Geophysical electromagnetic method data inversion method and system based on entropy constraint

Abstract

The invention belongs to the technical field of geophysical methods, and particularly discloses a geophysical electromagnetic method data inversion method and system based on entropy constraint, and the method comprises the steps: dividing an inversion space, setting a conductivity value, and constructing an initial inversion model; a magnetotelluric regularization inversion objective function based on entropy constraint is constructed; and adopting a Gaussian-Newton method to minimize the magnetotelluric regularization inversion objective function, updating the initial inversion model, obtaining a conductivity model, and realizing magnetotelluric three-dimensional inversion. The method can achieve the effect of focusing inversion so as to obtain a high-resolution conductivity model with a clear boundary, and serves the fields of petroleum, mineral resource exploration and the like.

Description

Technical Field

[0001] The present application belongs to the technical field of geophysical methods, and more specifically, to a geophysical electromagnetic data inversion method and system based on entropy constraints. Background Art

[0002] As an important geophysical method, magnetotelluric method has been widely used in many fields such as mineral resource exploration, geothermal resource exploration, and deep earth structure detection. As electromagnetic exploration gradually penetrates into areas with complex geological structures and the demand for fine exploration increases, high-precision three-dimensional electromagnetic exploration has gradually become a research hotspot. The fine interpretation of large-scale magnetotelluric data requires the development of efficient and stable three-dimensional forward and inverse algorithms.

[0003] High-precision three-dimensional forward algorithm is the basis of inversion algorithm, and the accuracy and speed of forward algorithm will have a great impact on the efficiency of inversion algorithm. The development of efficient inversion algorithm first requires the formation of high-precision and high-efficiency forward algorithm. Integral equation method and finite difference method are applied to electromagnetic three-dimensional forward simulation. Different methods have different advantages and disadvantages. The principle of finite difference method is simple and easy to implement, but it is difficult to accurately partition complex geometric structures, which is its irreparable disadvantage. The simulation accuracy of integral equation method is seriously dependent on the accuracy of coefficient matrix and dyadic Green's function solution. For large-scale complex problems, the demand for memory for solving linear equations is greatly increased, the solution speed is slow and the solution accuracy is reduced. Finite element method can simulate complex terrain, geological bodies and arbitrary reflection sources by using flexible unstructured grid partitioning technology. It has very high calculation accuracy and is most suitable for fine detection, but the calculation efficiency still needs to be improved. Finite volume method can also use unstructured grid to discretize the research area, but its accuracy is still not as good as finite element method.

[0004] Inversion algorithm is an indispensable part of electromagnetic data processing and interpretation. Although the three-dimensional magnetotelluric inversion based on Tikhonov regularization can obtain a stable solution, when there are sharp boundaries of underground electrical anomalies, the traditional inversion based on The boundaries of the electrical anomalies obtained by the magnetotelluric 3D inversion with normalized norm are relatively smooth, which brings certain difficulties to the subsequent geological and geophysical interpretation. Norm regularized non-smooth inversion method. Most non-smooth inversion methods use a certain function as the physical property model and minimize the objective function to obtain a model solution with a sharp boundary, such as the minimum support functional and the minimum gradient support functional. However, the inversion results depend on the selection of the focusing factor, are greatly affected by human experience, and lack a certain degree of stability. Summary of the invention

[0005] In view of the defects of the prior art, the purpose of this application is to provide a geophysical electromagnetic data inversion method and system based on entropy constraints, aiming to solve the problems of continuous diffusion of existing magnetotelluric smooth inversion results and lack of stability of focused inversion.

[0006] To achieve the above objectives, in a first aspect, the present application provides a geophysical electromagnetic data inversion method based on entropy constraints, comprising the following steps: Step 1: After dividing the inversion space, set the conductivity value and build the initial inversion model; Step 2: Based on the initial inversion model, construct the magnetotelluric regularization inversion objective function based on entropy constraints; Step 3: Use the Gauss-Newton method to minimize the magnetotelluric regularization inversion objective function, update the initial inversion model, obtain the conductivity model, and realize magnetotelluric three-dimensional inversion.

