Occam-based SATEM transverse constraint quasi-two-dimensional inversion method

Abstract

The invention relates to the technical field of exploration, and discloses an SATEM transverse constraint quasi-two-dimensional inversion method based on Occam. Firstly, one-dimensional SATEM forward modeling is carried out, and the precision of a numerical solution is verified. And then adding a transverse constraint weight factor in the inversion objective function, and adjusting the continuity strength of the electrical units of the adjacent measuring points. Setting a three-dimensional theoretical model, calculating three-dimensional forward modeling response, and selecting a plurality of sections for inversion; by adjusting the transverse constraint weight factor, the influence of the transverse constraint weight factor on the inversion effect is analyzed, and an inversion result is obtained. Compared with three-dimensional inversion, the method is higher in efficiency and lower in hardware requirement, has important value for preliminarily understanding underground structures and providing an initial model for three-dimensional inversion, and has better recovery capability for structures with high transverse continuity and stratified stratums.

Description

Technical Field

[0001] The invention relates to the field of exploration technology, and in particular to an Occam-based SATEM lateral constraint quasi-two-dimensional inversion method. Background Art

[0002] Mineral resources are vital to my country's economic development. The demand for them is huge, and the external dependence is high, which has largely restricted the high-quality development of the economy. The improvement of the level of basic geological survey work has led to the exhaustion of shallow and easily identifiable minerals. In order to alleviate the contradiction between supply and demand of mineral resources, it is urgent to develop an efficient electromagnetic exploration method and technology. The transmitter and signal receiver of the traditional ground transient electromagnetic method are laid on the surface, which not only has a slow data acquisition speed, but also makes it more difficult to move the observation system in areas with slightly complex terrain, which often requires a lot of costs. The semi-aeronautical transient electromagnetic method (SATEM) combines the advantages of ground and airborne transient electromagnetic systems. The high-power transmitter is laid on the ground, and the receiver is placed on the flying vehicle to measure the induced magnetic field in the coil. In recent years, it has developed into a new type of transient electromagnetic measurement method, such as Figure 1 As shown. The grounding wire source has the advantage of using electrodes to inject current into the ground, allowing low-frequency waveforms and larger offset distances, which means that under the same conditions, the electrical source can get a stronger response than the magnetic source, so the grounding wire source is more suitable for semi-aeronautical transient electromagnetic measurement (Becken et al., 2020). Compared with the ground transient electromagnetic system, this system has the characteristics of high efficiency, large detection range, repeatable observation, and high lateral resolution. It is suitable for exploration tasks in mountainous and undulating terrain. At the same time, it has more advantages in the division of underground electrical structures. It has become a hot spot for deep earth exploration and has been developed in geothermal resource surveys (Verma et al., 2010), volcanic structure surveys (Mogi et al., 2009, Ito et al., 2014, Allah and Mogi, 2016), and coastal zone surveys (Ito et al., 2011, Allah et al., 2013). It is widely used in underground cavities, resource and environmental monitoring, mineral exploration, etc. (Wu et al., 2019).

[0003] With the development of transient electromagnetic technology, the research on inversion methods for huge observation data has gradually followed up. Traditional gradient inversion relies on the initial geoelectric model. Li (2023) proposed a heuristic algorithm (WOA) suitable for nonlinear inversion to perform TEM data inversion. The inversion framework was optimized through back-propagation learning (OBL) and adaptive weighting factor (AWF), which enhanced the solution accuracy and ensured convergence stability. Sun et al. (2019) used a fully nonlinear one-dimensional inversion method of simulated annealing to restore the resistivity of multilayer media, but because the model update requires a large number of forward and inversion calculations, it is difficult to meet the actual requirements in terms of timeliness. Lei (2022) used the Jacobi matrix chain analysis method for calculation, and considered the calculation of the current waveform in the inversion. The measured data was inverted to obtain a more realistic underground resistivity structure. Chen and Sun (2020) studied the best detection area of ​​SATEM and theoretically proved that considering comprehensive factors such as sensitivity, resolution, and detection depth, it is easiest to obtain reasonable data by using a flying platform to measure the vertical component of the magnetic field.

