Terrestrial well controllable source electromagnetic method joint inversion method and system based on tensor source

Abstract

The invention belongs to the technical field of geophysical exploration, and particularly discloses a ground well controllable source electromagnetic method joint inversion method and system based on a tensor source, and the method comprises the steps: carrying out the forward modeling of an established three-dimensional electrical model through a CSEM in a ground well, and obtaining the impedance tensor and a tipper of a tensor controllable source; constructing a three-dimensional ground and in-well CSEM combined inversion objective function and a gradient of the inversion objective function by using the model roughness matrix and the data fitting item; and solving the gradient of the inversion objective function by adopting an improved L-BFGS optimization algorithm based on a momentum method, and inverting the underground electrical structure. According to the method, through joint inversion and in combination with controllable source electromagnetic data in the ground and the well, the transverse and longitudinal resolution of exploration is improved, the multiplicity of inversion is reduced, and the inversion result is more reliable.

Description

Technical Field

[0001] The present application belongs to the field of geophysical exploration technology, and more specifically, relates to a tensor source-based ground-well controlled source electromagnetic joint inversion method and system. Background Art

[0002] With the recent surge in oil, gas, and mineral resource extraction, shallow resources are becoming increasingly depleted, creating a severe supply situation for oil, gas, and important metals. The trend toward deeper oil, gas, and mineral exploration has become inevitable. However, due to the complexity of exploration targets, traditional single geophysical methods struggle to overcome the multi-solution nature of inversion, resulting in limitations and an inability to effectively identify the morphology and location of underground reservoirs, leading to increased exploration costs.

[0003] Controlled-source electromagnetic method (CSEM) is a geophysical exploration technique that uses artificial emission sources for excitation. It is widely used in geological exploration, environmental monitoring, and hydrogeological research. This method involves excitation of signals at the surface, recording the electromagnetic response via a receiving array, and inverting the recorded signal to detect subsurface electrical structures (Zhong Liancheng et al., 2024). CSEM has the advantages of strong anti-interference capabilities and a large detection depth. However, due to the skin effect, the electromagnetic field intensity decays exponentially with depth, reducing vertical resolution (Zhang Jiwei et al., 2024). Borehole CSEM data can mitigate the ambiguity that can occur during the inversion of ground-based CSEM data. The vertical magnetic field measurement points are located closer to the distribution of subsurface structures, helping to improve the accuracy of local stratum identification. However, borehole data are largely dependent on the wellbore location and also have limitations (Gao Shiqi, 2023).

[0004] CSEM can be divided into three types of observation devices: scalar, vector and tensor according to the emission source and the number of electromagnetic field components observed. Scalar CSEM uses one emission source and collects two orthogonal electromagnetic field tangential components ( 、 or 、 ); Vector CSEM uses a transmitting source and collects 5 electromagnetic field components ( 、 、 、 、 ); Tensor CSEM uses two sets of emission sources and collects 5 electromagnetic field components of each emission source ( 、 、 、 、 ), a total of 10 components. Due to the limited distribution range of the emission source signal, vector observation is rarely used (Wang Tao et al., 2017), making it difficult to recover complex deep electrical structures. CSEM has always mainly used a scalar observation mode with single-source excitation. In this mode, only scalar impedance can be obtained by measuring the electromagnetic field components. Therefore, this method is only suitable for the exploration of one-dimensional geological structures and the effect is relatively ideal. However, in actual exploration, underground electrical structures often exhibit complex two-dimensional or three-dimensional characteristics. This means that electrical parameters not only vary in the vertical direction, but also undergo significant changes in the dip and horizontal directions. In this case, the electrical parameters are expressed in tensor form. In this case, the traditional scalar CSEM method can no longer meet the exploration needs.

[0005] The above analysis reveals the following problems and shortcomings of existing technologies: Most currently employed inversion methods rely solely on single-scale geophysical data, making it difficult to accurately explore the distribution of underground electrical structures. Existing technologies are also unable to effectively identify the shape and location of complex underground oil and gas reservoirs and mineral distributions, failing to meet the requirements for refined inversion, resulting in increased costs for oil and gas extraction and mineral development. Summary of the Invention

[0006] In response to the defects of the existing technology, the purpose of this application is to provide a tensor source-based ground-well controlled source electromagnetic joint inversion method and system, aiming to solve the problem that the existing single ground or well electromagnetic method is difficult to overcome the multi-solution nature of geophysical problems, resulting in the inability to fully reflect the electrical distribution of underground media.

[0007] To achieve the above objectives, in a first aspect, the present application provides a tensor source-based ground-well controlled source electromagnetic joint inversion method, comprising the following steps: Step S1: constructing a three-dimensional electrical model including a tensor source, drilling electrical parameters, and formation electrical parameters, and performing forward modeling on the established three-dimensional electrical model using a CSEM in a surface well to obtain the impedance tensor and the tilt of the tensor controllable source; Step S2: Combining the impedance tensors and dipoles obtained in step S1, the model roughness matrix and the data fitting term are used to construct the three-dimensional ground and well CSEM joint inversion objective function and the gradient of the inversion objective function; Step S3: Using the improved L-BFGS optimization algorithm based on the momentum method to solve the gradient of the inversion objective function, invert the underground electrical structure.

