Boundary soft-supervised resistivity prediction method based on data-model double gradient constraint

Abstract

The application discloses a kind of boundary soft supervision resistivity prediction methods based on data-model double gradient constraint, belong to electromagnetic signal inversion technical field.Wherein, the method includes: constructing true value model field, determining true value boundary and distance;According to the difference between prediction model and true value, model fitting loss is constructed;Introduce the soft boundary label based on distance to construct boundary supervision loss;Fusion bidirectional gradient constraint, construct boundary gradient excitation loss and non-boundary gradient inhibition loss;According to the model range given by priori, model range constraint loss is constructed, and data consistency constraint loss is constructed;Weighted summation constructs total loss function, and the optimal model is output by minimizing total loss function.The application can capture the position and form of boundary by introducing electromagnetic gradient and model gradient double constraint in prediction framework, effectively restores boundary, significantly improves the precision and resolution of inversion result.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic signal inversion technology, and in particular to a boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints. Background Technology

[0002] Electromagnetic methods, which invert resistivity distribution by exciting electromagnetic fields and recording the response of subsurface media to these fields, are an important means of obtaining information on the electrical structure of subsurface materials. Resistivity, as a key parameter characterizing the composition, water content, fluid occurrence, and migration features of subsurface soil and rock media, is of great significance in mineral resource exploration, oil and gas exploration, groundwater monitoring, geothermal development, and geological hazard assessment. Accurately reconstructing subsurface resistivity distribution not only provides physical constraints for geological interpretation but also provides a scientific basis for engineering construction and environmental monitoring.

[0003] In existing technologies, traditional electromagnetic inversion methods rely on physical forward modeling operators to solve for resistivity models using the objective function of minimizing the difference between observed and simulated data. Typical Occam inversion, by introducing smoothing regularization, obtains stable and physically reasonable solutions, maintaining overall consistency even under noisy conditions. However, these methods generally suffer from two drawbacks: first, smoothing constraints can blur the subsurface electrical interface, making it difficult to accurately characterize the boundary; second, the algorithm is highly dependent on prior models and regularization parameters, and improper parameter settings can lead to significant deviations from the actual structure. Furthermore, in large-scale 3D applications, finite element, finite difference, or integral equation forward modeling methods all incur extremely high computational costs, severely limiting their widespread application in real-world scenarios. Although recent advancements in adaptive meshes, sparse constraints, and Lp-norm methods have improved boundary resolution and computational efficiency to some extent, they still cannot fundamentally resolve the contradiction between excessive model smoothing and insufficient interface clarity.

[0004] With the development of artificial intelligence and deep learning, the academic community has proposed using machine learning methods to directly predict subsurface resistivity models from electromagnetic data. Deep learning methods based on architectures such as Convolutional Neural Networks (CNN) and U-Net learn the nonlinear mapping relationship between electromagnetic response and subsurface electrical structure through a large number of training samples, enabling rapid prediction during the inference stage and avoiding the high computational cost required for iterative inversion. These methods exhibit strong nonlinear fitting capabilities and can achieve electrical structure imaging under complex geological conditions. However, these methods still have significant limitations: on the one hand, they are highly dependent on the quantity and diversity of training data; when the training set fails to cover the diversity of real geology, the generalization ability of the prediction model decreases significantly; on the other hand, the method lacks clear physical constraints, which may produce results with unreasonable physical properties or severe artifacts; at the same time, the output of deep networks is often generally smooth, making it difficult to accurately capture the location and morphology of subsurface electrical boundaries.

