A joint inversion method, system and electronic device based on cross-gradient function

Abstract

The present invention provides a joint inversion method, system and electronic device based on the cross-gradient function, including: performing grid meshing on the subsurface medium based on geophysical data from different sources to obtain an initial physical property model; calculating the cross-gradient function between different physical property models; separately performing individual inversions on the geophysical data to obtain model update amounts; combining the individual inversion physical property model update amounts and the cross-gradient function and solving a linear inversion equation system; determining whether the solution result meets the convergence criterion, if it meets, outputting the joint inversion physical property model update amount, if it does not meet, updating the physical property model using the joint inversion physical property model update amount and repeating the above steps. By constraining different physical property models through structural similarity, combining the separately inverted model update amounts with the cross-gradient function, the non-uniqueness of the joint inversion is effectively reduced, the resolution of the joint inversion is improved, and a more accurate subsurface medium physical property distribution result can be obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field of geophysical inversion, and more specifically, relates to a joint inversion method, system and electronic device based on a cross-gradient function. Background Art

[0002] The non-uniqueness of geophysical data inversion is inevitable, and it is often difficult to accurately explore underground targets. After long-term exploration by domestic and foreign scholars, various methods to weaken the non-uniqueness have been proposed. The most effective method is to add more information in the inversion, integrate various types of geological information into geophysical inversion, and use multiple geophysical exploration methods to observe the same research area to generate a model that conforms to both geological information and geophysical data, that is, joint inversion. The joint inversion method reduces the non-uniqueness of inversion by leveraging the complementarity of data, making the inversion result more consistent with the actual geological situation.

[0003] Joint inversion can be mainly divided into two categories: joint inversion methods based on rock relationships and joint inversion methods based on structural similarity. Joint inversion methods based on rock relationships rely on the functional or statistical relationships between different physical properties of rocks, which require certain costs and the support of geological information. The physical property relationships of different lithologies in different regions vary greatly, and a unified physical property relationship cannot be obtained. Therefore, the development of joint inversion based on rock physical property relationships is restricted. Joint inversion methods based on structural similarity use the structural similarity of physical property models for mutual constraints. Therefore, specific rock physical property relationships do not need to be obtained, and they are more applicable under geological conditions with complex physical property relationships. The cross-gradient function can more accurately represent the structural similarity between different physical property models, and joint inversion based on the cross-gradient function has gradually attracted the attention of the industry. Currently, there are still problems in joint inversion based on the cross-gradient function, such as large numerical differences in the sensitivity matrix, large differences in the inversion system, and storage and calculation of large sparse matrices. In response to these problems, a joint inversion method based on the cross-gradient function is expected, a joint inversion framework that combines model update amount and cross-gradient structure constraint, alternately performs data fitting and cross-gradient structure constraint respectively, and proposes a grid division strategy with separated forward and inverse grids, which balances calculation efficiency and accuracy. Summary of the Invention

[0004] The present invention provides a joint inversion method, system and electronic device based on a cross-gradient function, which effectively reduces the non-uniqueness of inversion and improves the resolution of inversion by constraining different physical property models through structural similarity, and can ensure both calculation efficiency and forward modeling accuracy under the supplementation of different physical property models.

[0005] To achieve the above object, the present invention provides a joint inversion method based on a cross-gradient function, including:

[0006] Step S1: Based on geophysical data from different sources, perform grid meshing on the subsurface medium to obtain an initial physical property model;

[0007] Step S2: Based on the initial physical property model, calculate the cross-gradient function between different physical property models;

[0008] Step S3: Perform separate inversions on the geophysical data from different sources respectively to obtain corresponding updated amounts of the separate inversion physical property models;

[0009] Step S4: Combine the updated amounts of the separate inversion physical property models and the cross-gradient function, and solve the linearly-constrained inversion equations with structural constraints to obtain a solution result;

[0010] Step S5: Determine whether the solution result meets the convergence criterion. If it meets, output the updated amount of the joint inversion physical property model; if it does not meet, update the physical property model using the updated amount of the joint inversion physical property model and repeat Steps S2 to S5.

