Nuclear magnetic resonance adaptive transverse constraint inversion method for complex geology

Abstract

The invention belongs to the technical field of geophysical signal processing, and particularly relates to a complex geology-oriented nuclear magnetic resonance adaptive transverse constraint inversion method, which comprises the following steps of: converting nuclear magnetic resonance signals on the same survey line into a target function by adopting a Tikhonov regularization algorithm; combining a smoothness matrix in the target function with a Spearman level correlation coefficient, and calculating an adaptive transverse constraint matrix; the self-adaptive transverse constraint matrix is used for transverse constraint of the water content, self-adaptive transverse constraint inversion is carried out, and an obtained inversion result is a nuclear magnetic resonance self-adaptive transverse constraint inversion result. According to the method, section abnormal information can be highlighted, and meanwhile, the transverse resolution of the nuclear magnetic resonance signals is effectively kept.

Description

Technical Field

[0001] The invention belongs to the technical field of geophysical signal processing, and in particular relates to a nuclear magnetic resonance adaptive lateral constraint inversion method for complex geology. Background Art

[0002] The underground aquifer images obtained by single-point one-dimensional inversion of nuclear magnetic resonance often have discontinuities and heterogeneities, which brings significant challenges to the subsequent geophysical interpretation work. To address this problem, researchers have proposed a nuclear magnetic resonance lateral constraint inversion method, which is particularly suitable for geological environments with good continuity (such as sedimentary rock areas). By introducing lateral constraints between adjacent measuring points, the lateral continuity of the aquifer is ensured. This is a quasi-two-dimensional inversion technology based on a one-dimensional model. However, in complex geological environments (such as urban geology, dams, etc.), there are both areas with good continuity and areas with poor continuity. Directly applying lateral constraint inversion will weaken the geological differences, resulting in incorrect interpretation of cross-sectional data. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a nuclear magnetic resonance adaptive lateral constraint inversion method for complex geology, so as to solve the problem that in complex geological environments, direct application of lateral constraint inversion will weaken geological differences, thereby leading to incorrect interpretation of cross-section data.

[0004] The present invention is achieved in this way. A nuclear magnetic resonance adaptive lateral constraint inversion method for complex geology, the method comprising the following steps: S1, the NMR signal on the same measuring line is converted into the objective function using the Tikhonov regularization algorithm; S2, combining the smoothness matrix in the objective function with the Spearman rank correlation coefficient to calculate the adaptive lateral constraint matrix; S3. Use the adaptive lateral constraint matrix for lateral constraint of water content, perform adaptive lateral constraint inversion, and the obtained inversion result is the NMR adaptive lateral constraint inversion result.

[0005] Furthermore, step S1 specifically includes: S11. The NMR signal in the quasi-two-dimensional inversion method is expressed in matrix form: Suppose there is a measuring line measuring points, each measuring point divides the underground space into layer, the NMR signal expression is: , in, is the matrix form of the NMR signal, represents the transpose of a matrix, Indicates the magnitude of the pulse moment, contained in the NMR signal; The measurement points are formed in the matrix List, Layers of underground space are formed in the matrix OK, Indicates that the NMR signal is located at Ledi The matrix elements of the rows, express The magnitude of the pulse moment underground space, represents one of the matrix elements, then The value range is 1 to , The value range is 1 to ; The quasi-two-dimensional sensitivity kernel function is expressed as: , in, represents a diagonal matrix, Indicates The elements in the diagonal matrix corresponding to the measurement points, Denotes the quasi-two-dimensional sensitivity kernel function, and uses represents an element in a diagonal matrix, then The value ranges from 1 to ; The underground space moisture content of each measuring point is combined into an unknown moisture content matrix: , is the unknown moisture content matrix, Indicates the moisture content corresponding to the first measuring point, Indicates the water content corresponding to the second measuring point, Indicates The moisture content corresponding to the measuring point; The NMR signal is expressed using an unknown water content matrix and a quasi-two-dimensional sensitivity kernel function as follows: , It is a NMR signal representation using an unknown water content matrix and a quasi-two-dimensional sensitivity kernel function; S12. The nuclear magnetic resonance signal is converted into an objective function using the Tikhonov regularization algorithm: , in, represents the objective function, is the data objective function, is the regularization parameter, is the model objective function, is the data weight obtained by calculating the uncertainty of observation noise, is the smoothness matrix, Indicates taking the minimum value.