[0007] Further preferably, the objective function of the magnetotelluric regularization inversion in step 2 is for:

[0008] in, is the inversion model parameter, and the inversion model parameter is the logarithmic conductivity; is the data fitting term; is the model roughness term; is the minimum entropy term; , is the regularization parameter; , , For the The model parameters of the inversion unit, , is the number of inversion units, is a very small positive number with magnitude .

[0009] Further preferably, in step 2, an approximate spectral analysis method is used to calculate the regularization parameter:

[0010]

[0011] in, is a random vector, In order to observe the sensitivity of magnetotelluric response data to the inversion model parameters, the adjoint forward modeling method is used to calculate. is the number of iterations, is a positive integer less than 3, is an empirical parameter, ; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion.

[0012] Further preferably, step three specifically includes the following steps: Step 3.1: Use the Gauss-Newton method with quasi-quadratic convergence rate to minimize the magnetotelluric regularization inversion objective function, and use the Taylor expansion formula to obtain the normal equation; Step 3.2: Convert the normal equation into the least square form, use the least square algorithm to obtain the inversion model update amount, and use the linear search method to obtain the model update step size, and then obtain the prediction model; Step 3.3: When the prediction model meets the preset conditions, the prediction model is used as the conductivity model.

[0013] Further preferably, step 3.3 is specifically as follows: Step 3.3.1: Perform three-dimensional magnetotelluric forward modeling on the prediction model based on the vector finite element method to obtain magnetotelluric response data of the prediction model; Step 3.3.2: Use the normalized error to evaluate the fit between the predicted model magnetotelluric response data and the observed magnetotelluric response data. If the normalized fit error reaches the set threshold, the predicted model is used as the conductivity model; otherwise, go to step 3.3.3: Step 3.3.3: Determine whether the current iteration is the maximum inversion iteration number. If so, use the predicted model as the conductivity model, otherwise go to step 3.2.

[0014] Further preferably, step one specifically includes the following steps: Step 1.1: Use unstructured tetrahedral grid to divide the inversion space; Step 1.2: In the unstructured tetrahedral mesh obtained in step 1.1, set the conductivity value and build the initial inversion model.

[0015] Further preferably, the normal equation is:

[0016]

[0017] in, is the model update amount; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion; , is the regularization parameter; is the sensitivity matrix; For the The data error between the predicted value and the observed value after iterations; For the Model parameters after iterations; is the prior model.

[0018] In a second aspect, the present application provides a geophysical electromagnetic method data inversion system based on entropy constraints, comprising: The model building module sets the conductivity value after dividing the inversion space and constructs the initial inversion model; An objective function construction module is used to construct an entropy-constrained magnetotelluric regularized inversion objective function based on the initial inversion model; The model updating module is used to minimize the magnetotelluric regularization inversion objective function using the Gauss-Newton method, update the initial inversion model, obtain the conductivity model, and realize magnetotelluric three-dimensional inversion.

[0019] Further preferably, the magnetotelluric regularization inversion objective function in the objective function construction module is for:

[0020] in, is the inversion model parameter, and the inversion model parameter is the logarithmic conductivity; is the data fitting term; is the model roughness term; is the minimum entropy term; , is the regularization parameter; , , For the The model parameters of the inversion unit, , is the number of inversion units, is a very small positive number with magnitude .

[0021] Further preferably, the objective function construction module uses an approximate spectral analysis method to calculate the regularization parameter:

[0022]

[0023] in, is a random vector, In order to observe the sensitivity of magnetotelluric response data to the inversion model parameters, the adjoint forward modeling method is used to calculate. is the number of iterations, is a positive integer less than 3, is an empirical parameter, ; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion.

[0024] Further preferably, the model updating module includes: A normal equation acquisition unit is used to minimize the magnetotelluric regularization inversion objective function using a Gauss-Newton method with a quasi-quadratic convergence speed, and to obtain the normal equation using a Taylor expansion formula; a prediction model acquisition unit is used to convert the normal equation into a least squares form, use a least squares algorithm to obtain the inversion model update amount, and use a linear search method to obtain the model update step size, and then obtain the prediction model; The condition determination unit is used to use the prediction model as the conductivity model when the prediction model meets the preset conditions.