[0008] Further preferably, step S1 specifically includes the following steps: Step S1.1: Construct the vector finite element governing equations in the three-dimensional electrical model based on the electric field intensity, electromagnetic wave angular frequency, magnetic permeability, electrical conductivity, and CSEM applied current source term; Step S1.2: Discretize the vector finite element governing equations, interpolate the electric field values within the finite element and then assemble them in the entire computational domain to obtain the complex linear algebraic equations; Step S1.3: After adding the Dirichlet boundary to the complex linear algebraic equation, obtain the electric field and magnetic field values on any element edge; Step S1.4: Based on the tensor CSEM observation method, the impedance tensor and the tensor controllable source tilter of the tensor controllable source are obtained according to the electric field value and the magnetic field value obtained in step S1.3.

[0009] Further preferably, step S2 specifically includes the following steps: Step S2.1: Constructing an inversion objective function based on the inversion model roughness matrix and data fitting terms; wherein the data fitting terms include surface CSEM data and well CSEM data; Step S2.2: Discretize the data fitting term in the inversion objective function and calculate the data residual contribution value in each grid cell through the interpolation basis function; Step S2.3: Express the roughness matrix using the smoothness constraint and the reference model constraint; Step S2.4: performing finite element discretization on the roughness matrix in step S2.3; Step S2.5: Calculate the gradient of the inversion objective function by combining the data residual and the constraint term, and continuously update the inversion model according to the gradient direction until the inversion objective function converges. Further preferably, the inversion objective function in step S2.1 is:

[0010] in, , , ; , ; is the roughness matrix of the inversion model; is the data fitting term; m is the inversion model; 、 、 、 and is the regularization factor; n =1 corresponds to the CSEM data on the ground; n =2 corresponds to the CSEM data in the well; the CSEM data includes the impedance tensor of the tensor controllable source and the tensor controllable source tilter; is the observed CSEM data; CSEM data obtained by forward modeling in step S1; is the error data covariance matrix; R is the inversion model smoothing matrix; is the prior constraint matrix of the inversion model; Inversion model for forward prediction.

[0011] Further preferably, the inversion model updating method in the L-BFGS iteration is:

[0012] in, is the update amount of the inversion model; k is the number of iterations; m is the inversion model; is the learning rate; V is the momentum factor; g is the gradient of the inversion objective function.

[0013] In a second aspect, the present application provides a tensor source-based ground-well controlled source electromagnetic method joint inversion system, comprising: The forward modeling module is used to construct a three-dimensional electrical model that includes tensor sources, drilling electrical parameters, and formation electrical parameters. The 3D electrical model is forward modeled using CSEM in a surface well to obtain the impedance tensor and tilt of the tensor controllable source. The objective function construction module is used to combine the impedance tensors and dipoles obtained from the forward modeling module, and to construct the three-dimensional surface and well CSEM joint inversion objective function and the gradient of the inversion objective function using the model roughness matrix and data fitting terms. The inversion module is used to solve the gradient of the inversion objective function and invert the underground electrical structure by using the L-BFGS optimization algorithm improved based on the momentum method.

[0014] Further preferably, the forward modeling module includes: The control equation construction unit is used to construct the vector finite element control equations in the three-dimensional electrical model based on the electric field intensity, electromagnetic wave angular frequency, magnetic permeability, electrical conductivity and CSEM external current source terms; A first data processing unit is used to discretize the vector finite element governing equations using an unstructured finite element method, interpolate the electric field values within the finite element units and then assemble them in the entire computational domain to obtain a complex linear algebraic equation; The electromagnetic field acquisition unit is used to obtain the electric field and magnetic field values on the edges of any unit after adding the Dirichlet boundary to the complex linear algebraic equation; The forward data acquisition unit is used to obtain the impedance tensor and the tensor controllable source tilter of the tensor controllable source based on the electric field value and the magnetic field value obtained by the electromagnetic field acquisition unit based on the tensor CSEM observation method.

[0015] Further preferably, the objective function building module includes: A first objective function construction unit is configured to construct an inversion objective function based on the inversion model roughness matrix and a data fitting term, wherein the data fitting term includes ground CSEM data and well CSEM data; The second data processing unit discretizes the data fitting term in the inversion objective function; a third data processing unit, configured to represent a roughness matrix using a smoothness constraint and a reference model constraint; a fourth data processing unit, configured to perform finite element discretization on the roughness matrix; The first objective function construction unit calculates the gradient of the inversion objective function and continuously updates the inversion model in the direction of the fastest gradient descent until the inversion objective function converges.

[0016] Further preferably, the inversion objective function in the objective function construction module is:

[0017] in, , , ; , ; is the roughness matrix of the inversion model; is the data fitting term; m represents the inversion model; 、 、 、 and is the regularization factor; n =1 corresponds to the CSEM data on the ground; n =2 corresponds to the CSEM data in the well; the CSEM data includes the impedance tensor of the tensor controllable source and the tensor controllable source tilter; is the observed CSEM data; CSEM data obtained by forward modeling in step S1; is the error data covariance matrix; R is the inversion model smoothing matrix; is the prior constraint matrix of the inversion model; Inversion model for forward prediction.

[0018] Further preferably, the inversion model updating method in the L-BFGS iteration in the inversion module is:

[0019] in, is the update amount of the inversion model; k is the number of iterations; m is the inversion model; is the learning rate; V is the momentum factor; g is the gradient of the inversion objective function.

[0020] In a third aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0021] In a fourth aspect, the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0022] In a fifth aspect, the present application provides a computer program product, which, when executed on a processor, enables the processor to execute the method described in the first aspect or any possible implementation of the first aspect.