[0011] Preferably, in Step S1, it includes: performing grid meshing on the subsurface medium, meshing it into fine grids and coarse grids, performing forward modeling on the fine grids and inversion on the coarse grids to obtain the initial physical property model.

[0012] Preferably, the convergence criterion includes at least one of: data fitting error threshold, model update amount threshold, cross-gradient value threshold.

[0013] Preferably, calculate the cross-gradient function between different physical property models through the following formula:

[0014]

[0015] where m1 and m2 are two physical property models, is the spatial gradient operator, and τ is the cross-gradient function between the two models.

[0016] Preferably, solve the linearly-constrained inversion equations with structural constraints through the following formula to obtain the solution result:

[0017]

[0018] where I is the identity matrix, Δm s and Δm g are respectively the updated amounts of the joint inversion physical property models of the two models after adding cross-gradient constraints, Δm s 0 and Δm g 0 are respectively the updated amounts of the separate inversion models of the two models, α s and α gParameters β for balancing the differences in the orders of magnitude of the updates of different physical property models respectively t A parameter τ for balancing data fitting and structural constraints, and τ is the cross-gradient function between two models

[0019] The present invention provides a joint inversion system based on a cross-gradient function to implement the joint inversion method based on the cross-gradient function described above, including:

[0020] An initial physical property model generation module, which is used to perform grid meshing on the underground medium based on geophysical data from different sources to obtain an initial physical property model

[0021] A cross-gradient function calculation module, which is used to calculate the cross-gradient function between different physical property models based on the initial physical property model

[0022] A separate inversion calculation module, which is used to perform separate inversions on the geophysical data from different sources respectively to obtain corresponding updates of the separate inversion physical property models

[0023] A joint inversion calculation module, which combines the updates of the separate inversion physical property models and the cross-gradient function to solve the linear inversion equations with structural constraints to obtain a solution result

[0024] A judgment module, which is used to judge whether the solution result meets the convergence criterion

[0025] An output module, which is used to output the update of the joint inversion physical property model if the solution result meets the convergence criterion

[0026] An update module, which is used to update the physical property model with the update of the joint inversion physical property model if the solution result does not meet the convergence criterion

[0027] Preferably, the convergence criterion includes at least one of: a data fitting error threshold, a model update threshold, and a cross-gradient value threshold

[0028] Preferably, the cross-gradient function calculation module calculates the cross-gradient function between different physical property models through the following formula:

[0029]

[0030] where m1 and m2 are two physical property models is the spatial gradient operator, and τ is the cross-gradient function between two models

[0031] Preferably, the joint inversion calculation module solves the linear inversion equation system with structural constraints through the following formula to obtain the solution result:

[0032]

[0033] where I is the identity matrix, and Δm s and Δm g are the updated amounts of the joint inversion physical property models of the two models after adding cross-gradient constraints respectively, and Δm s 0 and Δm g 0 are the updated amounts of the individual inversion models of the two models respectively, α s and α g are the parameters for balancing the magnitude differences of the updated amounts of different physical property models respectively, β t is the parameter for balancing data fitting and structural constraints, and τ is the cross-gradient function between the two models.

[0034] The present invention provides an electronic device, and the electronic device includes:

[0035] at least one processor; and,

[0036] a memory communicatively connected to the at least one processor, wherein,

[0037] the memory stores instructions executable by the at least one processor, and when the instructions are executed by the at least one processor, the at least one processor is enabled to execute the above-mentioned joint inversion method based on the cross-gradient function.

