Gravity inversion method and system based on unsupervised deep learning, and electronic device
By constructing a fully connected neural network and combining it with a specific loss function, the problem of dependence on the initial model and geological prior knowledge in gravity inversion is solved, realizing high-resolution and robust unsupervised gravity inversion, which is suitable for geophysical exploration.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- THE 4TH GEOLOGICAL BRIGADE OF SICHUAN
- Filing Date
- 2026-06-01
- Publication Date
- 2026-07-03
AI Technical Summary
Existing gravity inversion methods rely on initial models and prior geological knowledge, leading to biases in the inversion process. Furthermore, unsupervised learning is insufficient in terms of physical consistency, inversion resolution, and geological plausibility, and struggles to handle gravity field decay with depth and sparse geological body boundaries.
We employ an unsupervised deep learning approach to construct a fully connected neural network. Backpropagation is performed using loss functions consisting of data fitting terms, smoothing constraints, physical boundary constraints, and focus regularization terms. By combining L1 norm and L0 norm sparse constraints with a depth weighting matrix, we improve the physical consistency and geological rationality of the inversion results.
It achieves high-resolution gravity inversion without the need for labeled data, improving the robustness and geological rationality of the inversion results. It is suitable for scenarios in the early stages of exploration or when prior information is scarce. It can automatically extract features and reduce human intervention.
Smart Images
Figure CN122331002A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geophysical exploration technology, and in particular to gravity inversion methods, systems and electronic devices based on unsupervised deep learning. Background Technology
[0002] Gravity inversion is a core task in geophysical exploration, aiming to infer the spatial distribution characteristics of subsurface density using gravity anomaly data observed at the Earth's surface. This technique is widely used in mineral resource evaluation, oil and gas reservoir description, deep crustal structure research, and natural disaster monitoring. However, due to the complexity of geophysical problems, gravity inversion has long faced strong ambiguity and ill-conditioning.
[0003] Traditional inversion methods (such as least squares or gradient descent) are typically highly dependent on the accuracy of the initial model settings and prior geological knowledge. In practical applications, the non-ideal nature of the geological environment often leads to deviations in the inversion process, and improper parameter settings can result in signal loss or artifacts. Therefore, finding an automated inversion method that can reduce human intervention and directly extract features from data has become an urgent need for both academia and industry.
[0004] In recent years, artificial intelligence and machine learning methods (supervised learning and unsupervised learning) have been introduced into the field of gravity inversion. While supervised learning performs exceptionally well, its limitation lies in the need for a large amount of "labeled" data (i.e., pairing known subsurface density models with corresponding gravity anomaly data). However, in actual deep exploration, obtaining high-precision geological "true labels" is extremely difficult and costly. In contrast, unsupervised learning has shown unique application potential. It does not rely on pre-labeled data but focuses on discovering inherent patterns, correlation structures, or statistical distributions within the data, making it particularly effective in the early stages of exploration when known information is limited. For example, convolutional autoencoders extract key features from the latent space, which are then reconstructed by decoders. This mechanism not only effectively suppresses noise and recovers weak signals but also automatically extracts high-dimensional features without human intervention, thus simplifying the interpretation process. Furthermore, unsupervised techniques such as independent component analysis are also frequently used to separate mixed geophysical signals, improving the accuracy of inversion.
[0005] While unsupervised learning can avoid dependence on labels, existing unsupervised methods still have significant shortcomings in terms of physical consistency, inversion resolution, and geological rationality constraints. For example, they are difficult to effectively handle the sensitivity problem of gravity field decay with depth, lack the ability to focus on the boundaries of sparse geological bodies, and are difficult to integrate multidimensional regularization constraints in an unsupervised framework.
[0006] Therefore, there is an urgent need for a new unsupervised gravity inversion paradigm that can both break free from dependence on labeled data and integrate prior geophysical knowledge to improve inversion resolution and geological rationality. Summary of the Invention
[0007] The purpose of this invention is to overcome the problems existing in the prior art and to provide a gravity inversion method, system and electronic device based on unsupervised deep learning. It adopts an innovative unsupervised deep learning method to analyze geophysical exploration data. While taking into account the advantages of previous methods, it constructs a new physical loss function for backpropagation, aiming to propose a new paradigm for gravity inversion methods.
