Joint inversion method and system for borehole controlled source electromagnetic method based on tensor source

Abstract

The application belongs to the technical field of geophysical exploration, and specifically discloses a joint inversion method and system for geohole controlled source electromagnetic method based on a tensor source, which comprises the following steps: using the CSEM in the ground and the well to perform forward modeling on the established three-dimensional electrical model to obtain impedance tensors and tilts of the tensor controlled source; using a model roughness matrix and a data fitting term to construct a three-dimensional ground and well CSEM joint inversion objective function and a gradient of the inversion objective function; and using an L-BFGS optimization algorithm based on a momentum method to solve the gradient of the inversion objective function and to invert the underground electrical structure. Through joint inversion, the application combines the controlled source electromagnetic data in the ground and the well, improves the lateral and longitudinal resolution of exploration, reduces the multi-solution property of inversion, and makes the inversion result more reliable.

Description

Technical Field

[0001] This application belongs to the field of geophysical exploration technology, and more specifically, relates to a joint inversion method and system based on tensor source controlled source electromagnetic method for wells. Background Technology

[0002] With the large-scale exploitation of oil, gas, and mineral resources in recent years, shallow resources are gradually being depleted, and the supply situation of oil, gas, minerals, and important metals is severe. Exploring deeper reservoirs for oil, gas, and minerals has become an inevitable trend. However, due to the complexity of exploration targets, traditional single geophysical methods struggle to overcome the multiple solutions inherent in inversion, exhibiting certain limitations and failing 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 utilizes an artificial emission source for excitation. It is widely used in geological exploration, environmental monitoring, and hydrogeological research. This method involves exciting a signal on the ground, recording the electromagnetic response using a receiving array, and then inverting the recorded signal to detect subsurface electrical structures (Zhong et al., 2024). CSEM has advantages such as strong anti-interference capability and large detection depth, but due to the skin effect, the electromagnetic field intensity decreases exponentially with depth, reducing vertical resolution (Zhang et al., 2024). Borehole CSEM data can appropriately reduce the ambiguity problem that occurs during the inversion of surface CSEM data. The measurement points of the vertical magnetic field are closer to the distribution area of ​​subsurface structures, which helps improve the accuracy of local stratum identification. However, borehole data is largely dependent on the drilling location and also has limitations (Gao, 2023).

[0004] CSEMs can be categorized into three types based on the emission source and the number of observed electromagnetic field components: scalar, vector, and tensor. A scalar CSEM uses a single emission source and acquires two orthogonal tangential components of the electromagnetic field. , or , ); Vector CSEM uses a single emission source and acquires 5 electromagnetic field components ( , , , , Tensor CSEM uses two sets of emission sources and acquires five electromagnetic field components from each emission source. , , , , ), a total of 10 components. Limited by the distribution range of the emission source signal, vector observation is rarely used (Wang Tao et al., 2017), and it is difficult to recover deep complex electrical structure. All the time, CSEM mainly adopts the scalar observation mode of single source excitation. In this mode, only scalar impedance can be obtained by measuring electromagnetic field components, so this method is only suitable for one-dimensional geological structure exploration, and the effect is relatively ideal. However, in actual exploration, the underground electrical structure often shows complex two-dimensional or three-dimensional characteristics. This means that the electrical parameter not only changes in the vertical direction, but also changes significantly in the dip and horizontal directions, and the electrical parameter shows a tensor form. In this case, the traditional scalar CSEM method cannot meet the exploration needs.

[0005] Through the above analysis, the problems and defects of the prior art are that the current single geophysical data inversion is mostly used, and the single scale measurement data cannot accurately explore the underground electrical structure distribution. The existing technology cannot effectively identify the shape and position of complex underground oil and gas reservoirs and mineral distribution, does not meet the fine inversion requirements, and leads to the increase of the cost of oil and gas exploitation and mineral development. SUMMARY

[0006] In view of the defects of the prior art, the purpose of the present application is to provide a joint inversion method and system of borehole controlled source electromagnetic method based on tensor source, aiming at solving the multi-solution problem of the existing single ground or borehole electromagnetic method, which cannot overcome the geophysical problem, leading to the problem that the electrical distribution of underground medium cannot be fully reflected.

[0007] To achieve the above purpose, in a first aspect, the present application provides a joint inversion method of borehole controlled source electromagnetic method based on tensor source, comprising the following steps:

[0008] Step S1: A three-dimensional electrical model containing tensor source, drilling electrical parameters and formation electrical parameters is constructed, and the established three-dimensional electrical model is forward calculated using ground and borehole CSEM to obtain impedance tensor of tensor controlled source and dip of tensor controlled source;

[0009] Step S2: The impedance tensor and dip obtained in step S1 are combined to construct the inversion objective function and the gradient of the inversion objective function of the three-dimensional ground and borehole CSEM joint inversion, using the model roughness matrix and the data fitting term;

[0010] Step S3: The gradient of the inversion objective function is solved by using the L-BFGS optimization algorithm based on the momentum method, and the underground electrical structure is inverted.

[0011] Further preferably, step S1 specifically comprises the following steps:

[0012] Step S1.1: constructing a vector finite element control equation in a three-dimensional electrical property model based on an electric field intensity, an electromagnetic wave angular frequency, a magnetic permeability, an electric conductivity, and a CSEM impressed current source term;

[0013] Step S1.2: discretizing the vector finite element control equation, interpolating an electric field value in a finite element unit, and assembling the entire calculation domain to obtain a complex linear algebraic equation;

[0014] Step S1.3: obtaining an electric field value and a magnetic field value on an arbitrary unit edge after adding a Dirichlet boundary to the complex linear algebraic equation;

[0015] Step S1.4: obtaining a tensor controlled source impedance tensor and a tensor controlled source tilt based on a tensor CSEM observation mode and the electric field value and the magnetic field value obtained in step S1.3.