[0023] It can be understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0024] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the existing technologies: Compared to traditional scalar controlled-source electromagnetic methods, this application provides a joint inversion method for ground-based and well-based controlled-source electromagnetic methods based on tensor sources. This multi-source tensor controlled-source electromagnetic method can simultaneously excite and receive electromagnetic field components in multiple directions, obtaining richer subsurface structural information. By combining controlled-source electromagnetic data from the surface and wells, this joint inversion improves the lateral and vertical resolution of exploration, reduces the potential for multiple solutions, and makes the inversion results more reliable.

[0025] Unlike traditional regularized grids, this application provides a tensor source-based ground-well controlled source electromagnetic joint inversion method, which uses unstructured grids to divide the study area, can more flexibly construct the shape of terrain and underground anomalies, and at the same time use unstructured finite elements to save memory and improve calculation speed.

[0026] This application uses the L-BFGS optimization algorithm to reduce the inversion memory requirements, and introduces the momentum method in the model update of the three-dimensional joint inversion to achieve faster convergence.

[0027] The data acquisition efficiency of the tensor source in this application is high, and the joint inversion method can quickly process multi-source data, shorten the exploration cycle and reduce costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 This is a schematic diagram of tetrahedral unit nodes and edges provided in an embodiment of the present application; FIG2( a ) is a schematic diagram of a scalar method of a ground CSEM device provided in an embodiment of the present application; FIG2( b ) is a tensor diagram of a ground CSEM device provided in an embodiment of the present application; Figure 3 is a schematic diagram of a scalar method of a surface and well CSEM device provided in an embodiment of the present application; Figure 4 Schematic diagram of the tensor method of the surface and well CSEM devices provided in the embodiments of the present application; Figure 5 1 is a planar schematic diagram of the constraint items of the unstructured tetrahedron network model provided in an embodiment of the present application; Figure 6 This is a schematic diagram of the descent of the three-dimensional electromagnetic inversion objective function provided by an embodiment of the present application; Figure 7 This is a schematic diagram of a local polar area provided in an embodiment of the present application; FIG8( a ) is a schematic diagram of the xz section of the surface and well tensor CSEM theoretical model provided in Example 1 of the present application; FIG8( b ) is a schematic diagram of the yy section of the tensor CSEM theoretical model of the surface and well provided in Example 1 of the present application; FIG9( a ) is an xz plane slice diagram of the final inversion result provided in Example 1 of the present application; FIG9( b ) is an xy plane slice diagram of the final inversion result provided in Example 1 of the present application; Figure 10 (a) is the fitting item provided in Example 1 of this application , model constraints and Inversion convergence diagram of ; Figure 10 (b) is provided in Example 1 of this application and search step size Inversion convergence diagram of ; FIG10( c ) is an inversion convergence diagram of RMS and regularization factor provided in Example 1 of the present application; FIG11( a ) is a schematic diagram of an xz section of the tensor CSEM model provided in Example 2 of the present application; FIG11( b ) is a schematic diagram of an xy section of the tensor CSEM model provided in Example 2 of the present application; Figure 12 (a) is the ground data inversion provided in Example 2 of this application Result xz plane slice diagram y=0m; Figure 12 (b) shows the joint inversion of surface and well data provided in Example 2 of this application. Result xy plane slice diagram y=0m; Figure 12 (c) is the ground data inversion provided by Example 2 of this application Result xy plane slice diagram z=1400m; Figure 12 (d) shows the joint inversion of surface and well data provided in Example 2 of this application. Result xy plane slice diagram z=1400m; Figure 12 (e) is the ground data inversion provided in Example 2 of this application Result xy plane slice diagram z=3000m; Figure 12 (f) shows the joint inversion of surface and well data provided in Example 2 of this application. Result xy plane slice diagram z=3000m. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0030] The term "and / or" as used herein describes an association between related objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. The symbol " / " as used herein indicates that the related objects are in an "or" relationship, for example, A / B means either A or B.

[0031] The terms "first" and "second" and the like in the description and claims herein are used to distinguish different objects rather than to describe a specific order of the objects.

[0032] In the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be interpreted as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0033] This application provides a tensor source-based joint inversion method for controlled-source electromagnetic methods for underground and wells, which involves two methods: forward modeling and inversion. The following describes them in detail: Forward modeling: From model to simulation data, that is, calculating the electromagnetic response based on the model's electrical information and field source information; the specific steps are: Step a: Define the electrical parameters of the underground medium, build a forward model, and use an unstructured tetrahedral mesh for segmentation; Step b: construct the governing equations, i.e. the electromagnetic field relationships satisfied by the constructed forward model; Step c: discretize the control equations using vector basis functions, define interpolation functions of the electric field E on the grid edges, and transform the continuous equations into a system of linear equations; Step d: Apply boundary conditions, solve the linear equations, and obtain forward simulation data (such as impedance tensor and dipole, etc.).

[0034] Inversion: From data to underground model, that is, inferring the distribution of underground electrical parameters based on observed data. The specific steps are: Step a: Set the initial conductivity model for inversion (subsequent iterations start from the initial model) and define the inversion grid (usually the same as the forward grid); Step b: Construct an objective function, which includes a data fitting term (which measures the error between the forward modeling data and the observed data) and a model constraint term (which controls the complexity of the model, such as smoothness). Discretizing the data fitting term involves mapping the residuals between the observed data and the forward modeling results to grid cells, converting the continuous data error into discrete cell contributions. Discretizing the model constraint term involves discretizing the constraint term into a sparse matrix on the grid, enabling numerical calculation of the regularization term. Step c: Based on the discretized field values of the forward modeling grid, calculate the sensitivity coefficient (gradient) of each unit conductivity to the observed data, in order to establish a quantitative relationship between the impact of model parameter changes on the data; Step d: Update the inversion model along the gradient direction in the discrete parameter space, and update it iteratively until the inversion objective function converges.

