A three-dimensional transient electromagnetic inversion method including induced polarization effect

Abstract

The present invention relates to the field of geological exploration technology, and specifically to a method for three-dimensional transient electromagnetic inversion containing induced polarization effect. Arrange a square wireframe and set receiving points to obtain electromagnetic data containing induced polarization effect in the area to be surveyed; establish an initial parameter model for three-dimensional transient electromagnetic inversion containing induced polarization effect; use the Cole-Cole model to establish a description equation for the induced polarization effect in three-dimensional transient electromagnetic; use the Caputo operator to time discretize the description equation, and combine the vector finite element method to establish a three-dimensional forward equation; construct an objective function for three-dimensional transient electromagnetic inversion containing induced polarization effect; perform adjoint forward calculations according to the three-dimensional forward equation, obtain the gradient of the transient electromagnetic three-dimensional inversion objective function to construct an inversion equation; perform three-dimensional transient electromagnetic inversion containing induced polarization effect according to the electromagnetic data, the inversion equation and the initial parameter model. The present invention can effectively identify and invert minerals containing induced polarization effect.

Description

Technical Field

[0001] The invention relates to the technical field of geological exploration, and in particular to a transient electromagnetic three-dimensional inversion method including induced polarization effect. Background Art

[0002] Transient electromagnetic method is a cutting-edge geophysical exploration method that focuses on using transient electromagnetic fields to reveal the conductive properties of underground geological bodies. The core of this method is to capture and analyze the electromagnetic response caused by underground geological bodies through specific electromagnetic transmitting and receiving devices, thereby achieving effective detection of underground structures and electrical properties. As a geophysical method with high sensitivity and resolution, strong adaptability, high efficiency and low cost, transient electromagnetic method has been widely used in the exploration of metal mineral resources.

[0003] Polaroids are commonly developed in metal deposits, such as massive sulfide ores, copper-nickel ores, graphite ores, etc. The induced polarization effect caused by polaroids can cause transient electromagnetic data to be distorted in the late time channel, or even cause sign reversal. However, traditional inversion that only considers resistivity cannot effectively invert these data containing induced polarization effects, which has created obstacles to the application of transient electromagnetic methods in these areas. At the same time, traditional one-dimensional and two-dimensional inversion interpretations are not suitable for complex underground structure simulations and can no longer meet the technical requirements of detailed resource exploration and structural research. Therefore, a transient electromagnetic inversion method that considers the induced polarization effect and is suitable for complex three-dimensional models is needed. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention provides a method for three-dimensional inversion of transient electromagnetic with induced polarization effect, which comprises: laying out a square wireframe and setting receiving points to obtain electromagnetic data with induced polarization effect in the area to be investigated; establishing an initial parameter model for three-dimensional inversion of transient electromagnetic with induced polarization effect; establishing a description equation for induced polarization effect in three-dimensional transient electromagnetic using the Cole-Cole model; using the Caputo operator to time discretize the description equation, and establishing a three-dimensional forward equation in combination with the vector finite element method; constructing an objective function for three-dimensional inversion of transient electromagnetic with induced polarization effect; performing adjoint forward calculation according to the three-dimensional forward equation, obtaining the gradient of the objective function of three-dimensional inversion of transient electromagnetic to construct an inversion equation; and performing three-dimensional inversion of transient electromagnetic with induced polarization effect according to the electromagnetic data, the inversion equation and the initial parameter model. The present invention can effectively identify and invert minerals with induced polarization effect.

[0005] The present invention adopts the following technical scheme, a transient electromagnetic three-dimensional inversion method including induced polarization effect, comprising:

[0006] Arrange a square wireframe in the area to be surveyed and set receiving points to obtain electromagnetic data including induced polarization effect in the area to be surveyed;

[0007] Establishing an initial parameter model of transient electromagnetic three-dimensional inversion including induced polarization effect according to the electromagnetic data;

[0008] The Cole-Cole model is used to establish a description equation for the induced polarization effect in three-dimensional transient electromagnetics; the Caputo operator is used to time discretize the description equation, and the three-dimensional forward equation is established in combination with the vector finite element method;

[0009] According to the forward equation combined with regularization theory, an objective function of transient electromagnetic three-dimensional inversion including induced polarization effect is constructed;

[0010] Performing an adjoint forward calculation according to the three-dimensional forward equation, obtaining a gradient of a transient electromagnetic three-dimensional inversion objective function, and constructing an inversion equation according to the gradient of the objective function;

[0011] A three-dimensional transient electromagnetic inversion including induced polarization effect is performed according to the electromagnetic data, inversion equation and initial parameter model.