[0016] Further preferably, step S2 specifically includes the following steps:

[0017] Step S2.1: constructing an inversion objective function based on an inversion model roughness matrix and a data fitting term; wherein the data fitting term includes CSEM data on the ground and CSEM data in a well;

[0018] Step S2.2: discretizing the data fitting term in the inversion objective function, and calculating a data residual contribution value in each grid unit through an interpolation basis function;

[0019] Step S2.3: representing the roughness matrix by using a smoothness constraint and a reference model constraint;

[0020] Step S2.4: performing finite element discretization on the roughness matrix in step S2.3;

[0021] Step S2.5: jointly calculating a gradient of the inversion objective function by using the data residual and the constraint term, and constantly updating 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:

[0022]

[0023] wherein, , , ; , ; is an inversion model roughness matrix; is a data fitting term; m is an inversion model; 、 、 、 and is a regularization factor; n=1 corresponds to the ground CSEM data; n =2 corresponds to the well CSEM data; the CSEM data includes impedance tensor of the tensor source and the dip of the tensor source; is the observed CSEM data; is the CSEM data obtained by the forward step S1; is the error data covariance matrix; R is the inversion model smoothing matrix; is the inversion model prior constraint matrix; is the inversion model predicted by the forward prediction.

[0024] Further preferably, the inversion model updating method in the L-BFGS iteration is:

[0025]

[0026] wherein, is the update amount of the inversion model; k is the iteration number; m is the inversion model; is the learning rate; V is the momentum factor; g is the gradient of the inversion objective function.

[0027] In a second aspect, the application provides a tensor source-based joint inversion system for borehole CSEM, comprising:

[0028] A forward module is configured to construct a three-dimensional electrical model including a tensor source, a drilling electrical parameter, and a formation electrical parameter, perform forward calculation on the established three-dimensional electrical model using ground and well CSEM, and obtain impedance tensor of the tensor source and the dip of the tensor source;

[0029] An objective function construction module is configured to combine the impedance tensor and the dip obtained by the forward module to construct a three-dimensional ground and well CSEM joint inversion objective function and the gradient of the inversion objective function using a model roughness matrix and a data fitting term;

[0030] An inversion module is configured to solve the gradient of the inversion objective function using an L-BFGS optimization algorithm improved based on a momentum method, and to invert the underground electrical structure.

[0031] Further preferably, the forward module comprises:

[0032] A control equation construction unit is configured to construct a vector finite element control equation in the three-dimensional electrical model based on an electric field intensity, an electromagnetic wave angular frequency, a magnetic permeability, an electrical conductivity, and a CSEM external current source term;

[0033] A first data processing unit is configured to discretize the vector finite element control equation using a non-structural finite element method, interpolate the electric field value in the finite element unit, and assemble the entire calculation domain to obtain a complex linear algebraic equation.

[0034] an electromagnetic field acquisition unit, configured to acquire electric field values and magnetic field values on edges of any unit after adding Dirichlet boundary conditions in a complex linear algebraic equation;

[0035] a forward data acquisition unit, configured to acquire impedance tensors of tensor controlled sources and tensor controlled source tilts based on the electric field values and the magnetic field values acquired by the electromagnetic field acquisition unit according to a tensor CSEM observation mode.

[0036] Further preferably, the objective function construction module comprises:

[0037] a first objective function construction unit, configured to construct an inversion objective function according to the inversion model roughness matrix and a data fitting term; wherein the data fitting term comprises CSEM data on the ground and CSEM data in the well;

[0038] a second data processing unit, configured to discretize the data fitting term in the inversion objective function;

[0039] a third data processing unit, configured to represent the roughness matrix by using smoothness constraints and reference model constraints;

[0040] a fourth data processing unit, configured to perform finite element discretization on the roughness matrix;

[0041] The first objective function construction unit calculates the gradient of the inversion objective function and constantly updates the inversion model in the direction of the fastest gradient descent until the inversion objective function converges.

[0042] Further preferably, the inversion objective function in the objective function construction module is:

[0043]

[0044] wherein, , , ; , ; is the inversion model roughness matrix; is the data fitting term; m represents the inversion model; 、 、 、 and is a regularization factor; n =1 corresponds to CSEM data on the ground; n =2 corresponds to CSEM data in the well; the CSEM data comprises impedance tensors of tensor controlled sources and tensor controlled source tilts; is the observed CSEM data; is the CSEM data obtained by forward calculation in step S1. is the error data covariance matrix; R is the inversion model smoothing matrix; is the inversion model prior constraint matrix; is the forward predicted inversion model.

[0045] Further preferably, the inversion model updating method in the L-BFGS iteration in the inversion module is:

[0046]

[0047] wherein, is the update amount of the inversion model; k is the iteration number; m is the inversion model; is the learning rate; V is the momentum factor; g is the gradient of the inversion objective function.

[0048] In a third aspect, the present application provides an electronic device, comprising: at least one memory for storing a program; at least one processor for executing the program stored in the memory, and when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation manner of the first aspect.

[0049] In a fourth aspect, the present application provides a computer readable storage medium, and the computer readable storage medium stores a computer program, and when the computer program is run on a processor, the processor is configured to execute the method described in the first aspect or any possible implementation manner of the first aspect.

[0050] In a fifth aspect, the present application provides a computer program product, and when the computer program product is run on a processor, the processor is configured to execute the method described in the first aspect or any possible implementation manner of the first aspect.

[0051] It can be understood that the beneficial effects of the above-mentioned second aspect to fifth aspect can be referred to the related description in the first aspect, and will not be repeated here.

[0052] Overall, compared with the prior art, the above technical solutions conceived by the present application have the following beneficial effects:

[0053] Compared with the traditional scalar controllable source electromagnetic method, the present application provides a joint inversion method of tensor source ground well controllable source electromagnetic method, and the multi-source tensor controllable source electromagnetic method can simultaneously excite and receive multi-directional electromagnetic field components to obtain more abundant underground structure information. Through joint inversion, the controllable source electromagnetic data in the ground and the well are combined to improve the lateral and longitudinal resolution of exploration, reduce the multi-solution of inversion, and make the inversion result more reliable.

