A joint inversion method for transient electromagnetic and magnetic data

Abstract

This invention discloses a joint inversion method for transient electromagnetic and magnetic data, comprising the following steps: acquiring transient electromagnetic observation data and magnetic observation data; converting the transient electromagnetic observation data into transient electromagnetic moment data; constructing a joint inversion objective function based on the transient electromagnetic moment data and magnetic observation data, the joint inversion objective function including: data fitting residual terms and model constraint terms; using a multivariate Gaussian mixture model to parameterize the model constraint terms, obtaining the coupled model constraint terms; combining the data fitting residual terms and the coupled model constraint terms into the final objective function, and minimizing the final objective function through an optimization algorithm to obtain the electrical and magnetic parameters of the subsurface medium. This invention achieves joint inversion of transient electromagnetic and magnetic data, solves the problem of low computational efficiency in three-dimensional inversion by introducing transient electromagnetic moments, and utilizes rock physics constraints to couple electrical and magnetic parameters, making the inversion results more accurate and structurally consistent.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology, specifically to a method for joint inversion of transient electromagnetic and magnetic data. Background Technology

[0002] Transient electromagnetic methods and magnetic methods are two commonly used geophysical methods in underground space exploration, used to obtain resistivity and magnetic susceptibility parameters of underground media, respectively. In fields such as mineral resource exploration, these two parameters are typically highly sensitive for identifying target geological bodies (such as ore bodies). Therefore, in practice, these two methods are often used in combination in the same exploration area to obtain a complementary and more comprehensive understanding of the underground structure.

[0003] However, these two methods face a significant technical imbalance in data inversion. The field propagation in the transient electromagnetic method follows the computationally complex Helmholtz equations, and its three-dimensional numerical simulation requires discretization in both time and space, resulting in an extremely large computational burden. This bottleneck severely restricts the development and application of its three-dimensional inversion technology, causing current practical production to still mainly rely on approximate one-dimensional inversion methods. These simplified methods are insufficient for accurately characterizing complex three-dimensional geological structures.

[0004] In contrast, magnetic inversion, based on the relatively simple Poisson equation, is computationally efficient, and its high-precision three-dimensional inversion technology is quite mature and widely used in practical data processing. Thanks to this maturity, joint inversion studies using magnetic methods with other geophysical methods (such as gravity and seismic methods) have also yielded significant results.

[0005] Currently, in the collaborative detection of transient electromagnetic and magnetic methods, due to the technical bottleneck of transient electromagnetic methods in high-dimensional inversion, the data processing and interpretation of the two methods usually adopt a step-by-step mode of "independent inversion and comprehensive interpretation". However, geophysical inversion itself has strong nonlinearity and non-uniqueness of solutions. Under complex geological conditions, this step-by-step processing method can easily lead to deviations or even contradictions in the inversion results of the two methods, making it difficult to form a unified and reliable geological model.

[0006] Therefore, how to overcome the bottleneck of efficiency in three-dimensional inversion of transient electromagnetic methods and develop a joint inversion method that can effectively couple electrical and magnetic information to achieve integrated synchronous inversion of transient electromagnetic and magnetic data has become a key technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention introduces transient electromagnetic moments and their rapid simulation methods to solve the computational efficiency problem in the joint inversion of transient electromagnetic and magnetic data. Based on this, a joint inversion strategy with rock physics constraints is employed to achieve joint optimization of the time constant and magnetic susceptibility. Finally, the time constant in the results is converted into electrical conductivity, thereby realizing a high-precision three-dimensional joint inversion of transient electromagnetic and magnetic data.

[0008] To achieve the above objectives, this invention provides a method for joint inversion of transient electromagnetic and magnetic data, comprising the following steps:

[0009] Acquire transient electromagnetic observation data and magnetic observation data;

[0010] The transient electromagnetic observation data is converted into transient electromagnetic moment data;

[0011] Based on the transient electromagnetic moment data and the magnetic observation data, a joint inversion objective function is constructed, which includes: a data fitting residual term and a model constraint term.

[0012] The model constraint terms are parametrically coupled using a multivariate Gaussian mixture model to obtain the coupled model constraint terms.