[0004] In actual geological conditions, due to the influence of volume effects, it is obviously unreasonable to use a uniform layered model to simulate the distribution of three-dimensional geological bodies. The three-dimensional inversion technology has high hardware requirements, storage costs and time costs, and the calculation is very complex and inefficient. It is even more difficult for the semi-aeronautical transient electromagnetic law of mobile reception. It is mainly used for theoretical research and can be considered in the fine analysis of data. Due to the large amount of data, in practical applications, the interpretation of semi-aeronautical transient electromagnetic data is mainly based on one-dimensional inversion algorithms, mainly damped least squares method (Huang and Palacky, 1991, Yang Cong, 2020) and Occam inversion (Mao Qilin et al., 2011). The profile of one-dimensional single-point inversion often has poor lateral continuity of resistivity. Considering the actual geological conditions, the electrical parameters of the underground medium of several adjacent measuring points should have a certain degree of continuity in space. In addition, for the data recorded in the late period, it is greatly affected by noise. The introduced noisy data will also cause lateral mutations in the inversion results (He et al., 2022). The method of laterally constrained inversion (LCI) on the parameters of adjacent stratigraphic units (resistivity, thickness, etc.) can improve this problem. Based on the measured data obtained by vertical electrical sounding (CVES) and continuous electrical sounding (PACES), Auken and Christiansen (2004) pointed out that the layered model can often more accurately reflect the actual geological conditions. By constraining the electrical parameters between adjacent measuring points, the lateral continuity of the inversion results can be improved. Christiansen and Auken (2004) used Broyden update to approximate the Jacobian matrix and further improved the efficiency of two-dimensional inversion. The 1D-LCI method is used to invert the two-dimensional TEM data set synthesized by continuous sampling of three-dimensional near-surface resistivity changes, which can fully restore the morphology and resistivity of the concealed structure (Auken et al., 2008). Cai Jing (2014) first proposed an improved weighted lateral constraint inversion method in China and applied it to the inversion of airborne electromagnetic data. By introducing a weighting factor to change the constraint strength, the results are closer to the real model than the traditional inversion method. He Ke (2022) performed a constrained inversion of semi-airborne transient electromagnetic data based on the hybrid norm, considering that the signal is relatively weak in areas far from the grounding line source, and the inversion requirements are higher.

[0005] Therefore, it is necessary to provide an Occam-based SATEM lateral constraint quasi-two-dimensional inversion method to solve the above technical problems. Summary of the invention

[0006] The present invention provides a SATEM lateral constraint quasi-two-dimensional inversion method based on Occam, analyzes the sensitivity of SATEM response to underground resistivity from different angles, and explains the method of adding lateral constraints in the inversion objective function, then designs different three-dimensional models to calculate the three-dimensional forward response, and selects several profiles to analyze the influence of the size of the lateral weighting factor on the inversion effect, so as to verify the effectiveness and applicability of the inversion method proposed by the present invention in the theoretical model.

[0007] The Occam-based SATEM lateral constraint quasi-two-dimensional inversion method provided by the present invention comprises the following steps:

[0008] S1. Perform one-dimensional SATEM forward simulation to verify the accuracy of the numerical solution;

[0009] S2. Design a lateral constraint inversion objective function and introduce a lateral constraint weight factor into the inversion objective function to adjust the continuity of electrical units at adjacent measuring points;

[0010] S3. Design different three-dimensional theoretical models, adjust the lateral constraint weight factor, analyze its impact on the inversion effect, and obtain the inversion results.