[0054] Different from the traditional regular grid, the application provides a joint inversion method of tensor source-based surface-borehole controlled source electromagnetic method, which adopts unstructured grid to subdivide the research area, can more flexibly construct the shape of terrain and underground abnormal body, and can save memory and improve calculation rate by using non-structured finite element.

[0055] The application uses the L-BFGS optimization algorithm to reduce the inversion memory requirement, and introduces the momentum method in the model updating of three-dimensional joint inversion, so that the convergence is faster.

[0056] The data acquisition efficiency of the tensor source in the application is high, the joint inversion method can quickly process multi-source data, shorten the exploration period and reduce the cost. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 is a schematic diagram of a tetrahedral unit node and edge provided by an embodiment of the application;

[0058] Figure 2(a) is a schematic diagram of a scalar mode of a surface CSEM device provided by an embodiment of the application;

[0059] Figure 2(b) is a schematic diagram of a tensor mode of a surface CSEM device provided by an embodiment of the application;

[0060] Figure 3 is a schematic diagram of a scalar mode of a surface and borehole CSEM device provided by an embodiment of the application;

[0061] Figure 4 is a schematic diagram of a tensor mode of a surface and borehole CSEM device provided by an embodiment of the application;

[0062] Figure 5 is a schematic diagram of a non-structured tetrahedral network model constraint term plane provided by an embodiment of the application;

[0063] Figure 6 is a schematic diagram of a three-dimensional electromagnetic method inversion objective function descent provided by an embodiment of the application;

[0064] Figure 7 is a schematic diagram of a local minimum zone provided by an embodiment of the application;

[0065] Figure 8(a) is a schematic diagram of an x-z section of a surface and borehole tensor CSEM theoretical model provided by Embodiment 1 of the application;

[0066] Figure 8(b) is a schematic diagram of a y-y section of a surface and borehole tensor CSEM theoretical model provided by Embodiment 1 of the application;

[0067] Figure 9(a) is an x-z plane slice diagram of a final inversion result provided by Embodiment 1 of the application;

[0068] Figure 9(b) is an x-y plane slice of the final inversion result provided by Embodiment 1 of the present application;

[0069] Figure 10(a) is an inversion convergence plot of the fitting term , the model constraint term and provided by Embodiment 1 of the present application;

[0070] Figure 10(b) is an inversion convergence plot of and the search step size provided by Embodiment 1 of the present application;

[0071] Figure 10(c) is an inversion convergence plot of the RMS and the regularization factor provided by Embodiment 1 of the present application;

[0072] Figure 11(a) is a schematic diagram of an x-z slice of a tensor CSEM model provided by Embodiment 2 of the present application;

[0073] Figure 11(b) is a schematic diagram of an x-y slice of a tensor CSEM model provided by Embodiment 2 of the present application;

[0074] Figure 12(a) is an x-z plane slice at y=0m of the surface data inversion result provided by Embodiment 2 of the present application;

[0075] Figure 12(b) is an x-y plane slice at y=0m of the joint surface and borehole data inversion result provided by Embodiment 2 of the present application;

[0076] Figure 12(c) is an x-y plane slice at z=1400m of the surface data inversion result provided by Embodiment 2 of the present application;

[0077] Figure 12(d) is an x-y plane slice at z=1400m of the joint surface and borehole data inversion result provided by Embodiment 2 of the present application;

[0078] Figure 12(e) is an x-y plane slice at z=3000m of the surface data inversion result provided by Embodiment 2 of the present application;

[0079] Figure 12(f) is an x-y plane slice at z=3000m of the joint surface and borehole data inversion result provided by Embodiment 2 of the present application. DETAILED DESCRIPTION

[0080] In order to make the purposes, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and not used to limit the present application.

[0081] The term "and / or" used herein is used to describe an association relationship of associated objects, which means that there can be three relationships, for example, A and / or B can mean that A exists alone, A and B exist together, and B exists alone. The symbol " / " used herein means that the associated objects are or, for example, A / B means A or B.

[0082] The terms "first" and "second" and the like in the description and claims herein are used to distinguish different objects, and are not used to describe a specific order of the objects.

[0083] In the embodiments of the present application, the words "exemplary" or "for example" are used to mean serving as an example, instance, or illustration. Any embodiment or design described herein as "exemplary" or "for example" should not be construed as being more preferred or advantageous than other embodiments or designs. Rather, the use of "exemplary" or "for example" is intended to present concepts in a concrete manner.

[0084] The present application provides a joint inversion method of borehole controlled source electromagnetic method based on tensor source, which involves two methods, forward and inversion, which will be described in detail as follows:

[0085] Forward: from model to simulation data, that is, according to the electrical information and field source information of the model, the electromagnetic response is calculated; the specific steps are as follows:

[0086] Step a: define the electrical parameters of the underground medium, build a forward model, and use unstructured tetrahedral mesh for partitioning;

[0087] Step b: build control equations, that is, the electromagnetic field relationship satisfied by the built forward model;

[0088] Step c: use vector basis functions to discretize the control equation, define the interpolation function of the electric field E on the grid edge, and convert the continuous equation into a linear equation set;

[0089] Step d: apply boundary conditions, solve the linear equation set, and obtain the simulation data (such as impedance tensor and dip) of the forward.