[0025] Further preferably, in the normal equation acquisition unit, the normal equation is:

[0026]

[0027] in, is the model update amount; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion; , is the regularization parameter; is the sensitivity matrix; For the The data error between the predicted value and the observed value after iterations; For the Model parameters after iterations; is the prior model.

[0028] Further preferably, the condition determination unit includes: A data collector is used to perform three-dimensional magnetotelluric forward modeling on the prediction model based on the vector finite element method to obtain magnetotelluric response data of the prediction model; The prediction model condition determiner is used to evaluate the fit between the prediction model magnetotelluric response data and the observed magnetotelluric response data using normalized error. If the normalized fit error reaches a set threshold, the prediction model is used as the conductivity model. The iteration number determiner is used to determine whether the current iteration is the maximum inversion iteration number. If so, the prediction model is used as the conductivity model.

[0029] Further preferably, the model building module includes: A meshing unit, used to mesh the inversion space using unstructured tetrahedral meshes; The conductivity filling unit is used to set the conductivity value in the unstructured tetrahedral grid and build the initial inversion model.

[0030] In a third aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the programs stored in the memory are executed, the processor is used to execute the method described in the first aspect or further preferably in the first aspect.

[0031] In a fourth aspect, the present application provides a computer-readable storage medium storing a computer program, which, when executed on a processor, enables the processor to execute the method described in the first aspect or any further preferred aspect of the first aspect.

[0032] In a fifth aspect, the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method described in the first aspect or any further preferred aspect of the first aspect.

[0033] It can be understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0034] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the prior art: The present application provides a method for geophysical electromagnetic data inversion based on entropy constraints. During the inversion process, based on the idea of ​​minimum entropy regularization, the minimum entropy stable functional is added to the objective function, and it is expressed as a pseudo-quadratic functional of the model parameters. In combination with the unstructured grid characteristics, a suitable diagonal minimum entropy weighted matrix is ​​constructed by introducing the tetrahedral unit volume. The objective function is converted into a least squares problem using a high-speed-Newton method equation with a quasi-quadratic convergence speed, the model update amount is obtained, and a linear search is used to obtain the optimal model update step size. Not only can the resolution of the inversion result be improved, a focused inversion effect can be achieved, and a clear physical property boundary can be obtained, but there is no need to determine reasonable focusing parameters, thereby reducing the influence of human factors and having good stability and applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of a geophysical electromagnetic data inversion method based on entropy constraints provided in an embodiment of the present application; FIG2 (a) is a slice diagram of y=0m obtained by using a theoretical model provided in an embodiment of the present application; FIG2( b ) is a y=0m slice image obtained by smooth inversion provided in an embodiment of the present application; FIG2( c ) is a slice image of y=0m obtained by using minimum entropy constrained inversion provided in an embodiment of the present application; FIG2( d ) is a slice image at z=500 m obtained by using a theoretical model provided in an embodiment of the present application; FIG2( e ) is a slice image of z=500 m obtained by smooth inversion according to an embodiment of the present application; FIG2( f ) is a slice image of z=500 m obtained by using minimum entropy constrained inversion provided in an embodiment of the present application; Figure 3 An embodiment of the present application provides a schematic diagram of an electronic device. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0037] The term "and / or" in this article is a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. The symbol " / " in this article indicates that the associated objects are in an or relationship, for example, A / B means A or B.

[0038] The terms “first”, “second” and the like in the specification and claims herein are used to distinguish different objects rather than to describe a specific order of the objects.

[0039] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0040] In the description of the embodiments of the present application, unless otherwise specified, “plurality” means two or more than two.