[0011] Preferably, in the one-dimensional SATEM forward simulation of step S1, a long wire source with a length of 2L is placed on the horizontal surface along the X direction, the center of the line source is the origin of the right-handed downward coordinate system, and the vertical magnetic field component of the center point of the receiving coil is calculated by an integral expression containing Hankel transform.

[0012] Preferably, in step S1, verifying the accuracy of the numerical solution includes comparing the one-dimensional forward numerical simulation with the analytical solution and the influence of resistivity on the forward response and sensitivity analysis.

[0013] Preferably, the inversion objective function is based on the Tikhonov regularization concept, including data fitting terms and model constraint terms. A regularization factor is introduced to adjust the relationship between model constraints and data fitting. At the same time, a model roughness constraint term and a lateral constraint term are introduced to make the model smoother and enhance lateral continuity.

[0014] Preferably, in step S3, the three-dimensional theoretical model includes:

[0015] A low-resistance body model to explore the ability of SATEM to detect the depth of low-resistance bodies;

[0016] A step model consisting of three plates to explore the ability of SATEM to detect the depth of high-resistance bodies and the influence of the strength of the constraint on the inversion effect;

[0017] A low-resistance ore body model invading deep underground to simulate more complex and realistic geological conditions;

[0018] By comparing the inversion results of different models, the effectiveness and applicability of the inversion method are verified.

[0019] Compared with the related art, the SATEM lateral constraint quasi-two-dimensional inversion method based on Occam provided by the present invention has the following beneficial effects:

[0020] 1. Compared with 3D inversion, the lateral constrained quasi-2D inversion method has higher computational efficiency and lower hardware requirements. It can obtain preliminary underground structural information in a shorter time and provide a reference for subsequent detailed exploration.

[0021] 2. By adding a lateral constraint weight factor to the inversion objective function, the lateral continuity of the inversion result can be effectively improved, so that the electrical parameters of the underground medium at adjacent measuring points have more reasonable continuity in space and more accurately reflect the actual geological conditions.

[0022] 3. For structures with strong lateral continuity and layered strata, this method has better recovery ability and can more clearly restore the geometric shape and electrical change trend of each part, providing a more effective technical means for the exploration of complex geological bodies.

[0023] 4. The inversion results obtained by this method can be used as the initial model for 3D inversion, providing a more accurate starting point for 3D inversion and further improving the accuracy and efficiency of 3D inversion.

[0024] 5. In the inversion work, by reasonably selecting the lateral constraint weight factor, it is possible to reduce unnecessary calculations, reduce inversion costs, and improve the economy of exploration work while ensuring the inversion accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Schematic diagram of SATEM detection system;

[0026] Figure 2 Comparison between the numerical solution and analytical solution of the one-dimensional response in the present invention;

[0027] Figure 3 denoted the influence of different resistivities (ρ=10, 100, 1000, 5000Ω·m) on the attenuation curve in the present invention;

[0028] Figure 4 It is the sensitivity of the field value to the resistivity in the present invention. The horizontal axis is time and the vertical axis is depth;

[0029] Figure 5 It is the basic flow chart of Occam inversion in the present invention;

[0030] Figure 6The three-dimensional theoretical model and the inversion results of different anomaly body burial depths in the present invention are as follows: (1) is the electrical parameter distribution of the three-dimensional theoretical model and the size of the anomaly body, (a), (b), and (c) are the resistivity inversion results of different anomaly body burial depths respectively;

[0031] Figure 7 The three-dimensional theoretical model, the two-dimensional inversion result diagram with different weight factors and the RMS of each point in the present invention: (1) is the distribution of electrical parameters of each part of the three-dimensional theoretical model; (a), (b) and (c) are the weight factors λ l =0, 0.05, 0.1 when the resistivity inversion results;

[0032] Figure 8 The three-dimensional theoretical model, the two-dimensional inversion result diagram with different weight factors and the RMS of each point in the present invention are shown as follows: (1) is the distribution of parameters of each layer of the three-dimensional theoretical model; (a), (b) and (c) are the weight factors λ l = Inversion resistivity when 0, 0.02, 0.05;