[0090] Inversion: from data to underground model, that is, according to the observed data to infer the distribution of underground electrical parameters, the specific steps are as follows:

[0091] Step a: set the initial conductivity model for inversion (start from the initial model in subsequent iterations), define the inversion grid (usually consistent with the forward grid);

[0092] Step b: construct the objective function, including the data fitting term (measure the error between the forward simulation data and the observed data) and the model constraint term (control the complexity of the model, such as smoothness); the data fitting term discretization is to map the residual between the observed data and the forward simulation results to the grid cells, and to convert the continuous data error into discrete cell contribution values; the model constraint term discretization is to discretize the constraint term on the grid into a sparse matrix, realizing the numerical calculation of the regularization term;

[0093] Step c: based on the discretized field values of the forward grid, calculate the sensitivity coefficient (gradient) of each cell conductivity to the observed data, the purpose is to establish the quantitative relationship between the change of model parameters and the influence on the data;

[0094] Step d: update the inversion model in the direction of the gradient in the discrete parameter space, and update through continuous iteration until the inversion objective function converges.

[0095] The embodiments of the present application will be described below in conjunction with the drawings in the embodiments of the present application.

[0096] The present application provides a joint inversion method based on tensor source for surface-well controlled source electromagnetic method, specifically including the following steps:

[0097] Step S1: construct a three-dimensional electrical property model containing tensor source, well and formation electrical property parameters, use the surface-well CSEM to perform forward simulation on the established three-dimensional electrical property model, and obtain the impedance tensor and tilt response of the tensor controlled source;

[0098] Step S2: joint inversion of surface and well data to construct an objective function;

[0099] Step S3: calculate the sensitivity matrix and store the data;

[0100] Step S4: use a regularization method to constrain the inversion model, and use the L-BFGS optimization algorithm improved based on the momentum method to invert the underground electrical property structure.

[0101] More specifically, step S1 performs surface-well CSEM (controlled source electromagnetic method) forward based on tensor source to obtain electromagnetic data that can reflect the underground electromagnetic characteristics; more specifically, it includes the following steps:

[0102] Step S1.1: construct the control equation;

[0103] For CSEM forward, assume the time-harmonic factor and ignore the displacement current, the three-dimensional CSEM satisfies the vector finite element control equation:

[0104] (1)

[0105] where, is the electric field intensity; is the angular frequency; is the magnetic permeability; is the electric conductivity; is the CSEM impressed current source term;

[0106] Step S1.2: Discretize the control equation by using unstructured finite element method;

[0107] Discretize the control equation (1) by using Galerkin method to obtain the weak form of finite element method:

[0108] (2)

[0109] where, is the discretized domain; is the unstructured tetrahedral vector basis function;

[0110] Discretize the discretized domain by using tetrahedral mesh and corresponding vector basis function, divide the discretized domain into a finite number of non-overlapping tetrahedral elements, Figure 1 is the local node and edge number of the tetrahedral element;

[0111] Substitute the finite element dimensional interpolation function e into equation (2) in the element , where, is the approximate solution of finite element method, is the electric field value on the edge of the element, and according to the generalized variational principle, the discretization of each element can be obtained:

[0112] (3)

[0113] where, the expression of each element matrix is:

[0114]

[0115] Assemble the element matrix in the above formula in the entire calculation domain to obtain a large complex linear algebraic equation:

[0116] (4)

[0117] where, is the total synthesis matrix; S is the right end term of the equation; after imposing the Dirichlet boundary condition on equation (4), the electric field value on any element edge can be obtained, and according to Faraday's law, the magnetic field on the edge can be obtained:

[0118] (5)

[0119] For the traditional scalar CSEM as shown in Fig. 2(a), the electromagnetic field at the ground measuring point can be obtained by solving equation (5), and the scalar apparent resistivity and impedance phase of the scalar controlled source response function can be further obtained:

[0120] , (6)

[0121] wherein, is the impedance; is the apparent resistivity of the scalar controlled source response function; is the impedance phase of the scalar controlled source response function;

[0122] For the tensor CSEM observation mode, the source term matrix of two mutually orthogonal electric sources needs to be solved respectively as shown in Fig. 2(b), and two corresponding forward calculations are performed, so that the response function of the tensor controlled source can be obtained, and the impedance tensor of the tensor controlled source can be defined:

[0123] (7)

[0124] wherein, 1 and 2 represent two groups of tensor sources; after calculating the impedance tensor, the controlled source apparent resistivity and phase can be obtained, and the expression is the same as equation (6);

[0125] For the CSEM observation mode of the ground and the well (as shown in Figs. Figure 3 and Figure 4 The z-direction electromagnetic field measurement can be easily realized at the well CSEM receiving point;

[0126] S1.3: Tilt Description

[0127] The tensor controlled source method in the present application sets a base station to measure the horizontal magnetic field component on the ground (as shown in Fig. Figure 4 ), measures the vertical magnetic field component z in the well, and defines the tensor controlled source tilt T to represent the conversion function from the horizontal magnetic field to the vertical direction; according to the relationship between the tilt and the magnetic field component:

[0128] (8)

[0129] Similar to the method of obtaining the impedance component, the tilt component can be represented by using two groups of vertical mode excitation sources:

[0130] (9)

[0131] Step S2: Ground-well CSEM joint inversion based on the tensor source

[0132] The three-dimensional ground-well CSEM joint inversion objective function can be represented as:

[0133] (10)

[0134] where, is the inverse model roughness matrix, m represents the inverse model, is the regularization factor, is the data fitting term:

[0135] , (11)

[0136] where, n =1 corresponds to the surface CSEM data (electromagnetic field components , impedance tensor , dipole moment or apparent resistivity and phase ), n =2 corresponds to the borehole CSEM data (electromagnetic field components or defined tensor controllable source dipole moment ); is the observed data; is the predicted value; is the error data covariance matrix; is the model roughness matrix;

[0137] Based on the non-structured finite element method, the in equation (11) can be expressed as:

[0138] (12)

[0139] where, is the number of grid elements, and are the measured data and the electromagnetic data obtained by forward calculation respectively, e n is the data error; the data is arranged according to the real part and the imaginary part; for the model constraint term , the combination of smoothness constraint and reference model constraint is adopted, and the two constraints are respectively set as and to obtain:

[0140] (13)

[0141] where, and are the regularization factors, and their values are:

[0142] , (14)