[0006] Furthermore, S2 specifically includes: S21. Solve the Spearman rank correlation coefficient between adjacent measurement points: , in, Indicates Spearman rank correlation coefficient; Indicates The initial amplitude array corresponding to the measurement points, Indicates The average value of the initial amplitude array corresponding to the measurement points; Indicates The initial amplitude array corresponding to the measurement points, Indicates The average value of the initial amplitude array corresponding to the measurement points; S22, the smoothness matrix It is expressed as: , In the formula, is the longitudinal constraint matrix, which is used to constrain the parameters of adjacent measuring points in the longitudinal direction; is the lateral constraint matrix. By performing difference calculation on two adjacent measuring points at the same position, the size change of the mutual constraint between the two adjacent measuring points is realized. Among them, the lateral constraint matrix The expression is as follows: , Maintain the vertical constraint matrix No change, change the lateral constraint matrix , calculate the Spearman rank correlation coefficient between adjacent measuring points, and the results form a new lateral constraint matrix , the expression is: , in, Represents the number of model parameters for each measuring point, and obtains the adaptive lateral constraint matrix related to the difference coefficient of the data of adjacent measuring points for: , in, express In .

[0007] Furthermore, S3 specifically includes: S31. Linearize the NMR signal representation using the unknown water content matrix and the quasi-two-dimensional sensitivity kernel function: , in, The quasi-sensitivity kernel function is applied using the Jacobian matrix method The result of the function after any variable space transformation, where No meaning, Together they represent the Jacobian matrix transformation; represents the moisture content matrix increment, represents the initial amplitude of the change; , in, use express, represents the water content signal contained in the water content matrix, is the representation of the water content matrix containing the water content signal, To include and The representation of the quasi-two-dimensional sensitivity kernel function is: represents the real part, represents the imaginary part; S32, for unknown moisture content matrix Iterations, from the initial moisture matrix Start to solve step by step Iteration moisture matrix increment , the iteration equation is as follows: , in, is the current iteration number, It is The moisture content matrix of the iteration, is the iteration step length, Indicates The moisture content matrix of the iteration; The Gauss-Newton iteration formula is used to further solve the Iteration moisture matrix increment : , in, express The transpose of express The transpose of express The transpose of S33, establish an iterative step The forward calculation expression of is: , By the objective function The inversion process of iterative solution obtains the optimal iteration step size of the current iteration. The optimal iteration step size corresponds to the minimum value of the objective function. The objective function is solved for the moisture content information of each layer at each measuring point on the same measuring line, where: represents the forward calculation, Yes Join The data objective function representation is: Represents the model objective function representation with the iteration step added.

[0008] Compared with the prior art, the present invention has the following beneficial effects: The method of the present invention can automatically identify the measuring points with good continuity and the measuring points with obvious water content difference during the inversion process, and impose appropriate lateral constraints on the measuring points with good continuity, while reducing or not imposing lateral constraints on the measuring points with poor continuity. This method can not only highlight the abnormal information of the cross section, but also effectively maintain the lateral resolution of the nuclear magnetic resonance signal, which is of great significance for realizing high-precision nuclear magnetic resonance data interpretation under complex geological conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 A flow chart of a nuclear magnetic resonance adaptive lateral constraint inversion method for complex geology provided by an embodiment of the present invention; Figure 2 A schematic diagram of a theoretical model of nuclear magnetic resonance in complex geology containing discontinuities adopted in an embodiment of the present invention; Figure 3 The traditional Smooth inversion result of the discontinuous complex geological model provided by the embodiment of the present invention; Figure 4 The conventional lateral constraint inversion result of the discontinuous complex geological model provided by the embodiment of the present invention; Figure 5 The embodiment of the present invention provides an inversion result of the method of the present invention on a discontinuous complex geological model. DETAILED DESCRIPTION

[0010] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0011] See also Figure 1 As shown, a NMR adaptive lateral constraint inversion method for complex geology includes: S1. The NMR signal on the same measuring line is converted into the objective function using the Tikhonov regularization algorithm; S2, combining the smoothness matrix in the objective function with the Spearman rank correlation coefficient to calculate the adaptive lateral constraint matrix; S3. Use the adaptive lateral constraint matrix for lateral constraint of water content, perform adaptive lateral constraint inversion, and the obtained inversion result is the NMR adaptive lateral constraint inversion result.

[0012] like Figure 2 As shown, the embodiment of the present invention adopts a nuclear magnetic resonance theoretical model containing discontinuous complex geology to implement and verify the method of the present invention.