[0033] Fig. 9 (a) The RMS curve diagram of model 2 and (b) the RMS curve diagram of model 3 in the present invention. DETAILED DESCRIPTION

[0034] The present invention proposes a SATEM lateral constraint quasi-two-dimensional inversion method based on Occam. Firstly, the sensitivity of SATEM response to underground resistivity is analyzed from different angles, and the method of adding lateral constraint in the inversion objective function is explained. Then, different three-dimensional models are designed to calculate the three-dimensional forward response, and several profiles are selected to analyze the influence of the size of the lateral weighting factor on the inversion effect, so as to verify the effectiveness and applicability of the inversion method proposed by the present invention in the theoretical model.

[0035] The present invention will be further described in detail below in conjunction with the accompanying drawings and implementation modes.

[0036] 1. One-dimensional SATEM forward modeling

[0037] A long wire source with a length of 2L is placed on the horizontal surface along the X direction, and the center of the wire source is the origin of the right-hand downward coordinate system. Then in the time domain, the vertical magnetic field component H at the center point (x, y, h) of the receiving coil is z It can be given by the following integral expression involving Hankel transform:

[0038]

[0039] R=[(xx Dipole ) 2 +y 2 ] 1 / 2(2)

[0040] In the above formula: R is the horizontal offset; r TE is the reflection coefficient, which can be obtained from the underground admittance; λ is the wave number; J 1 is a first-order Bessel function; x Dipole is the horizontal coordinate of the electric dipole.

[0041] Perform sine and cosine transform on (1) to obtain the time derivative of the vertical magnetic field component in the time domain:

[0042]

[0043] Im(H z ) is the imaginary part of the magnetic field, Δ is the sampling interval, W n are the coefficients of the sine-cosine transform, and n is the number of coefficients.

[0044] 1.1 Comparison between one-dimensional forward numerical simulation and analytical solution

[0045] In order to verify the correctness of the written program, the numerical solution and analytical solution of the uniform half space are compared, and the underground resistivity is set to 100Ω·m. Figure 2 As shown in the figure, the attenuation curves of the two are in good agreement, and the actual relative error is less than 1%, which verifies the correctness of the program.

[0046] 1.2 Effect of resistivity on forward modeling response and sensitivity analysis

[0047] In addition to the thickness and burial depth of the target, its resistivity is the main factor affecting the attenuation curve. For this reason, the present invention fixes the measuring point height to 50m and the transmitting and receiving distance to 500m, and analyzes the influence of the change of the resistivity of the second layer in the three-layer medium on the response. The transmitting current is 1A and the wire length is 100m.

[0048] From the above figure, we can draw the following conclusions: when the resistivity of the second layer is low, the curve shape will be greatly distorted compared to the uniform half space. When it is high resistance, it has little effect on the response. This also confirms the phenomenon that electromagnetic methods are generally insensitive to high resistance.

[0049] In order to quantify the effect of resistivity on the response and consider the efficiency and accuracy in the subsequent inversion, the present invention performs a sensitivity analysis on the Jacobian matrix by obtaining the values ​​of the elements in the Jacobian matrix.

[0050] The above figure shows that the response is more sensitive to changes in shallow resistivity. In addition, the early response is strongly affected by resistivity, while the mid- and late-stage responses are not sensitive enough to resistivity changes.

[0051] 2. Laterally constrained quasi-two-dimensional inversion method

[0052] 2.1 Objective function of lateral constraint inversion

[0053] Based on the idea of ​​Tikhonov regularization, the objective function of the inversion can be written as follows:

[0054]

[0055] in, and They represent the data fitting term and the model constraint term respectively, and m is the model parameter matrix of the entire profile. The regularization factor λ is introduced, and its value changes continuously through linear search during the inversion process to adjust the relationship between model constraints and data fitting. From the profile data covariance matrix W d , observation data d obs and the forward operator F(m).