[0143] where R is the model smoothing matrix; is the model prior constraint matrix; is the prediction model;

[0144] The tensor CIP objective function can be expressed as:

[0145] (15)

[0146] As shown in FIG. 1, based on the unstructured tetrahedral mesh, R in formula (14) can be solved by the difference between each element and adjacent elements; Figure 5 The reciprocal of the volume of the current model can be used to express, and thus:

[0147] , (16)

[0148] where is the volume of the current element corresponding element; i is the number of adjacent elements of the current element; is the distance between the centers of adjacent elements; i is the weight coefficient of the i-th adjacent element; is the model parameter difference of the adjacent element; and j The definition of and is respectively: , (17)

[0149] Let the i-th grid element center point be (xi, yi, zi), and thus:

[0150] (18)

[0151] (19)

[0152] The gradient of the data fitting term can be expressed as:

[0153] (20)

[0154]

[0155] (21)

[0156] Therefore, for the i-th element, we have: k

[0157] (21)​​​​​​​​

[0158] where, is conjugate; denotes the operator taking the real part of a complex number;

[0159] In the solution process, these partial derivatives shown in equations (20) and (21) can be applied to the forward equation solution equation (4) with being the magnetic field component of the measured point magnetic field interpolated from the electric field vector at given frequency and transmitter source , then:

[0160] , (22)

[0161] Similarly, we can define , , , and similarly to equation (22) we have:

[0162] , (23)

[0163] Taking the derivative of equation (4) with respect to for both source modes, we have:

[0164] , (24)

[0165] According to the above derivation, equation (21) can be rewritten as:

[0166] (25)

[0167] where, and depend on different tensor CSEM response components, for example, for the corresponding and are and ; define the first simulation under the orthogonal source mode as the first forward, then equation (25) requires four forward calculations at each frequency; among them, two forward calculations are for calculating , and impedance and dipole responses; in addition, two times the right end term are the adjoint forward with and , where, and are:

[0168] , (26)

[0169] Let and satisfy:

[0170] , (27)

[0171] Two adjoint forward problems can be defined:

[0172] , (28)

[0173] The complete calculation of equation (25) can be obtained from equation (28). Compared with the data fitting term , the model constraint term can be directly analytically solved:

[0174] (29)

[0175] (30)

[0176] Step S4: Calculation and storage of sensitivity

[0177] The sensitivity of the corresponding inversion data is denoted by J, and the forward data set is where To obtain the spatial interpolation operator of different types of data, specific data types can be selected; according to equations (27) and (28), the sensitivity of the data with respect to the isotropic conductivity component is:

[0178] , (31)

[0179] where the sensitivity information can be obtained from the adjoint forward formula (28);

[0180] Step S5: L-BFGS optimization algorithm based on momentum method

[0181] In gradient-based optimization methods, the search direction of the model is ; for three-dimensional joint inversion of data, the L-FBGS algorithm obtains an approximate by double-loop recursion to reduce memory; at this time, only the gradient of the objective function needs to be calculated:

[0182] , (32)

[0183] where, and can be directly calculated, By formula (31) is constructed, the model update of three-dimensional joint inversion is:

[0184] (33)

[0185] Using L-BFGS optimization algorithm can reduce the memory requirements of inversion, and then realize the three-dimensional large-scale joint inversion calculation, Figure 6 Three-dimensional electromagnetic method inversion from random model, and along the gradient method trajectory descent process schematic diagram; inversion from the initial model into the green ditch, in order to reach the global minimum point must cross the ditch, that is, a series of local minimum value in the inversion; The target function in the local minimum interval repeatedly oscillates, the curvature of the decline is pathological, not along the optimal descent trajectory to reach the global minimum; for the traditional gradient method inversion, because 1 Direction of gradient component than 2 Direction is much larger, the inversion is extremely slow in the local minimum value near the decline, resulting in three-dimensional inversion is forced to terminate at the local minimum value;

[0186] Three-dimensional inversion into local minimum problem, very similar to the training stagnation problem in machine learning; In machine learning, heuristic algorithm is often used to guide the optimization process, and the momentum method is introduced in the model update of three-dimensional joint inversion. The model update amount in three-dimensional inversion can be compared to momentum, and the model update in L-BFGS iteration is modified as follows:

[0187] (34)

[0188] Where, momentum factor V And learning rate Need to be reasonably selected according to the theory and the law of measured data inversion summary; The improved model update of momentum method not only considers the gradient of the current objective function, but also uses the previous gradient to estimate its momentum; According to formula (32), the subsequent Update of the gradient information of the previous objective function is weighted sum, the closer the gradient, the higher the weight; Combined with Figure 7 , the gradient of the objective function of each iteration is decomposed into 1 And 2 Direction, in the process of multiple iteration update, 1 Direction of gradient component in the weighted sum is constantly reduced, while the component in 2 Direction is strengthened. This shows that the model update based on momentum method can accumulate the gradient component in 2 Direction, and reduce The component in the 1 direction can effectively guide the inversion algorithm based on the gradient method to proceed along the optimal descending direction, thereby avoiding the three-dimensional joint inversion from falling into a local minimum.

[0189] Compared with the prior art, the present application has the following advantages:

[0190] Compared with the traditional scalar controllable source electromagnetic method, the multi-source tensor controllable source electromagnetic method used in the present application can simultaneously excite and receive electromagnetic field components in multiple directions, thereby obtaining more abundant underground structure information.

[0191] Unlike the traditional regular grid, the present application uses an unstructured grid to subdivide the study area, which can more flexibly construct the shape of the terrain and underground anomaly body, and at the same time, the use of unstructured finite elements can save memory and improve the calculation rate.

[0192] Through joint inversion, the controllable source electromagnetic data on the ground and in the well are combined to improve the lateral and longitudinal resolution of exploration, reduce the multi-solution of inversion, and make the inversion result more reliable.

