A joint inversion method and device based on cross-gradient term weight factor

Abstract

The present application provides a joint inversion method and apparatus based on a cross-gradient term weight factor, the method comprising: assigning an initial parameter value of a uniform half-space to each grid cell in an underground grid as an initial model for the joint inversion, wherein the underground grid is obtained by gridding a study area, and the data range of the study area is determined based on the data range of the observation area; constructing an objective function for the joint inversion, wherein the objective function comprises a cross-gradient term and a first weight factor, wherein the first weight factor comprises a coefficient matrix and a weight constant, wherein each matrix element in the coefficient matrix corresponds to each grid cell in the underground grid, and the values ​​of the matrix elements corresponding to the grid cells in different regions of the underground grid are different; and utilizing apparent resistivity data and apparent polarizability data, performing a minimization calculation on the objective function to update the initial model and obtain a resistivity model and a polarizability model. The present application can improve the accuracy of the inversion results.

Description

Technical Field

[0001] The present application relates to the field of geophysical exploration technology, and in particular to a joint inversion method and device based on cross-gradient term weight factors. Background Art

[0002] Geophysical inversion is an important concept in geophysics. It refers to the process of using geophysical observation data (such as seismic wave records, gravity measurement data, magnetic measurement data, etc.) to infer the physical properties of the earth's interior (such as velocity structure, density distribution, magnetic distribution, etc.) and geological structure. During the inversion process, there may be a variety of different underground structures or models that can fit the same set of observation data. This is the multi-solution nature of geophysical inversion. The multi-solution nature of geophysical inversion comes from many aspects. Mathematically, nonlinearity and ill-posedness will cause the solution to be non-unique; in physical models, the geological structure is complex and the properties are equivalent, and multiple combinations can produce similar responses; the observation data are limited, incomplete, and lack precision and resolution. These factors are intertwined, resulting in multiple possibilities for the inversion results.

[0003] The cross-gradient joint inversion method is currently a mainstream structural coupling joint inversion method. By multiplying the gradients of different physical properties, the boundaries of different physical properties are constrained to each other, which can improve the similarity of the inversion results of different physical properties in spatial structure. It mainly realizes the joint inversion process by introducing cross-gradient terms into the objective function. By minimizing the objective function, the underground model can be obtained.

[0004] When minimizing the objective function, the selection of weighting factors is crucial. Too small a weighting factor will limit its constraining effect, while too large a value will have the opposite effect, reducing the accuracy of the inversion results. However, there is currently no optimal method for selecting the weighting factor for the cross-gradient term. This is because the cross-gradient term does not always hold a value; it only holds a value when both models change, and the directions of change are inconsistent. Therefore, it is crucial to determine the weighting factor for the cross-gradient term to ensure its optimal performance during the inversion process. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a joint inversion method and device based on cross-gradient term weight factors, which reduces the multi-solution of joint inversion by selecting effective cross-gradient term weight factors, and helps to improve the accuracy of inversion results.

[0006] In a first aspect, an embodiment of the present application provides a joint inversion method based on a cross-gradient term weight factor, the joint inversion method comprising:

[0007] Obtaining apparent resistivity data and apparent polarizability data based on a plurality of survey lines pre-arranged in an observation area of ​​the underground medium;

[0008] Assigning initial parameter values ​​of a uniform half-space to each grid cell in a subsurface grid as an initial model for joint inversion, the initial parameter values ​​including initial resistivity values ​​and initial polarizability values, the subsurface grid being obtained by gridding a study area, and the data range of the study area being determined based on the data range of the observation area;

[0009] Constructing an objective function for joint inversion, the objective function including a cross-gradient term and a first weight factor corresponding to the cross-gradient term, the first weight factor including a coefficient matrix and a weight constant, each matrix element in the coefficient matrix corresponding to each grid cell in the underground grid, the values ​​of the matrix elements corresponding to grid cells in different areas of the underground grid being different, and the weight constant being used to adjust the proportion of the cross-gradient term in the objective function;

[0010] The objective function is minimized using the apparent resistivity data and the apparent polarizability data to update the initial model and obtain a resistivity model and a polarizability model.

[0011] In an optional embodiment, multiple survey lines are arranged in an observation area of ​​the underground medium, and each survey line is provided with a transmitting electrode and a receiving electrode. Obtaining apparent resistivity data and apparent polarizability data based on the multiple survey lines pre-arranged in the observation area of ​​the underground medium includes:

[0012] When the transmitting electrode on each survey line is powered, the adjacent receiving electrodes on the corresponding survey line receive power to obtain apparent resistivity data and apparent polarizability data.

[0013] In an optional embodiment, the data range of the study area is determined by the following steps:

[0014] Obtaining the X-direction data range, Y-direction data range, and Z-direction data range of the observation area;

[0015] A target multiple is set for the X-direction data range, the Y-direction data range, and the Z-direction data range to obtain the data range of the study area in the X-direction, the Y-direction, and the Z-direction; wherein the target multiple is between 3 times and 5 times.

[0016] In an optional embodiment, the objective function also includes a data term, a model term and a second weight factor corresponding to the model term, the data term is used to calculate the difference between the apparent resistivity data and the resistivity data of the inversion response, and the difference between the apparent polarizability data and the polarizability data of the inversion response, the model term is used to calculate the smoothness of the resistivity model and the polarizability model, and the second weight factor represents the proportion of the model term in the objective function.