[0056]

[0057] The model complexity will increase with the iteration of inversion. Therefore, the model roughness constraint term ||W is introduced. v m|| 2 To make the model smoother. To solve the problem of insufficient lateral continuity and unclear identification of stratum interface, the lateral constraint term || W is introduced. l m|| 2 , the electrical parameters of adjacent stratigraphic units are correlated with each other, and the present invention can obtain the following objective function:

[0058]

[0059] 2.2 Occam inversion and lateral constraint addition method

[0060] As an algorithm with little dependence on the initial model and aimed at generating a smooth model, Occam inversion regards the forward operator as a differentiable function at a certain point. Substituting it into equation (7), we can obtain the k+1th model parameter matrix, λ l is the lateral constraint weight factor.

[0061]

[0062] J is the Jacobian matrix, which is obtained by differentiating the model parameters through the forward operator, and n is the number of measurement points on the profile:

[0063]

[0064] m k is the k-th model parameter matrix.

[0065] m k =[ρ 1k ,ρ2k ,···,ρ nk ] T (10)

[0066] For the depth constraint matrix W z , lateral constraint matrix W l According to the idea that the adjacent layers of the same measuring point are continuous and the parameters of the same layer of adjacent measuring points are related, they can be represented by the following matrices:

[0067]

[0068] in i is the i-th layer, M is the number of stratigraphic units, and N is the number of measuring points. In order to control the strength of the lateral constraint, the weight factor λ is introduced l , can be adjusted according to actual needs during the inversion process. The k-th data fitting error (RMS) is expressed as:

[0069]

[0070] d i,obs is the observed data, F i (m k ) is the kth forward response, ε i is noise data. Adding noise to theoretical data can generate synthetic data. obs is the number of the entire profile data. Therefore, the present invention is as follows Figure 5 The inversion process is shown.

[0071] The inversion termination conditions are set as follows: (1) To prevent overfitting, the maximum number of inversions is set to 15; (2) when abs[(RMS k+1 -RMS k ) / RMS k ]<5%, the present invention considers that the inversion tends to be stable and stops iterating; (3) the data fitting error is lower than the preset threshold. Theoretically, the RMS is 1. Considering the existence of noise, the present invention sets it to 1.5, that is, when the RMS in the inversion process is <1.5, the iteration is stopped and the result is output.

[0072] 3. 3D theoretical model inversion results and analysis

[0073] The present invention sets up a simple low-resistance body model and two more complex models to study the recovery effect of the developed program on the model parameters. The response under the long wire source is simulated by three-dimensional forward modeling, and some system parameters are shown in Table 1. The synthetic data of several measuring points on the survey line with a length of 1 km parallel to the field source are analyzed. In order to fit the actual data collected in the field, the present invention assumes that the synthetic data is contaminated by 5% Gaussian noise. In the inversion process, the present invention fixes the range of the inverted resistivity to [1,5000]Ω·m.

[0074] Table 1. Some parameters of SATEM system

[0075] Emission current Source length Flight altitude Offset Y Time channel Dot Pitch 20A 1km 50m 500m 100 25m

[0076] 3.1 Model 1

[0077] In order to study the ability of SATEM to detect the depth of low-resistance anomalies, the present invention sets up the following Figure 6 In the model 1 shown in (1), the size of the anomaly is 200x200x100m. It is placed at the top interface with a burial depth of 50m and 75m, and the bottom interface with a burial depth of 150m and 175m, respectively. Its resistivity is set to 10Ω.m, and the background resistivity is set to 100Ω.m. The conventional parameters are set as follows: the direction of the field source is the same as the positive direction of the X-axis, the receiving and transmitting distance in the Y direction is 1km, and the field source coordinates of the present invention are: (-500,0,0), (500,0,0), with a total of 74 time channels, which are logarithmically evenly distributed in [10 -6 ,10 -1 ]s, using 41 measuring points with a point spacing of 25m. For the initial inversion model, a 15-layer half-space (ρ = 100Ω·m) uniform grid was selected, with the first layer thickness of 10m and each subsequent layer increasing by 1.05 times the thickness of the previous layer.