[0035] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0036] This application provides a tensor source-based ground-well controlled source electromagnetic joint inversion method, which specifically includes the following steps: Step S1: construct a three-dimensional electrical model including the tensor source, drilling and formation electrical parameters, and use the CSEM in the surface well to perform forward simulation on the established three-dimensional electrical model to obtain the impedance tensor and tilt response of the tensor controllable source; Step S2: Jointly invert the surface and well data to construct the objective function; Step S3: Calculate the sensitivity matrix and store the data; Step S4: Regularization method is used to constrain the inversion model, and the L-BFGS optimization algorithm improved based on the momentum method is used to invert the underground electrical structure.

[0037] More specifically, step S1 performs surface-to-well CSEM (controlled source electromagnetic method) forward modeling based on a tensor source to obtain electromagnetic data that can reflect underground electromagnetic characteristics. More specifically, the following steps are included: Step S1.1: Construct the governing equations; For CSEM forward modeling, it is assumed that the time harmonic factor , and ignoring the displacement current, the three-dimensional CSEM satisfies the vector finite element governing equation: (1) in, is the electric field strength; is the angular frequency; is the magnetic permeability; is the conductivity; is the CSEM external current source term; Step S1.2: Discretize the governing equations using the unstructured finite element method; Using the Galerkin method to discretize the governing equation (1), we obtain the weak form of the finite element method: (2) in, is a discrete area; is the unstructured tetrahedron vector basis function; The tetrahedral mesh and the corresponding vector basis function are used for discretization, and the discrete area is It is divided into a finite number of non-overlapping tetrahedral elements. Figure 1 Number the local nodes and edges of the tetrahedral elements; Formula (2) in the unit e Substitute the finite element dimension interpolation function ,in, is the approximate solution of the finite element method, is the electric field value on the edge of the unit. According to the generalized variational principle, the discretization of each unit can be obtained: (3) Among them, the expression of each unit matrix is:

[0038] Assembling the unit matrix in the above formula in the entire computational domain can obtain a large complex linear algebraic equation system: (4) in, is the overall synthesis matrix; S is the right-hand side of the equation; after imposing the Dirichlet boundary condition on formula (4), the electric field value on any unit edge can be obtained, and the magnetic field on the edge can be obtained by Faraday's theorem : (5) For the traditional scalar CSEM as shown in Figure 2(a), solving formula (5) can obtain the electromagnetic field of the ground measuring point, and can also obtain the apparent resistivity and impedance phase of the scalar controllable source response function: , (6) in, is impedance; is the apparent resistivity of the scalar controllable source response function; is the impedance phase of the scalar controllable source response function; For the tensor CSEM observation method, it is necessary to obtain the source term matrices of two mutually orthogonal electrical sources as shown in Figure 2(b), and perform two corresponding forward modelings to obtain the response function of the tensor controllable source. The impedance tensor of the tensor controllable source can be defined as: (7) Where 1 and 2 represent two sets of tensor sources. After calculating the impedance tensor, the apparent resistivity and phase of the controllable source can be obtained, and the expression is the same as formula (6). For CSEM observation methods on the surface and in wells (such as Figure 3 and Figure 4 As shown in Figure 2), it is easy to measure the electromagnetic field in the z direction at the CSEM receiving point in the well; S1.3: Description of the tipper The tensor controlled source method in this application sets up a base station on the surface to measure the horizontal magnetic field component (such as Figure 4 ), the vertical magnetic field component z is measured in the well, and the tensor controllable source tilter T is defined to characterize the conversion function from the horizontal magnetic field to the vertical direction; according to the relationship between the tilter and the magnetic field component: (8) Similar to the method of obtaining the impedance component, using two sets of perpendicular mode excitation sources, the dipole component can be expressed as: (9) Step S2: Joint surface-well CSEM inversion based on tensor source The objective function of the 3D surface and well CSEM joint inversion can be expressed as: (10) in, is the roughness matrix of the inversion model, m represents the inversion model, is the regularization factor, Fit the term to the data: , (11) in, n =1 corresponds to the CSEM data on the ground (electromagnetic field component , impedance tensor , Qingzi Or apparent resistivity and phase ), n=2 corresponds to the CSEM data in the well (electromagnetic field component Or defined tensor controllable source tilter ); is the observation data; is the predicted value; is the error data covariance matrix; is the model roughness matrix; Based on the unstructured finite element method, the formula (11) It can be expressed as: (12) in, is the number of grid cells, and are the measured data and the electromagnetic data obtained by forward modeling, e n is the data error; the data are arranged according to the real part and the imaginary part; for the model constraint , the combination of smoothness constraint and reference model constraint is adopted, and the two constraints are set as and get: (13) in, and is the regularization factor, and its value is: , (14) Among them, R is the model smoothing matrix; is the model prior constraint matrix; For the prediction model; Then the isotropic objective function of the tensor controllable source can be expressed as: (15) like Figure 5 As shown, based on the unstructured tetrahedral mesh, R in formula (14) can be solved by the difference between each element and its adjacent elements; It can be expressed as the inverse of the volume of the current model: , (16) in, For the current unit i The volume of the corresponding unit; For the current unit i The number of adjacent units; is the distance between the centers of adjacent cells; For the j The weight coefficients of adjacent units; is the model parameter difference between adjacent units; and The definitions are: , (17) Let the center point of the i-th grid cell be ( , , ),but: (18) In summary, the gradient of the objective function can be expressed as: (19) The gradient of the data fitting term can be expressed as: (20) Therefore, for the k The units are: (twenty one) in, is conjugated; An operator representing the real part of a complex number; In the solution process, these partial derivatives shown in formulas (20) and (21) can be applied to the forward equation solution In formula (4), let For a given frequency and emission source, the electric field vector The interpolated Magnetic field components of the magnetic field at the measuring point ,but: , (twenty two) Similarly, we can define , , , , similar to formula (22) are: , (twenty three) The forward equation (4) of the tensor controlled source electromagnetic method under two source modes is about Taking the derivative we get: , (twenty four) According to the above derivation, formula (21) can be rewritten as: (25) in, and Depending on the different tensor CSEM response components, for example for Corresponding and for and ; Define the orthogonal source mode under a simulation is called a forward model, then formula (25) requires four forward calculations at each frequency; among them, two forward calculations are for calculation 、 and impedance and tilt response; in addition, two right-hand-side terms are required: and The accompanying forward, where and for: , (26) set up and satisfy: , (27) From this we can define two adjoint forward models: , (28) The complete calculation of formula (25) can be obtained by formula (28); compared with the data fitting term , model constraints It can be directly analyzed to obtain: (29) (30) Step S4: Calculation and storage of sensitivity The sensitivity of the corresponding inversion data is represented by J. Assume that the forward data set ,in In order to obtain spatial interpolation operators for different types of data, they can be selected according to the specific data type; according to formulas (27) and (28), the data is about the isotropic conductivity component The sensitivity is: , (31) Among them, the sensitivity information can be obtained by the adjoint forward formula (28); Step S5: L-BFGS optimization algorithm improved based on momentum method In the gradient optimization method, the search direction of the model is ; For the joint inversion of three-dimensional data, the L-FBGS algorithm obtains an approximate , to reduce memory; at this time, only the gradient of the objective function needs to be taken: , (32) in, and can be directly analyzed and calculated, and Constructed by formula (31), the three-dimensional joint inversion model is updated as follows: (33) The use of L-BFGS optimization algorithm can reduce the inversion memory requirements, thereby achieving three-dimensional large-scale joint inversion calculations. Figure 6 The figure shows the process of 3D electromagnetic inversion starting from a random model and descending along the gradient method trajectory. The inversion starts from the initial model and enters the green gully. In order to reach the global extreme point, the gully must be crossed, which is a series of local minima in the inversion. The objective function oscillates repeatedly in the local minimum interval, and the curvature of the descent is pathological, rather than quickly reaching the global minimum along the optimal descent trajectory. For the traditional gradient method inversion, due to Gradient component ratio in 1 direction 2 direction is much larger, and the inversion drops extremely slowly near the local minimum, causing the 3D inversion to be forced to terminate at the local minimum; The problem of three-dimensional inversion falling into local minima is very similar to the training stagnation problem in machine learning. In machine learning, heuristic algorithms are often used to guide the optimization process. This application introduces the momentum method in the model update of three-dimensional joint inversion. It can be compared to momentum and the model update in L-BFGS iteration is modified as follows: (34) Among them, the momentum factor V and learning rate It is necessary to reasonably select according to the rules summarized by the inversion of theoretical and measured data; the model update after the momentum method is improved should not only consider the gradient of the current objective function, but also use the previous gradient to estimate its momentum; According to formula (32), the subsequent The update performs a weighted summation of the gradient information of the previous objective function, and the closer the gradient, the higher the weight; combined with Figure 7 , decompose the objective function gradient of each iteration into 1 and In the 2nd direction, after improvement in multiple iterative updates, The gradient component in the 1 direction is continuously reduced in the weighted sum, while The component in the 2-direction is strengthened. This shows that the model update based on the momentum method can accumulate Gradient components in 2 directions, cut The component in the 1 direction can effectively guide the inversion algorithm based on the gradient method to proceed along the optimal descent direction, thereby preventing the three-dimensional joint inversion from falling into the local minimum.

[0039] Compared with the existing technology, this application has the following advantages: Compared with the traditional scalar controlled source electromagnetic method, the multi-source tensor controlled source electromagnetic method adopted in this application can simultaneously excite and receive electromagnetic field components in multiple directions, thereby obtaining richer underground structure information.

[0040] Unlike traditional regular grids, this application uses unstructured grids to divide the study area, which can more flexibly construct the shape of terrain and underground anomalies. At the same time, the use of unstructured finite elements can save memory and improve calculation speed.

[0041] Through joint inversion, combined with controlled source electromagnetic data on the surface and in the well, the lateral and vertical resolution of exploration is improved, the multi-solution of inversion is reduced, and the inversion results are more reliable.

[0042] This application uses the L-BFGS optimization algorithm to reduce the inversion memory requirements, and introduces the momentum method in the model update of the three-dimensional joint inversion to achieve faster convergence.

[0043] The data acquisition efficiency of the tensor source in this application is high, and the joint inversion method can quickly process multi-source data, shorten the exploration cycle and reduce costs.