[0041] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0042] like Figure 1As shown, the present application provides a geophysical electromagnetic method data inversion method based on entropy constraints, comprising the following steps: Step S1: obtaining observed magnetotelluric response data for inversion, including collecting actual observed magnetotelluric response data on the ground and obtaining theoretical observed magnetotelluric response data through magnetotelluric three-dimensional forward modeling using a theoretical model; the theoretical model is a simulation model that can obtain theoretical observed magnetotelluric response data; Among them, the three-dimensional magnetotelluric forward modeling in this application adopts the vector finite element method of unstructured tetrahedral grid; specifically: Since the frequency band used in the magnetotelluric method is a low frequency band, the influence of the displacement current can be ignored, and the frequency domain Maxwell equations are obtained: (1) (2) (3) (4) in, is the magnetic field strength; is the electric field strength; is the magnetic permeability in vacuum; is the angular frequency; is an imaginary unit; is the conductivity; taking the rotation on both sides of formula (2), we can get: (5) Substituting formula (1) into formula (5), we can obtain: (6) The quadratic field algorithm is used to solve the three-dimensional magnetotelluric forward problem, and the following equation is used: (7) in, is the background electric field of the layered medium, which is solved by analytical method; is the value of the secondary electric field; Substituting formula (7) into formula (6), we obtain the control equation satisfied by the secondary electric field: (8) in, is the background model conductivity.

[0043] Using the simplest Dirichlet boundary condition: ; in, is the normal vector at the boundary.

[0044] The weighted residual method is used to solve the above equation. Taking the vector basis function as the weight function, the following residual function can be obtained: : (9) in, is the vector basis function for each computational unit; To calculate the unit volume; is the computational unit domain; Then, applying the first vector Green theorem, we can get the discrete form of formula (9): (10) in, , For computing unit Secondary and primary fields on edges; is the total number of computing units; , For computing unit The stiffness matrix of ; can be expressed as:

[0045]

[0046] in, , is the vector basis function within unit e.

[0047] Finally, formula (10) can be assembled into the following large sparse equation system: (11) in, is the overall stiffness matrix; is the right-hand side term of the loading boundary condition; Here, a direct solver based on matrix decomposition is used to solve the sparse equations.

[0048] After solving equation (11) to obtain the secondary electric field, the secondary magnetic field value is obtained according to Ampere's law: , after obtaining the secondary magnetic field, add it to the background magnetic field to get the total magnetic field value: (12) (13) in, is the magnetic field response of a one-dimensional layered medium, which can be solved analytically; after the electric field and magnetic field are obtained, the impedance is calculated according to the following formula : (14) Among them, subscript 1 and subscript 2 refer to and Electromagnetic field data obtained by polarization method; , , , is the impedance tensor value; , is the magnetic field component value; , is the electric field component value; , are two directions that are orthogonal to each other.

[0049] Step S2: using unstructured tetrahedral grids to divide the inversion space; wherein the inversion space is the underground space corresponding to the measuring point and the preset extension range near it; This application uses an unstructured tetrahedral grid method to discretize the inversion space. By using an unstructured grid, local refinement of key areas (such as measuring points) can be easily achieved; refinement around the measuring points can obtain very accurate simulation results; Step S3: setting the conductivity value in the unstructured tetrahedral grid obtained in step S2 to construct an initial inversion model; In three-dimensional inversion, the selection of the initial inversion model will affect the inversion effect and convergence speed. Selecting an initial inversion model that is significantly different from the true model may result in non-convergence of magnetotelluric inversion and poor inversion results. Therefore, constructing a suitable initial inversion model is of great significance for obtaining high-quality inversion results. In general, a simple initial inversion model can be established by referring to the existing drilling, geological and geophysical prior information. However, in areas with less prior information and more complex geological conditions, a one-dimensional inversion can be performed first, and the one-dimensional inversion result can be used as the initial model. Step S4: constructing a magnetotelluric regularization inversion objective function based on entropy constraints; Traditional based on The anomaly boundary obtained by the norm-regularized magnetotelluric three-dimensional inversion is often smooth. The solution with focused inversion effect can be obtained by using the minimum entropy-based regularization objective function. The regularization objective function is: (15) in, is the data fitting term; is the model roughness term; is the minimum entropy term; , is the regularization parameter; , and They are defined as: (16) (17) (18) Will Expressed as a pseudo-quadratic functional of the model parameters: (19) in, is the inversion model parameter. In order to ensure is a non-negative number, so that the model parameters have physical meanings, and the conductivity in the logarithmic domain is taken as the model parameter; is the data weighting matrix; represents the initial inversion model parameters The forward response of The observed magnetotelluric response data at the measuring point; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion; are the reference model parameters containing prior information; , For the The model parameters of the inversion unit, , is the number of inversion units, is a very small positive number, usually .

