and reasonably controlling the update frequency of G( ^mk ) in solving the first problem can not only reduce the cost of forward modeling in the entire imaging iteration process, but also better protect the sharp boundary information and improve imaging efficiency.

4) When ||m ^k+1 -m ^k ||<∈ _m and ||H ^k+1 -H ^k ||<∈ _H , the iteration ends and the slowness estimate of the area to be detected is output And get the ray tracing matrix estimate End and exit the result, otherwise, return to step 3), ∈ _m is the slowness matrix iteration error, ∈ _{H is} the ray tracing matrix iteration error.

5) Inversion imaging is performed based on the estimated value of the slowness matrix, the estimated value of the ray tracing matrix, and the grid structure of the area to be detected to obtain the final inversion result image of the structure of the area to be observed.

Taking the grid structure of the area to be detected as the spatial position and the slowness matrix estimation value as the pixel value, the inversion imaging result shown in FIG5 can be drawn. The path nodes are determined by the ray tracing matrix estimation value to draw the discrete ray tracing path shown in FIG3.

As shown in Figures 5 and 6, the inversion results and iteration errors are obtained. The iteration error of the slowness matrix m mainly shows that the error is getting smaller and smaller during the solution process, and the numerical results are convergent and stable. The general numerical calculation process is verified in this way. This method can reduce the forward calculation cost, improve the inversion calculation efficiency and the stability of the numerical results.

System Example:

The present invention provides a regularized cross-pore imaging system, comprising:

Region segmentation module: used to discretize the area to be detected into several grid points evenly according to the positions of the signal transmitting points and receiving points in the geological area to be detected; and obtain the observation data of the receiving points.

Model construction module: used to construct a regularized iterative inversion formula through the observation data, the slowness matrix of the area to be observed, the ray tracing matrix, and the ray tracing operator, wherein the ray tracing matrix is the projection matrix of the ray tracing operator on the slowness matrix.

Iteration module: used to use the regularized iterative inversion formula according to the initial value of the slowness matrix and the initial value of the ray tracing matrix of the given area to be observed, to alternately iteratively update the ray tracing matrix and the slowness matrix in the regularized iterative inversion formula, and to obtain the estimated value of the slowness matrix and the estimated value of the ray tracing matrix of the area to be observed according to the iteration end condition.

Image generation module: Inversion imaging is performed based on the estimated value of the slowness matrix, the estimated value of the ray tracing matrix and the grid structure of the area to be detected to obtain the final inversion result image of the structure of the area to be observed.

Device Embodiment

The present invention provides a computer device, including a memory and a processor, wherein the memory stores computer execution instructions, and the processor executes the computer execution instructions stored in the memory to implement a regularized cross-pore imaging method as described above, wherein the method has been described in detail in the method embodiment and will not be repeated here.

Storage Medium Embodiments

The present invention provides a computer-readable storage medium for storing computer-executable instructions. When the computer-executable instructions are executed by a processor, they are used to implement a regularized cross-pore imaging method as described above, wherein the method has been described in detail in a method embodiment and will not be repeated here.

It should be noted that the above-described specific implementation methods can enable those skilled in the art to more fully understand the invention, but do not limit the invention in any way. Therefore, although the present specification and embodiments have described the invention in detail, those skilled in the art should understand that the invention can still be modified or replaced by equivalents; and all technical solutions and improvements that do not deviate from the spirit and scope of the invention are included in the protection scope of the patent for the invention. Any figure mark in the claims should not be regarded as limiting the claims involved.

Claims (9)