[0017] In an optional embodiment, the objective function is expressed by the following formula:

[0018] Φ(m ρ )=Φ d (m ρ )+λ1Φ m (m ρ )+γ1KΦ cg (m ρ ,m η )

[0019] Φ(m η )=Φ d (m η )+λ2Φ m (m η )+γ2KΦ cg (m η ,m ρ )

[0020] Among them, m ρ Represents the resistivity model of the underground, m η represents the underground polarizability model, Φ(m ρ ) represents the objective function of the resistivity method in the joint inversion of the resistivity method and the induced polarization method, Φ(m η ) represents the objective function of the induced polarization method in the joint inversion of the resistivity method and the induced polarization method, Φ d (m ρ ) represents the data item of the resistivity method, Φ d (m η ) represents the data item of the induced polarization method, Φ m (m ρ ) represents the model term of the resistivity method, Φ m (m η ) represents the model term of the induced polarization method, Φ cg (, ρ ,m η ) represents the cross gradient term of the resistivity method, Φ cg (m η ,m ρ) represents the cross-gradient term of the induced polarization method, λ1 represents the second weight factor of the model term in the objective function of the resistivity method, λ2 represents the second weight factor of the model term in the objective function of the induced polarization method, γ1 represents the weight constant of the cross-gradient term in the objective function of the resistivity method, γ2 represents the weight constant of the cross-gradient term in the objective function of the induced polarization method, and K represents the coefficient matrix.

[0021] In an optional embodiment, the research area includes a first sub-study area, a second sub-study area and a third sub-study area. In the XY direction, the center of the first sub-study area coincides with the center of the research area, the second sub-study area is wrapped around the periphery of the first sub-study area, and the third sub-study area is wrapped around the periphery of the second sub-study area; in the Z direction, the detection depths corresponding to the first sub-study area, the second sub-study area and the third sub-study area respectively increase gradually; the data range of the first sub-study area and the area range of the second sub-study area constitute the data range of the observation area; the grid cells in the first sub-study area correspond to the first matrix element values, the grid cells in the second sub-study area correspond to the second matrix element values, and the grid cells in the third sub-study area correspond to the third matrix element values. The first matrix element value is greater than the second matrix element value, and the second matrix element value is greater than the third matrix element value.

[0022] In an optional embodiment, the X-direction data range of the first sub-study area is 2 / 3 of the X-direction data range of the observation area, the Y-direction data range of the first sub-study area is 1 / 2 of the Y-direction data range of the observation area, and the Z-direction data range of the first sub-study area is 2 / 3 of the Z-direction data range of the observation area.

[0023] In an optional embodiment, the value of the first matrix element is 1, the value of the second matrix element is 0.1, and the value of the third matrix element is 0.

[0024] In an optional embodiment, the setting value of the weight constant makes the cross gradient term account for 5% to 10% of the objective function.

[0025] In a second aspect, an embodiment of the present application further provides a joint inversion device based on a cross-gradient term weight factor, the joint inversion device comprising:

[0026] A data acquisition module, configured to acquire apparent resistivity data and apparent polarizability data based on a plurality of survey lines pre-arranged in an observation area of ​​the underground medium;

[0027] a model construction module, configured to assign initial parameter values ​​of a uniform half-space to each grid cell in a subsurface grid as an initial model for joint inversion, wherein the initial parameter values ​​include initial resistivity values ​​and initial polarizability values, wherein the subsurface grid is obtained by gridding a study area, and wherein a data range of the study area is determined based on a data range of the observation area;

[0028] a function construction module, configured to construct an objective function for joint inversion, wherein the objective function includes a cross-gradient term and a first weight factor corresponding to the cross-gradient term, wherein the first weight factor includes a coefficient matrix and a weight constant, wherein each matrix element in the coefficient matrix corresponds to each grid cell in the underground grid, and the values ​​of the matrix elements corresponding to grid cells in different areas of the underground grid are different, and the weight constant is used to adjust the proportion of the cross-gradient term in the objective function;

[0029] A model updating module is used to use the apparent resistivity data and the apparent polarizability data to perform a minimization calculation on the objective function to update the initial model and obtain a resistivity model and a polarizability model.

[0030] In a third aspect, an embodiment of the present application further provides an electronic device comprising: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the steps of the joint inversion method as described above are performed.

[0031] In a fourth aspect, an embodiment of the present application further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the joint inversion method as described above are executed.

[0032] An embodiment of the present application provides a joint inversion method and apparatus based on a cross-gradient term weight factor. The joint inversion method includes: first, obtaining apparent resistivity data and apparent polarizability data based on multiple survey lines pre-arranged in an observation area of ​​a subsurface medium; then assigning initial parameter values ​​of a uniform half-space to each grid cell in a subsurface grid as an initial model for the joint inversion, wherein the initial parameter values ​​include initial resistivity values ​​and initial polarizability values, the subsurface grid is obtained by gridding a study area, and the data range of the study area is determined based on the data range of the observation area; then, constructing an objective function for the joint inversion, wherein the objective function includes a cross-gradient term and a first weight factor corresponding to the cross-gradient term, the first weight factor including a coefficient matrix and a weight constant, wherein each matrix element in the coefficient matrix corresponds to each grid cell in the subsurface grid, and the matrix element values ​​corresponding to grid cells in different areas of the subsurface grid are different, and the weight constant is used to adjust the proportion of the cross-gradient term in the objective function; finally, using the apparent resistivity data and the apparent polarizability data, the objective function is minimized to update the initial model to obtain a resistivity model and a polarizability model. This application uses coefficient matrices and weight constants to select effective weight factors for cross-gradient terms, thereby exerting a better constraint on the resistivity model and polarizability model, reducing the multiplicity of solutions in the joint inversion, and helping to improve the accuracy of the inversion results.