[0012] Furthermore, the Cole-Cole model is used to establish a description equation for the induced polarization effect in three-dimensional transient electromagnetics, specifically:

[0013] According to the Maxwell equations in the time domain, the electric field diffusion equation satisfied by three-dimensional transient electromagnetic is:

[0014] ;

[0015] Where r represents the position vector, t represents the time, and E(r, t) represents the electric field intensity at r at time t. represents the conduction current density at r at time t, represents the current density of the external current source at time t at r, μ is the magnetic permeability, is the gradient operator;

[0016] After the electric field diffusion equation is time discretized using the second-order backward Euler, the descriptive equation established using the Cole-Cole model is:

[0017] ;

[0018] in, is the zero-frequency conductivity, that is, the real conductivity when there is no induced polarization effect in the formation; m is the charging rate, which characterizes the intensity of the induced polarization effect of the polarized body; τ is the time constant, which characterizes the charging and discharging speed of the polarized body; c is the frequency correlation coefficient, which characterizes the uniformity of the mineral distribution in the polarized body, and its value range is ; i is the imaginary unit, ω is the angular frequency.

[0019] Furthermore, the description equation is time discretized, specifically:

[0020] Substituting the described equation into Ohm's law and performing inverse Fourier transformation to obtain the time domain Ohm's law expression including induced polarization effect;

[0021] The Ohm's law expression is time discretized by introducing an implicit differential discretization format of the Caputo operator, and the discretized Ohm's law expression is substituted into the electric field diffusion equation satisfied by three-dimensional transient electromagnetics to obtain the electric field diffusion equation.

[0022] Furthermore, the three-dimensional forward equations are established by combining the vector finite element method, including:

[0023] Unstructured tetrahedral grids are used to discretize the three-dimensional space, and vector interpolation basis functions are introduced to interpolate and approximate the electric field in the grid unit to obtain the electric field expression in any tetrahedral grid unit.

[0024] The electric field diffusion equation is discretized by finite element method using Galerkin method;

[0025] Applying Dirichlet boundary conditions to the electric field expression and assembling all time channels, the forward equations are:

[0026] ;

[0027] Where A is the coefficient matrix, E is the electric field value to be determined on each edge of the tetrahedral mesh unit, and b is the source term.

[0028] Furthermore, the objective function of transient electromagnetic three-dimensional inversion including induced polarization effect is constructed, and the expression is:

[0029] ;

[0030] in, is the data covariance matrix, is the model roughness operator, , are the observed data vector and the forward response data vector, respectively. is the regularization factor, , are the calculation model parameter vector and the reference model parameter vector respectively.

[0031] Further, adjoint forward modeling is performed according to the three-dimensional forward modeling equation to obtain the gradient of the transient electromagnetic three-dimensional inversion objective function, including:

[0032] In the objective function, the partial derivatives of the model parameter m are obtained at both ends to obtain the gradient of the objective function:

[0033] ;

[0034] In the formula, is the model roughness operator, , are the observed data vector and the forward response data vector, respectively. is the regularization factor, , are the calculation model parameter vector and the reference model parameter vector, respectively, J is the sensitivity matrix, and the superscript T indicates the transpose of the matrix;

[0035] The sensitivity matrix is ​​solved by the adjoint forward modeling method, and the solved sensitivity matrix is ​​substituted into the above formula to calculate the gradient of the objective function.

[0036] Furthermore, an inversion equation is constructed according to the gradient of the objective function, including:

[0037] For the kth iteration, the inversion equation is constructed based on the gradient of the objective function and is expressed as:

[0038] ;

[0039] in, , is a positive definite matrix, representing the approximate Hessian matrix of the kth iteration, is the objective function gradient at the kth iteration.