[0013] The data fitting residuals and coupled model constraints are combined to form the final objective function, and the electrical and magnetic parameters of the underground medium are obtained by minimizing the final objective function through an optimization algorithm.

[0014] Preferably, the steps for converting transient electromagnetic observation data into transient electromagnetic moment data include:

[0015] The transient electromagnetic moment is defined based on the power product of the transient electromagnetic field pulse response and time.

[0016] The transient electromagnetic moment is subjected to an integral transformation to obtain transient electromagnetic moment data for inversion.

[0017] Preferably, the transient electromagnetic moment is a first-order transient electromagnetic moment, and its expression is:

[0018]

[0019] in, t 0 indicates the time to close the ramp at its midpoint; Represents the current function; Apparent magnetic field impulse response.

[0020] Preferred methods for conducting three-dimensional numerical simulations based on transient electromagnetic moment data include:

[0021] The underground medium is discretized into cubic units, and the electrical parameters of each unit are characterized by a time constant.

[0022] The magnetic dipole response of each unit under a single magnetic field is calculated using Biot-Savart's law;

[0023] The total response of the transient electromagnetic first moment is obtained by superimposing the responses of all elements.

[0024] Preferably, the time constant and conductivity are converted using the following relationship:

[0025]

[0026] in, τ It is a time constant; σ Electrical conductivity; μ Permeability of free space; l is the side length of the grid cell.

[0027] Preferably, the method for parametrically coupling model constraint terms using a multivariate Gaussian mixture model includes:

[0028] Based on prior geological and rock physics information, a multivariate Gaussian mixture model is constructed.

[0029] Based on the aforementioned multivariate Gaussian mixture model, the prior distribution of the model parameters is defined;

[0030] Rock physics constraints are constructed using negative log-likelihood functions to couple electrical and magnetic parameters.

[0031] Preferably, the joint inversion objective function is expressed as:

[0032]

[0033] in, Represents the data fitting residual term; Represents rock physics constraints; Represents the model regularization term; β , αs , αp , v These are the weighting coefficients; x , y , z These represent the three directions of the Cartesian coordinate system in space; v represents the direction index; m represents the model vector containing the electrical and magnetic parameters of all grid cells.

[0034] Preferably, the data fitting residual term is calculated using the following formula:

[0035]

[0036] in,k An index for geophysical data types; r The total number of geophysical data types participating in the joint inversion; For numerical simulation operators; This represents the k-th type of observation data; For the first k Error weighting matrix for class data.

[0037] Preferably, the model constraints include rock physics constraints and spatial regularization terms, wherein the rock physics constraints are constructed using the negative log-likelihood function of a multivariate Gaussian mixture model.

[0038] Preferred methods for minimizing the objective function through optimization algorithms include:

[0039] Set the initial model parameters and inversion control parameters;

[0040] Iteratively update the model parameters until the data fitting residuals and model constraint terms satisfy the preset convergence conditions;

[0041] Output the final electrical and magnetic parameter models.

[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0043] (1) This patent realizes the joint inversion of transient electromagnetic data and magnetic data, so that the recovered electrical and magnetic structures remain consistent in the inversion of these two types of data, and the obtained model can satisfy the observation data and prior information.

[0044] (2) By introducing transient electromagnetic moments, the efficiency problem of transient electromagnetic three-dimensional numerical simulation was solved, and three-dimensional joint inversion of transient electromagnetic and magnetic data was realized.

[0045] (3) Compared with conventional single inversion methods, the model obtained by the method of this patent not only conforms to prior knowledge, but also effectively utilizes the correlation between conductivity and magnetization to obtain more accurate model parameters. Attached Figure Description

[0046] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a schematic diagram of a model according to an embodiment of the present invention; (a) in the figure is a schematic diagram of the designed test model; (b) and (c) are... Planar plots of magnetic susceptibility and conductivity; (d) and (e) are... Cross-sectional view of the model at the location;

[0048] Figure 2 This is a schematic diagram of the magnetic TMI and transient electromagnetic data generated according to an embodiment of the present invention; (a) in the figure is a multi-channel plot of transient electromagnetic data at y = 0; (b) in the figure is the corresponding transient electromagnetic first moment; (c) is the magnetic TMI number; (d) is the planar distribution plot of the transient electromagnetic first moment.