[0013] Assuming that the underground is a uniform half-space, the geomagnetic field strength B0 = 54720 nT, the geomagnetic field inclination angle is 60°, and the calculated Larmor frequency is 2330 Hz. The excitation pulse moment is composed of 20 points between 0 and 0.6 A·s according to the exponential distribution; A total of 20 measuring points were set up on the ground at a horizontal distance of 38 m. They were evenly distributed at positions between 0 and 38 m, with an overlapping structure of side length a = 2 m, 16 turns of the transmitting coil, and 64 turns of the receiving coil, and were measured by laying them side by side; The complex underground aquifer can be divided into two parts: the first part is at 0 ~ 18 m, and the aquifer is located in the shallow underground layer of 1 ~ 3 m; the second part is at 22 ~ 38 m, and the aquifer is located in the shallow underground layer of 1.2 ~ 3.2 m; the maximum aquifer thickness of the two parts is 2m, the minimum aquifer thickness is 0.1m, and the water content is 20%; the water content of the aquiclude is 1%.

[0014] In order to approach the actual noise conditions, 5% random noise was added to the water body model.

[0015] right Figure 2 The Tikhonov regularization algorithm is used in the theoretical model of nuclear magnetic resonance under complex geological conditions containing discontinuities. After converting the nuclear magnetic resonance signal into the objective function, the adaptive lateral constraint matrix is ​​solved.

[0016] S1 specifically includes: S11. The NMR signal in the quasi-two-dimensional inversion method is expressed in matrix form: Suppose there is a measuring line measuring points, each measuring point divides the underground space into layer, and the NMR signal is represented as: , in, is the matrix form of the NMR signal, represents the transpose of a matrix, Indicates the magnitude of the pulse moment, contained in the NMR signal; The measurement points are formed in the matrix List, Layers of underground space are formed in the matrix OK, Indicates that the NMR signal is located at Ledi The matrix elements of the rows, express The magnitude of the pulse moment underground space, represents one of the matrix elements, then The value range is 1 to , The value range is 1 to ; The quasi-two-dimensional sensitivity kernel function is expressed as: , in, represents a diagonal matrix, Indicates The elements in the diagonal matrix corresponding to the measurement points, Denotes the quasi-two-dimensional sensitivity kernel function, and uses represents an element in a diagonal matrix, then The value ranges from 1 to ; The underground space moisture content of each measuring point is combined into an unknown moisture content matrix: , is the unknown moisture content matrix, Indicates the moisture content corresponding to the first measuring point, Indicates the water content corresponding to the second measuring point, Indicates The moisture content corresponding to the measuring point; The unknown water content matrix here refers to a matrix used to describe the distribution of water content in underground media in geophysical exploration. Here, the water content values ​​at different measuring points represented by the elements in this matrix are unknown.

[0017] The NMR signal is expressed using an unknown water content matrix and a quasi-two-dimensional sensitivity kernel function as follows: , It is a NMR signal representation using an unknown water content matrix and a quasi-two-dimensional sensitivity kernel function; S12. The NMR signal matrix is ​​converted into the objective function using the Tikhonov regularization algorithm: , in, represents the objective function, is the data objective function, is the regularization parameter, is the model objective function, is the data weight obtained by calculating the uncertainty of observation noise, is the smoothness matrix, Indicates taking the minimum value.

[0018] In step S2, the adaptive lateral constraint matrix includes a smoothness matrix and a Spearman rank correlation coefficient, specifically including: S21. Solve the Spearman rank correlation coefficient between adjacent measurement points: , in, Indicates Spearman rank correlation coefficient; Indicates The initial amplitude array corresponding to the measurement points, Indicates The average value of the initial amplitude array corresponding to the measurement points; Indicates The initial amplitude array corresponding to the measurement points, Indicates The average value of the initial amplitude array corresponding to the measurement points; Spearman rank correlation coefficient By The measurement points and The corresponding measurement points are also To indicate the order.

[0019] S22, the smoothness matrix It is expressed as: , In the formula, is the longitudinal constraint matrix, which is used to constrain the parameters of adjacent measuring points in the longitudinal direction to ensure that the parameter sizes of adjacent measuring points in the longitudinal direction are controlled by subtraction; is the lateral constraint matrix. By performing difference calculation on two adjacent measuring points at the same position, the size change of the mutual constraint between the two adjacent measuring points is realized. Among them, the lateral constraint matrix The expression is as follows: , Maintain the vertical constraint matrix No change, change the lateral constraint matrix , S21 is used to calculate the Spearman rank correlation coefficient between adjacent measuring points, and the results obtained constitute a new lateral constraint matrix , the expression is: , in, Represents the number of model parameters for each measuring point, and obtains the adaptive lateral constraint matrix related to the difference coefficient of the data of adjacent measuring points for: , in, express In , The closer the value is to 1, the higher the correlation between two adjacent measuring points; if the result is close to 0, it means there is no correlation between the two measuring points. At this point, the calculation of the adaptive lateral constraint matrix is ​​completed.