[0040] Furthermore, the transient electromagnetic three-dimensional inversion including induced polarization effect is carried out, including:

[0041] Iteratively solving the inversion equation by a finite memory quasi-Newton method, and obtaining an updated model parameter vector after each iteration;

[0042] Perform forward modeling on the updated model parameter vector after each iteration to obtain the electromagnetic response data after each iteration;

[0043] The data fitting difference is obtained based on the electromagnetic response data after each iteration and the electromagnetic data including the induced polarization effect;

[0044] When the data fitting error meets the set conditions, the inversion is terminated and the model parameter vector at this time is output.

[0045] Furthermore, the data fitting difference is obtained based on the electromagnetic response data after each iteration and the electromagnetic data containing the induced polarization effect, including:

[0046] ;

[0047] in, is the ith noise standard deviation, is the number of data, , are the observation data vector and the forward response data vector, respectively.

[0048] Furthermore, the setting conditions include:

[0049] When the RMS value drops to 1, the inversion is terminated;

[0050] When the number of iterations reaches a given upper limit, the inversion is terminated;

[0051] When the RMS value no longer changes, the inversion is terminated.

[0052] The beneficial effects of the present invention are as follows: in a three-dimensional inversion method of transient electromagnetic with induced polarization effect provided by the present invention, the time domain Ohm's law with induced polarization effect is discretized by an implicit differential discretization format based on the Caputo operator, so that the three-dimensional forward and inversion calculation of transient electromagnetic with induced polarization effect can be directly performed in the time domain, and the calculation accuracy is higher, and higher-precision mineral exploration results can be provided; modeling is performed by unstructured tetrahedral grids, so that complex geological conditions can be better simulated, and the adaptability of the exploration method can be greatly improved; the parameter model with induced polarization effect obtained by inversion can effectively identify metal ore bodies with induced polarization effect, and provide strong guarantee for national mineral demand; the three-dimensional inversion method is adopted to realize three-dimensional imaging and interpretation of underground structural structures, so that the three-dimensional information of underground geological structures can be more comprehensively understood, and a powerful method support is provided for the positioning of exploration targets and the judgment of properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0054] Figure 1 A schematic flow chart of a transient electromagnetic three-dimensional inversion method including induced polarization effect according to an embodiment of the present invention;

[0055] Figure 2 A schematic diagram of a transient electromagnetic data acquisition strategy according to an embodiment of the present invention;

[0056] Figure 3 A schematic diagram of forward modeling and inverse modeling of a horizontal plate model according to an embodiment of the present invention;

[0057] Figure 4 A three-dimensional inversion resistivity result diagram of an embodiment of the present invention;

[0058] Figure 5 A three-dimensional inversion charging rate result diagram of an embodiment of the present invention;

[0059] Figure 6 A three-dimensional inversion time constant result diagram of an embodiment of the present invention;

[0060] Figure 7 This is a three-dimensional inversion frequency correlation coefficient result diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0062] When the induced polarization effect exists in the exploration area, the transient electromagnetic measurement data may be distorted or even reversed in sign. The inversion method that does not consider the induced polarization effect cannot effectively invert the exploration area. In order to solve this problem, Ohm's law including the induced polarization effect is introduced into the forward and inverse equations for relevant calculations, thereby performing three-dimensional transient electromagnetic inversion including the induced polarization effect. The present invention can invert the four model parameters related to the induced polarization effect, namely the resistivity, charging rate, time constant and frequency correlation coefficient of the exploration area, to provide effective assistance for the identification of minerals with induced polarization effect. Based on the above concept, Figure 1 As shown, an embodiment of the present invention provides a transient electromagnetic three-dimensional inversion method including induced polarization effect, comprising:

[0063] Arrange a square wireframe in the area to be surveyed and set receiving points to obtain electromagnetic data including induced polarization effect in the area to be surveyed;

[0064] Establishing an initial parameter model of transient electromagnetic three-dimensional inversion including induced polarization effect according to the electromagnetic data;

[0065] The Cole-Cole model is used to establish a description equation for the induced polarization effect in three-dimensional transient electromagnetics; the Caputo operator is used to time discretize the description equation, and the three-dimensional forward equation is established in combination with the vector finite element method;

[0066] According to the forward equation combined with regularization theory, an objective function of transient electromagnetic three-dimensional inversion including induced polarization effect is constructed;

[0067] Performing adjoint forward calculation according to the three-dimensional forward equation, obtaining the gradient of the transient electromagnetic three-dimensional inversion objective function, and constructing the inversion equation according to the gradient of the objective function;