[0050] Combined with the unstructured grid features, the tetrahedral unit volume is introduced to construct a suitable diagonal minimum entropy weighting matrix: (20) in, , , is the inversion unit volume; is the number of inversion units, For the The model parameters of the inversion unit, For the The prior model of the inversion unit is constructed by adding tetrahedral unit volume to eliminate the influence of different unit volume sizes in the unstructured grid on the inversion results.

[0051] According to the closest distance to the inversion unit The roughness matrix is ​​constructed by the weight of the volume and distance of the inversion unit, which is expressed as follows: (twenty one) (twenty two) in, is the first Line The elements of the column, For the distance The most recent inversion unit The cell number of the cell in the inversion grid; , The distance The most recent inversion unit and The volume of a unit; is the number of adjacent units, It is The volume of the inversion unit; Indicates From the center of the inversion unit to the The distance between the nearest unit centers; and Respectively Inversion unit and The center coordinates of the inversion unit.

[0052] The regularization parameter plays an important role in balancing the data fitting term and the model constraint term (model roughness term and minimum entropy term). The choice of the regularization parameter affects the stability and convergence speed of the algorithm. The regularization parameter is calculated using the approximate spectral analysis method: (twenty three) (twenty four) in, is a random vector, To observe the sensitivity of magnetotelluric response data to inversion model parameters, is the number of iterations, is a positive integer less than 3, is an empirical parameter, usually taken as ; Step S5: Calculate the sensitivity matrix using the adjoint forward modeling method; First, obtain the sensitivity matrix of the electromagnetic field components at the measuring point under different polarization modes , and then the impedance sensitivity matrix is ​​obtained by the chain rule ; Sensitivity matrix of electromagnetic field components can be written as: (25) Taking partial derivatives of the model parameters on both sides, we get: (26) in, is the overall stiffness matrix; is the right-hand side term of the loading boundary condition.

[0053] Therefore, the partial derivatives of the quadratic field with respect to the model parameters can be obtained: (27) Substituting into the above formula, we get: (28) in The order of is the number of edges, is the number of inversion units); The number of columns is , in order to solve the sensitivity matrix , need to do This will consume a lot of computing time; since the coefficient matrix It is symmetric, and we can transpose the above formula to get: (29) This is how to solve Only need to carry out (number of measurement points) times quasi-forward calculation, because the number of measurement points is much smaller than the number of model parameters, it has higher calculation efficiency; Step S6: Use the LSQR method to solve the least squares problem of the equivalent Gauss-Newton method equation to obtain the model update amount, perform linear search to obtain the optimal model update step size, and update the prediction model; The Gauss-Newton method with quasi-quadratic convergence rate is used to minimize the objective function. The Taylor expansion formula is applied to the objective function, and the following normal equation can be obtained by ignoring high-order terms:

[0054] (30) in, is the model update amount; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion; , is the regularization parameter; is the sensitivity matrix; For the The data error between the predicted value and the observed value after iterations; For the Model parameters after iterations; is the prior model.