[0038] The beneficial effects of the technical solution of the present invention are as follows:

[0039] By constraining different physical property models through structural similarity, and combining the updated amounts of the models obtained by separately inverting different types of data with the cross-gradient function under the supplementation of different physical property models, the multi-solution property of the joint inversion is effectively reduced, the resolution of the joint inversion is improved, and a more accurate underground medium physical property distribution result can be obtained;

[0040] At the same time, by using the method of different-precision meshing of forward and inverse models, while improving the calculation efficiency, it does not affect the resolution of the joint inversion, and effectively solves the problems of storage and solution of cross-gradient partial derivatives in joint inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] By describing the exemplary embodiments of the present invention in more detail in conjunction with the drawings, the above and other objects, features, and advantages of the present invention will become more obvious. Among them, in the exemplary embodiments of the present invention, the same reference numerals generally represent the same components.

[0042] Figure 1 Flow chart of a joint inversion method based on cross-gradient function of the present invention;

[0043] Figure 2 Schematic structural diagram of a joint inversion system based on cross-gradient function of the present invention;

[0044] Figure 3 Abnormal model diagram of a prism adopted in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0045] Figure 4 Schematic diagram of forward and inverse modeling grid division in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0046] Figure 5 Flow chart of the gravity and seismic joint inversion method in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0047] Figure 6a Vertical profile at Y = 10 km after separate inversion of the velocity model in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0048] Figure 6b Horizontal profile at Z = 7 km after separate inversion of the velocity model in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0049] Figure 6c Vertical profile at Y = 10 km after separate inversion of the density model in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0050] Figure 6d Horizontal profile at Z = 4 km after separate inversion of the density model in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0051] Figure 7a Vertical profile at Y = 10 km after joint inversion of the velocity model in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0052] Figure 7b Horizontal profile at Z = 7 km after joint inversion of the velocity model in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0053] Figure 7c Vertical profile at Y = 10 km after joint inversion of the density model in an embodiment of the joint inversion method based on cross-gradient function of the present invention;

[0054] Figure 7d The horizontal profile at Z = 4 km after the joint inversion of the density model in an embodiment of the joint inversion method based on the cross-gradient function of the present invention.

[0055] Explanation of reference numerals:

[0056] 1. Initial physical property model generation module; 2. Cross-gradient function calculation module; 3. Separate inversion calculation module; 4. Joint inversion calculation module; 5. Judgment module; 6. Output module; 7. Update module. Detailed implementation manners

[0057] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to make the present invention more thorough and complete, and to fully convey the scope of the present invention to those skilled in the art.

[0058] It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0059] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but it is not limited to the present invention.

[0060] Referring to Figure 1 As shown, the present invention provides a joint inversion method based on the cross-gradient function, including:

[0061] Step S1: Based on geophysical data from different sources, perform grid meshing on the underground medium to obtain an initial physical property model;

[0062] Step S2: Based on the initial physical property model, calculate the cross-gradient function between different physical property models;

[0063] Step S3: Perform separate inversions on geophysical data from different sources respectively to obtain corresponding updated amounts of the separate inversion physical property models;

[0064] Step S4: Combine the updated amounts of the separate inversion physical property models and the cross-gradient function, and solve the linearly constrained inversion equations to obtain a solution result;

[0065] Step S5: Determine whether the solution result meets the convergence criterion. If it meets, output the updated amount of the joint inversion physical property model; if it does not meet, update the physical property model using the updated amount of the joint inversion physical property model and repeat steps S2 to S5.

[0066] A preferred example is that in step S1, it includes: performing grid meshing on the underground medium, meshing it into fine grids and coarse grids, performing forward modeling on the fine grids, and performing inversion on the coarse grids to obtain an initial physical property model.

[0067] A preferred example is that the convergence criterion includes at least one of: data fitting error threshold, model update amount threshold, and cross-gradient value threshold.

[0068] A preferred example is that the cross-gradient function between different physical property models is calculated by the following formula:

[0069]

[0070] where m1 and m2 are two physical property models, is the spatial gradient operator, and τ is the cross-gradient function between the two models.