[0068] Perform three-dimensional transient electromagnetic inversion including induced polarization effect based on electromagnetic data, inversion equations and initial parameter models;

[0069] The inversion equation is iteratively solved by the finite memory quasi-Newton method, and an updated model parameter vector is obtained after each iteration; the updated model parameter vector after each iteration is forward modeled to obtain the electromagnetic response data after each iteration;

[0070] The data fitting difference is obtained based on the electromagnetic response data after each iteration and the electromagnetic data containing the induced polarization effect; when the data fitting difference meets the set conditions, the inversion is terminated and the model parameter vector at this time is output.

[0071] In another specific embodiment of the present invention:

[0072] A large square wireframe is laid out on the ground as a transmitting source, and receiving points are laid out inside the transmitting wireframe to receive electromagnetic signals in the survey area and obtain observed electromagnetic data; Figure 2 As shown, Figure 2 (a) is a schematic diagram of the 3D wireframe laying model. Figure 2 (b) is a plane diagram. In the embodiment of the present invention, a 200×200 m square transmitting wireframe is laid on the surface, and 81 measuring points are arranged on the surface within the wireframe with a point spacing of 20 m. Thus, a horizontal plate with a size of 100×100×30 m and a central burial depth of 60 m is designed for numerical experiments. The resistivity of the horizontal plate is 10 ohm-m, the charging rate is 0.5, the time constant is 0.1s, and the frequency correlation coefficient is 0.6. The resistivity of the surrounding rock is 100 ohm-m, the charging rate is 0.1, the time constant is 0.01 s, and the frequency correlation coefficient is 0.1.

[0073] Establish the initial parameter model required for transient electromagnetic three-dimensional inversion including induced polarization effect; Figure 3 As shown, the embodiment of the present invention adopts unstructured tetrahedral mesh for unit division. Figure 3 The forward modeling grid containing the horizontal plate in (a) is discretized into 386610 tetrahedral units. The initial inversion model adopted in the embodiment of the present invention is a uniform half space with a resistivity of 100 ohm-m, a charging rate of 0.1, a time constant of 0.01 s, and a frequency correlation coefficient of 0.1. Figure 3 The inversion grid in (b) is discretized into 322643 tetrahedral elements.

[0074] The Cole-Cole model is introduced to describe the induced polarization effect, and the time-domain Ohm's law is time-discretized based on the Caputo operator. The three-dimensional forward equation is established by combining the vector finite element method and the second-order backward Euler method. A forward calculation is performed on the given initial parameter model to obtain the electromagnetic response data. The embodiment of the present invention starts from the differential form of the Maxwell equations in the time domain, introduces the constitutive relationship, ignores the displacement current and eliminates the magnetic field, and can derive the electric field diffusion equation satisfied by the three-dimensional transient electromagnetic:

[0075] ;

[0076] Where r represents the position vector, t represents the time, and E(r, t) represents the electric field intensity at r at time t. represents the conduction current density at r at time t, represents the current density of the external current source at time t at r, μ is the magnetic permeability, is the gradient operator.

[0077] Using the second-order backward Euler method to time discretize the electric field diffusion equation, we can obtain:

[0078] ∇×∇× E ( r, t k ) + μ 1 2 Δ t k - 1 [ 3 j ( r, t k ) − 4 j ( r, t k − 1 ) + j ( r, t k − 2 ) ] + μ 1 2 Δ t k - 1 [ 3 j s ( r, t k ) − 4 j s ( r, t k − 1 ) + j s ( r, t k − 2 ) ] = 0 ;

[0079] When the dielectric has induced polarization effect, the conductivity is related to the frequency. The embodiment of the present invention adopts the Cole-Cole model to describe it, that is, the description equation is:

[0080] ;

[0081] in, is the zero-frequency conductivity, that is, the real conductivity when there is no induced polarization effect in the formation; m is the charging rate, which characterizes the intensity of the induced polarization effect of the polarized body; τ is the time constant, which characterizes the charging and discharging speed of the polarized body; c is the frequency correlation coefficient, which characterizes the uniformity of the mineral distribution in the polarized body, and its value range is ; i is the imaginary unit, ω is the angular frequency.