[0193] The use of the L-BFGS optimization algorithm in the present application can reduce the memory requirement of inversion, and the introduction of the momentum method in the model updating of three-dimensional joint inversion makes the convergence faster.

[0194] The data acquisition efficiency of the tensor source in the present application is high, the joint inversion method can quickly process multi-source data, shorten the exploration period and reduce the cost.

[0195] Embodiment 1

[0196] A horizontal ground model is set to test the effectiveness of the data on the ground and in the well, as shown in Fig. 8 (a), 100 A single well is set in a homogeneous half-space, and the wellhead is located on the ground (-2.5km, 0km, 0km), as shown in Fig. 8 (b). The well measurement points are set from -330m to -3050m in the longitudinal direction, and 35 measurement points are set; a low-resistance anomaly body is set below the center of the measurement area (0km, 0km, 0km), the top surface of the anomaly body is buried 1km deep, the resistivity is 10 , and the size is 2km 2km 1km; as shown in FIG. 8 (b) above the anomaly body, 169 measuring points are uniformly arranged with the coordinate origin as the center, the line distance and the point distance are both 0.5km, and there are 13 measuring lines; the orthogonal transmitting source is a tensor source, which is arranged along the x and y directions respectively, the center point coordinates of the transmitting source are (6km, 0km, 0km), and the length of the transmitting source is 1km; in order to realize the measurement of the dipmeter data, the base station for measuring the horizontal magnetic field is arranged at (20km, 0km, 0km), and the measurement frequency of the tensor controllable source is 1000Hz, 100Hz, 10Hz and 1Hz; the tensor impedance data of the forward response ground of the tensor controllable source of the model and the dipmeter data in the well are simulated and measured, and 5% noise is added; the whole calculation area of the theoretical model contains 333695 unit numbers; the inversion area is 8km 8km 4km, the initial model is a half space with 100 , and the termination target RMS is 1.05; the prior model is set as a half space with 100 ; the initial regularization factor is set as 0.01 during the inversion process, and the additional regularization factors and are 1 and 1 respectively; the cooling principle is used to change in the iteration process, and when the reduction of the RMS of the adjacent iterations is less than 2%, the is reduced by the proportion coefficient 0.9 ;

[0197] The inversion results are shown in FIG. 9 (a) and FIG. 9 (b), and the joint inversion of the ground and well data can obtain the resistivity of the low-resistance anomaly body of about 10 , and the spatial distribution of the low-resistance anomaly body can accurately reflect the electrical structure of the underground true model without redundant structure; the effectiveness of the joint inversion of the ground and well controllable source electromagnetic method data based on the isotropic medium is proved.

[0198] As shown in FIG. 10 (a) to FIG. 10 (c), the inversion is terminated after 116 iterations, the data fitting term is reduced from 352.8 to 4.5, the reduction speed is fast in the early stage of the iteration, and then the reduction speed becomes slow until the inversion converges; the model constraint terms and are very small close to zero at the beginning of the inversion, increase sharply after one time, then increase slowly to gradually decrease, and then increase slowly to a stable state; as shown in FIG. 10 (b), the maximum is 3, and the search step In most iterative process for 1, it is illustrated that the L-BGFS algorithm based on the improved momentum method approximates the inverse matrix of the Hessian matrix in most iterative processes, has approached the true value, and the fixed unit step length can satisfy the Wolfe condition, only one forward calculation is required in the iterative process, the number of forward calculations is effectively reduced, and the inversion efficiency is improved; Fig. 10 (c) shows that the RMS finally drops to 2.02, and the regularization factor does not become smaller in the iterative process, and Figs. 10 (a) to 10 (c) illustrate that the application based on the isotropic surface and borehole controlled source electromagnetic method joint inversion algorithm has certain stability and efficiency.

[0199] Example 2

[0200] A three-dimensional surface and borehole controlled source electromagnetic data fracturing monitoring theoretical model is set as shown in Figs. 11 (a) and 11 (b), and a 100 m thick isotropic half-space model is set, and a 150 Ω abnormal body with a resistivity of 150 Ω is arranged at 1200m-1600m of the uniform half-space, the center of the abnormal body model is (0m, 0m, -1400m), and the size is 2km 2km 0.4km; an abnormal body model with a resistivity of 20 Ω is arranged at a 2500m-3500m horizon, the center of the model is (-2000km, 0m, 0km), as shown in Figs. 11 (a) and 11 (b), 35 measuring points are arranged in the longitudinal direction from -330m to -3050m of the anisotropic body penetrating the bottom. The center of the measuring area is the coordinate origin, 49 measuring points are uniformly arranged, the line distance and point distance are both 1km, and there are 7 measuring lines; the transmitting source is an orthogonal tensor source, which is arranged along the x and y directions respectively, the center point coordinates of the transmitting source are (6km, 0km, 0km), the transmitting source length is 1km, and the transmitting current is 30A; wherein the measuring frequency is 0.1 to 100Hz logarithmic interval, 11 frequency points are taken, the forward response tensor impedance of the model tensor controlled source and the borehole dip data are simulated, and 5% noise is added to the measured data. The inversion region is 8km 8km 4km, the initial model is a half-space of 100 Ω, and the termination target RMS is 1.05; the prior model is set as a half-space of 100 Ω. In order to compare the effectiveness of the surface and borehole data joint inversion, the three-dimensional inversion result of the single surface data is set as a comparison model.