[0008] The objective of this invention is achieved through the following technical solution: A first aspect of the present invention provides a gravity inversion method based on unsupervised deep learning, comprising the following steps: S1. Obtain gravity anomaly data from surface observations through forward modeling; S2. Construct a fully connected neural network based on the gravity anomaly data to map the input gravity anomaly data into a three-dimensional underground density distribution; wherein, the loss function of the fully connected neural network includes: The data fitting term measures the difference between observed gravity anomaly data and the predicted gravity field. A smoothing constraint term is used to constrain the gradient of the underground density model in three-dimensional space based on the L1 norm. Physical boundary constraints are used to limit the density prediction value within a preset physical reasonable range; Focusing on regularization terms, including L0 norm sparse constraints based on the differentiability approximation of the Sigmoid function and depth weighting matrices, we aim to compensate for the sensitivity loss of deep gravity anomaly signals. S3. An optimizer is used to perform unsupervised training on the fully connected neural network to minimize the loss function; S4. Input the actual observed gravity anomaly data into the trained fully connected neural network, and output the corresponding underground three-dimensional density distribution model.
[0009] In some embodiments, the loss function is specifically as follows:
[0010] in, Represents the total loss function. Represents the data fitting term. Represents the smoothing constraint term. Represents physical boundary constraint terms. This indicates focusing on the regularization term. , , Weighting parameters to balance the contributions of each loss term.
[0011] In some embodiments, the data fitting term is calculated using the following formula:
[0012] in, Let A be a weighted matrix of data, and A be a forward operator. The output of the network shows the underground three-dimensional density distribution. To observe gravity anomaly data, This represents the L2 norm.
[0013] In some embodiments, the smoothness constraint term is calculated using the following formula:
[0014] in, These are the first-order spatial derivative operators of the underground density model in the x, y, and z directions, respectively. A three-dimensional magnetization model. 1 represents the L1 norm.
[0015] In some embodiments, the physical boundary constraint term is calculated using the following formula:
[0016] in, Indicates the lower limit of density. Indicates the upper limit of density, This represents the total number of three-dimensional mesh cells corresponding to the underground density model. Indicates the index of the grid cell.
[0017] In some embodiments, the focus regularization term is calculated using the following formula:
[0018] Here, mean(⋅) performs the mean operation, normalizing the loss to [0,1]. For the Sigmoid activation function, Steepness coefficient, The threshold for determining non-zero values. Let m be the depth-weighted matrix, and m represent the density.
[0019] In some embodiments, the depth-weighted matrix is calculated using the following formula:
[0020] in, This represents the depth of the grid corresponding to the underground density model; For reference depth, The parameter is used to control the rate of change of weights with depth. This represents a diagonal matrix.
[0021] In some embodiments, the fully connected neural network takes a flattened one-dimensional vector of two-dimensional gravity anomaly data as input and outputs a one-dimensional vector of underground three-dimensional density distribution. The fully connected neural network is trained using the Adam optimizer and employs a learning rate decay strategy.
[0022] A second aspect of the present invention provides a gravity inversion system based on unsupervised deep learning, comprising: The gravity anomaly data acquisition module is used to acquire gravity anomaly data observed on the Earth's surface through forward modeling. A fully connected neural network construction module is used to construct a fully connected neural network based on the gravity anomaly data, mapping the input gravity anomaly data to a subsurface three-dimensional density distribution; wherein, the loss function of the fully connected neural network includes: The data fitting term measures the difference between observed gravity anomaly data and the predicted gravity field. A smoothing constraint term is used to constrain the gradient of the underground density model in three-dimensional space based on the L1 norm. Physical boundary constraints are used to limit the density prediction value within a preset physical reasonable range; Focusing on regularization terms, including L0 norm sparse constraints based on the differentiability approximation of the Sigmoid function and depth weighting matrices, we aim to compensate for the sensitivity loss of deep gravity anomaly signals. A fully connected neural network training module is used to perform unsupervised training on the fully connected neural network using an optimizer to minimize the loss function; The gravity inversion output module is used to input actual observed gravity anomaly data into a trained fully connected neural network and output the corresponding underground three-dimensional density distribution model.