[0082] Substituting the descriptive equation into Ohm's law and performing an inverse Fourier transform, the expression of Ohm's law in the time domain including the induced polarization effect can be obtained as follows:

[0083] ;

[0084] The embodiment of the present invention further introduces the implicit differential discretization format of the Caputo operator:

[0085] 0 C D t α f ( t k ) = 1 Γ ( 2 − α ) { ∑ p = 0 k − 1 f ( t p + 1 ) − f ( t p ) Δ t p [ ( t k − t p ) 1 − α − ( t k − t p + 1 ) 1 − α ] } = 1 Γ ( 2 − α ) { ∑ p = 0 k − 2 f ( t p + 1 ) − f ( t p ) Δ t p [ ( t k − t p ) 1 − α − ( t k − t p + 1 ) 1 − α ] + [ f ( t k ) − f ( t k − 1 ) ] Δ t k - 1 − α } ;

[0086] Among them, c is the abbreviation of Caputo operator, Γ is the Gamma function, which is a basic function commonly used in fractional-order calculations, and α represents the order of fractional derivatives. express The pth time channel among the first k time channels of the time channel, The formula is applied to the p+1th time channel in the first k time channels to discretize the Ohm's law expression in the time domain including the induced polarization effect, and the result is:

[0087] σ 0 E ( r, t k ) + τ c σ 0 1 Γ ( 2 − c ) { ∑ p = 0 k − 2 E ( r, t p + 1 ) − E ( r, t p ) Δ t p [ ( t k − t p ) 1 − c − ( t k − t p + 1 ) 1 − c ] + [ E ( r, t k ) − E ( r, t k − 1 ) ] Δ t k - 1 − c } = j ( r, t k ) + τ c ( 1 − m ) 1 Γ ( 2 − c ) { ∑ p = 0 k − 2 j ( r, t p + 1 ) − j ( r, t p ) Δ t p [ ( t k − t p ) 1 − c − ( t k − t p + 1 ) 1 − c ] + [ j ( r, t k ) − j ( r, t k − 1 ) ] Δ t k - 1 − c } ;

[0088] Substituting the discretized expression into the electric field diffusion equation satisfied by three-dimensional transient electromagnetic, the diffusion equation of the electric field can be obtained as follows:

[0089] 1 μ ∇×∇× E ( r, t k ) + 1 2 Δ t k - 1 [ 3 j s ( r, t k ) − 4 j s ( r, t k − 1 ) + j s ( r, t k − 2 ) ] + 1 2 Δ t k - 1 [ 3 ( σ 0 g 0 + σ 0 g 1 ) E ( r, t k ) − 3 σ 0 g 1 E ( r, t k - 1 ) + 3 g 1 ( 1 − m ) j ( r, t k - 1 ) + 3 σ 0 ∑ p = 0 k − 2 ( g 2 ( p ) [ E ( r, t p + 1 ) − E ( r, t p ) ] ) − 3 ∑ p = 0 k − 2 ( g 2 ( p ) ( 1 − m ) [ j ( r, t p + 1 ) − j ( r, t p ) ] ) − 4 j ( r, t k − 1 ) + j ( r, t k − 2 ) ] = 0 ;

[0090] The embodiment of the present invention uses an unstructured tetrahedral grid to discretize the three-dimensional space, and introduces a vector interpolation basis function to interpolate and approximate the electric field in the grid unit. Then, the electric field in any tetrahedral grid unit can be expressed as:

[0091] ;

[0092] In the formula, is the vector interpolation basis function of the ith edge of the nth grid cell, is the tangential electric field on the i-th edge of the n-th grid unit.

[0093] Finite element discretization of the electric field diffusion equation using the Galerkin method:

[0094] ;

[0095] Applying Dirichlet boundary conditions to the electric field expression in any tetrahedral grid unit and assembling all time channels, the forward equations are:

[0096] ;

[0097] Wherein, A is a coefficient matrix, E is the electric field value to be determined on each edge of the tetrahedral mesh unit, and b is a source term. In the embodiment of the present invention, the MUMPS direct solver can be used to solve the forward equations.