[0005] While existing electromagnetic inversion and machine learning prediction methods have advantages in various aspects, they still have significant shortcomings in boundary identification and precise interface localization. Traditional inversion tends to "smooth out" interfaces, and while machine learning prediction is fast, it lacks physical guidance; neither can simultaneously ensure boundary clarity and overall stability. Especially in application scenarios where interface resolution is extremely important, such as ore body boundaries, fault planes, and the top and bottom interfaces of aquifers, the limitations of existing technologies severely restrict the application effectiveness of electromagnetic methods. Summary of the Invention

[0006] This invention addresses the problems of interface ambiguity, lack of physical consistency in results, and high dependence of predictions on training data in existing technologies. It proposes a boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints. The electromagnetic field spatial gradient is extremely sensitive to abrupt changes in the medium, often exhibiting extreme responses at resistivity abrupt boundary points; while the model gradient directly reflects the boundary position and clarity during the prediction process. By introducing dual constraints of electromagnetic gradient and model gradient into the prediction framework, this invention not only enhances boundary recognition capabilities but also effectively suppresses false boundaries in homogeneous regions, thus balancing boundary clarity and overall physical plausibility.

[0007] This invention enables more accurate localization of underground electrical interfaces, significantly improving the resolution and reliability of resistivity imaging results. In mineral exploration, it can more precisely delineate ore body boundaries and extent; in groundwater and geothermal surveys, it can reliably identify the interface between aquifers and impermeable layers; and in engineering geology and environmental monitoring, it can significantly enhance the detection capabilities of discontinuous structures such as faults, cavities, and pollution zones. Therefore, this invention not only theoretically overcomes the limitations of existing technologies but also possesses significant value and broad prospects in practical applications.

[0008] According to one aspect of the present invention, a boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints is provided, comprising: constructing a ground truth model field and determining the ground truth boundary based on the spatial gradient of the ground truth model, and calculating the distance from each point in the ground truth model field to the ground truth boundary; constructing a model fitting loss based on the difference between the predicted model and the ground truth; introducing a distance-based soft boundary label and constructing a boundary supervision loss by combining BCE and Dice coefficients, wherein the soft boundary label is a soft mask of the ground truth boundary, is 1 at the boundary, and gradually decays as it moves away from the boundary; setting a minimum gradient threshold, and constructing a boundary gradient excitation using the ReLU function based on the gradient of the predicted model. The model fit loss, boundary supervision loss, boundary gradient excitation loss, non-boundary gradient suppression loss, model range constraint loss, and data consistency constraint loss are constructed by weighting the non-boundary region probabilities. The model fit loss, boundary supervision loss, boundary gradient excitation loss, non-boundary gradient suppression loss, model range constraint loss, and data consistency constraint loss are weighted and summed to construct the total loss function. The optimal model is output by minimizing the total loss function. The model range constraint loss and data consistency constraint loss are optional when the true value model is available and mandatory when the true value model is not available.

[0009] Optionally, constructing the truth model field and determining the truth boundary based on the spatial gradient of the truth model includes: Constructing a truth model field , Indicates spatial location The truth model parameters at that location; Calculate the spatial gradient of the true model : ; Points whose spatial gradient exceeds a preset boundary threshold are used as boundary points to construct a set of truth boundaries: In the formula, Represent the set of truth boundaries; Represents the spatial coordinates that satisfy the boundary conditions; To preset boundary thresholds, .

[0010] Optionally, calculating the distance from each point in the truth model field to the truth boundary includes: For any grid point Its Euclidean distance to the nearest truth boundary point is: ; On a discrete grid, if the grid spacing is , The calculation method is as follows: ; in, The minimum distance from a point to the truth boundary. These are the coordinates of the boundary points. For the set of truth boundaries, It is the set of boundary grid points. Boundary grid points Direction index coordinates, For any grid point The index coordinates of the direction.

[0011] Optionally, constructing the model fitting loss based on the difference between the predicted model and the true value includes: When a true value model is available, the mean squared error between the predicted model and the true value is used as the model fitting loss: ; in, The model fitting loss; To predict the model's values ​​in the grid; The values ​​of the truth model in the grid; This represents the total number of grid points; If no true value is found, then zero value, prior, or interval constraints are used as the model fitting loss.