[0049] Figure 3 This invention presents the results of magnetic susceptibility and time constant obtained from generated magnetic TMI data and transient electromagnetic data using smooth inversion in an embodiment of the invention; wherein, (a) and (b) in the figure are... Plan view of the location; (c) and (d) are Cross-sectional view at the location;

[0050] Figure 4 This embodiment of the invention provides a multivariate Gaussian mixture model for constraining the joint inversion of transient electromagnetic and magnetic methods in rock physics, wherein the intersection plot represents the constraint relationship between magnetic susceptibility and electrical conductivity.

[0051] Figure 5 This invention provides the magnetic susceptibility and time constant results obtained from the generated magnetic TMI data and transient electromagnetic data using joint inversion in an embodiment of the invention; figures (a) and (b) show... Plan view of the location; (c) and (d) Cross-sectional view at the location;

[0052] Figure 6 The survey line distribution of transient electromagnetic and magnetic methods for the exploration of the Bell porphyry copper-gold deposit in Canada, as described in this embodiment of the invention;

[0053] Figure 7 The above are conventional smooth inversion results of embodiments of the present invention; (a) and (b) in the figure are planar distribution maps at an altitude of 400 meters; (c) and (d) are depth profiles with north coordinates = 6098652 m;

[0054] Figure 8 The magnetic susceptibility and resistivity models obtained from the joint inversion of magnetic and mouse electromagnetic data of the Bell deposit in this embodiment of the invention are shown in (a) and (b) in the figure, which are planar distribution maps at an altitude of 400 meters; (c) and (d) are depth profiles with north coordinates of 6098652m. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] Example 1

[0058] This embodiment provides a method for joint inversion of transient electromagnetic and magnetic data, the steps of which include:

[0059] S1. Acquire transient electromagnetic observation data and magnetic observation data.

[0060] S2. Convert transient electromagnetic observation data into transient electromagnetic moment data.

[0061] magnetic field pulse response With time t of n The product of powers is defined as the transient electromagnetic moment. Assume the midpoint of the turn-off ramp of the transient electromagnetic source signal is... t 0, transient electromagnetic n The step moment is defined in the following form:

[0062] (1)

[0063] The integral transform defined in the above equation can be used to simplify and accelerate the numerical simulation of transient electromagnetic events. This invention will use the first moment from the above equation for calculation, namely:

[0064] (2)

[0065] in, t 0 indicates the time to close the ramp at its midpoint; Represents the current function; Apparent magnetic field impulse response; t Represents a time variable.

[0066] After introducing the transient electromagnetic moment, the transient electromagnetic data used for inversion is the first-order transient electromagnetic moment. At this point, the model parameters for inversion are not the conductivity used in conventional inversion, but rather the time constant of each subsurface element. The time constant τ describes the exponential decay rate of the transient electromagnetic response. In the joint inversion of this patent, the following conversion relationship is used to convert conductivity to time constant.

[0067] (3)

[0068] in, σ conductivity μ Permeability in vacuum l is the side length of the grid cell.

[0069] Based on the transformation relationship established by equations (2) and (3), the transient electromagnetic first moment will be used as data and the time constant will be used as the model parameter in the joint inversion scheme of this embodiment.

[0070] S3. Based on transient electromagnetic moment data and magnetic observation data, a joint inversion objective function is constructed, which includes: data fitting residual term and model constraint term.