[0098] According to the forward equation combined with the regularization theory, the objective function of transient electromagnetic three-dimensional inversion including induced polarization effect is constructed; in the embodiment of the present invention, an objective function based on Tikhonov regularization is adopted, and its expression is:

[0099] ;

[0100] In the formula, is the data covariance matrix, is the model roughness operator, , are the observed data vector and the forward response data vector, respectively. is the regularization factor, , are the calculation model parameter vector and the reference model parameter vector, respectively; it is worth noting that due to the introduction of the Cole-Cole model, the model parameters here have four dimensions, namely conductivity, charging rate, time constant and frequency correlation coefficient.

[0101] According to the three-dimensional forward modeling equation, an adjoint forward modeling calculation is performed to obtain the gradient of the transient electromagnetic three-dimensional inversion objective function, and an inversion equation is constructed according to the gradient of the objective function; the embodiment of the present invention calculates the sensitivity matrix information through an adjoint forward modeling once, and further calculates the objective function gradient, and the specific steps are as follows:

[0102] Taking partial derivatives of the left and right ends of the objective function with respect to the model parameter m, the gradient of the objective function can be obtained as:

[0103] ;

[0104] Where J is the sensitivity matrix, which can be expressed as:

[0105] ;

[0106] The transpose of the sensitivity matrix can be expressed as:

[0107] ;

[0108] In the formula, L is the interpolation operator, which means that the electric field on the edge is interpolated to the observation point to generate the predicted data; it can be seen that the direct calculation It is very difficult, so the embodiment of the present invention adopts the method of adjoint forward modeling to calculate, by calculating the product of the transpose of the sensitivity matrix and a vector, to implicitly calculate the sensitivity information, that is:

[0109] ;

[0110] make , then , so far, we only need to solve the linear equations to get , further substitute it into the expression of calculating the product of the transpose of the sensitivity matrix and a vector to calculate the sensitivity information. When the vector assigned to the expression is: , the calculation result can be directly substituted into the expression for obtaining the gradient value of the objective function for solution.

[0111] According to the electromagnetic data, the inversion equation and the initial parameter model, the transient electromagnetic three-dimensional inversion including the induced polarization effect is performed; in the embodiment of the present invention, for the kth iteration, the inversion equation is constructed according to the gradient of the objective function and is expressed as:

[0112] ;

[0113] in, , is a positive definite matrix representing the approximate Hessian matrix of the kth iteration, is the objective function gradient at the kth iteration. It can be updated using the Limited-Memory Quasi-Newton (L-BFGS) method.

[0114] The inversion equation is iteratively solved by the finite memory quasi-Newton method, and an updated model parameter vector is obtained after each iteration; the updated model parameter vector after each iteration is forward modeled to obtain the electromagnetic response data after each iteration;

[0115] The data fitting error is obtained based on the electromagnetic response data after each iteration and the electromagnetic data containing induced polarization effect; the data fitting error is specifically expressed as:

[0116] RMS = ∑ i = 1 N [ ( d obs ( i ) − d pre ( i ) ) 2 / e i 2 ] N ;

[0117] in, is the ith noise standard deviation, is the number of data, , are the observation data vector and the forward response data vector, respectively.

[0118] When the data fitting error meets the set conditions, the inversion is terminated and the model parameter vector at this time is output. The set conditions that need to be met for terminating the inversion include:

[0119] When the RMS value drops to 1, the inversion is terminated;

[0120] When the number of iterations reaches a given upper limit, the inversion is terminated;

[0121] When the RMS value no longer changes, the inversion is terminated.

[0122] In another specific embodiment of the present invention:

[0123] like Figure 4 FIG. 1 is a cross-sectional view of a three-dimensional resistivity inversion result obtained by a transient electromagnetic inversion method including induced polarization effect provided by an embodiment of the present invention, wherein: Figure 4 (a) is the resistivity two-dimensional section result at Y=0m. Figure 4 (b) is the resistivity two-dimensional section result at a depth of 60 m, Figure 4 It can be seen that the inversion results of resistivity can roughly describe the position and distribution of the horizontal plate-like body and delineate the boundary of the horizontal plate-like body to a certain extent. The inverted resistivity of the horizontal plate-like body fits the real resistivity of the actual model well.