[0071] A preferred example is that the solution result is obtained by solving the linear inversion equation system with structural constraints through the following formula:

[0072]

[0073] where I is the identity matrix, Δm s , Δm g are respectively the updated amounts of the joint inversion physical property models of the two models after adding cross-gradient constraints, Δm s 0 , Δm g 0 are respectively the updated amounts of the individual inversion models of the two models, α s , α g are respectively the parameters for balancing the magnitude differences of the updated amounts of different physical property models, β t is the parameter for balancing data fitting and structural constraints, and τ is the cross-gradient function between the two models.

[0074] Specifically, according to the original geophysical data from different sources, the underground medium in the study area is meshed, and the inversion grid is processed by downward merging on the basis of the forward modeling grid, and a suitable initial physical property model for inversion is selected.

[0075] Calculate the cross-gradient function between different physical property models. The formula is as follows:

[0076]

[0077] where m1 and m2 are two physical property models, is the spatial gradient operator, which is obtained by using the central difference method, and τ is the cross-gradient function between the two models.

[0078] Perform single - type data inversion on geophysical data from different sources to obtain the corresponding updated physical property model Δm s 0 and Δm g 0 .

[0079] Combine the updated physical property models obtained from separate inversions of different types of data with the cross - gradient function constraint, and solve the linear inversion equations with structural constraints. The formula is as follows:

[0080]

[0081] where I is the identity matrix, Δm s and Δm g are the updated physical property models of two models after adding the cross - gradient constraint respectively, Δm s 0 and Δm g 0 are the updated physical property models obtained from separate inversions of the two models respectively, α s and α g are the parameters for balancing the magnitude differences of the updated models of different models, which can be determined by pre - evaluating the magnitudes of the updated models of separate inversion models. β t is the parameter for balancing data fitting and structural constraints. The larger its value, the greater the weight of the structural constraint. By adjusting the three parameters α s , α g , and β t , the balance of various constraints in the inversion process is achieved.

[0082] Calculate the fitting error of the solution of this set of equations, and determine whether the result meets the convergence criteria. The convergence criteria are generally the data fitting error threshold, the updated model threshold, the cross - gradient value threshold, etc. If it meets the criteria, the updated physical property model of the joint inversion is obtained. If it does not meet the criteria, update the physical property model using the updated physical property model of the joint inversion and repeat steps S2 to S5.

[0083] By constraining different physical property models through structural similarity, with the supplementation of different physical property models, the non - uniqueness of the joint inversion is effectively reduced, and the resolution of the joint inversion is improved. At the same time, by using the method of different - precision meshing of forward and inverse models, the computational efficiency is improved, and the resolution of the joint inversion is not affected. The problem of storing and solving the partial derivatives of the cross - gradient function in the joint inversion is effectively solved.

[0084] The present invention also provides a joint inversion system based on the cross - gradient function to implement the above - mentioned joint inversion method based on the cross - gradient function, including:

[0085] Initial physical property model generation module 1, which is used to perform grid division on the subsurface medium based on geophysical data from different sources to obtain an initial physical property model;

[0086] Cross-gradient function calculation module 2, which is used to calculate the cross-gradient function between different physical property models based on the initial physical property model;

[0087] Separate inversion calculation module 3, and the separate inversion module 3 is used to perform separate inversions on geophysical data from different sources respectively to obtain corresponding separate inversion physical property model update amounts;

[0088] Joint inversion calculation module 4, and the joint inversion module 4 combines the separate inversion physical property model update amounts and the cross-gradient function to solve the linearly-constrained inversion equations with structural constraints to obtain a solution result;

[0089] Judgment module 5, which is used to judge whether the solution result meets the convergence criteria;

[0090] Output module 6, and the output module 6 is used to output the joint inversion physical property model update amount if the solution result meets the convergence criteria;

[0091] Update module 7, and the update module 7 is used to update the physical property model using the joint inversion physical property model update amount if the solution result does not meet the convergence criteria.

[0092] A preferred example, the convergence criteria include at least one of: data fitting error threshold, model update amount threshold, cross-gradient value threshold.