[0033] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0035] Figure 1 A flowchart of a joint inversion method based on a cross-gradient term weight factor provided in an embodiment of the present application;

[0036] Figure 2 A schematic diagram of measurement line distribution provided in an embodiment of the present application;

[0037] Figure 3 A schematic diagram of an underground grid divided into different areas provided in an embodiment of the present application;

[0038] Figure 4 Classification of the research area in the XY direction in the embodiment of this application;

[0039] Figure 5 Classification of the research area in the XZ direction in the embodiment of this application;

[0040] Figure 6 A comparison chart of resistivity and polarizability inversion results of the conventional method and the method of the present invention provided in the embodiments of the present application;

[0041] Figure 7 Schematic diagram of cross-gradient values ​​for resistivity and polarizability calculations obtained by the conventional method and the method of the present invention provided in the embodiments of the present application;

[0042] Figure 8 A schematic structural diagram of a joint inversion device based on a cross-gradient term weight factor provided in an embodiment of the present application;

[0043] Figure 9 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application for which protection is claimed, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, each other embodiment obtained by those skilled in the art without making creative work falls within the scope of protection of the present application.

[0045] First, the application scenarios to which this application is applicable are introduced. This application can be applied to the field of geophysical exploration technology. Geophysical inversion is an important concept in geophysics. It refers to the process of using geophysical observation data (such as seismic wave records, gravity measurement data, magnetic measurement data, etc.) to infer the physical properties of the earth's interior (such as velocity structure, density distribution, magnetic distribution, etc.) and geological structure. During the inversion process, there may be a variety of different underground structures or models that can fit the same set of observation data. This is the multi-solution nature of geophysical inversion. The multi-solution nature of geophysical inversion comes from many aspects. Mathematically, nonlinearity and ill-posedness will cause the solution to be non-unique; in physical models, the geological structure is complex and the properties are equivalent, and multiple combinations can produce similar responses; the observation data are limited, incomplete, and have insufficient precision and resolution. These factors are intertwined, resulting in multiple possibilities for the inversion results.

[0046] The cross-gradient joint inversion method is currently a mainstream structural coupling joint inversion method. By multiplying the gradients of different physical properties, the boundaries of different physical properties are constrained to each other, which can improve the similarity of the inversion results of different physical properties in spatial structure. It mainly realizes the joint inversion process by introducing cross-gradient terms into the objective function. By minimizing the objective function, the underground model can be obtained.

[0047] When minimizing the objective function, the selection of weighting factors is crucial. Too small a weighting factor will limit its constraining effect, while too large a value will have the opposite effect, reducing the accuracy of the inversion results. However, there is currently no optimal method for selecting the weighting factor for the cross-gradient term. This is because the cross-gradient term does not always hold a value; it only holds a value when both models change, and the directions of change are inconsistent. Therefore, it is crucial to determine the weighting factor for the cross-gradient term to ensure its optimal performance during the inversion process.

[0048] Based on this, an embodiment of the present application provides a joint inversion method based on a cross-gradient term weight factor. By selecting an effective cross-gradient term weight factor, the multi-solution property of the joint inversion is reduced, which helps to improve the accuracy of the inversion result.

[0049] See also Figure 1 , Figure 1 This is a flow chart of a joint inversion method based on a cross gradient term weight factor provided in an embodiment of the present application. Figure 1 As shown in , the joint inversion method provided in the embodiment of the present application includes:

[0050] S101, acquiring apparent resistivity data and apparent polarizability data according to a plurality of survey lines pre-arranged in an observation area of ​​an underground medium;

[0051] S102, assigning initial parameter values ​​of the uniform half-space to each grid cell in the underground grid as an initial model for joint inversion, wherein the initial parameter values ​​include initial resistivity values ​​and initial polarizability values. The underground grid is obtained by gridding the study area, and the data range of the study area is determined based on the data range of the observation area.

[0052] S103, constructing an objective function for joint inversion, where the objective function includes a cross-gradient term and a first weight factor corresponding to the cross-gradient term, the first weight factor including a coefficient matrix and a weight constant, each matrix element in the coefficient matrix corresponds to each grid cell in the underground grid, and the values ​​of the matrix elements corresponding to grid cells in different areas of the underground grid are different. The weight constant is used to adjust the proportion of the cross-gradient term in the objective function;

[0053] S104 , using the apparent resistivity data and the apparent polarizability data, performing a minimization calculation on the objective function to update the initial model and obtain a resistivity model and a polarizability model.

[0054] In the above steps S101 to S104, the coefficient matrix and weight constant are used to select effective weight factors of the cross-gradient terms, thereby exerting a good constraint on the resistivity model and the polarizability model, reducing the multiplicity of solutions of the joint inversion, and helping to improve the accuracy of the inversion results.

[0055] The above steps S101 to S104 are exemplarily described below through a specific embodiment:

[0056] In step S101 , apparent resistivity data and apparent polarizability data are acquired based on a plurality of survey lines pre-arranged in an observation area of ​​a subsurface medium.

[0057] Here, a survey line is a line arranged along a straight line at a certain scale for observing underground media, consisting of a series of observation points. Underground media include but are not limited to mineral resources, oil and gas resources, groundwater, and archaeological relics. For example, taking groundwater as an example, different geological structures will affect the migration of groundwater. Arranging survey lines to obtain apparent resistivity data and apparent polarizability data can help analyze underground geological structures, such as the location and scale of faults and fissures. The area where the survey lines are arranged is defined as the observation area.