[0071] Numerical simulation of the transient electromagnetic first moment is similar to that of magnetic simulation, except that the source of the primary magnetic field originates from the Earth's magnetic field, while the source of the transient electromagnetic moment originates from a transmitter. The subsurface medium is discretized into cubic cells, with the electrical parameters of each cell characterized by a time constant. Using the Biot-Savart law, a magnetic field is calculated at the center of each cell, exciting a magnetic dipole whose strength is proportional to the magnetic field amplitude and the time constant of each cell. In the... i Within each unit, the magnetic dipole at the observation point The transient electromagnetic first-order magnetic moment generated at the location for:

[0072] (4)

[0073] Among them, geometric coupling factor for:

[0074] (5)

[0075] in, From the observation point to the i The position vector of the center of each unit It is the time constant of this unit. It is the amplitude of the magnetic field at the center of the unit. It is the volume of the unit. Is with Parallel unit vectors Is with Parallel unit vectors It is the distance from the center of the unit cell to the observation point. Transient electromagnetic first-order moment response. The superposition of the dipole responses of all units and the background transient electromagnetic moment sum:

[0076] (6)

[0077] The transient electromagnetic moment in the three-dimensional model can be obtained by superposition using equation (6). The magnetic data can be solved by solving the Poisson equation satisfied by the potential field.

[0078] S4. Use a multivariate Gaussian mixture model to perform parameter coupling on the model constraint terms and obtain the coupled model constraint terms.

[0079] When conducting joint inversion using transient electromagnetic and magnetic methods, it is necessary to constrain resistivity and magnetic susceptibility to optimize them jointly during the inversion process. This embodiment uses a Geophysical Model (GMM) to encapsulate prior rock physical and geological information, guiding the joint optimization of resistivity and magnetic susceptibility during the inversion. For [the specific rock type / structure]... q A physical property parameter describes c Each lithological unit The lithological characteristics are represented by a multivariate Gaussian probability distribution. To characterize, among which It is the size of q The mean vector, It is the size of q × q The covariance matrix, It is the proportion of this category.

[0080] Then, assuming the model vector Depend on n Subvectors on each grid cell Composition, each subvector contains the first i Unit q Individual physical property parameter values. The multivariate Gaussian distributions of each lithological unit are weighted and superimposed to establish a multivariate Gaussian mixture model, used to characterize the geophysical model type. m The prior distribution of the GMM. At this point, the probability distribution of the GMM can be represented in the following form:

[0081] (7)

[0082] in, Represents the set of parameters of the GMM; It is the first i Geological classification of individual grid units (i.e., the category to which a particular lithological unit belongs). It is the first i The unit belongs to the first j The prior probability of a lithological unit (this probability can be a constant within a region). Alternatively, it can be determined locally based on prior geological knowledge. It is a diagonal weighted matrix, often used for depth-weighted or sensitivity-weighted calculations.

[0083] The negative log-likelihood function of the Gaussian mixture model (GMM) defined by Equation (7) can be used to construct a single rock physics "smallness term" to couple multiple physical properties. This negative log-likelihood can be approximated as a least-squares norm form.

[0084] (8)

[0085] Among them, the reference model Minimum degree weighted matrix It is constructed using the mean and variance extracted from the GMM:

[0086] (9)

[0087] (10)

[0088] in, It's an upper triangular matrix. The cell's ownership... Determined by maximizing the posterior probability:

[0089] (11)

[0090] S5. Combine the data fitting residuals with the coupled model constraints to form the final objective function, and minimize the final objective function through an optimization algorithm to obtain the electrical and magnetic parameters of the underground medium.

[0091] Geophysical inversion is achieved by minimizing an objective function. Under the numerical simulation methods for transient electromagnetic and magnetic methods, as well as the joint optimization method defined above, by constructing the inversion objective function and combining it with the optimization method, a geophysical model that simultaneously fits the data and parameter constraints can be obtained as the inversion solution. In the joint inversion scheme proposed in this invention, the following objective function is adopted. :

[0092] (12)

[0093] in, The fitting residuals of the transient electromagnetic and magnetic data involved in the inversion are... β To balance the constant factors of the data fitting residuals and model constraint terms, Terms related to model constraints, including regularization terms. The constraints are shown in equation (8). Therefore, the objective function can be expressed as:

[0094] (13)

[0095] The data fitting residual term is:

[0096] (14)

[0097] in, Represents numerical simulation operators. For the transient electromagnetic or magnetic data observed, This is the error weighting matrix for the data.

[0098] Regularization term, r This indicates the number of geophysical data types participating in the joint inversion scheme in this embodiment. r =2. Regularization term of model constraints. The smoothness of the model parameters in the longitudinal or transverse direction can be constrained and defined within the framework of Equation (13) to improve the stability of the inversion.