[0093] A preferred example, the cross-gradient function calculation module calculates the cross-gradient function between different physical property models through the following formula:

[0094]

[0095] where m1 and m2 are two physical property models, is the spatial gradient operator, and τ is the cross-gradient function between the two models.

[0096] A preferred example, the joint inversion calculation module solves the linearly-constrained inversion equations with structural constraints through the following formula to obtain a solution result:

[0097]

[0098] where I is the identity matrix, Δm s and Δm g are the joint inversion physical property model update amounts of the two models after adding cross-gradient constraints respectively, and Δm s 0 and Δmg 0 They are the individual inversion model update amounts for the two models, α s and α g They are parameters for balancing the order-of-magnitude differences in the update amounts of different physical property models, β t is a parameter for balancing data fitting and structural constraints, and τ is the cross-gradient function between the two models.

[0099] Specifically, to verify the correctness and effectiveness of the joint inversion method based on the cross-gradient function of the present invention, an initial physical property model generation module 1 is used to perform grid meshing on the subsurface medium based on geophysical data from different sources to obtain an initial physical property model; a cross-gradient function calculation module 2 is used to calculate the cross-gradient function between different physical property models based on the initial physical property model; an individual inversion module 3 is used to perform individual inversion on geophysical data from different sources respectively to obtain the corresponding individual inversion physical property model update amounts; a joint inversion module 4 combines the individual inversion physical property model update amounts and the cross-gradient function to solve the linear inversion equations with structural constraints to obtain a solution result; a judgment module 5 is used to judge whether the solution result meets the convergence criterion; an output module 6 is used to output the joint inversion physical property model update amount if the solution result meets the convergence criterion; an update module 7 is used to perform iterative update on the physical property model using the joint inversion physical property model update amount if the solution result does not meet the convergence criterion, and return to the cross-gradient function calculation module 2 to continue the joint inversion calculation.

[0100] By constraining different physical property models through structural similarity, and with the supplementation of different physical property models, the non-uniqueness of joint inversion is effectively reduced, and the resolution of joint inversion is improved. At the same time, by using the method of different-precision meshing of forward and inverse grids, the computational efficiency is improved, and the resolution of joint inversion is not affected, effectively solving the problems of storage and solution of the partial derivatives of the cross-gradient function in joint inversion.

[0101] The present invention also provides an electronic device, which includes:

[0102] At least one processor; and,

[0103] A memory communicatively connected to the at least one processor, wherein,

[0104] The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the above-mentioned joint inversion method based on the cross-gradient function.

[0105] Specifically, the at least one processor runs the executable instructions in the memory and executes the following steps:

[0106] Step S1: Based on geophysical data from different sources, perform grid meshing on the subsurface medium to obtain an initial physical property model;

[0107] Step S2: Based on the initial physical property model, calculate the cross-gradient function between different physical property models;

[0108] Step S3: Perform separate inversions on geophysical data from different sources respectively to obtain corresponding updated amounts of the separately inverted physical property models;

[0109] Step S4: Combine the updated amounts of the separately inverted physical property models and the cross-gradient function, and solve the linearly inverted equations with structural constraints to obtain a solution result;

[0110] Step S5: Determine whether the solution result meets the convergence criterion. If it meets, output the updated amount of the jointly inverted physical property model; if not, update the physical property model using the updated amount of the jointly inverted physical property model and repeat Steps S2 to S5.

[0111] Based on the above steps, by constraining different physical property models with structural similarity, and with the supplementation of different physical property models, the non-uniqueness of the joint inversion is effectively reduced, and the resolution of the joint inversion is improved. At the same time, by using the method of different precision meshing of the forward and inverse grids, while improving the calculation efficiency, it does not affect the resolution of the joint inversion, and effectively solves the problems of storage and solution of the partial derivatives of the cross-gradient function in the joint inversion.