[0201] Fig. 12(a)-Fig. 12(f) are anisotropic horizontal resistivity result maps of the ground data inversion alone and the ground-well data joint inversion; from Fig. 12(a) and Fig. 12(b), for the ground data inversion result, a high-resistance and low-resistance anomaly region can be roughly inverted, wherein the low-resistance anomaly has a higher resolution, and the high-resistance anomaly is about 120 ~150 , but the region boundary of the anomaly body is not obvious; for the ground and well data joint inversion result, an obvious low-resistance anomaly region and some local high-resistance regions can be inverted, wherein the region boundary of the low-resistance anomaly is very obvious, and the low-resistance anomaly is about 25 ; the same point of the inversions of the x-z sections is that the low-resistance anomaly can be highly resolved, and the resolution of the high-resistance is low; the different point of the inversions of the x-z sections is that the depths of the high and low-resistance anomaly bodies obtained by the ground inversion are higher than the true positions, while the ground and well data joint inversion can obtain the depth of the underground anomaly body more accurately; from Fig. 12(c) and Fig. 12(d), for the ground data inversion result, a low-resistance false anomaly is inverted above the true bottom anomaly body in the y direction, and the high-resistance anomaly region boundary is not obvious but exceeds the correct range; for the ground and well data joint inversion result, although the position of the high-resistance anomaly is not obviously inverted, no low-resistance false anomaly appears; from Fig. 12(e) and Fig. 12(f), for the ground data inversion result, a relatively correct anomaly range is obtained. Comprehensive analysis of Fig. 12(a)-Fig. 12(f) shows that the addition of the well data can improve the inversion depth and resolution, and the resistivity value of the low-resistance anomaly body is closer to the true value.

[0202] The following describes a ground-well CSEM joint inversion system based on a tensor source provided in the present application, which can be mutually referred to the ground-well CSEM joint inversion method based on a tensor source described above.

[0203] The present application provides a ground-well CSEM joint inversion system based on a tensor source, comprising:

[0204] A forward modeling module is configured to construct a three-dimensional electrical property model comprising a tensor source, drilling electrical property parameters and formation electrical property parameters, perform forward modeling on the established three-dimensional electrical property model using ground and well CSEM to obtain impedance tensors of the tensor controllable source and the dip of the tensor controllable source;

[0205] A target function construction module is configured to combine the impedance tensors and the dip of the ground and well obtained by the forward modeling module to construct a three-dimensional ground and well CSEM joint inversion target function and the gradient of the inversion target function with a model roughness matrix and a data fitting term;

[0206] The inversion module is configured to solve the gradient of the inversion objective function by using an L-BFGS optimization algorithm improved based on a momentum method, and to invert the underground electrical structure.

[0207] Further preferably, the forward module comprises:

[0208] The control equation construction unit is configured to construct a vector finite element control equation based on an electric field intensity, an angular frequency, a magnetic permeability, an electrical conductivity, and a CSEM impressed current source term.

[0209] The first data processing unit is configured to discretize the vector finite element control equation by using a non-structured finite element method, to interpolate the electric field value in the finite element unit, and to assemble the entire calculation domain to obtain a complex linear algebraic equation.

[0210] The electromagnetic field acquisition unit is configured to obtain the electric field value and the magnetic field value on any unit edge after adding a Dirichlet boundary to the complex linear algebraic equation.

[0211] The forward data acquisition unit is configured to obtain an impedance tensor of a tensor CSEM and a tensor controllable source dip based on the electric field value and the magnetic field value obtained by the electromagnetic field acquisition unit according to a tensor CSEM observation mode.

[0212] Further preferably, the objective function construction module comprises:

[0213] The first objective function construction unit is configured to construct the inversion objective function according to the inversion model roughness matrix and the data fitting term, wherein the data fitting term comprises the CSEM data on the ground and the CSEM data in the well.

[0214] The second data processing unit is configured to perform grid division and grid representation on the data fitting term in the inversion objective function by using the non-structured finite element method.

[0215] The third data processing unit is configured to represent the roughness matrix by using a smoothness constraint and a reference model constraint.

[0216] The fourth data processing unit is configured to perform grid division and grid representation on the roughness matrix by using a non-structured tetrahedral grid.

[0217] The first objective function construction unit is configured to update the inversion objective function based on the grid-represented data fitting term and the roughness matrix, and to obtain the gradient representation of the inversion objective function.

[0218] Further preferably, the inversion objective function in the objective function construction module is:

[0219]

[0220] wherein, , , ; , ; 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 of the ground surface; n =2 corresponds to the CSEM data in the well; the CSEM data includes the impedance tensor of the tensor controlled source and the dip of the tensor controlled source; is the observed CSEM data; is the CSEM data obtained by the forward step S1; is the error data covariance matrix; R is the smoothing matrix of the inversion model; is the prior constraint matrix of the inversion model; is the inversion model predicted by the forward prediction.

[0221] Further preferably, the inversion model updating method in the L-BFGS iteration in the inversion module is:

[0222]

[0223] wherein, is the update amount of the inversion model; k is the iteration number; m is the inversion model; is the learning rate; V is the momentum factor; g is the gradient of the inversion objective function.

[0224] It can be understood that the detailed function implementation of each unit / module described above can refer to the description in the foregoing method embodiments, and will not be repeated here.

[0225] It should be understood that the above system is used to execute the method in the above embodiments, and the corresponding program modules in the system have similar implementation principles and technical effects to the description in the above method, and the working process of the system can refer to the corresponding process in the above method, which will not be repeated here.

[0226] Those skilled in the art can easily understand that the above only describes the preferred embodiments of the present application, and is not intended to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A joint inversion method of tensor source-based borehole controlled source electromagnetic method, characterized in that, The method comprises the following steps: Step S1: constructing a three-dimensional electrical property model containing tensor source, drilling electrical property parameters and formation electrical property parameters, using the established three-dimensional electrical property model to perform forward modeling on the surface and in the well CSEM to obtain impedance tensor and dip response of the tensor controllable source; Step S2: combining the impedance tensor and dip response obtained in step S1 to construct an inversion objective function and a gradient of the inversion objective function of the three-dimensional surface and well CSEM joint in combination with a model roughness matrix and a data fitting term; Step S3: solving the gradient of the inversion objective function by using an L-BFGS optimization algorithm based on the momentum method to invert the underground electrical property structure; In the L-BFGS iteration, the inversion model updating method is: wherein, is the update of the model for the k th iteration; is the update of the model for the k th iteration; k is the number of iterations; is the model for the k th iteration; is the model for the k th iteration; is the learning rate; V is the momentum factor; is the gradient of the objective function for the k th iteration; is the gradient of the objective function for the k th iteration.