1. A regularized cross-pore imaging method, characterized in that it comprises the following steps: According to the positions of the signal transmitting points and receiving points in the geological detection area, the detection area is evenly discretized into a number of grid points, and the observation data of the receiving points are obtained; A regularized iterative inversion formula is constructed through the relationship between the observation data, the slowness matrix, the ray tracing matrix and the ray tracing operator, wherein the ray tracing matrix is a projection matrix of the ray tracing operator on the slowness matrix; According to the given initial value of the slowness matrix of the area to be observed, the initial value of the ray tracing matrix and the observed data value, the regularized iterative inversion formula is used to alternately iteratively update the ray tracing matrix and the slowness matrix in the regularized iterative inversion formula, and the estimated value of the slowness matrix and the estimated value of the ray tracing matrix of the area to be observed are obtained according to the iteration end condition; The final reconstructed image of the structure of the area to be observed is obtained according to the estimated value of the slowness matrix, the estimated value of the ray tracing matrix and the grid structure of the area to be detected. 2. The regularized cross-hole imaging method according to claim 1 is characterized in that the iteration termination conditions include: the norm of the difference between the slowness matrix of the current iteration and the slowness matrix of the previous iteration is less than the set slowness matrix iteration error, and the norm of the difference between the ray tracing matrix of the current iteration and the ray tracing matrix of the previous iteration is less than the set ray tracing matrix iteration error. 3. The regularized cross-hole imaging method according to claim 1, characterized in that the specific relationship of the regularized iterative inversion formula is as follows: in, is the slowness matrix estimation matrix of the area to be observed, is the ray tracing matrix estimation matrix, H is the ray tracing matrix, α, λ _m , λ _H are weight coefficients, represents the L ¹ regularization (norm) of H, ||m|| _TV represents the TV regularization of m, m is the slowness matrix, ||·|| ₂ represents the L ² regularization (norm), It is the partial derivative of the vector, and R represents the regularization operation of H. 4. The regularized cross-hole imaging method according to claim 1, characterized in that the step of performing alternating iterative updating on the ray tracing matrix in the regularized iterative inversion formula is as follows: The iterative update formula of the ray tracing matrix H is: Use Bregman iteration and Gauss-Seidel iteration to alternately iterate the ray tracing matrix. The specific iteration formula is as follows: Among them, V, b are auxiliary variables, H is the ray tracing matrix, m is the slowness matrix, ξ is the regularization parameter, α, λ _H are weight coefficients, It is the partial derivative of a vector. 5. The regularized cross-hole imaging method according to claim 1, characterized in that the step of performing alternating iterative updating on the slowness matrix in the regularized iterative inversion formula is as follows: The iterative update formula of the slowness matrix m is: Use Bregman iteration and Gauss-Seidel iteration to alternately iterate the slowness matrix m. The specific iteration formula is as follows: [(H ^k ) ^T H ^k -ξΔ]m ^k+1 = (H ^k ) ^T d+ξΔ·(w ^k+1 -p ^k+1 ) Among them, w, p are auxiliary variables, H is the ray tracing matrix, m is the slowness matrix, ξ is the regularization parameter, α, λ _m are weight coefficients, It is the partial derivative of a vector. 6. The regularized cross-hole imaging method according to claim 1, characterized in that the step of obtaining a reconstructed image of the structure of the final area to be observed according to the estimated value of the slowness matrix, the estimated value of the ray tracing matrix and the grid structure of the area to be detected comprises: The path nodes are determined by the ray tracing matrix estimation value to draw the discrete ray tracing path; the grid structure of the area to be detected is used as the spatial position, and the slowness matrix estimation value is used as the pixel value to draw the inversion imaging result of the structure of the area to be observed. 7. A regularized cross-well imaging system, comprising: Region segmentation module: used to discretize the area to be detected into several grid points evenly according to the positions of the signal transmitting points and receiving points in the geological area to be detected, and obtain the observation data of the receiving points; Model construction module: used to construct a regularized iterative inversion formula through the relationship between observation data, slowness matrix, ray tracing matrix, and ray tracing operator, wherein the ray tracing matrix is a projection matrix of the ray tracing operator on the slowness matrix; Iteration module: used for performing alternate iterative updates on the ray tracing matrix and the slowness matrix in the regular iterative inversion formula according to the given initial value of the slowness matrix of the area to be observed, the initial value of the ray tracing matrix and the observed data value, and obtaining the estimated value of the slowness matrix and the estimated value of the ray tracing matrix of the area to be observed according to the iteration end condition; Image generation module: used to obtain a reconstructed image of the structure of the area to be observed based on the estimated value of the slowness matrix, the estimated value of the ray tracing matrix and the grid structure of the area to be detected. 8. A computer device comprising a memory and a processor, wherein the memory stores computer execution instructions, and the processor executes the computer execution instructions stored in the memory to implement the regularized cross-hole imaging method as described in any one of claims 1-6. 9. A computer-readable storage medium, characterized in that the computer-readable storage medium is used to store computer-executable instructions, and when the computer-executable instructions are executed by a processor, they are used to implement the regularized cross-pore imaging method as described in any one of claims 1-6.