[0112] Example 1

[0113] Provide a joint inversion method based on the cross-gradient function, including:

[0114] Step S1: Based on geophysical data from different sources, perform grid meshing on the subsurface medium to obtain an initial physical property model;

[0115] Step S2: Based on the initial physical property model, calculate the cross-gradient function between different physical property models;

[0116] Step S3: Perform separate inversions on geophysical data from different sources respectively to obtain corresponding updated amounts of the separately inverted physical property models;

[0117] Step S4: Combine the updated amounts of the separately inverted physical property models and the cross-gradient function, and solve the linearly inverted equations with structural constraints to obtain a solution result;

[0118] Step S5: Determine whether the solution result meets the convergence criterion. If it meets, output the updated amount of the jointly inverted physical property model; if not, update the physical property model using the updated amount of the jointly inverted physical property model and repeat Steps S2 to S5.

[0119] In this embodiment, step S1 includes: performing grid meshing on the underground medium, meshing it into fine grids and coarse grids, performing forward modeling on the fine grids, and performing inversion on the coarse grids to obtain an initial physical property model.

[0120] In this embodiment, the convergence criteria include at least one of: a data fitting error threshold, a model update amount threshold, and a cross-gradient value threshold.

[0121] In a preferred example, the cross-gradient function between different physical property models is calculated by the following formula:

[0122]

[0123] where m1 and m2 are two physical property models, is the spatial gradient operator, and τ is the cross-gradient function between the two models.

[0124] In this embodiment, the solution result is obtained by solving the linear inversion equations with structural constraints through the following formula:

[0125]

[0126] where I is the identity matrix, Δm s , Δm g are the updated amounts of the joint inversion physical property models of the two models after adding cross-gradient constraints, Δm s 0 , Δm g 0 are the updated amounts of the individual inversion models of the two models, α s , α g are the parameters for balancing the magnitude differences of the updated amounts of different physical property models, β t is the parameter for balancing data fitting and structural constraints, and τ is the cross-gradient function between the two models.

[0127] To verify the correctness and effectiveness of the above method, a velocity-density coupling model is designed below for joint inversion verification of repeated seismic data.

[0128] Design three prism anomaly models, as Figure 3As shown in the figure, the geometric parameters are as follows: for the small prism, the length is 2 km, the width is 4 km, the height is 2 km, and the top surface burial depth is 3 km; for the medium prism, the length is 3 km, the width is 4 km, the height is 3 km, and the top surface burial depth is 2 km; for the large prism, the length is 4 km, the width is 4 km, the height is 4 km, and the top surface burial depth is 1 km. The physical property parameters of the three prism anomalies are the same, with a residual density of 1 g / cm3, a seismic wave velocity of 6 km / s, and a surrounding rock velocity of 4 km / s. It is assumed that there is a seismic reflection interface (Z = 7 km plane) below the anomalies in the model. The seismic observation system is ground-based. 25 shot points and 66 receiver points are evenly arranged on the ground (Z = 0 plane). The seismic wave propagates downward from the shot points, is reflected by the interface, and then propagates to the receiver points, without considering the reflection at the anomaly interface. 400 gravity data observation points are evenly set up on the Z = 0 observation plane, with a measurement point interval of 1 km. The results of the forward calculation are added with 3% Gaussian noise as the observed data for inversion. The initial inversion model is set as a homogeneous model with physical property parameters of 0 g / cm3 and 4 km / s, and separate inversion and joint inversion are carried out. Each inversion grid is divided into a 5×5×5 grid, forming a denser forward grid (black grid lines) for the forward calculation of seismic wave travel time, as Figure 4 shown. According to Figure 5 the flow chart of the gravity-seismic joint inversion method shown, the separate inversion and joint inversion results are obtained, and the Y = 10 km vertical profile and Z = 4 km horizontal profile are made for the results respectively. In the separate inversion results, as Figure 6c - 6d shown, the density model profile cannot distinguish the three prisms, and only the larger prism anomaly is recovered well. As Figure 6a - 6b shown, the velocity model can accurately recover the three prism anomalies, but there are certain deviations in their shapes, amplitudes and the real situation. Compared with the separate inversion, the joint inversion results have been greatly improved in terms of the recovery of the anomaly shape and physical property values. As Figure 7c - 7d shown, the three prism anomalies can be effectively distinguished in the density model. As Figure 7a - 7b shown, the velocity model is closer to the real situation in terms of the recovery of the anomaly shape and amplitude. Through the supplement of seismic data, the resolution of gravity inversion has been significantly improved. At the same time, under the constraint of gravity data, the seismic inversion results are more in line with the actual situation. The joint inversion is verified by the embodiment to effectively reduce the non-uniqueness of inversion, improve the resolution of inversion, and ensure both the calculation efficiency and the forward accuracy.