[0078] Figure 6 The single-point inversion results of resistivity at different burial depths are given. It can be seen that the geometric shape and electrical property change trend of the anomaly are well restored, but as the depth of the top interface of the anomaly increases, the resistivity recovery effect weakens, indicating that SATEM's detection capability for deep targets is limited.

[0079] 3.2 Model 2

[0080] The construction of model 2 is as follows Figure 7As shown in (1), it is a step model composed of three plate-like bodies, with the bottom buried at Z = 200m and the top buried at Z = 50m. The ranges of the three plate-like bodies from deep to shallow are [-200, 0], [-100, 100], and [0, 200], respectively. The resistance values ​​are all set to 10Ω.m, the background resistivity is set to 100Ω.m, and the high-resistance substrate with a resistance value of 1000Ω.m is 200m below. Since the continuity of the model in the horizontal direction is not strong, the present invention sets three different horizontal constraints λ l (0, 0.05, 0.1 respectively) to study the influence of constraint strength on inversion effect. For the initial inversion model, a uniform half-space with resistivity ρ = 1500Ω·m was selected, and the number of inversion layers was increased to 20.

[0081] Figure 7 The quasi-two-dimensional inversion results of resistivity under different weight factor constraints are given. It can be seen that inverting the entire profile together can restore the geometric shape and electrical property change trend of each part more clearly, and as the weight factor increases, the lateral continuity of the target body is enhanced, but the enhancement effect becomes weaker. The RMS of most points is less than the threshold (1.5). Fig. 9 (a) From the total RMS of the inversion given, adding lateral constraints can speed up the inversion convergence.

[0082] 3.3 Model 3

[0083] Transient electromagnetic method was originally used to find disseminated sulfide ore bodies. In order to simulate more complex and realistic geological conditions, such as Figure 8 As shown, the present invention sets a low-resistance ore body model invading deep underground, which is an inverse "L" model composed of a low-resistance channel invading downward, and its surface is covered by a low-resistance layer, the thickness of the covering layer is 50m, the bottom of the intrusion body is buried at Z = 200m, the top is buried at Z = 50m, connected to the covering layer, the range in the X direction is [-300, 300]m, the range in the Y direction is [400, 600]m, the resistance is 10Ω.m, the resistance of the covering layer is 500Ω.m, the resistivity of the surrounding rock is high resistance, and the resistivity is set to 2000Ω.m. In order to speed up the inversion speed while retaining the inversion accuracy, the present invention will appropriately reduce the value of the weight factor.

[0084] Figure 8 The quasi-two-dimensional inversion results of resistivity under different weight factor constraints are given. l=0, it is a single-point one-dimensional inversion. It can be seen that the results of the single-point inversion can roughly distinguish the position of the target body, and the position and size of the downward channel mouth of the intrusion body can also be reflected, but the effect is not obvious enough. In the inversion results with the addition of lateral constraints, more obvious false anomalies appeared on both sides of the abnormal body. The above phenomenon is inferred to have two reasons: First, the resistance of the upper covering layer is large, which to a certain extent masks the appearance of the low-resistance range; second, the observed data in the numerical simulation of the three-dimensional abnormal body is not only affected by the abnormal body, but there is a volume effect, which reduces the resolution of the inversion result. Due to the lateral constraint, the underground units of adjacent measuring points are connected, so the lateral range is stretched. Analysis shows that when the weight factor increases, the lateral continuity of the target body is enhanced, but too strong constraints will lead to the appearance of false anomalies. The RMS of each point is mostly higher than the threshold at the target body. Combined with the single-point RMS curve of model 2, the following results can be obtained: at the abnormal body, the data is often more difficult to fit, while it is easier to fit in other layered surrounding rocks. From Fig. 9 (b) shows that the inversion results converge quickly, indicating that the data of the entire profile is well fitted. l When =0.05, the inversion convergence is the fastest.