[0020] In S3, the adaptive lateral constraint matrix is ​​used for the lateral constraint of water content, and the adaptive lateral constraint inversion is performed. The data objective function, the model objective function and the adaptive lateral constraint matrix are generally integrated to form a final objective function, which specifically includes: S31. Linearize the NMR signal representation using the unknown water content matrix and the quasi-two-dimensional sensitivity kernel function: , in, The quasi-sensitivity kernel function is applied using the Jacobian matrix method The result of the function after any variable space transformation, where No meaning, Together they represent the Jacobian matrix transformation; It indicates the increment of the moisture content matrix. It should be noted that the increment of the moisture content matrix here is a definite value and is no longer an unknown value. represents the initial amplitude of the change; , in, use express, represents the water content signal contained in the water content matrix, is the representation of the water content matrix containing the water content signal, To include and The representation of the quasi-two-dimensional sensitivity kernel function is: represents the real part, Represents the imaginary part; it should be noted that in this calculation, the moisture content matrix represents a moisture content matrix with a certain value.

[0021] S32, for unknown moisture content matrix Iterations, from the initial moisture matrix Start to solve step by step Iteration moisture matrix increment , the iteration equation is as follows: , in, is the current iteration number, It is The moisture content matrix of the iteration, is the iteration step length, Indicates Iteration moisture matrix; it should be noted that the initial moisture matrix here is and The moisture content matrix of each iteration has a certain value and is no longer called an unknown moisture content matrix.

[0022] In order to reduce the amount of calculation and improve the convergence speed, the Gauss-Newton iterative formula is used to further solve the Iteration moisture matrix increment : , in, express The transpose of express The transpose of express The transpose of S33, establish an iterative step The forward calculation expression of is: , By the objective function The inversion process of iterative solution obtains the optimal iteration step size of the current iteration. The optimal iteration step size corresponds to the minimum value of the objective function. The solution is the moisture content information of each layer at each measuring point on the same measuring line, where: represents the forward calculation, Yes Join The data objective function representation is: Represents the model objective function representation with the iteration step added.

[0023] In the above process, forward modeling refers to the known or observed water content data. In the process of inverting the objective function, the water content data obtained by each iteration is compared with the observed water content data until the difference between the two is minimized, that is, the optimal iteration step length of the current iteration is obtained. The optimal iteration step length corresponds to the minimum value of the objective function.

[0024] The results of comparing the method of the present invention with the existing method are as follows: Figure 3 The traditional Smooth inversion results for the discontinuous complex geological model are shown. Smooth inversion is a regularization-based inversion method that optimizes the inversion results through smoothness constraints. It can be seen that the water content fit of the inversion results is poor. The area marked by the dotted line shows that the layer interface is not smooth. Figure 4 The imaging results of the traditional lateral constraint inversion are shown. See the dotted line mark. It can be seen that although the traditional lateral constraint inversion is much better than the traditional Smooth inversion results, and the water content in the middle is relatively close, there is still the problem of uneven layer interface, and the model is relatively distorted; Figure 5 The inversion results of the method of the present invention for a discontinuous complex geological model are demonstrated. Compared with the traditional Smooth inversion and the traditional lateral constraint inversion, the inversion imaging results of the method of the present invention are closer to the real theoretical model. The layer interface in the area marked by the dotted line is smoother, and the section zone information can be prepared to be presented, which has good application value.

[0025] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A NMR adaptive lateral constraint inversion method for complex geology, characterized in that: The method comprises the following steps: S1, the NMR signal on the same measuring line is converted into the objective function using the Tikhonov regularization algorithm; S2, combining the smoothness matrix in the objective function with the Spearman rank correlation coefficient to calculate the adaptive lateral constraint matrix; S3. Use the adaptive lateral constraint matrix for lateral constraint of water content, perform adaptive lateral constraint inversion, and the obtained inversion result is the NMR adaptive lateral constraint inversion result.