[0023] A third aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores computer instructions executable on the processor, and the processor executes the gravity inversion method based on unsupervised deep learning as described in the first aspect when executing the computer instructions.
[0024] It should be further noted that the technical features corresponding to the above-mentioned options and embodiments can be combined or substituted with each other to form new technical solutions without conflict.
[0025] Compared with the prior art, the beneficial effects of the present invention are: 1. No labeled data required: It adopts an unsupervised learning framework, completely eliminating the dependence on underground real density labels, greatly reducing the cost and data acquisition difficulty in actual exploration, and is suitable for scenarios in the early stage of exploration or when prior information is scarce.
[0026] 2. Combining physical consistency and geological rationality: By introducing L1 smoothing constraints, density upper and lower limit physical boundary constraints, L0 sparse focusing constraints, and depth weighted compensation, the inversion results outperform traditional methods in terms of spatial continuity, boundary clarity, sparsity representation, and depth resolution.
[0027] 3. High resolution and robustness: The combination of the L0 norm differentiable Sigmoid approximation and depth weighting effectively overcomes the problems of "volume effect" and "depth sensitivity attenuation" in gravity inversion, enabling high-resolution imaging of both shallow and deep geological bodies.
[0028] 4. High automation and versatility: Neural networks automatically extract features in a data-driven manner, reducing human intervention, adapting to different geological environments, and having good generalization ability. Attached Figure Description
[0029] Figure 1 The flowchart illustrates the gravity inversion method based on unsupervised deep learning in an embodiment of the present invention. Figure 2 This is a schematic diagram of a geological body density model (three-dimensional stepped model) shown in an embodiment of the present invention; Figure 3 This is a gravity forward model diagram shown in an embodiment of the present invention; Figure 4 Different embodiments of the present invention are shown. The graph of the Sigmoid function with varying values; Figure 5 The images of different norms and the Sigmoid approximation function are shown in the embodiments of the present invention. Figure 6 This is a schematic diagram of a fully connected neural network structure shown in an embodiment of the present invention; Figure 7 The following are graphs illustrating the various loss terms in an embodiment of the present invention; Figure 8 This is a slice of a real model with x=1600m shown in an embodiment of the present invention; Figure 9 This is a slice of the real model with z=2220m shown in an embodiment of the present invention; Figure 10 The inversion slice with x=1600m shown in the embodiment of the present invention; Figure 11 This is a slice of the z=220m inversion model shown in an embodiment of the present invention. Detailed Implementation
[0030] The technical solution 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, not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. 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.
[0031] It should be noted that the defects in the solutions in the prior art are all the results of the inventors' practice and careful research. Therefore, the discovery process of the above problems and the solutions proposed by the embodiments of this application in the following text should be the inventors' contributions to this application in the process of invention and creation, and should not be understood as technical content known to those skilled in the art.
[0032] To address the technical problems identified in the background section, this invention proposes using an unsupervised learning framework for gravity inversion. This aims to overcome the reliance on labeled data and leverage the advantages of machine learning in data analysis and modeling to automatically discover the nonlinear mapping relationship between gravity data and subsurface density structure. By constructing a specific network architecture, parameter redundancy is reduced while improving the robustness of the inversion results, thereby providing geological experts with a more accurate and objective reference for subsurface models.
[0033] In one exemplary embodiment, a gravity inversion method based on unsupervised deep learning is provided, such as... Figure 1 As shown, it includes the following steps: S1. Obtain gravity anomaly data from surface observations through forward modeling; S2. Construct a fully connected neural network based on the gravity anomaly data to map the input gravity anomaly data into a three-dimensional underground density distribution; wherein, the loss function of the fully connected neural network includes: The data fitting term measures the difference between observed gravity anomaly data and the predicted gravity field. A smoothing constraint term is used to constrain the gradient of the underground density model in three-dimensional space based on the L1 norm. Physical boundary constraints are used to limit the density prediction value within a preset physical reasonable range; Focusing on regularization terms, including L0 norm sparse constraints based on the differentiability approximation of the Sigmoid function and depth weighting matrices, we aim to compensate for the sensitivity loss of deep gravity anomaly signals. S3. An optimizer is used to perform unsupervised training on the fully connected neural network to minimize the loss function; S4. Input the actual observed gravity anomaly data into the trained fully connected neural network, and output the corresponding underground three-dimensional density distribution model.