[0099] Example 2

[0100] To test and verify the joint inversion method proposed in this invention, a three-dimensional model for method testing was designed, see [link to model]. Figure 1 The model consists of two blocks with different electrical and magnetic characteristics. Each block measures 100 m × 100 m × 300 m and is located at... At (400 m, 0 m), the top of the blocks is buried at a depth of 100 m. The first block (Block-1) has high electrical conductivity (100 mS / m) and medium magnetic susceptibility (0.01 SI); the second block (Block-2) has low electrical conductivity (10 mS / m) and high magnetic susceptibility (0.02 SI). Both blocks are embedded in a high resistivity, non-magnetic background medium with a background conductivity of 1 mS / m and zero magnetic susceptibility.

[0101] Synthetic total magnetic anomaly (TMI) data and first-order transient electromagnetic moment responses were generated, such as... Figure 2 As shown in the figure. Subsequently, conventional smoothing inversion algorithm and joint inversion algorithm were used to invert the two sets of data for comparative analysis.

[0102] In the smoothing inversion, the initial value of the magnetic susceptibility model was set to 0.0001 SI, and the reference model was set to 0; the initial value of the time constant model was 0.0001 ms, and the reference model was also set to 0. Smoothing inversions were performed for 10 iterations on the total magnetic anomaly (TMI) data and the first-order transient electromagnetic moment data, respectively. The final data fitting errors were 0.61 and 0.59, respectively, indicating good agreement between the inversion results and the observed data. To ensure the physical validity of the inversion results, non-negative lower limits (lower limit of 0) were set for both magnetic susceptibility and time constant. The target value for the data fitting error was set to 1.

[0103] The magnetic susceptibility and time constant model obtained by smooth inversion is as follows: Figure 3 As shown, the positions and geometries of the two blocks are generally well recovered. However, Block-2 is not effectively identified in the time constant model, due to the low sensitivity of transient electromagnetic data to high-resistivity bodies. Furthermore, the recovered magnetic susceptibility is generally lower than the true value, mainly due to the smoothing effect of the depth-weighted function.

[0104] In the joint inversion, the lithology-constrained joint inversion uses a Gaussian mixture model (GMM) to express the prior petrophysical knowledge of rock units, thereby constraining the inversion process. This GMM is constructed based on the real physical property parameters of the synthetic model, such as... Figure 4 As shown. In the inversion, electrical conductivity is expressed as a time constant and calculated according to formula (3) combined with the grid cell volume. After the inversion is completed, it is converted back to electrical conductivity for comparison with the actual rock physical property values. The initial β ratio is set to 10. -4 The model was incremented by a factor of 2 in each iteration. The target data fitting error was set to 1, and the target rock property fitting error was set to 0.1. Due to high confidence in the synthetic rock property information, the GMM remained unchanged throughout the inversion process. The joint inversion was completed after 5 iterations, and the target data fitting errors for both datasets reached 0.73, indicating that the obtained model was consistent with the observed data.

[0105] Figure 5 The magnetic susceptibility and time constant models obtained from the joint inversion are presented. The inversion results show a well-structured and compactly bounded anomaly with contours highly consistent with real geological units. Notably, the high resistivity Block-2, which failed to be resolved in the smoothing inversion, was effectively imaged in the time constant model.

[0106] Furthermore, the converted electrical conductivity and magnetic susceptibility are in high agreement with the actual values, indicating that lithology-constrained inversion can more accurately reflect subsurface physical properties using electrical conductivity compared to smooth inversion results characterized by time constants. The consistency between the two models is also reflected in… Figure 4 In the cross plot shown, the inverted values ​​cluster closely around the true mean rock properties. This indicates that the lithology-constrained joint inversion not only generates a model consistent with rock property knowledge, but also effectively captures the common geological features between the magnetic susceptibility and electrical conductivity models.