[0058] In an optional embodiment, multiple survey lines are arranged in the observation area of ​​the underground medium, and each survey line is provided with a transmitting electrode and a receiving electrode. Step S101 specifically includes:

[0059] When the transmitting electrode on each survey line is powered, the adjacent receiving electrodes on the corresponding survey line receive power to obtain apparent resistivity data and apparent polarizability data.

[0060] For example, Figure 2 As shown in the figure, five survey lines, L1 to L5, were deployed for groundwater exploration in the Chaobai River Basin in Miyun District, Beijing. Triangles on the lines represent the locations of transmitting electrodes, and circles represent the locations of receiving electrodes. Each survey line was observed using a three-pole setup. When the transmitting electrode was powered, the adjacent receiving electrode on the corresponding line received the signal. A total of 24,540 apparent resistivity and polarizability data points were obtained. These data were collated to obtain the apparent resistivity and polarizability values, observation errors, and coordinates of the transmitting and receiving points for each data point. The receiving point coordinates ranged from -96 to 96 m in the X direction and -70 to 70 m in the Y direction, with a detection depth of 0 to 80 m.

[0061] In step S102, the initial parameter values ​​of the uniform half space are assigned to each grid cell in the underground grid as the initial model of the joint inversion. The initial parameter values ​​include initial resistivity values ​​and initial polarizability values. The underground grid is obtained by gridding the study area, and the data range of the study area is determined based on the data range of the observation area.

[0062] Here, a uniform half-space means that the medium within it has uniform physical properties. For example, in terms of electrical properties, the resistivity is uniform throughout the half-space, with no resistivity variation; in terms of polarization properties, the polarizability is also uniform throughout the half-space. In this example, a uniform half-space with a resistivity of 200 Ω·m and a polarizability of 0.01 was selected as the initial model.

[0063] Among them, the main purpose of gridding the study area is to facilitate the mathematical description and numerical calculation of the underground space. Since the underground space is a continuous three-dimensional area, it is very difficult to analyze and calculate it directly. Through grid division, the continuous underground space is discretized into many small units, so that each unit can be analyzed and processed separately, thereby simplifying the calculation process. For example, in the embodiment of the present application, there are 155 grid nodes in the X direction, 19 grid nodes in the Y direction, and 90 grid nodes in the Z direction.

[0064] In the present embodiment, after meshing the study area, the resulting collection of discrete small cells constitutes a subsurface grid. Each grid cell has a specific location and number, and can be assigned corresponding physical parameters (such as resistivity and polarizability). By calculating and analyzing each grid cell, an inversion result of the subsurface conditions of the entire study area can be obtained.

[0065] In other words, the underground space is divided into many grid units, and a value is assigned to each grid unit first, which is the initial model. The inversion is to continuously change the value of each grid unit by minimizing the objective function, and finally obtain a model that meets the minimization of the objective function.

[0066] Optionally, step S102 determines the data range of the study area by the following steps:

[0067] Step 1021: Obtain the data range in the X direction, the data range in the Y direction, and the data range in the Z direction of the observation area.

[0068] Here, the X-direction data range, Y-direction data range and Z-direction data range of the observation area can be determined according to the X-direction range, Y-direction data range and Z-direction data range of the receiving point coordinates. Figure 2The data collected along the survey line shown is the basis for analysis. The receiving point coordinates range from -96m to 96m in the X direction and -70m to 70m in the Y direction, with a detection depth of 0 to 80m. Furthermore, the data range in the observation area is -96m to 96m in the X direction, -70m to 70m in the Y direction, and 0 to 80m in the Z direction.

[0069] Step 1022: Set target multiples for the X-direction data range, the Y-direction data range, and the Z-direction data range to obtain the data range of the study area in the X-direction, the Y-direction, and the Z-direction; wherein the target multiples are between 3 times and 5 times.

[0070] Here, the data ranges of the study area in the X, Y and Z directions are determined based on the data ranges of the observation area in the X, Y and Z directions. The data ranges of the study area in the X, Y and Z directions are the data ranges of the initial model in the X, Y and Z directions. Figure 2 The data collected by the survey line shown is the basis for analysis. The data range of the study area in the X direction can be defined as -300m to 300m, the data range in the Y direction is -300m to 300m, and the data range in the Z direction is 0 to 250m.

[0071] In the embodiment of the present application, if the entire spatial range of the study area is set too small, a boundary effect will occur during the inversion process and the inversion result will be poor. Therefore, the data range of the study area is generally set to 3 to 5 times the data range of the observation area, which can obtain more accurate inversion results, thereby reducing the boundary effect in the inversion process and improving the accuracy of the inversion results.

[0072] In step S103, an objective function of the joint inversion is constructed. The objective function includes a cross-gradient term and a first weight factor corresponding to the cross-gradient term. The first weight factor includes a coefficient matrix and a weight constant. Each matrix element in the coefficient matrix corresponds to each grid cell in the underground grid. The values ​​of the matrix elements corresponding to the grid cells in different areas of the underground grid are different. The weight constant is used to adjust the proportion of the cross-gradient term in the objective function.