[0012] Optionally, the soft boundary label is defined as: , ; in, For soft-border labels; It is the minimum distance from the point to the truth boundary; To control the scale parameter of the boundary blur width, ; Border surveillance loss Defined as: , ; The Dice coefficient is: , ; in, To predict boundary probabilities; This is a hyperparameter that controls the weight of the Dice coefficient in the loss. This is a smoothing term.

[0013] Optionally, a minimum gradient threshold can be set. The boundary gradient excitation loss Defined as: ; ; ; in, To predict the magnitude of the gradient of the model at that point; The minimum gradient magnitude that the boundary must satisfy; For activation functions; This represents the total number of grid points; To predict boundary probabilities; To predict the model's values ​​in the grid; The non-boundary gradient suppression loss Defined as: ; in, The mask represents the probability of non-boundary regions.

[0014] Optionally, the model range constraint loss Defined as: ; in, The model range is given a priori; To predict the model's values ​​in the grid; This represents the total number of grid points; The data consistency constraint loss Defined as: ; in, For predictive models at frequency The forward response under these conditions; To observe electromagnetic data; This represents the number of frequency points.

[0015] Optionally, the formula for the total loss function is expressed as: ; in, For the total loss, The model fitting loss, For the loss of border surveillance, For boundary gradient excitation loss, For non-boundary gradient suppression loss, For data consistency constraint loss, For model range constraint loss, These are the weighting coefficients for each item, and all are greater than zero.

[0016] The beneficial effects of this invention are: The smoothing constraints introduced by existing technologies often lead to blurred interfaces and inaccurate boundary characterization. The algorithms are highly dependent on prior models and regularization parameters and lack clear physical constraints. This invention introduces dual constraints of electromagnetic gradient and model gradient in the prediction framework. The electromagnetic gradient is highly sensitive to abrupt changes in the medium, while the model gradient can capture the position and shape of the boundary. Under the dual constraints, the boundary is effectively recovered, significantly improving the accuracy and resolution of the results and reducing the dependence on the initial model.

[0017] This invention integrates electromagnetic data gradient and model gradient information for underground resistivity prediction, enabling accurate location of underground electrical interfaces and significantly improving the reliability of resistivity imaging results. Compared with existing technologies, this invention theoretically overcomes the limitations of traditional methods and can be applied to fields such as mineral exploration, groundwater and geothermal surveys, engineering geology, and environmental monitoring. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints according to an embodiment of the present invention; Figure 2 This is a comparison chart of the inversion results of the three-dimensional resistivity model using the method of the present invention and the traditional Gaussian smoothing method. The first row is the real model, the second row is the inversion result chart using the method of the present invention, and the third row is the inversion result chart using the traditional method. Each column sequentially displays the three-dimensional stereoscopic effect and key slice features in the xy, xz, and yz directions. Figure 3 The resistivity inversion error analysis diagram systematically compares the inversion accuracy differences between the method of this invention and the traditional Gaussian smoothing method from three perspectives: error spatial distribution, multi-index statistical bar chart, and error probability density distribution. Detailed Implementation

[0019] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, and not all of them. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present application can be combined with each other.

[0020] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0021] The terms “comprising” and “having”, and any variations thereof, in the specification and claims of this application are intended to cover non-exclusive inclusion, for example, a process, method, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or apparatus.

[0022] Example 1: This embodiment of the invention provides a boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints. This method introduces dual constraints of electromagnetic data gradient and model gradient information to predict subsurface resistivity. Compared with traditional inversion methods, this method can predict subsurface resistivity models more accurately, making the imaging results more reliable.

[0023] Reference Figure 1 , Figure 1 This is a flowchart of a boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints according to an embodiment of the present invention, as follows: Figure 1 As shown, the method includes: S1, construct the true value model field and determine the true value boundary and distance; The true model field is the parameter field of the initially considered two-dimensional model, set as follows: , indicating the position The parameters of the truth model, Represents the horizontal axis, i.e., the horizontal position. Represents the vertical coordinate, i.e., the depth position (none). The axis is designed to adapt to the physical scenario of "horizontal-depth" in underground two-dimensional profiles.