[0055] Convert the normal equation to the least squares form as follows: (31) The least squares (LSQR) algorithm is used to solve equation (31) to obtain the model update amount, and the linear search method is used to find the optimal model update step size. , the model update equation can be expressed as: (32) Step S7: Prediction model based on vector finite element method Conduct three-dimensional magnetotelluric forward modeling to obtain the magnetotelluric response data of the prediction model; combine the direct solver, MPI (Message Passing Interface) and OpenMP parallel computing technology in the forward modeling to improve the computing efficiency; Step S8: using the normalized error to evaluate the fit between the model prediction data and the observation data, judging whether a preset threshold is reached, and judging whether a maximum number of iterations is reached; To determine whether the observed magnetotelluric response data and the predicted magnetotelluric response data are fit, the data normalized fit difference between the observed magnetotelluric response data and the predicted magnetotelluric response data can be expressed by the following formula: (33) When the data normalization fitting error reaches the set threshold or convergence stops, the inversion algorithm is terminated and the inversion result is output; if the set minimum data normalization fitting error is not reached, it is determined whether the maximum number of inversion iterations has been reached. If the current number of iterations is less than the set number, the next iteration is looped. If the set number is reached, the inversion iteration is stopped and the inversion result is output; Step S9: Iterate steps S5 to S8 until the set termination condition is reached, obtain the conductivity model, and realize the three-dimensional magnetotelluric inversion.

[0056] Example 1 In order to verify the effectiveness of the magnetotelluric inversion method based on minimum entropy constraint provided by the present application, the present application embodiment provides a two-low-resistance model of a mountain topography. The height of the mountain is 300m relative to the ground, the side length of its upper base is 450m, the side length of its lower base is 1800m, and the resistivity of the background half space is 100 The two anomalies are 1000m×1000m×500m in size and have a resistivity of 10 , the center coordinates of the anomaly are (-1000m, 0m, 500m) and (1000m, 0m, 500m) respectively. A total of 121 measuring points are arranged, the frequency number is 5 (100Hz~1.668Hz), the number of forward modeling grids is 350418, and 2% Gaussian noise is added to the forward impedance data to simulate the measured data. In the inversion process, the number of grids in the inversion area is 175816, and the initial model and prior model are both set to 100 The uniform half space of the Gauss-Newton model is set to 40. When the inversion reaches the maximum number of iterations or the calculated normalized error is less than the specified error, the inversion stops. Figures 2 (a) and 2 (d) are theoretical models, Figures 2 (b) and 2 (e) are smooth inversion results, and Figures 2 (c) and 2 (f) are minimum entropy inversion results. The white dots in the figures are the locations of the measurement points, and the black rectangular boxes are the locations of the anomalies. It can be seen that the minimum entropy constrained inversion can better restore the resistivity value of the anomaly and the boundary of the anomaly.

[0057] Example 2 The present application provides a geophysical electromagnetic method data inversion system based on entropy constraints, comprising: The model building module is used to set the conductivity value after dividing the inversion space and build the initial inversion model; An objective function construction module is used to construct an entropy-constrained magnetotelluric regularized inversion objective function based on the initial inversion model; The model updating module is used to minimize the magnetotelluric regularization inversion objective function using the Gauss-Newton method, update the initial inversion model, obtain the conductivity model, and realize magnetotelluric three-dimensional inversion.

[0058] Further preferably, the magnetotelluric regularization inversion objective function in the objective function construction module is for:

[0059] in, is the inversion model parameter, and the inversion model parameter is the logarithmic conductivity; is the data fitting term; is the model roughness term; is the minimum entropy term; , is the regularization parameter; , , For the The model parameters of the inversion unit, , is the number of inversion units, is a very small positive number, usually .

[0060] Further preferably, the objective function construction module uses an approximate spectral analysis method to calculate the regularization parameter:

[0061]

[0062] in, is a random vector, In order to observe the sensitivity of magnetotelluric response data to the inversion model parameters, the adjoint forward modeling method is used to calculate. is the number of iterations, is a positive integer less than 3, is an empirical parameter, ; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion.

[0063] Further preferably, the model updating module includes: A normal equation acquisition unit is used to minimize the magnetotelluric regularization inversion objective function using a Gauss-Newton method with a quasi-quadratic convergence speed, and to obtain the normal equation using a Taylor expansion formula; a prediction model acquisition unit is used to convert the normal equation into a least squares form, use a least squares algorithm to obtain the inversion model update amount, and use a linear search method to obtain the model update step size, and then obtain the prediction model; The condition determination unit is used to use the prediction model as the conductivity model when the prediction model meets the preset conditions.