[0034] Specifically, in step S1, a three-dimensional rectangular block is used as the density model of the underground geological body (underground density model), and the forward model is as follows: Figure 2 As shown, the vertical component of gravity at the surface observation plane is obtained through forward modeling. This provides input data for unsupervised learning models. Forward modeling strictly follows potential field theory, based on the analytical solution of the potential field of a rectangular block, for observation points. Integrating the coordinate difference with the vertex of the block yields the forward modeling formula for the vertical component. Let the block be in... The difference in vertex coordinates in the direction is , The distance from the observation point to the vertex of the block, with a sign factor. The formula for calculating the vertical component is as follows:
[0035] Among them, the gravitational constant For the remaining density, Figure 2 The remaining density is Gravity normal performance field Figure 3 As shown.
[0036] For example, in step S2, the loss function is constructed by combining a data fitting term and multiple geophysical regularization terms. While ensuring consistency between the predicted data and the observed data, it constrains the geological rationality of the inversion model, achieving a balance between the two. The specific loss function is as follows:
[0037] in, Represents the total loss function. Represents the data fitting term. Represents the smoothing constraint term. This represents the physical boundary constraint term (used to limit the density value within a reasonable range). This indicates the focus regularization term (including depth-weighted and L0 focus terms). , , The weighting parameters for balancing the contributions of each loss term are ultimately determined through training.
[0038] The data fitting term, used to measure the difference between observed gravity anomalies and predicted gravity fields, is defined as the weighted L2 norm:
[0039] in, This is a data weighting matrix, which assigns greater weight to data points with higher signal-to-noise ratios, effectively reducing the impact of observation noise on the inversion results. A is the forward modeling operator. The output of the network shows the underground three-dimensional density distribution. To observe gravity anomaly data, This represents the L2 norm.
[0040] To avoid drastic fluctuations without geological significance in the inversion model and to improve its spatial continuity and stability, a smoothing constraint term is introduced to constrain the density gradient. Considering that density volumes typically possess continuous geological characteristics in three-dimensional space, the L1 norm is used to constrain the gradients in the x, y, and z spatial directions.
[0041] in, These are the first-order spatial derivative operators of the underground density model in the x (east-west), y (north-south), and z (vertical) directions, respectively. A three-dimensional magnetization model. 1 represents the L1 norm. Compared to the L2 norm, the L1 norm constraint is better able to preserve the edge features of the model: it can effectively suppress random fluctuations and avoid blurring of the magnetic source body boundary due to excessive smoothing, thus ensuring that the inversion results not only conform to the continuous distribution law of geological bodies, but also clearly characterize the spatial morphological boundary of the magnetic source body.
[0042] To ensure the inversion results have physical meaning, density constraints are added to the loss function. The physical boundary constraint term is defined as follows:
[0043] in, Indicates the lower limit of density. Indicates the upper limit of density, This represents the total number of three-dimensional mesh cells corresponding to the underground density model. This indicates the index of the grid cell. This constraint penalizes density values that exceed physically reasonable limits, thereby preventing unconstrained and geologically unreliable inversion results.
[0044] Gravity has a strong volume effect, which often leads to low resolution in inversion results. Target geological bodies exhibit a sparse spatial distribution. The L0 norm can effectively constrain the sparsity of the magnetic model, but since the L0 norm is not differentiable, this method uses the Sigmoid function to construct a differentiable approximation.