2. The joint borehole-surface CSEM inversion method of claim 1, wherein, Step S1 specifically comprises the following steps: Step S1.1: constructing a vector finite element control equation in the three-dimensional electrical property model based on the electric field intensity, electromagnetic wave angular frequency, magnetic permeability, electrical conductivity and CSEM external current source term; Step S1.2: discretizing the vector finite element control equation, interpolating the electric field value in the finite element unit and assembling the entire calculation domain to obtain a complex linear algebraic equation; Step S1.3: adding the Dirichlet boundary in the complex linear algebraic equation to obtain the electric field value and magnetic field value on the edge of any unit; Step S1.4: based on the tensor CSEM observation mode, the electric field value and magnetic field value obtained in step S1.3 are used to obtain the impedance tensor of the tensor controllable source and the tensor controllable source dip.

3. The joint inversion method of surface-borehole CSEM according to claim 1 or 2, characterized in that, Step S2 specifically comprises the following steps: Step S2.1: constructing an inversion objective function according to the inversion model roughness matrix and the data fitting term; wherein the data fitting term contains the CSEM data of the surface and the CSEM data in the well; Step S2.2: discretizing the data fitting term in the inversion objective function to calculate the data residual contribution value in each grid unit by using an interpolation basis function; Step S2.3: constructing a roughness matrix by using a smoothness constraint and a reference model constraint; Step S2.4: performing finite element discretization on the roughness matrix in step S2.3; Step S2.5: solving the gradient of the inversion objective function by combining the data residual and the constraint term, and constantly updating the inversion model according to the gradient direction until the inversion objective function converges.

4. The surface-borehole CSEM joint inversion method of claim 3, wherein, The inversion objective function in step S2.1 is: wherein, , , ; , ; is a roughness matrix of the inversion model; is a data fitting term; m is the inversion model; , , , and is a regularization factor; n = 1 corresponds to CSEM data on the surface; n = 2 corresponds to CSEM data in the well; CSEM data includes impedance tensor of the tensor source and the tensor source dip; is the observed CSEM data; is the CSEM data obtained by forward modeling in step S1; is the error data covariance matrix; R is a smoothing matrix of the inversion model; is a priori constraint matrix of the inversion model; is the inversion model predicted by forward modeling.

5. A tensor source based joint inversion system for borehole controlled source electromagnetic method, characterized in that, It comprises: a forward modeling module, which is used to construct a three-dimensional electrical property model containing tensor source, drilling electrical property parameters and formation electrical property parameters, to use the established three-dimensional electrical property model to perform forward modeling on the surface and in the well CSEM to obtain impedance tensor and dip response of the tensor controllable source; a target function construction module, which is used to combine the impedance tensor and dip obtained by the forward modeling module to construct an inversion objective function and a gradient of the inversion objective function of the three-dimensional surface and well CSEM joint in combination with a model roughness matrix and a data fitting term; an inversion module, which is used to solve the gradient of the inversion objective function by using an L-BFGS optimization algorithm based on the momentum method to invert the underground electrical property structure; In the L-BFGS iteration in the inversion module, the inversion model updating method is: wherein, is the update of the model for the k th iteration; is the update of the model for the k -1th iteration; k is the iteration number; is the model for the k th iteration; is the model for the k +1th iteration; is the learning rate; V is the momentum factor; is the gradient of the objective function for the k th iteration; is the gradient of the objective function for the k -1th iteration.

6. The borehole controlled source electromagnetic method joint inversion system of claim 5, wherein, The forward modeling module comprises: The control equation construction unit is configured to construct a vector finite element control equation in a three-dimensional electrical property model based on an electric field intensity, an electromagnetic wave angular frequency, a magnetic permeability, an electric conductivity, and a CSEM impressed current source term; The first data processing unit is configured to discretize the vector finite element control equation by using a non-structure finite element method, interpolate an electric field value in a finite element unit, assemble the electric field value in an entire calculation domain, and obtain a complex linear algebraic equation; The electromagnetic field acquisition unit is configured to obtain electric field values and magnetic field values on any unit edge after adding a Dirichlet boundary to the complex linear algebraic equation. The forward data acquisition unit is configured to obtain an impedance tensor of a tensor CSEM and a tensor controllable source dip based on a tensor CSEM observation mode and the electric field values and the magnetic field values obtained by the electromagnetic field acquisition unit.

7. The surface-borehole CSEM joint inversion system of claim 5 or 6, wherein, The objective function construction module includes: The first objective function construction unit is configured to construct an inversion objective function according to an inversion model roughness matrix and a data fitting term, wherein the data fitting term includes CSEM data on the ground and CSEM data in a well; The second data processing unit is configured to perform finite element discretization on the data fitting term in the inversion objective function; The third data processing unit is configured to represent the roughness matrix by using a smoothness constraint and a reference model constraint; The fourth data processing unit is configured to perform finite element discretization on the roughness matrix; The first objective function construction unit is configured to calculate a gradient of the inversion objective function, and constantly update the inversion model according to the gradient direction until the inversion objective function converges.

8. The borehole controlled source electromagnetic method joint inversion system of claim 5, wherein, The inversion objective function in the objective function construction module is: wherein, , , ; , ; is the inverse model roughness matrix; is the data fitting term; m represents the inverse model; , , , and is the regularization factor; n = 1 corresponds to the surface CSEM data; n = 2 corresponds to the borehole CSEM data; the CSEM data includes the impedance tensor of the tensor controlled source and the tensor controlled source dip; is the observed CSEM data; is the CSEM data obtained by the forward model; is the error data covariance matrix; R is the inverse model smoothing matrix; is the inverse model prior constraint matrix; is the inverse model predicted by the forward prediction.

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