[0073] In this step, the first weighting factor for the cross-gradient term introduces a coefficient matrix K and constants γ1 and γ2. The number of matrix elements in the coefficient matrix K is the same as the number of cells in the subsurface grid, allowing us to set a different value for each cell in the subsurface grid. γ1 and γ2 are used to adjust the weight of the cross-gradient term in the objective function.

[0074] Specifically, the matrix element values ​​corresponding to the grid cells in different areas of the underground grid are different. Each grid cell is assigned a value according to the area where the grid cell is located. Each grid cell in the underground grid corresponds to each matrix element in the coefficient matrix, and then the coefficient matrix can be obtained.

[0075] For example, Figures 3 to 5 As shown in , the entire cube represents the study area, which includes the first sub-study area A, the second sub-study area B and the third sub-study area C. Figure 4 As shown, in the XY direction, the center of the first sub-study area A coincides with the center of the study area, the second sub-study area B is wrapped around the periphery of the first sub-study area A, and the third sub-study area C is wrapped around the periphery of the second sub-study area B; Figure 5 As shown, in the Z direction, the detection depths corresponding to the first sub-study area A, the second sub-study area B and the third sub-study area C gradually increase; the data range of the first sub-study area A and the area range of the second sub-study area B constitute the data range of the observation area; the grid cells in the first sub-study area A correspond to the first matrix element values, the grid cells in the second sub-study area B correspond to the second matrix element values, and the grid cells in the third sub-study area C correspond to the third matrix element values. The first matrix element value is greater than the second matrix element value, and the second matrix element value is greater than the third matrix element value.

[0076] Optionally, the X-direction data range of the first sub-study area A is 2 / 3 of the X-direction data range of the observation area, the Y-direction data range of the first sub-study area A is 1 / 2 of the Y-direction data range of the observation area, and the Z-direction data range of the first sub-study area A is 2 / 3 of the Z-direction data range of the observation area.

[0077] Exemplarily, the value of the first matrix element may be 1, the value of the second matrix element may be 0.1, and the value of the third matrix element may be 0.

[0078] For example, Figure 2 The data collected along the survey line shown in the figure are the basis for analysis. Figures 4 and 5As shown in Figure 1, the underground grid is divided into three different areas, A, B, and C. A represents the first study area, whose coordinate range is -60m to 60m in the X direction, -30m to 30m in the Y direction, and 0m to 60m in the Z direction. The corresponding values ​​of the grid cells in the first study area in the coefficient matrix K are set to 1; B represents the second study area, whose coordinate range is -96m to 96m in the X direction, -70m to -30m and 30m to 70m in the Y direction, and 60m to 80m in the Z direction. The corresponding values ​​of the grid cells in the second study area in the coefficient matrix K are set to 0.1; C represents the third study area, whose coordinate range is -300m to -96m and 96m to 300m in the X direction, -300m to -70m and 70m to 300m in the Y direction, and 80m to 250m in the Z direction. The corresponding values ​​of the grid cells in the third study area in the coefficient matrix K are set to 0.

[0079] The above method makes the constraint effect of the cross-gradient term in the joint inversion process mainly concentrated in the first study area, avoiding the data observation boundary from having a large impact on the inversion results. The final resistivity and polarizability inversion results are also more similar in structure within the first study area.

[0080] Optionally, the weight constant is set to a value such that the cross gradient term accounts for 5% to 10% of the objective function.

[0081] The embodiment of the present application sets the weight constant γ1 of the resistivity model and the weight constant γ2 of the polarizability model, which are mainly used to adjust the proportion of the cross gradient term in the objective function. After a large number of tests, the present invention found that by adjusting γ1 and γ2 so that the proportion of the entire cross gradient term in the objective function is 5% to 10%, a better inversion effect can be achieved. In the embodiment of the present application, Figure 2 The data collected by the survey line shown is the basis for analysis. γ1 can be selected as 500 and γ2 can be selected as 2000.

[0082] In an optional embodiment, the objective function also includes a data term, a model term and a second weight factor corresponding to the model term, the data term is used to calculate the difference between the apparent resistivity data and the resistivity data of the inversion response, and the difference between the apparent polarizability data and the polarizability data of the inversion response, the model term is used to calculate the smoothness of the resistivity model and the polarizability model, and the second weight factor represents the proportion of the model term in the objective function.

[0083] Here, the data term, model term, and second weight factor cooperate with each other in geophysical inversion and act together on the objective function to guide the optimization and adjustment of the model, ultimately obtaining a more accurate and reasonable underground model.

[0084] For example, the objective function is expressed by the following formula:

[0085] Φ(m ρ )=Φ d (m ρ )+λ1Φ n (m ρ )+γ1KΦ cg (m ρ ,m η )

[0086] Φ(m η )=Φ d (m η )+λ2Φ m (m η )+γ2KΦ cg (m η ,m ρ )

[0087] Among them, m ρ Represents the resistivity model of the underground, m η represents the underground polarizability model, Φ(m ρ ) represents the objective function of the resistivity method in the joint inversion of the resistivity method and the induced polarization method, Φ(m η ) represents the objective function of the induced polarization method in the joint inversion of the resistivity method and the induced polarization method, Φ d (m ρ ) represents the data item of the resistivity method, Φ d (m η ) represents the data item of the induced polarization method, Φ m (m ρ ) represents the model term of the resistivity method, Φ m (m η ) represents the model term of the induced polarization method, Φ cg (m ρ ,m η ) represents the cross gradient term of the resistivity method, Φ cg (m η ,m ρ ) represents the cross-gradient term of the induced polarization method, λ1 represents the second weight factor of the model term in the objective function of the resistivity method, λ2 represents the second weight factor of the model term in the objective function of the induced polarization method, γ1 represents the weight constant of the cross-gradient term in the objective function of the resistivity method, γ2 represents the weight constant of the cross-gradient term in the objective function of the induced polarization method, and K represents the coefficient matrix.