[0044] Example 1 A horizontal surface model is set to test the validity of the ground and well data, as shown in Figure 8(a) at 100 A single well is set in the uniform half-space with the wellhead located at the ground (-2.5 km, 0 km, 0 km). As shown in Figure 8(b), 35 well measurement points are set vertically from -330 m to -3050 m. A low-resistance anomaly is set below the center of the measurement area (0 km, 0 km, 0 km). The top surface of the anomaly is buried at a depth of 1 km and the resistivity is 10 , with a size of 2km 2km 1km; as shown in Figure 8 (b) above the anomaly, 169 measuring points are evenly arranged with the coordinate origin as the center, with a line spacing and a point spacing of 0.5km, and a total of 13 measuring lines; the orthogonal transmitting source tensor source is arranged along the x and y directions respectively, with the center point coordinates of the transmitting source (6km, 0km, 0km), the length of the transmitting source is 1km, and the transmitting current is 30A; in order to realize the measurement of the dipole data, this application sets the base station for measuring the horizontal magnetic field at (20km, 0km, 0km), and sets the measurement frequency of the tensor controllable source to 1000Hz, 100Hz, 10Hz and 1Hz; for the forward response of the tensor controllable source of the model, the tensor impedance data of the ground and the dipole data in the well are used, and 5% noise is added to simulate the measured tensor controllable source electromagnetic method data on the ground and in the well; the entire calculation area of the theoretical model contains 333695 units; the inversion area is 8km 8km 4km, the initial model is 100 The half space of the termination target RMS is 1.05; the prior model is set to 100 half-space; set the initial regularization factor during the inversion process is 0.01, additional regularization factor and 1 and 1 respectively; this application adopts the cooling principle to change , when the RMS decrease of adjacent iterations is less than 2% during the iteration process, the proportional coefficient is reduced by 0.9 ; The inversion results are shown in Figure 9 (a) and Figure 9 (b). The resistivity of the low-resistance anomaly body obtained by the joint inversion of surface and well data is about 10 , and the spatial distribution of low-resistance anomalies can accurately reflect the electrical structure of the real underground model without redundant structures; this proves the effectiveness of the joint inversion of ground and well controlled source electromagnetic data based on isotropic media in this application.

[0045] According to Figures 10(a) to 10(c), the inversion is terminated after 116 iterations, reaching convergence. The data fitting term decreases from 352.8 to 4.5. The decrease is fast in the early stage of the iteration, and then the decrease rate begins to slow down until the inversion converges. The model constraint term and At the beginning of the inversion, it is very small and close to zero. After a sharp increase, it slowly increases and then gradually decreases, and then slowly increases to a stable state. As can be seen from Figure 10 (b), the maximum value of this application in the iterative process is is 3, and search step size It is 1 in most iterations, indicating that the L-BGFS algorithm improved based on the momentum method approximates the inverse matrix of the Hessian matrix in most iterations and has approached the true value. A fixed unit step size can satisfy the Wolfe condition. Only one forward calculation is required in the iteration process, which effectively reduces the number of forward calculations and improves the inversion efficiency. Figure 10 (c) shows that the RMS finally drops to 2.02, and the regularization factor does not decrease during the iteration process. Figures 10 (a) to 10 (c) illustrate that the joint inversion algorithm based on isotropic ground and well controlled source electromagnetic methods in this application has certain stability and efficiency.

[0046] Example 2 The theoretical model of controlled source electromagnetic data fracturing monitoring in a 3D surface well is shown in Figure 11(a) and Figure 11(b). A resistivity of 150 is set at 1200m-1600m in the uniform half space. The center of the anomaly model is (0m, 0m, -1400m) and the size is 2km 2km 0.4km; set a resistivity of 20 in the 2500m~3500m layer. The anomaly model is centered at (-2000km, 0m, 0km). As shown in Figures 11(a) and 11(b), 35 well measurement points are set vertically from -330m to -3050m, penetrating the anisotropic body at the bottom. 49 measurement points are evenly arranged at the center of the survey area as the coordinate origin, with a line spacing and point spacing of 1km, for a total of 7 survey lines. The transmitter is an orthogonal tensor source, arranged along the x and y directions respectively. The center point coordinates of the transmitter are (6km, 0km, 0km), the transmitter length is 1km, and the transmitter current is 30A. The measurement frequency is 0.1 to 100Hz, with 11 frequency points taken at equal intervals. 5% noise is added to the forward response tensor impedance and well dip sub-data of the model's tensor controllable source to simulate the measured data. The inversion area is 8km 8km 4km, the initial model is 100 The half space of the termination target RMS is 1.05; the prior model is set to 100 In order to compare the effectiveness of the joint inversion of surface and well data, the 3D inversion results of the surface data alone are set as the comparison model.

[0047] Figures 12(a) to 12(f) show the anisotropic horizontal resistivity results of the surface data inversion alone and the surface-well data joint inversion. From the analysis of Figures 12(a) and 12(b), we can roughly invert a high-resistance and low-resistance anomaly area for the surface data inversion results. The low-resistance anomaly has a higher resolution, and the high-resistance anomaly is about 120 ~150 , but the regional boundary of the anomaly is not obvious; for the joint inversion results of surface and well data, obvious low-resistance anomaly areas and some local high-resistance areas can be inverted, among which the regional boundary of the low-resistance anomaly is obvious, and the low-resistance anomaly is about 25 The similarities between the two inversions for the xz slice are that they can highly resolve low-resistivity anomalies, while the resolution for high-resistivity anomalies is very low. The differences between the two inversions for the xz slice are that the depths of both high- and low-resistivity anomalies obtained by the surface inversion are higher than their true locations, while the joint inversion of surface and borehole data can obtain more accurate depths of the subsurface anomalies. Analysis of Figures 12(c) and 12(d) shows that the false low-resistivity anomaly inverted above the true bottom anomaly exhibits significant stretching in the y direction, and the boundary of the high-resistivity anomaly region is not clear, but it exceeds the correct range. Although the joint inversion results for the surface and borehole data do not clearly invert the location of the high-resistivity anomaly, no false low-resistivity anomaly appears. Analysis of Figures 12(e) and 12(f) shows that the surface data inversion results obtain a more accurate anomaly range. A comprehensive analysis of Figures 12(a) to 12(f) demonstrates that the inclusion of borehole data improves the inversion depth and resolution, and the resistivity values of the low-resistivity anomaly obtained are closer to the true values.