[0024] The truth boundary set is the set of points in the truth model field whose spatial gradient exceeds a preset boundary threshold, expressed as: ; in, Represent the set of truth boundaries; The spatial gradient of the truth model. ; The spatial location that satisfies the boundary conditions, i.e., the coordinates of the boundary points; The threshold for detecting the boundary, i.e., the preset boundary threshold, and Any location where the gradient exceeds the threshold is considered a "boundary".

[0025] The minimum distance from each point in the ground truth model field to the boundary (which is constructed by the set of points whose gradients exceed a threshold) is calculated, and then the soft label of the boundary to be introduced is generated.

[0026] The minimum distance from a point to the boundary is , For the current grid point Coordinates of direction.

[0027] For any grid point The formula for the Euclidean distance from the nearest truth boundary point is expressed as: ; On a discrete grid, if the grid spacing is , The calculation method is as follows: ; in, It is the set of boundary grid points; It is the set of boundary grid points The coordinates of a point in the middle.

[0028] S2 represents the overall distribution fitting loss of the constrained model. To ensure that the distribution of overall resistivity or conductivity fits the true value, when the true value model is available (available means that the model can accurately reflect the true parameter distribution of the target physical scene, that is, the parameter distribution must be consistent with the true parameters of the actual physical scene and have complete and reasonable effective values), the mean square error is used to measure the difference between the prediction model and the true value. The model fitting loss formula is expressed as: ; in, The model fitting loss; To predict the model's values ​​in the grid; The values ​​of the truth model in the grid; This represents the total number of grid points.

[0029] This model fit loss calculates the mean squared error between the predicted model and the true value across all grid points. When no true value is available, this option can be removed, or prior or interval constraints can be used instead.

[0030] S3 introduces soft labels and constructs a boundary-supervised loss; Boundary supervision loss is used to make the model pay more attention to the boundary region, thereby improving the boundary segmentation effect and increasing the model's segmentation accuracy of the target boundary.

[0031] To avoid hard labels being too sharp, distance-based soft boundary labels are introduced, expressed by the formula: , ; in, To control the scale parameter of the boundary blur width and , The width of the boundary soft label is usually set to 1 to 3 grid spacings.

[0032] The soft mask is used as the truth boundary. The soft boundary label has a value of 1 at the boundary and gradually decays away from the boundary, which effectively avoids the discreteness of hard labels and provides a stable training signal for subsequent boundary supervision.

[0033] Boundary probability map for network synchronization prediction based on soft boundary labels. The boundary supervision loss is constructed by combining BCE (Binary Cross Entropy Loss) and Dice coefficient. BCE ensures that the predicted probability of each boundary point is close to the soft true value, while Dice ensures that the overall boundary shape is consistent and alleviates the class imbalance problem.

[0034] The formula for boundary supervision loss is expressed as: , ; The Dice coefficient is calculated as follows: , ; in, To predict the boundary probability, ; This is a hyperparameter that controls the weight of the Dice coefficient in the loss. The set of predicted boundary probabilities for all grid points; It is a set consisting of all soft boundary labels; This is a smoothing term.

[0035] S4 incorporates bidirectional gradient constraints to achieve encouragement at the boundary and suppression at non-boundary areas; Incorporating bidirectional spatial gradient physical constraints, this part includes two loss terms: one that encourages large gradients at the boundary and the other that suppresses gradients at non-boundary locations. The boundary gradient excitation loss is used to enhance model changes in the boundary region, while the non-boundary gradient suppression loss term is used to suppress gradients at non-boundary locations, thereby enhancing boundary recognition capabilities and suppressing false boundaries in homogeneous regions.