[0088] Here, the inversion is achieved by continuously minimizing the objective function, m ρ and m η It will continue to change, and eventually the resistivity model and polarizability model that best fits the underground conditions will be obtained.

[0089] In step S104, the objective function is minimized using the apparent resistivity data and the apparent polarizability data to update the initial model and obtain a resistivity model and a polarizability model.

[0090] In this step, after multiple iterations and minimization of the objective function, the final resistivity and polarizability models are obtained when certain convergence conditions are met (such as the objective function value no longer decreases significantly or the parameter change is less than a certain threshold). The resistivity model describes the distribution of the resistivity of the underground medium, and the polarizability model describes the distribution of the polarizability of the underground medium. These models can intuitively display the electrical properties of different underground locations and provide important references for geological interpretation, resource exploration (such as searching for mineral resources and groundwater resources), and engineering construction (such as assessing foundation stability).

[0091] For example, Figure 6 The comparison of the resistivity and polarizability inversion results of the traditional method and the method of the present invention is shown in the figure. It can be seen that the structural similarity of the resistivity and polarizability models obtained by the method used in the present invention is significantly improved compared with the traditional method. Figure 7 The cross-gradient values ​​for resistivity and polarizability calculated using the conventional method and the method of the present invention are shown in the figure. The cross-gradient value for the first study area is smaller using the method of the present invention, indicating that the cross-gradient term in the first study area has a more pronounced effect. In the third study area, the cross-gradient value remains essentially unchanged, indicating that the method of the present invention avoids the influence of the third study area on the first study area.

[0092] The embodiment of the present application provides a joint inversion method based on cross-gradient term weight factors, which uses a coefficient matrix and a weight constant to select effective cross-gradient term weight factors, thereby exerting a good constraint on the resistivity model and the polarizability model, reducing the multi-solution of the joint inversion, and helping to improve the accuracy of the inversion results.

[0093] Based on the same inventive concept, an embodiment of the present application also provides a joint inversion device based on a cross-gradient term weight factor corresponding to the joint inversion method based on a cross-gradient term weight factor. Since the principle of solving the problem by the device in the embodiment of the present application is similar to the above-mentioned joint inversion method based on a cross-gradient term weight factor in the embodiment of the present application, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be repeated.

[0094] See also Figure 8 , Figure 8 This is a schematic diagram of the structure of a joint inversion device based on a cross gradient term weight factor provided in an embodiment of the present application. Figure 8 As shown in , the joint inversion device 800 includes:

[0095] The data acquisition module 801 is used to acquire apparent resistivity data and apparent polarizability data based on a plurality of survey lines pre-arranged in the observation area of ​​the underground medium;

[0096] A model building module 802 is configured to assign initial parameter values ​​of a uniform half-space to each grid cell in a subsurface grid as an initial model for joint inversion, wherein the initial parameter values ​​include initial resistivity values ​​and initial polarizability values. The subsurface grid is obtained by gridding a study area, and the data range of the study area is determined based on the data range of the observation area.

[0097] A function construction module 803 is used to construct an objective function for joint inversion, wherein the objective function includes a cross-gradient term and a first weight factor corresponding to the cross-gradient term, wherein the first weight factor includes a coefficient matrix and a weight constant, wherein each matrix element in the coefficient matrix corresponds to each grid cell in the underground grid, and the values ​​of the matrix elements corresponding to grid cells in different areas of the underground grid are different. The weight constant is used to adjust the proportion of the cross-gradient term in the objective function;

[0098] The model updating module 804 is configured to perform a minimization calculation on the objective function using the apparent resistivity data and the apparent polarizability data to update the initial model and obtain a resistivity model and a polarizability model.

[0099] In an optional embodiment, multiple survey lines are arranged in the observation area of ​​the underground medium, and each survey line is provided with a transmitting electrode and a receiving electrode. The data acquisition module 801 is specifically used to:

[0100] When the transmitting electrode on each survey line is powered, the adjacent receiving electrodes on the corresponding survey line receive power to obtain apparent resistivity data and apparent polarizability data.

[0101] In an optional embodiment, the model building module 802 is configured to determine the data range of the study area through the following steps:

[0102] Obtaining the X-direction data range, Y-direction data range, and Z-direction data range of the observation area;

[0103] A target multiple is set for the X-direction data range, the Y-direction data range, and the Z-direction data range to obtain the data range of the study area in the X-direction, the Y-direction, and the Z-direction; wherein the target multiple is between 3 times and 5 times.

[0104] In an optional embodiment, the objective function also includes a data term, a model term and a second weight factor corresponding to the model term, the data term is used to calculate the difference between the apparent resistivity data and the resistivity data of the inversion response, and the difference between the apparent polarizability data and the polarizability data of the inversion response, the model term is used to calculate the smoothness of the resistivity model and the polarizability model, and the second weight factor represents the proportion of the model term in the objective function.