[0129] Embodiment 2

[0130] Referring to Figure 2 shown, this embodiment provides a joint inversion system based on the cross-gradient function to implement the above-mentioned joint inversion method based on the cross-gradient function, including:

[0131] Initial physical property model generation module 1, which is used to perform grid division on the underground medium based on geophysical data from different sources to obtain an initial physical property model;

[0132] Cross-gradient function calculation module 2, which is used to calculate the cross-gradient function between different physical property models based on the initial physical property model;

[0133] Separate inversion calculation module 3, which is used to perform separate inversion on geophysical data from different sources respectively to obtain corresponding separate inversion physical property model update amounts;

[0134] Joint inversion calculation module 4, which combines the separate inversion physical property model update amounts and the cross-gradient function, and solves the linearly constrained inversion equations to obtain a solution result;

[0135] Judgment module 5, which is used to judge whether the solution result meets the convergence criterion;

[0136] Output module 6, which is used to output the joint inversion physical property model update amount according to the solution result meeting the convergence criterion;

[0137] Update module 7, which is used to update the physical property model with the joint inversion physical property model update amount according to the solution result not meeting the convergence criterion.

[0138] In this embodiment, the convergence criterion includes at least one of: data fitting error threshold, model update amount threshold, and cross-gradient value threshold.

[0139] In this embodiment, the cross-gradient function calculation module calculates the cross-gradient function between different physical property models through the following formula:

[0140]

[0141] where m1 and m2 are two physical property models, is the spatial gradient operator, and τ is the cross-gradient function between the two models.

[0142] In this embodiment, the joint inversion calculation module solves the linearly constrained inversion equations through the following formula to obtain a solution result:

[0143]

[0144] where I is the identity matrix, Δm s and Δm g are the joint inversion physical property model update amounts of the two models after adding cross-gradient constraints respectively, and Δm s 0 and Δm g0 They are the individual inversion model update amounts for the two models, α s , α g They are the parameters for balancing the order-of-magnitude differences in the update amounts of different physical property models, β t is the parameter for balancing data fitting and structural constraints, and τ is the cross-gradient function between the two models.

[0145] In summary, the present invention utilizes the structural coupling relationship of geophysical data sensitive to different physical properties, and with the supplementation of different physical property models, combines the model update amounts obtained from the individual inversion of different types of data with the cross-gradient function for joint inversion, reduces the non-uniqueness existing in the inversion of a single type of geophysical data, improves the resolution of the inversion, and can obtain a more accurate result of the physical property distribution of the underground medium.

[0146] The embodiments of the present invention have been described above. The above description is exemplary and not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A joint inversion method based on the cross-gradient function, characterized in that, Including: Step S1: Based on geophysical data from different sources, perform grid meshing on the subsurface medium to obtain an initial physical property model. Step S2: Based on the initial physical property model, calculate the cross-gradient function between different physical property models. Step S3: Perform separate inversions on the geophysical data from different sources respectively to obtain corresponding updated amounts of the separate inversion physical property models. Step S4: Combine the updated amounts of the separate inversion physical property models and the cross-gradient function, and solve the linearly-constrained inversion equations with structural constraints to obtain a solution result. Step S5: Determine whether the solution result meets the convergence criteria. If it meets, output the updated amount of the joint inversion physical property model; if it does not meet, update the physical property model using the updated amount of the joint inversion physical property model and repeat Steps S2 to S5.