[0036] S41, In the boundary region, sufficiently strong model changes are required, thus encouraging large gradients at the boundary and setting a minimum gradient threshold. ,Require Define boundary gradient excitation loss The formula is expressed as: ; in, , where is the magnitude of the gradient of the prediction model at that point; The minimum gradient magnitude that the boundary should satisfy is the set minimum gradient threshold, which can be taken as 0.1~0.3 after normalization. , is a commonly used activation function in deep learning, used to correct linear units.

[0037] When the gradient is insufficient, i.e., when the gradient is insufficient. Less than the set minimum gradient threshold At this time , If the function outputs this positive value, a penalty is applied; when the gradient is sufficient, i.e., when the threshold is reached, , The function output is 0, indicating that there is no penalty and the loss is 0 (no more loss will be added), ensuring the non-negativity and numerical stability of the loss.

[0038] S42. In homogeneous regions, the model should be as smooth as possible to avoid spurious structures in non-boundary regions. A non-boundary gradient suppression loss should be constructed. When the all-directional constraint is to smooth only the x-direction or z-direction, the square of the gradient in the corresponding direction is taken, and the formula is expressed as: ; in, For the mask, To predict the boundary probability, then For non-boundary regions, the probability is represented by a larger weight. At the confirmed boundary points, The mask weight is 0, meaning there is no penalty at the boundary; at certain non-boundary points, The mask weight is 1, the gradient is completely penalized, the gradient is almost entirely included in the loss, and the gradient is suppressed at non-boundary locations.

[0039] S5, construct the model range constraint loss and the data consistency constraint loss; For application scenarios where there is no true value (where model fitting loss cannot be used), this invention provides two alternative constraint losses: model range constraint loss and data consistency constraint loss. The model range constraint loss is used to constrain the predicted value to not exceed the prior range, and the data consistency constraint loss is used to constrain the model prediction to fit the true value, so as to ensure that the prediction result is reasonable and the model response is consistent with the observation.

[0040] When the truth value is available, these two losses can be used as auxiliary constraints to enhance the rationality of the model. That is, when the truth value is available, these two losses are an option to further improve the rationality of the model.

[0041] In order to ensure that the prediction results are reasonable and do not exceed the limits, the model range constraint loss is used. The formula is expressed as: ; in, This is the range of the model given in the prior knowledge. It ensures that the predicted values ​​do not exceed the prior range, thus guaranteeing the reasonableness of the results.

[0042] To ensure that the response of the prediction model is consistent with the observations, i.e., physical constraints, data consistency constraint loss. The formula is expressed as: ; in, For predictive models at frequency The forward response under these conditions; To observe electromagnetic data; The frequency point number is used. The difference between model fitting loss and data consistency constraint loss is that model fitting loss aims to make the predicted model's parameter values ​​close to the true values, and its calculation is based on the model parameter values ​​themselves. Data consistency constraint loss aims to match the predicted model's physical response with the actual observed data, and its calculation is based on the electromagnetic response data after transformation by the forward operator.

[0043] S6, the weighted summation total loss function, outputs the optimal model by minimizing the total loss.

[0044] The final total loss is a weighted sum of the losses of multiple non-negative sub-sub ... The function expression is: ; in, All weighted coefficients are greater than zero; it is recommended that each coefficient be set to a value of [value missing]. , , , , , By minimizing the total loss function, such as by iteratively adjusting the model parameters using gradient descent, the loss function value is continuously reduced, ultimately outputting a model that achieves optimal performance in terms of overall distribution, boundary shape, physical rationality, and data fit.

[0045] Reference Figure 2 , Figure 2A direct comparison of the 3D spatial distribution and key slice features of the real resistivity model, the method of this invention, and traditional methods was conducted. The real model employs a smoothly gradient ellipsoidal low-resistivity anomaly design, closely conforming to the electrical distribution patterns of real geological bodies. The method of this invention, relying on the dual constraints of electromagnetic gradient and model gradient, accurately reconstructs the morphology, spatial location, and smooth gradient characteristics of the anomaly, without diffusion distortion or false boundaries. Its boundary recognition accuracy and morphological restoration are significantly superior to traditional methods. Traditional methods, due to excessive Gaussian smoothing, result in diffuse diffusion and blurred boundaries in the low-resistivity region, leading to significant deviations from the real model. Overall, the method of this invention has a significant core advantage in balancing boundary clarity and physical plausibility, accurately reproducing the real underground resistivity results, thus verifying the inversion performance of the method of this invention.