2. The method of adaptive lateral constraint inversion of nuclear magnetic resonance for complex geology according to claim 1, characterized in that: S1 specifically includes: S11. The NMR signal in the quasi-two-dimensional inversion method is expressed in matrix form: Suppose there is a measuring line measuring points, each measuring point divides the underground space into layer, and the NMR signal is represented as: ， in, is the matrix form of the NMR signal, represents the transpose of a matrix, Indicates the magnitude of the pulse moment, contained in the NMR signal; The measurement points are formed in the matrix List, Layers of underground space are formed in the matrix OK, Indicates that the NMR signal is located at Ledi The matrix elements of the rows, express The magnitude of the pulse moment underground space, represents one of the matrix elements, then The value range is 1 to , The value range is 1 to ; The quasi-two-dimensional sensitivity kernel function is expressed as: ， in, represents a diagonal matrix, Indicates The elements in the diagonal matrix corresponding to the measurement points, Denotes the quasi-two-dimensional sensitivity kernel function, and uses represents an element in a diagonal matrix, then The value ranges from 1 to ; The underground space moisture content of each measuring point is combined into an unknown moisture content matrix: ， is the unknown moisture content matrix, Indicates the moisture content corresponding to the first measuring point, Indicates the water content corresponding to the second measuring point, Indicates The moisture content corresponding to the measuring point; The NMR signal is expressed using an unknown water content matrix and a quasi-two-dimensional sensitivity kernel function as follows: ， It is a NMR signal representation using an unknown water content matrix and a quasi-two-dimensional sensitivity kernel function; S12. The nuclear magnetic resonance signal is converted into an objective function using the Tikhonov regularization algorithm: ， in, represents the objective function, is the data objective function, is the regularization parameter, is the model objective function, is the data weight obtained by calculating the uncertainty of observation noise, is the smoothness matrix, Indicates taking the minimum value.

3. The method of adaptive lateral constraint inversion of nuclear magnetic resonance for complex geology according to claim 2, characterized in that: S2 specifically includes: S21. Solve the Spearman rank correlation coefficient between adjacent measurement points: ， in, Indicates Spearman rank correlation coefficient; Indicates The initial amplitude array corresponding to the measurement points, Indicates The average value of the initial amplitude array corresponding to the measurement points; Indicates The initial amplitude array corresponding to the measurement points, Indicates The average value of the initial amplitude array corresponding to the measurement points; S22, the smoothness matrix It is expressed as: ， In the formula, is the longitudinal constraint matrix, which is used to constrain the parameters of adjacent measuring points in the longitudinal direction; is the lateral constraint matrix. By performing difference calculation on two adjacent measuring points at the same position, the size change of the mutual constraint between the two adjacent measuring points is realized. Among them, the lateral constraint matrix The expression is as follows: ， Maintain the vertical constraint matrix No change, change the lateral constraint matrix , calculate the Spearman rank correlation coefficient between adjacent measuring points, and the results form a new lateral constraint matrix , the expression is: ， in, Represents the number of model parameters for each measuring point, and obtains the adaptive lateral constraint matrix related to the difference coefficient of the data of adjacent measuring points for: ， in, express In .

4. The method of adaptive lateral constraint inversion of nuclear magnetic resonance for complex geology according to claim 3, characterized in that: S3 specifically includes: S31. Linearize the NMR signal representation using the unknown water content matrix and the quasi-two-dimensional sensitivity kernel function: ， in, The quasi-sensitivity kernel function is applied using the Jacobian matrix method The result of the function after any variable space transformation, where No meaning, Together they represent the Jacobian matrix transformation; represents the moisture content matrix increment, represents the initial amplitude of the change; ， in, use express, represents the water content signal contained in the water content matrix, is the representation of the water content matrix containing the water content signal, To include and The representation of the quasi-two-dimensional sensitivity kernel function is: represents the real part, represents the imaginary part; S32, for unknown moisture matrix Iterations, from the initial moisture matrix Start to solve step by step Iteration moisture matrix increment , the iteration equation is as follows: ， in, is the current iteration number, It is The moisture content matrix of the iteration, is the iteration step length, Indicates The moisture content matrix of the iteration; The Gauss-Newton iteration formula is used to further solve the Iteration moisture matrix increment : ， in, express The transpose of express The transpose of express The transpose of S33, establish an iterative step The forward calculation expression of is: ， By the objective function The inversion process of iterative solution obtains the optimal iteration step size of the current iteration. The optimal iteration step size corresponds to the minimum value of the objective function. The objective function is solved for the moisture content information of each layer at each measuring point on the same measuring line, where: represents the forward calculation, Yes Join The data objective function representation is: Represents the model objective function representation with the iteration step added.

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