[0105] In an optional embodiment, the objective function is expressed by the following formula:

[0106] Φ(m ρ )=Φ d (m ρ )+λ1Φ m (m ρ )+γ1KΦ cg (m ρ ,m η )

[0107] Φ(m η )=Φ d (m η )+λ2Φ m (m η )+γ2KΦ cg (m η ,m ρ )

[0108] Among them, m ρ Represents the resistivity model of the underground, m η represents the underground polarizability model, Φ(m ρ ) represents the objective function of the resistivity method in the joint inversion of the resistivity method and the induced polarization method, Φ(m η ) represents the objective function of the induced polarization method in the joint inversion of the resistivity method and the induced polarization method, Φ d (m ρ ) represents the data item of the resistivity method, Φ d (m η ) represents the data item of the induced polarization method, Φ m (m ρ ) represents the model term of the resistivity method, Φ m (m η ) represents the model term of the induced polarization method, Φ cg (m ρ ,m η ) represents the cross gradient term of the resistivity method, Φ cg (m η ,m ρ) represents the cross-gradient term of the induced polarization method, λ1 represents the second weight factor of the model term in the objective function of the resistivity method, λ2 represents the second weight factor of the model term in the objective function of the induced polarization method, γ1 represents the weight constant of the cross-gradient term in the objective function of the resistivity method, γ2 represents the weight constant of the cross-gradient term in the objective function of the induced polarization method, and K represents the coefficient matrix.

[0109] In an optional embodiment, the research area includes a first sub-study area, a second sub-study area and a third sub-study area. In the XY direction, the center of the first sub-study area coincides with the center of the research area, the second sub-study area is wrapped around the periphery of the first sub-study area, and the third sub-study area is wrapped around the periphery of the second sub-study area; in the Z direction, the detection depths corresponding to the first sub-study area, the second sub-study area and the third sub-study area respectively increase gradually; the data range of the first sub-study area and the area range of the second sub-study area constitute the data range of the observation area; the grid cells in the first sub-study area correspond to the first matrix element values, the grid cells in the second sub-study area correspond to the second matrix element values, and the grid cells in the third sub-study area correspond to the third matrix element values. The first matrix element value is greater than the second matrix element value, and the second matrix element value is greater than the third matrix element value.

[0110] In an optional embodiment, the X-direction data range of the first sub-study area is 2 / 3 of the X-direction data range of the observation area, the Y-direction data range of the first sub-study area is 1 / 2 of the Y-direction data range of the observation area, and the Z-direction data range of the first sub-study area is 2 / 3 of the Z-direction data range of the observation area.

[0111] In an optional embodiment, the value of the first matrix element is 1, the value of the second matrix element is 0.1, and the value of the third matrix element is 0.

[0112] In an optional embodiment, the setting value of the weight constant makes the cross gradient term account for 5% to 10% of the objective function.

[0113] The embodiment of the present application provides a joint inversion device based on a cross-gradient term weight factor, which uses a coefficient matrix and a weight constant to select an effective cross-gradient term weight factor, thereby exerting a good constraint on the resistivity model and the polarizability model, reducing the multi-solution of the joint inversion, and helping to improve the accuracy of the inversion results.

[0114] See also Figure 9 , Figure 9This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. Figure 9 As shown in FIG, the electronic device 900 includes a processor 901, a memory 902 and a bus 903.

[0115] The memory 902 stores machine-readable instructions executable by the processor 901. When the electronic device 900 is running, the processor 901 communicates with the memory 902 via the bus 903. When the machine-readable instructions are executed by the processor 901, the above-mentioned Figure 1 The steps of the joint inversion method based on the cross gradient term weight factor in the method embodiment shown are specifically implemented in accordance with the method embodiment, and will not be described in detail here.

[0116] The embodiment of the present application also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the computer program can execute the above-mentioned Figure 1 The steps of the joint inversion method based on the cross gradient term weight factor in the method embodiment shown are specifically implemented in accordance with the method embodiment, and will not be described in detail here.

[0117] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0118] In the several embodiments provided in this application, it should be understood that the disclosed systems, devices and methods can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is merely a logical function division. There may be other division methods in actual implementation. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed may be through some communication interface, indirect coupling or communication connection of devices or units, which may be electrical, mechanical or other forms.

[0119] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0120] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0121] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a non-volatile computer-readable storage medium that is executable by a processor. 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. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0122] Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present application, which are used to illustrate the technical solutions of the present application, rather than to limit them. The scope of protection of the present application is not limited thereto. Although the present application has been described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily conceive of changes to the technical solutions described in the above-mentioned embodiments within the technical scope disclosed in the present application, or perform equivalent replacements for some of the technical features thereof. These modifications, changes, or replacements do not deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A joint inversion method based on a cross gradient term weight factor, characterized in that: The joint inversion method includes: Obtaining apparent resistivity data and apparent polarizability data based on a plurality of survey lines pre-arranged in an observation area of ​​the underground medium; Assigning initial parameter values ​​of a uniform half-space to each grid cell in a subsurface grid as an initial model for joint inversion, the initial parameter values ​​including initial resistivity values ​​and initial polarizability values, the subsurface grid being obtained by gridding a study area, and the data range of the study area being determined based on the data range of the observation area; Constructing an objective function for joint inversion, the objective function including a cross-gradient term and a first weight factor corresponding to the cross-gradient term, the first weight factor including a coefficient matrix and a weight constant, each matrix element in the coefficient matrix corresponding to each grid cell in the underground grid, the values ​​of the matrix elements corresponding to grid cells in different areas of the underground grid being different, and the weight constant being used to adjust the proportion of the cross-gradient term in the objective function; The objective function is minimized using the apparent resistivity data and the apparent polarizability data to update the initial model and obtain a resistivity model and a polarizability model.