[0064] Further preferably, in the normal equation acquisition unit, the normal equation is:

[0065]

[0066] in, is the model update amount; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion; , is the regularization parameter; is the sensitivity matrix; For the The data error between the predicted value and the observed value after iterations; For the Model parameters after iterations; is the prior model.

[0067] Further preferably, the condition determination unit includes: A data collector is used to perform three-dimensional magnetotelluric forward modeling on the prediction model based on the vector finite element method to obtain magnetotelluric response data of the prediction model; The prediction model condition determiner is used to evaluate the fit between the prediction model magnetotelluric response data and the observed magnetotelluric response data using normalized error. If the normalized fit error reaches a set threshold, the prediction model is used as the conductivity model. The iteration number determiner is used to determine whether the current iteration is the maximum inversion iteration number. If so, the prediction model is used as the conductivity model.

[0068] Further preferably, the model building module includes: A meshing unit, used to mesh the inversion space using unstructured tetrahedral meshes; Conductivity filling cells are used to construct the initial inversion model in an unstructured tetrahedral grid.

[0069] In summary, compared with the prior art, the present application has the following advantages: The present application provides a method for focusing inversion of magnetotelluric method. When obtaining observed magnetotelluric response data, based on the secondary field theory, the high-order partial differential equation satisfied by the secondary electric field is derived from the frequency domain Maxwell equations, and the differential equation is converted into a finite element equation in integral form using the weighted residual method; the Dirichlet boundary condition is adopted, it is assumed that the electric field disappears at the boundary of the modeling area, the condition that the electric field is zero is set, and the modeling area of ​​the theoretical model is expanded, the grid is encrypted near the measuring point, and the size of the grid is gradually increased in other areas, and the setting of the boundary conditions and the setting of the grid are completed; the magnetotelluric response of complex geological structures can be accurately simulated.

[0070] In the inversion process, based on the idea of ​​minimum entropy regularization, the minimum entropy stable functional is added to the objective function and expressed as a pseudo-quadratic functional of the model parameters. Combined with the unstructured grid characteristics, the appropriate diagonal minimum entropy weighted matrix is ​​constructed by introducing the tetrahedral unit volume. The high-speed-Newton method equation with a quasi-quadratic convergence rate is used to transform the objective function into a least squares problem, with a quasi-quadratic convergence rate, to obtain the model update amount, and a linear search is used to obtain the optimal model update step. It can not only improve the resolution of the results, achieve the effect of focused inversion, obtain clear physical property boundaries, but also does not need to determine reasonable focusing parameters, thereby reducing the influence of human factors, and has good stability and applicability.

[0071] It should be understood that the above-mentioned system is used to execute the methods in the above-mentioned embodiments. The implementation principles and technical effects of the corresponding program modules in the system are similar to those described in the above-mentioned methods. The working process of the system can refer to the corresponding process in the above-mentioned method and will not be repeated here.

[0072] Based on the method in the above embodiment, Figure 3As shown, an embodiment of the present application provides an electronic device, which may include: a processor (Processor) 810, a communication interface (Communications Interface) 820, a memory (Memory) 830 and a communication bus 840, wherein the processor 810, the communication interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 can call the logic instructions in the memory 830 to execute the method in the above embodiment.

[0073] In addition, the logic instructions in the above-mentioned memory 830 can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application.

[0074] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0075] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0076] It is understandable that the processor in the embodiment of the present application may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, transistor logic devices, hardware components or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0077] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, and the software modules can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an ASIC.

[0078] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented by software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions may be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions may be transmitted from a website site, a computer, a server or a data center to another website site, a computer, a server or a data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or a data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)), etc.