[0048] The following describes the tensor source-based ground-well controlled source electromagnetic method joint inversion system provided in this application. The tensor source-based ground-well controlled source electromagnetic method joint inversion system described below and the tensor source-based ground-well controlled source electromagnetic method joint inversion method described above can be referenced to each other.

[0049] The present application provides a tensor source-based ground-well controlled source electromagnetic method joint inversion system, comprising: The forward modeling module is used to construct a three-dimensional electrical model that includes tensor sources, drilling electrical parameters, and formation electrical parameters. The 3D electrical model is forward modeled using CSEM in a surface well to obtain the impedance tensor and tilt of the tensor controllable source. The objective function construction module is used to combine the impedance tensors and dipoles obtained from the forward modeling module, and to construct the three-dimensional surface and well CSEM joint inversion objective function and the gradient of the inversion objective function using the model roughness matrix and data fitting terms. The inversion module is used to solve the gradient of the inversion objective function and invert the underground electrical structure by using the L-BFGS optimization algorithm improved based on the momentum method.

[0050] Further preferably, the forward modeling module includes: A control equation construction unit is used to construct the vector finite element control equation based on the electric field intensity, angular frequency, magnetic permeability, electrical conductivity and CSEM external current source terms; A first data processing unit is used to discretize the vector finite element governing equations using an unstructured finite element method, interpolate the electric field values within the finite element units and then assemble them in the entire computational domain to obtain a complex linear algebraic equation; The electromagnetic field acquisition unit is used to obtain the electric field and magnetic field values on the edges of any unit after adding the Dirichlet boundary to the complex linear algebraic equation; The forward data acquisition unit is used to obtain the impedance tensor and the tensor controllable source tilter of the tensor controllable source based on the electric field value and the magnetic field value obtained by the electromagnetic field acquisition unit based on the tensor CSEM observation method.

[0051] Further preferably, the objective function building module includes: A first objective function construction unit is configured to construct an inversion objective function based on the inversion model roughness matrix and a data fitting term, wherein the data fitting term includes ground CSEM data and well CSEM data; The second data processing unit is used for performing mesh division and mesh representation on the data fitting term in the inversion objective function by using the unstructured finite element method; a third data processing unit, configured to represent a roughness matrix using a smoothness constraint and a reference model constraint; A fourth data processing unit is used for dividing the roughness matrix into unstructured tetrahedral grids and then performing gridding representation; The first objective function construction unit is used to update the inversion objective function based on the data fitting term and the roughness matrix represented by the grid, and obtain the gradient representation of the inversion objective function.

[0052] Further preferably, the inversion objective function in the objective function construction module is:

[0053] in, , , ; , ; is the roughness matrix of the inversion model; is the data fitting term; m represents the inversion model; 、 、 、 and is the regularization factor; n =1 corresponds to the CSEM data on the ground; n =2 corresponds to the CSEM data in the well; the CSEM data includes the impedance tensor of the tensor controllable source and the tensor controllable source tilter; is the observed CSEM data; CSEM data obtained by forward modeling in step S1; is the error data covariance matrix; R is the inversion model smoothing matrix; is the prior constraint matrix of the inversion model; Inversion model for forward prediction.

[0054] Further preferably, the inversion model updating method in the L-BFGS iteration in the inversion module is:

[0055] in, is the update amount of the inversion model; k is the number of iterations; m is the inversion model; is the learning rate; V is the momentum factor; g is the gradient of the inversion objective function.

[0056] It is understandable that the detailed functional implementation of each of the above units / modules can be found in the introduction of the aforementioned method embodiment, and will not be repeated here.

[0057] It should be understood that the above-mentioned system is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the system are similar to those described in the above-mentioned method. The working process of the system can refer to the corresponding process in the above-mentioned method and will not be repeated here.

[0058] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the scope of protection of the present application.

Claims

1. A tensor source-based ground-well controlled source electromagnetic joint inversion method, characterized in that: The following steps are involved: Step S1: constructing a three-dimensional electrical model including a tensor source, drilling electrical parameters, and formation electrical parameters, and performing forward modeling on the established three-dimensional electrical model using a CSEM in a surface well to obtain the impedance tensor and tilt response of the tensor controllable source; Step S2: Combining the impedance tensor and dipole response of the surface and well obtained in step S1, constructing the three-dimensional surface and well CSEM joint inversion objective function and the gradient of the inversion objective function using the model roughness matrix and the data fitting term; Step S3: Using the L-BFGS optimization algorithm modified based on the momentum method to solve the gradient of the inversion objective function, invert the underground electrical structure.

2. The underground-well controlled source electromagnetic method joint inversion method according to claim 1 is characterized in that: Step S1 specifically includes the following steps: Step S1.1: Construct the vector finite element governing equations in the three-dimensional electrical model based on the electric field intensity, electromagnetic wave angular frequency, magnetic permeability, electrical conductivity, and CSEM applied current source term; Step S1.2: Discretize the vector finite element governing equations, interpolate the electric field values within the finite element and then assemble them in the entire computational domain to obtain a complex linear algebraic equation; Step S1.3: After adding the Dirichlet boundary to the complex linear algebraic equation, obtain the electric field and magnetic field values on any element edge; Step S1.4: Based on the tensor CSEM observation method, the impedance tensor and the tensor controllable source tilter of the tensor controllable source are obtained according to the electric field value and the magnetic field value obtained in step S1.