[0046] Figure 3 This is a resistivity inversion error analysis diagram. The error calculation in the diagram is based on the smooth and gradual true value model, and the absolute error is used as the accuracy evaluation index. The larger the error value, the darker the color, which intuitively presents the error distribution pattern and accuracy gap between the two methods.

[0047] The first row, left figure, shows the absolute error distribution of the xy slices obtained by the method of this invention. The error is mainly concentrated in the boundary region of the anomaly, and the value is small with no obvious diffusion. The right figure shows the error distribution of the traditional method. The error is widely diffused in the anomaly region, and the value is significantly larger than that of the method of this invention, reflecting the problem of blurred anomaly boundaries and morphological distortion caused by the excessive smoothing of the traditional method. The second row, left figure, compares the four core error indicators of the two methods horizontally—mean error, maximum error, root mean square error (RMSE), and 95th percentile error. It shows that the indicators of the method of this invention are significantly better than those of the traditional method, which verifies the accuracy advantage of the method of this invention from a quantitative perspective. The right figure shows the overall distribution of errors of the two methods. The error distribution of the method of this invention is peak-shaped, mainly concentrated in the low error range, indicating that the inversion results of most grid points are highly consistent with the true values. The error distribution of the traditional method is broad and flat, with a large range of error intervals, and the probability density of the high error interval is significantly higher than that of the method of this invention, indicating that the stability and reliability of its inversion results are poor.

[0048] The results show that the figure comprehensively demonstrates the significant advantages of the method of this invention in reducing inversion error and improving the accuracy and stability of the results by integrating the dual constraints of electromagnetic gradient and model gradient from three dimensions: spatial distribution, quantitative indicators and statistical regularities.

[0049] This invention provides a novel method for constructing deep learning loss functions. This loss function framework, through a combination of ground truth model constraints, boundary soft supervision, gradient physical constraints, and prior / data consistency, ensures that the prediction model not only fits the overall resistivity distribution but also quasi-stablely recovers the boundary positions and geometric features.

[0050] This invention achieves accurate prediction of complex underground resistivity by introducing dual constraints of electromagnetic gradient and model gradient into the prediction framework. It overcomes the shortcomings of traditional inversion methods with blurred boundaries and can output resistivity imaging results with clear electrical interfaces.

[0051] Example 2: This example provides a boundary soft-supervised resistivity prediction device based on data-model dual gradient constraints, including: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to realize the boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints proposed in the above example.

[0052] The device can be a terminal, including a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the device casing, or an external keyboard, touchpad, or mouse.

[0053] Embodiments of the present invention also provide a storage medium storing a computer program, wherein the computer program is configured to execute the steps in any of the above method embodiments when running.

[0054] Optionally, in this embodiment, the storage medium may include, but is not limited to, various media capable of storing computer programs, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0055] The sequence numbers of the above embodiments are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. The descriptions of each embodiment in the above embodiments have different emphases; for parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0056] The steps in the method of this invention can be adjusted, combined, or deleted according to actual needs. The technical features can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the embodiments are described. However, as long as the combinations of these technical features do not contradict each other, they should all be considered within the scope of this invention.