[0124] Figure 51 is a schematic diagram of a two-dimensional section result of a charging rate inverted by a three-dimensional transient electromagnetic inversion method including induced polarization effect provided by an embodiment of the present invention, wherein: Figure 5 (a) is the two-dimensional section result of the charging rate at Y=0m. Figure 5 (b) is the two-dimensional section result of the charging rate at a depth of 60m, Figure 5 It can be seen that the inversion results of the charging rate can better describe the position and distribution of the horizontal plate-like body, and at the same time can well delineate the boundary of the horizontal plate-like body. The inverted horizontal plate charging rate well restores the charging rate of the actual real model.

[0125] Figure 6 is a two-dimensional section result of a time constant inverted by a three-dimensional transient electromagnetic inversion method including induced polarization effect provided by an embodiment of the present invention, wherein: Figure 6 (a) is the two-dimensional section result of the time constant at Y=0m. Figure 6 (b) is the two-dimensional section result of the time constant at a depth of 60 m, given by Figure 6 It can be seen that the inversion results of the time constant can well describe the position and distribution of the horizontal plate-like body, and can also well delineate the boundary of the horizontal plate-like body. The time constant of the horizontal plate-like body obtained by inversion can be clearly distinguished from the time constant of the surrounding rock.

[0126] Figure 7 It is a two-dimensional section result of the frequency correlation coefficient inverted by a three-dimensional transient electromagnetic inversion method including induced polarization effect provided by an embodiment of the present invention, wherein: Figure 7 (a) is the two-dimensional section result of the frequency correlation coefficient at Y=0m. Figure 7 (b) is the two-dimensional cross-sectional result of the frequency correlation coefficient at a depth of 60m, Figure 7 It can be seen that the inversion results of the frequency correlation coefficient can well describe the position and distribution of the horizontal plate-like body, and can also well delineate the boundary of the horizontal plate-like body. The frequency correlation coefficient of the horizontal plate-like body obtained by inversion can well restore the true frequency correlation coefficient of the actual model.

[0127] In summary, from Figure 4 , Figure 5 , Figure 6 and Figure 7 It can be seen that the inversion method provided in the embodiment of the present invention has an inversion result that is in good agreement with the real model, indicating that the three-dimensional inversion algorithm for transient electromagnetic with induced polarization effect provided in the embodiment of the present invention is reliable, and can overcome the problem that the traditional inversion method that does not consider the induced polarization effect cannot effectively invert the electromagnetic observation data in the area containing the induced polarization effect, and can provide high-resolution inversion results for the exploration area containing the induced polarization effect, playing an important role in mineral exploration.

[0128] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A transient electromagnetic three-dimensional inversion method including induced polarization effect, characterized in that: include: Arrange a square wireframe in the area to be surveyed and set receiving points to obtain electromagnetic data including induced polarization effect in the area to be surveyed; Establishing an initial parameter model of transient electromagnetic three-dimensional inversion including induced polarization effect according to the electromagnetic data; The Cole-Cole model is used to establish a description equation for the induced polarization effect in three-dimensional transient electromagnetics; the Caputo operator is used to time discretize the description equation, and the three-dimensional forward equation is established in combination with the vector finite element method; According to the forward equation combined with regularization theory, an objective function of transient electromagnetic three-dimensional inversion including induced polarization effect is constructed; Performing an adjoint forward calculation according to the three-dimensional forward equation, obtaining a gradient of a transient electromagnetic three-dimensional inversion objective function, and constructing an inversion equation according to the gradient of the objective function; A three-dimensional transient electromagnetic inversion including induced polarization effect is performed according to the electromagnetic data, inversion equation and initial parameter model.

2. The method for three-dimensional transient electromagnetic inversion including induced polarization effect according to claim 1, characterized in that: The Cole-Cole model is used to establish a description equation for the induced polarization effect in three-dimensional transient electromagnetics, specifically: According to the Maxwell equations in the time domain, the electric field diffusion equation satisfied by three-dimensional transient electromagnetic is: ； Where r represents the position vector, t represents the time, and E(r, t) represents the electric field intensity at r at time t. represents the conduction current density at r at time t, represents the current density of the external current source at time t at r, μ is the magnetic permeability, is the gradient operator; After the electric field diffusion equation is time discretized using the second-order backward Euler, the descriptive equation established using the Cole-Cole model is: ； in, is the zero-frequency conductivity, that is, the real conductivity when there is no induced polarization effect in the formation; m is the charging rate, which characterizes the intensity of the induced polarization effect of the polarized body; τ is the time constant, which characterizes the charging and discharging speed of the polarized body; c is the frequency correlation coefficient, which characterizes the uniformity of the mineral distribution in the polarized body, and its value range is ; i is the imaginary unit, ω is the angular frequency.