[0079] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0080] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A geophysical electromagnetic data inversion method based on entropy constraints, characterized in that: The following steps are involved: Step 1: After dividing the inversion space, set the conductivity value and build the initial inversion model; Step 2: Based on the initial inversion model, construct the magnetotelluric regularization inversion objective function based on entropy constraints; Step 3: Use the Gauss-Newton method to minimize the magnetotelluric regularization inversion objective function, update the initial inversion model, obtain the conductivity model, and realize magnetotelluric three-dimensional inversion; The objective function of the magnetotelluric regularization inversion in step 2 for: in, is the inversion model parameter, and the inversion model parameter is the logarithmic conductivity; is the data fitting term; is the model roughness term; is the minimum entropy term; , is the regularization parameter; , , For the The model parameters of the inversion unit, , is the number of inversion units, is a very small positive number with magnitude ; In step 2, the regularization parameter is calculated using the approximate spectral analysis method: in, is a random vector, In order to observe the sensitivity of magnetotelluric response data to the inversion model parameters, the adjoint forward modeling method is used to calculate. is the number of iterations, is a positive integer less than 3, is an empirical parameter, ; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion.

2. The geophysical electromagnetic method data inversion method according to claim 1, characterized in that: Step three specifically includes the following steps: Step 3.1: Use the Gauss-Newton method with quasi-quadratic convergence rate to minimize the magnetotelluric regularization inversion objective function, and use the Taylor expansion formula to obtain the normal equation; Step 3.2: Convert the normal equation into the least square form, use the least square algorithm to obtain the inversion model update amount, and use the linear search method to obtain the model update step size, and then obtain the prediction model; Step 3.3: When the prediction model meets the preset conditions, the prediction model is used as the conductivity model.

3. The geophysical electromagnetic data inversion method according to claim 2, characterized in that: Step 3.3 specifically includes the following steps: Step 3.3.1: Perform three-dimensional magnetotelluric forward modeling on the prediction model based on the vector finite element method to obtain magnetotelluric response data of the prediction model; Step 3.3.2: Use the normalized error to evaluate the fit between the predicted model magnetotelluric response data and the observed magnetotelluric response data. If the normalized fit error reaches the set threshold, the predicted model is used as the conductivity model; otherwise, go to step 3.3.3; Step 3.3.3: Determine whether the current iteration is the maximum inversion iteration number. If so, use the predicted model as the conductivity model, otherwise go to step 3.

2.

4. The geophysical electromagnetic data inversion method according to claim 1, characterized in that: Step 1 specifically includes the following steps: Step 1.1: Use unstructured tetrahedral grid to divide the inversion space; Step 1.2: In the unstructured tetrahedral mesh obtained in step 1.1, set the conductivity value and build the initial inversion model.

5. The geophysical electromagnetic method data inversion method according to claim 2, characterized in that: The normal equation is: in, is the model update amount; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion; , is the regularization parameter; is the sensitivity matrix; For the The data error between the predicted value and the observed value after iterations; For the Model parameters after iterations; is the prior model.

6. A geophysical electromagnetic data inversion system based on entropy constraints, characterized in that: include: The model building module sets the conductivity value after dividing the inversion space and constructs the initial inversion model; An objective function construction module is used to construct an entropy-constrained magnetotelluric regularized inversion objective function based on the initial inversion model; The model update module is used to minimize the magnetotelluric regularization inversion objective function using the Gauss-Newton method, update the initial inversion model, obtain the conductivity model, and realize the magnetotelluric three-dimensional inversion; Magnetotelluric regularization inversion objective function in the objective function building module for: in, is the inversion model parameter, and the inversion model parameter is the logarithmic conductivity; is the data fitting term; is the model roughness term; is the minimum entropy term; , is the regularization parameter; , , For the The model parameters of the inversion unit, , is the number of inversion units, is a very small positive number with magnitude ; The objective function building block uses an approximate spectral analysis method to calculate the regularization parameter: in, is a random vector, In order to observe the sensitivity of magnetotelluric response data to the inversion model parameters, the adjoint forward modeling method is used to calculate. is the number of iterations, is a positive integer less than 3, is an empirical parameter, ; is the data weighting matrix; is the model roughness matrix; is the diagonal minimum entropy matrix for focusing inversion.

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