2. The joint inversion method according to claim 1, wherein In Step S1, it includes: Performing grid meshing on the subsurface medium, dividing it into fine grids and coarse grids, performing forward modeling on the fine grids, and performing inversion on the coarse grids to obtain the initial physical property model.

3. The joint inversion method according to claim 1, wherein The convergence criteria include at least one of: data fitting error threshold, model update amount threshold, cross-gradient value threshold.

4. The joint inversion method according to claim 1, wherein Calculate the cross-gradient function between different physical property models through the following formula: where, m1 and m2 are two physical property models, is a spatial gradient operator, and τ is a cross-gradient function between the two models.

5. The joint inversion method according to claim 4, wherein Solve the linearly-constrained inversion equations with structural constraints to obtain a solution result through the following formula: where \(I\) is the identity matrix, \(\Delta m\) s and \(\Delta m\) g are the updated amounts of the joint inversion physical property models of the two models after adding the cross-gradient constraint, \(\Delta m\) s 0 and \(\Delta m\) g 0 are the updated amounts of the individual inversion models of the two models respectively, \(\alpha\) s and \(\alpha\) g are the parameters for balancing the magnitude differences of the updated amounts of different physical property models respectively, \(\beta\) t is the parameter for balancing data fitting and structural constraint, and \(\tau\) is the cross-gradient function between the two models.

6. A joint inversion system based on the cross-gradient function, which implements the joint inversion method based on the cross-gradient function described in any one of claims 1-5, characterized in that, Including: Initial physical property model generation module, which is used to perform grid meshing on the subsurface medium based on geophysical data from different sources to obtain an initial physical property model. Cross-gradient function calculation module, which is used to calculate the cross-gradient function between different physical property models based on the initial physical property model. Separate inversion calculation module, the separate inversion module is used to perform separate inversions on the geophysical data from different sources respectively to obtain corresponding updated amounts of the separate inversion physical property models. Joint inversion calculation module, the joint inversion module combines the updated amounts of the separate inversion physical property models and the cross-gradient function, and solves the linearly-constrained inversion equations with structural constraints to obtain a solution result. Judgment module, which is used to determine whether the solution result meets the convergence criteria. Output module, which is used to output the updated amount of the joint inversion physical property model if the solution result meets the convergence criteria. Update module, which is used to update the physical property model using the updated amount of the joint inversion physical property model if the solution result does not meet the convergence criteria.

7. The joint inversion system according to claim 6, wherein The convergence criteria include at least one of: data fitting error threshold, model update amount threshold, cross-gradient value threshold.

8. The joint inversion system according to claim 6, wherein The cross-gradient function calculation module calculates the cross-gradient function between different physical property models through the following formula: where m1 and m2 are two physical property models, is the spatial gradient operator, and τ is the cross-gradient function between the two models.

9. The joint inversion system according to claim 8, wherein The joint inversion calculation module solves the linearly-constrained inversion equations with structural constraints to obtain a solution result through the following formula: where I is the identity matrix, and Δm s and Δm g are the updated amounts of the joint inversion physical property models of the two models after adding the cross-gradient constraint, and Δm s 0 and Δm g 0 are the updated amounts of the individual inversion models of the two models respectively. α s and α g are the parameters for balancing the order-of-magnitude differences of the updated amounts of different physical property models respectively. β t is the parameter for balancing data fitting and structural constraint, and τ is the cross-gradient function between the two models.

10. An electronic device, characterized in that, The electronic device includes: At least one processor; and, A memory communicatively connected to the at least one processor, where, The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the joint inversion method based on the cross-gradient function according to any one of claims 1-5.

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