[0085] 4. Conclusion

[0086] This paper proposes a lateral constraint quasi-two-dimensional inversion method for SATEM observation data based on Occam. First, starting from a one-dimensional forward method, the accuracy of the numerical solution is verified. Then, a lateral constraint weight factor is added to the inversion objective function to adjust the continuity strength of the electrical units at adjacent measuring points. Finally, two complex three-dimensional models are set for inversion work to obtain the inversion results. The analysis has the following three conclusions:

[0087] (1) Compared with 3D inversion, lateral constraint quasi-2D inversion is more efficient and has lower hardware requirements. Therefore, the results obtained by this method are necessary for a preliminary understanding of underground structures and have a certain reference value for the initial model of 3D inversion.

[0088] (2) By studying two models with different lateral continuity, the present invention finds that the inversion with added constraints will produce different degrees of false anomalies in the results. This is due to the volume effect and the inadaptability of the quasi-two-dimensional inversion method itself to three-dimensional structures. The resistance value of a single point will be further diffused to the surrounding measuring points and even the entire profile through the constraint strength, but compared with the single-point one-dimensional result, its inversion efficiency is improved to varying degrees with the change of the weight factor. From the analysis of the RMS results of each measuring point, it can be concluded that the quasi-two-dimensional inversion method proposed in the present invention has better recovery capabilities for structures with strong lateral continuity and quasi-layered strata;

[0089] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A quasi-two-dimensional inversion method for SATEM lateral constraints based on Occam, characterized in that: The following steps are involved: S1. Perform one-dimensional SATEM forward simulation to verify the accuracy of the numerical solution; S2. Design a lateral constraint inversion objective function and introduce a lateral constraint weight factor into the inversion objective function to adjust the continuity of electrical units at adjacent measuring points; S3. Design different three-dimensional theoretical models, adjust the lateral constraint weight factor, analyze its impact on the inversion effect, and obtain the inversion results.

2. The Occam-based SATEM lateral constraint quasi-two-dimensional inversion method according to claim 1, characterized in that: In the one-dimensional SATEM forward modeling simulation of step S1, a long wire source with a length of 2L is placed on the horizontal surface along the X direction, the center of the wire source is the origin of the right-handed downward coordinate system, and the vertical magnetic field component of the center point of the receiving coil is calculated by an integral expression containing Hankel transformation.

3. The Occam-based SATEM lateral constraint quasi-two-dimensional inversion method according to claim 1, characterized in that: In the step S1, verifying the accuracy of the numerical solution includes comparing the one-dimensional forward numerical simulation with the analytical solution and the influence of resistivity on the forward response and sensitivity analysis.

4. The Occam-based SATEM lateral constraint quasi-two-dimensional inversion method according to claim 1, characterized in that: The inversion objective function is based on the Tikhonov regularization idea, including data fitting terms and model constraint terms. A regularization factor is introduced to adjust the relationship between model constraint and data fitting. At the same time, a model roughness constraint term and a lateral constraint term are introduced to make the model smoother and enhance lateral continuity.

5. The Occam-based SATEM lateral constraint quasi-two-dimensional inversion method according to claim 1, characterized in that: In step S3, the three-dimensional theoretical model includes: A low-resistance body model to explore the ability of SATEM to detect the depth of low-resistance bodies; A step model consisting of three plates to explore the ability of SATEM to detect the depth of high-resistance bodies and the influence of the strength of the constraint on the inversion effect; A low-resistance ore body model invading deep underground to simulate more complex and realistic geological conditions; By comparing the inversion results of different models, the effectiveness and applicability of the inversion method are verified.

Images