[0107] The inversion method in this embodiment mainly consists of numerical simulation, model parameter constraints, and optimization methods. In the transient electromagnetic numerical simulation, a transient electromagnetic moment is introduced, and a three-dimensional numerical simulation is conducted based on this transient electromagnetic moment to address the efficiency problem of numerical simulation of high-dimensional transient electromagnetics, achieving joint inversion of two types of data in a three-dimensional model space. After converting conventional transient electromagnetic data into a transient electromagnetic moment, the inversion yields a time constant for the subsurface medium. To further connect the subsurface physical parameters, a conversion relationship between the time constant and conductivity is introduced, enabling bidirectional conversion between the numerical simulation and inversion results.

[0108] This embodiment utilizes a joint inversion algorithm framework to fit transient electromagnetic and magnetic data. To address the synergistic optimization problem of electrical and magnetic properties, a multivariate Gaussian mixture model is introduced to encapsulate prior geological and geophysical information. Based on this, by establishing a joint inversion objective function, geophysical inversion optimization methods are employed to obtain electrical and magnetic parameters from the observed transient electromagnetic and magnetic data.

[0109] The method described in this embodiment can fit transient electromagnetic and magnetic data within a joint inversion framework, and the obtained model exhibits good consistency. Compared with individual smoothing inversion, the method of this patent can more accurately obtain the electrical conductivity and magnetic susceptibility of the medium. Furthermore, the obtained model not only fits the observed data but also generates a model that conforms to prior knowledge, effectively capturing the common geological features between magnetic susceptibility and electrical conductivity.

[0110] Example 3

[0111] This embodiment utilizes data from the combined transient electromagnetic and magnetic detection methods conducted at the Bell porphyry copper-gold mine in Canada to verify the effectiveness of the method. The survey line layout is shown below. Figure 6 As shown, avionics and magnetic data were collected in this region using an airborne transient electromagnetic system based on a helicopter pod and a cesium optically pumped magnetometer. Before inversion, the collected data underwent the following preprocessing: for magnetic data, TMI underwent hysteresis correction, peak elimination, day / night correction, and IGRF correction; for incidental electromagnetic data, the derivative of the magnetic field over time was normalized using the emission current, and a Savitzky-Golay filter (polynomial degree 3, window size 5 points) was used to smooth out spikes that might produce artifacts in the inversion model. Then, the processed data was used for inversion studies.

[0112] To demonstrate the effectiveness of the method, both the conventional smoothing inversion method and the joint inversion method proposed in this patent were used to invert transient electromagnetic and magnetic data of the survey area. The results are as follows: Figure 7 and Figure 8As shown. In the conventional smoothing inversion, the inversion converged after 7 iterations, with a fitting residual of 0.74 for the TMI data and 0.64 for the transient electromagnetic data. (From...) Figure 7 It can be seen that the resistivity and magnetic susceptibility are generally consistent and can restore the shape of the underground target body with consistent structure. However, the details of the two are scattered, indicating that the two models did not capture the same geological features.

[0113] For the joint inversion, the target fitting residual for the magnetic and transient electromagnetic data was 1, and the target fitting residual for the rock physical data was 0.5. The inversion converged after 20 iterations, with a fitting residual of 0.74 for the TMI data and 0.68 for the transient electromagnetic data. Figure 8 As can be seen, compared with conventional smoothing inversion, the joint inversion clearly recovers the dense, well-defined rock mass. Therefore, under the same magnetic and transient electromagnetic data, introducing the joint inversion method proposed in this invention can fully utilize the cross-constraints of magnetic and electrical structures by magnetic and transient electromagnetic methods, and can also obtain better inversion results by further introducing rock physics-based constraint methods.

[0114] This invention proposes a method for joint inversion of transient electromagnetic and magnetic data. The joint inversion method mainly consists of numerical simulation, model parameter constraints, and optimization methods. In the transient electromagnetic numerical simulation, this invention introduces a transient electromagnetic moment and conducts three-dimensional numerical simulations based on this moment to address the efficiency problem of numerical simulation of high-dimensional transient electromagnetic data, achieving joint inversion of the two types of data in a three-dimensional model space. After converting conventional transient electromagnetic data into a transient electromagnetic moment, the inversion yields a time constant for the subsurface medium. To further connect the subsurface physical parameters, a conversion relationship between the time constant and conductivity is introduced, enabling bidirectional conversion between the numerical simulation and inversion results.