3. The method for three-dimensional transient electromagnetic inversion including induced polarization effect according to claim 1, characterized in that: The description equation is time discretized, specifically: Substituting the described equation into Ohm's law and performing inverse Fourier transformation to obtain the time domain Ohm's law expression including induced polarization effect; The Ohm's law expression is time discretized by introducing an implicit differential discretization format of the Caputo operator, and the discretized Ohm's law expression is substituted into the electric field diffusion equation satisfied by three-dimensional transient electromagnetics to obtain the electric field diffusion equation.

4. The method for three-dimensional transient electromagnetic inversion including induced polarization effect according to claim 3, characterized in that: Combined with the vector finite element method, the three-dimensional forward equation is established, including: Unstructured tetrahedral grids are used to discretize the three-dimensional space, and vector interpolation basis functions are introduced to interpolate and approximate the electric field in the grid unit to obtain the electric field expression in any tetrahedral grid unit. The electric field diffusion equation is discretized by finite element method using Galerkin method; Applying Dirichlet boundary conditions to the electric field expression and assembling all time channels, the forward equations are: ； Where A is the coefficient matrix, E is the electric field value to be determined on each edge of the tetrahedral mesh unit, and b is the source term.

5. The method for three-dimensional transient electromagnetic inversion including induced polarization effect according to claim 1, characterized in that: The objective function of the transient electromagnetic three-dimensional inversion including induced polarization effect is constructed, and the expression is: ； in, is the data covariance matrix, is the model roughness operator, , are the observed data vector and the forward response data vector, respectively. is the regularization factor, , are the calculation model parameter vector and the reference model parameter vector respectively.

6. The method for three-dimensional transient electromagnetic inversion including induced polarization effect according to claim 1, characterized in that: Performing adjoint forward calculation according to the three-dimensional forward equation to obtain the gradient of the transient electromagnetic three-dimensional inversion objective function includes: In the objective function, the partial derivatives of the model parameter m are obtained at both ends to obtain the gradient of the objective function: ； In the formula, is the model roughness operator, , are the observed data vector and the forward response data vector, respectively. is the regularization factor, , are the calculation model parameter vector and the reference model parameter vector, respectively, J is the sensitivity matrix, and the superscript T indicates the transpose of the matrix; The sensitivity matrix is ​​solved by the adjoint forward modeling method, and the solved sensitivity matrix is ​​substituted into the above formula to calculate the gradient of the objective function.

7. The method for three-dimensional transient electromagnetic inversion including induced polarization effect according to claim 1, characterized in that: An inversion equation is constructed according to the gradient of the objective function, including: For the kth iteration, the inversion equation is constructed based on the gradient of the objective function and is expressed as: ； in, , is a positive definite matrix, representing the approximate Hessian matrix of the kth iteration, is the objective function gradient at the kth iteration.

8. The method for three-dimensional transient electromagnetic inversion including induced polarization effect according to claim 1, characterized in that: Perform 3D transient electromagnetic inversion with IP effect, including: Iteratively solving the inversion equation by a finite memory quasi-Newton method, and obtaining an updated model parameter vector after each iteration; Perform forward modeling on the updated model parameter vector after each iteration to obtain the electromagnetic response data after each iteration; The data fitting difference is obtained based on the electromagnetic response data after each iteration and the electromagnetic data including the induced polarization effect; When the data fitting error meets the set conditions, the inversion is terminated and the model parameter vector at this time is output.

9. The method for three-dimensional transient electromagnetic inversion including induced polarization effect according to claim 8, characterized in that: The data fitting difference is obtained based on the electromagnetic response data after each iteration and the electromagnetic data containing induced polarization effect, including: ； in, is the ith noise standard deviation, is the number of data, , are the observation data vector and the forward response data vector, respectively.

10. The method for three-dimensional transient electromagnetic inversion including induced polarization effect according to claim 8, characterized in that: The setting conditions include: When the RMS value drops to 1, the inversion is terminated; When the number of iterations reaches a given upper limit, the inversion is terminated; When the RMS value no longer changes, the inversion is terminated.

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