3.

3. The underground-well controlled source electromagnetic method joint inversion method according to claim 1 or 2, characterized in that: Step S2 specifically includes the following steps: Step S2.1: Constructing an inversion objective function based on the inversion model roughness matrix and data fitting terms; wherein the data fitting terms include surface CSEM data and well CSEM data; Step S2.2: Discretize the data fitting term in the inversion objective function and calculate the data residual contribution value in each grid cell through the interpolation basis function; Step S2.3: Construct the roughness matrix using the smoothness constraint and the reference model constraint; Step S2.4: performing finite element discretization on the roughness matrix in step S2.3; Step S2.5: Combine the data residual and the constraint term to calculate the gradient of the inversion objective function, and continuously update the inversion model according to the gradient direction until the inversion objective function converges.

4. The underground-well controlled source electromagnetic method joint inversion method according to claim 2 is characterized in that: The inversion objective function in step S2.1 is: in, , , ; , ; is the roughness matrix of the inversion model; is the data fitting term; m is the inversion model; 、 、 、 and is the regularization factor; n =1 corresponds to the CSEM data on the ground; n =2 corresponds to the CSEM data in the well; the CSEM data includes the impedance tensor of the tensor controllable source and the tensor controllable source tilter; is the observed CSEM data; CSEM data obtained by forward modeling in step S1; is the error data covariance matrix; R is the inversion model smoothing matrix; is the prior constraint matrix of the inversion model; Inversion model for forward prediction.

5. The underground-well controlled source electromagnetic method joint inversion method according to any one of claims 1 to 4, characterized in that: The inversion model update method in L-BFGS iteration is: in, is the update amount of the inversion model; k is the number of iterations; m is the inversion model; is the learning rate; V is the momentum factor; g is the gradient of the inversion objective function.

6. A tensor source-based ground-well controlled source electromagnetic method joint inversion system, characterized by: include: The forward modeling module is used to construct a three-dimensional electrical model that includes tensor sources, drilling electrical parameters, and formation electrical parameters. The 3D electrical model is forward modeled using CSEM in a surface well to obtain the impedance tensor and inclination of the tensor controllable source. The objective function construction module is used to combine the impedance tensors and dipoles obtained from the forward modeling module, and to construct the three-dimensional surface and well CSEM joint inversion objective function and the gradient of the inversion objective function using the model roughness matrix and data fitting terms. The inversion module is used to solve the gradient of the inversion objective function and invert the underground electrical structure using the L-BFGS optimization algorithm modified based on the momentum method.

7. The underground-well controlled source electromagnetic method joint inversion system according to claim 6, characterized in that: The forward modeling module includes: The control equation construction unit is used to construct the vector finite element control equations in the three-dimensional electrical model based on the electric field intensity, electromagnetic wave angular frequency, magnetic permeability, electrical conductivity and CSEM external current source terms; A first data processing unit is used to discretize the vector finite element governing equations using an unstructured finite element method, interpolate the electric field values within the finite element units and then assemble them in the entire computational domain to obtain a complex linear algebraic equation; The electromagnetic field acquisition unit is used to obtain the electric field and magnetic field values on the edges of any unit after adding the Dirichlet boundary to the complex linear algebraic equation; The forward data acquisition unit is used to obtain the impedance tensor and the tensor controllable source tilter of the tensor controllable source based on the electric field value and the magnetic field value obtained by the electromagnetic field acquisition unit based on the tensor CSEM observation method.

8. The underground-well controlled source electromagnetic method joint inversion system according to claim 6 or 7, characterized in that: The objective function building blocks include: A first objective function construction unit is configured to construct an inversion objective function based on the inversion model roughness matrix and a data fitting term, wherein the data fitting term includes ground CSEM data and well CSEM data; A second data processing unit is used to perform finite element discretization on the data fitting term in the inversion objective function; a third data processing unit, configured to represent a roughness matrix using a smoothness constraint and a reference model constraint; a fourth data processing unit, configured to perform finite element discretization on the roughness matrix; The first objective function construction unit calculates the gradient of the inversion objective function and continuously updates the inversion model according to the gradient direction until the inversion objective function converges.

9. The underground-well controlled source electromagnetic method joint inversion system according to claim 6, characterized in that: The inversion objective function in the objective function building module is: in, , , ; , ; is the roughness matrix of the inversion model; is the data fitting term; m represents the inversion model; 、 、 、 and is the regularization factor; n =1 corresponds to the CSEM data on the ground; n =2 corresponds to the CSEM data in the well; the CSEM data includes the impedance tensor of the tensor controllable source and the tensor controllable source tilter; is the observed CSEM data; CSEM data obtained by forward modeling in step S1; is the error data covariance matrix; R is the inversion model smoothing matrix; is the prior constraint matrix of the inversion model; Inversion model for forward prediction.

10. The underground-well controlled source electromagnetic method joint inversion system according to any one of claims 6 to 9, characterized in that: The inversion model update method in the L-BFGS iteration in the inversion module is: in, is the update amount of the inversion model; k is the number of iterations; m is the inversion model; is the learning rate; V is the momentum factor; g is the gradient of the inversion objective function.

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