[0115] This invention utilizes a joint inversion algorithm framework to fit transient electromagnetic and magnetic data. To address the problem of co-optimizing electrical and magnetic properties, a multivariate Gaussian mixture model is introduced to encapsulate prior geological and geophysical information. Based on this, by establishing a joint inversion objective function and employing geophysical inversion optimization methods, electrical and magnetic parameters are obtained from the observed transient electromagnetic and magnetic data.

[0116] The method of this invention enables the fitting of transient electromagnetic and magnetic data within a joint inversion framework, resulting in a model with good consistency. Compared with individual smoothing inversions, the method of this invention can more accurately obtain the electrical conductivity and magnetic susceptibility of the medium. Furthermore, the obtained model not only fits the observed data but also generates a model that conforms to prior knowledge, effectively capturing the common geological features between magnetic susceptibility and electrical conductivity.

[0117] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for joint inversion of transient electromagnetic and magnetic data, characterized in that, Includes the following steps: Acquire transient electromagnetic observation data and magnetic observation data; The transient electromagnetic observation data is converted into transient electromagnetic moment data. The steps include: defining a transient electromagnetic moment based on the power product of the transient electromagnetic field impulse response and time; performing an integral transform on the transient electromagnetic moment to obtain transient electromagnetic moment data for inversion; the transient electromagnetic moment is a first-order transient electromagnetic moment, and its expression is: ； in, t 0 indicates the time to close the ramp at its midpoint; Represents the current function; Apparent magnetic field impulse response; t Represents a time variable; Based on the transient electromagnetic moment data and the magnetic observation data, a joint inversion objective function is constructed, which includes: a data fitting residual term and a model constraint term; the joint inversion objective function is expressed as: ； in, Represents the data fitting residual term; Represents rock physics constraints; Represents the model regularization term; β , αs , αp , v These are the weighting coefficients; x , y , z These represent the three directions of the Cartesian coordinate system in space; v represents the direction index; m represents the model vector containing the electrical and magnetic parameters of all grid cells; The data fitting residual term is calculated using the following formula: ； in, k An index for geophysical data types; r The total number of geophysical data types participating in the joint inversion; For numerical simulation operators; This represents the k-th type of observation data; For the first k Error weighting matrix for class data; The model constraints include rock physics constraints and spatial regularization terms, wherein the rock physics constraints are constructed using the negative log-likelihood function of a multivariate Gaussian mixture model; the model constraints are parameter-coupled using a multivariate Gaussian mixture model to obtain the coupled model constraints; the method includes: Based on prior geological and rock physics information, a multivariate Gaussian mixture model is constructed. Based on the aforementioned multivariate Gaussian mixture model, the prior distribution of the model parameters is defined; Rock physics constraints are constructed using the negative log-likelihood function to couple electrical and magnetic parameters. The data fitting residuals and coupled model constraints are combined to form the final objective function, and the electrical and magnetic parameters of the underground medium are obtained by minimizing the final objective function through an optimization algorithm.

2. The method for joint inversion of transient electromagnetic and magnetic data according to claim 1, characterized in that, Methods for conducting three-dimensional numerical simulations based on transient electromagnetic moment data include: The underground medium is discretized into cubic units, and the electrical parameters of each unit are characterized by a time constant. The magnetic dipole response of each unit under a single magnetic field is calculated using Biot-Savart's law; The total response of the transient electromagnetic first moment is obtained by superimposing the responses of all elements.

3. The method for joint inversion of transient electromagnetic and magnetic data according to claim 2, characterized in that, The time constant and conductivity can be converted using the following relationship: ； in, σ Electrical conductivity; μ The vacuum permeability; l is the side length of the grid cell.

4. The method for joint inversion of transient electromagnetic and magnetic data according to claim 1, characterized in that, Methods for minimizing the objective function through optimization algorithms include: Set the initial model parameters and inversion control parameters; Iteratively update the model parameters until the data fitting residuals and model constraint terms satisfy the preset convergence conditions; Output the final electrical and magnetic parameter models.

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