[0057] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints, characterized in that, include: Construct a truth value model field, which is the initially considered two-dimensional model parameter field, set as follows: , indicating the position The parameters of the truth model, Represents the horizontal axis, i.e., the horizontal position. Represents the vertical coordinate, i.e. the depth position, and determines the truth boundary based on the spatial gradient of the truth model, calculating the distance from each point in the truth model field to the truth boundary; Construct a model fitting loss based on the difference between the prediction model and the true value; A distance-based soft boundary label is introduced, and a boundary supervision loss is constructed by combining BCE and Dice coefficients. The soft boundary label is a soft mask of the truth boundary, which is 1 at the boundary and gradually decays as it moves away from the boundary. Set a minimum gradient threshold, construct the boundary gradient excitation loss using the ReLU function based on the gradient of the prediction model, and construct the non-boundary gradient suppression loss using probability weighting of non-boundary regions. A model range constraint loss is constructed based on the prior given model range, and a data consistency constraint loss is constructed based on the difference between the forward response of the predicted model and the observed data. The model range constraint loss... Defined as: ; The model range is given a priori. To predict the model's values ​​on the grid, The total number of grid points; the data consistency constraint loss. Defined as: ; For predictive models at frequency The forward response under the following conditions To observe electromagnetic data, Number of frequency points; The model fitting loss, boundary supervision loss, boundary gradient activation loss, non-boundary gradient suppression loss, model range constraint loss, and data consistency constraint loss are weighted and summed to construct a total loss function. The optimal model is output by minimizing the total loss function. The model range constraint loss and data consistency constraint loss are optional when the true value model is available, and mandatory when the true value model is not available.

2. The boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints according to claim 1, characterized in that, The construction of the truth model field and the determination of the truth boundary based on the spatial gradient of the truth model include: Constructing a truth model field , Indicates spatial location The truth model parameters at that location; Calculate the spatial gradient of the true model : ; Points whose spatial gradient exceeds a preset boundary threshold are used as boundary points to construct a set of truth boundaries: In the formula, Represent the set of truth boundaries; Represents the spatial coordinates that satisfy the boundary conditions; To preset boundary thresholds, .

3. The boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints according to claim 1, characterized in that, The calculation of the distance from each point in the truth model field to the truth boundary includes: For any grid point Its Euclidean distance to the nearest truth boundary point is: ； On a discrete grid, if the grid spacing is , The calculation method is as follows: ； in, The minimum distance from a point to the truth boundary. These are the coordinates of the boundary points. For the set of truth boundaries, It is the set of boundary grid points. Boundary grid points Direction index coordinates, For any grid point The index coordinates of the direction.

4. The boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints according to claim 1, characterized in that, The method of constructing the model fitting loss based on the difference between the predicted model and the true value includes: When a true value model is available, the mean squared error between the predicted model and the true value is used as the model fitting loss: ； in, The model fitting loss; To predict the model's values ​​in the grid; The values ​​of the truth model in the grid; This represents the total number of grid points; If no true value is found, then zero value, prior, or interval constraints are used as the model fitting loss.

5. The boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints according to claim 1, characterized in that, The soft boundary label is defined as: ， ； in, For soft-border labels; It is the minimum distance from the point to the truth boundary; To control the scale parameter of the boundary blur width, ; Border surveillance loss Defined as: ， ； The Dice coefficient is: ， ； in, To predict boundary probabilities; This is a hyperparameter that controls the weight of the Dice coefficient in the loss. This is a smoothing term.

6. The boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints according to claim 1, characterized in that, Set minimum gradient threshold The boundary gradient excitation loss Defined as: ； ； ； in, To predict the magnitude of the gradient of the model at that point; The minimum gradient magnitude that the boundary must satisfy; For activation functions; This represents the total number of grid points; To predict boundary probabilities; To predict the model's values ​​in the grid; The non-boundary gradient suppression loss Defined as: ； in, The mask represents the probability of non-boundary regions.

7. The boundary soft-supervised resistivity prediction method based on data-model dual gradient constraints according to claim 1, characterized in that, The formula for the total loss function is expressed as follows: ； in, For the total loss, For model fitting loss, For the loss of border surveillance, For boundary gradient excitation loss, For non-boundary gradient suppression loss, For data consistency constraint loss, For model range constraint loss, These are the weighting coefficients for each item, and all are greater than zero.

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