2. The joint inversion method according to claim 1, characterized in that: Multiple survey lines are arranged in an observation area of ​​the underground medium, and each survey line is provided with a transmitting electrode and a receiving electrode. Obtaining apparent resistivity data and apparent polarizability data according to the multiple survey lines pre-arranged in the observation area of ​​the underground medium includes: When the transmitting electrode on each survey line is powered, the adjacent receiving electrodes on the corresponding survey line receive power to obtain apparent resistivity data and apparent polarizability data.

3. The joint inversion method according to claim 1, characterized in that: Determine the data extent of the study area by following these steps: Obtaining the X-direction data range, Y-direction data range, and Z-direction data range of the observation area; A target multiple is set for the X-direction data range, the Y-direction data range, and the Z-direction data range to obtain the data range of the study area in the X-direction, the Y-direction, and the Z-direction; wherein the target multiple is between 3 times and 5 times.

4. The joint inversion method according to claim 1, characterized in that: The objective function also includes a data item, a model item, and a second weight factor corresponding to the model item. The data item is used to calculate the difference between the apparent resistivity data and the resistivity data of the inversion response, and the difference between the apparent polarizability data and the polarizability data of the inversion response. The model item is used to calculate the smoothness of the resistivity model and the polarizability model. The second weight factor represents the proportion of the model item in the objective function.

5. The joint inversion method according to claim 4, characterized in that: The objective function is expressed by the following formula: Φ(m ρ )=Φ d (m ρ )+λ1Φ m (m ρ )+γ1KΦ cg (m ρ ,m η ) Φ(m η )=Φ d (m η )+λ2Φ m (m η )+γ2KΦ cg (m η ,m ρ ) Among them, m ρ Represents the resistivity model of the underground, m η represents the underground polarizability model, Φ(m ρ ) represents the objective function of the resistivity method in the joint inversion of the resistivity method and the induced polarization method, Φ(m η ) represents the objective function of the induced polarization method in the joint inversion of the resistivity method and the induced polarization method, Φ d (m ρ ) represents the data item of the resistivity method, Φ d (m η ) represents the data item of the induced polarization method, Φ m (m ρ ) represents the model term of the resistivity method, Φ m (m η ) represents the model term of the induced polarization method, Φ cg (m ρ ,m η ) represents the cross gradient term of the resistivity method, Φ cg (m η ,m ρ ) represents the cross-gradient term of the induced polarization method, λ1 represents the second weight factor of the model term in the objective function of the resistivity method, λ2 represents the second weight factor of the model term in the objective function of the induced polarization method, γ1 represents the weight constant of the cross-gradient term in the objective function of the resistivity method, γ2 represents the weight constant of the cross-gradient term in the objective function of the induced polarization method, and K represents the coefficient matrix.

6. The joint inversion method according to claim 1, characterized in that: The research area includes a first sub-study area, a second sub-study area and a third sub-study area. In the XY direction, the center of the first sub-study area coincides with the center of the research area, the second sub-study area is wrapped around the periphery of the first sub-study area, and the third sub-study area is wrapped around the periphery of the second sub-study area; in the Z direction, the detection depths corresponding to the first sub-study area, the second sub-study area and the third sub-study area respectively increase gradually; the data range of the first sub-study area and the area range of the second sub-study area constitute the data range of the observation area; the grid cells in the first sub-study area correspond to the first matrix element values, the grid cells in the second sub-study area correspond to the second matrix element values, and the grid cells in the third sub-study area correspond to the third matrix element values. The first matrix element value is greater than the second matrix element value, and the second matrix element value is greater than the third matrix element value.

7. The joint inversion method according to claim 6, characterized in that: The X-direction data range of the first sub-study area is 2 / 3 of the X-direction data range of the observation area, the Y-direction data range of the first sub-study area is 1 / 2 of the Y-direction data range of the observation area, and the Z-direction data range of the first sub-study area is 2 / 3 of the Z-direction data range of the observation area.

8. The joint inversion method according to claim 6, characterized in that: The value of the first matrix element is 1, the value of the second matrix element is 0.1, and the value of the third matrix element is 0.

9. The joint inversion method according to claim 1, characterized in that: The setting value of the weight constant makes the proportion of the cross gradient term in the objective function between 5% and 10%.

10. A joint inversion device based on a cross gradient term weight factor, characterized in that: The joint inversion device comprises: A data acquisition module, configured to acquire apparent resistivity data and apparent polarizability data based on a plurality of survey lines pre-arranged in an observation area of ​​the underground medium; a model construction module, configured to assign initial parameter values ​​of a uniform half-space to each grid cell in a subsurface grid as an initial model for joint inversion, wherein the initial parameter values ​​include initial resistivity values ​​and initial polarizability values, wherein the subsurface grid is obtained by gridding a study area, and wherein a data range of the study area is determined based on a data range of the observation area; a function construction module, configured to construct an objective function for joint inversion, wherein the objective function includes a cross-gradient term and a first weight factor corresponding to the cross-gradient term, wherein the first weight factor includes a coefficient matrix and a weight constant, wherein each matrix element in the coefficient matrix corresponds to each grid cell in the underground grid, and the values ​​of the matrix elements corresponding to grid cells in different areas of the underground grid are different, and the weight constant is used to adjust the proportion of the cross-gradient term in the objective function; A model updating module is used to use the apparent resistivity data and the apparent polarizability data to perform a minimization calculation on the objective function to update the initial model and obtain a resistivity model and a polarizability model.

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