[0045] in, Using the sigmoid activation function, implement the step approximation. . The steepness coefficient (set to 10 in this embodiment) is the larger the value, the closer it is to the step characteristics of the L0 norm; The non-zero threshold (set to 0.01 in this embodiment) distinguishes between "zero" and "non-zero" density values; mean(⋅) performs mean calculation, normalizing the loss to [0,1] to suit the magnitude of other loss terms. The Sigmoid function approximates the L0 norm curve as shown below. Figures 4-5 As shown, Figure 4 Indicates different The graph of the Sigmoid function with different values. Figure 5 This represents the graphs of the Sigmoid approximation function for different norms.
[0046] Furthermore, to address the issue of gravity sensitivity decreasing with depth, depth-weighted summation and an L0 focusing term are introduced to improve the inversion resolution of deep gravity. The final focusing regularization term is calculated using the following formula:
[0047] in, It is a depth-weighted matrix. This represents the depth of the grid corresponding to the underground density model; This serves as a reference depth to avoid outliers in shallow areas; m represents density. The parameter is used to control the rate of change of weights with depth. This represents a diagonal matrix, which is set to 3 in this embodiment. This sub-item assigns greater weight to the deep model mesh, effectively compensating for the sensitivity loss of deep gravity anomaly signals. This ensures that the inversion results maintain high resolution in both shallow and deep regions.
[0048] Furthermore, this embodiment employs a fully connected neural network (FNN) as the implicit parameterization carrier for the underground density model, such as... Figure 6 As shown, this network takes two-dimensional gravity anomaly data (spatial format: 64×64 matrix, flattened into a 4096-dimensional vector) as input features and outputs a three-dimensional density distribution in the form of an 8000×1-dimensional one-dimensional vector. Specifically, the 8000-dimensional output vector is predefined as a three-dimensional mesh mapped to the subsurface model (e.g., divided into 20×20×20 grid cells in the x, y, and z directions, for a total of 8000 grid cells), and each element in the output vector corresponds to the density value m(x, y, z) of a single three-dimensional grid cell. This design makes the neural network a continuous and flexible representation tool for the subsurface model, and the network parameter θ implicitly encodes the subsurface three-dimensional density distribution information.
[0049] In step S3, the network hyperparameters θ are optimized using the Adam optimizer, which is highly efficient in deep learning optimization tasks. The initial learning rate is set to 10. −4A learning rate decay strategy (decreasing by 50% every 200 training epochs) is employed to stabilize the convergence process. The total number of training epochs is 1000. When the relative change in the total loss function is less than... The optimization process terminates at that point.
[0050] To ensure optimal performance of the deep learning model in the gravity anomaly inversion task, a series of system comparison experiments were conducted on the model's core hyperparameters. The optimal hyperparameter combination balancing model efficiency and inversion performance was ultimately determined, and the specific parameter settings are shown in Table 1.
[0051] Table 1. Hyperparameter values for unsupervised learning
[0052] Based on the above-mentioned method principle, this invention implements an unsupervised neural network inversion algorithm. To verify the correctness and effectiveness of the inversion method, this invention designs a relatively complex single-step staircase model. Each step of the unidirectional staircase is 800m long, 320m wide, and 80m high, as shown below. Figure 2 As shown, the density is 1 g / cm³. The coordinate range of the designed planar computational domain is from 0 to 3200 m, and the mesh size is [missing information]. m, co-division Data from each node.
[0053] An unsupervised deep learning method was used to invert gravity anomalies in a single-order model. The inversion process involved 1000 iterations and took 3.2 minutes. The final data fitting error reached 0.01 mGal. The loss terms are as follows: Figure 7 As shown. The cross-section (x=1600m) and section (z=2220m) obtained from the inversion are as follows. Figures 8-11 As shown, Figure 8 This represents a slice of the real model at x=1600m. Figure 9 This represents a slice of the real model at z=2220m. Figure 10 This represents the inversion slice at x=1600m. Figure 11 The inversion model slice for z=2220m shows that the position of the inversion model is basically consistent with the theoretical model, and it can restore the model's state of existence well.
[0054] In another exemplary embodiment, based on the same inventive concept as the method embodiment, a gravity inversion system based on unsupervised deep learning is provided, comprising: The gravity anomaly data acquisition module is used to acquire gravity anomaly data observed on the Earth's surface through forward modeling. A fully connected neural network construction module is used to construct a fully connected neural network based on the gravity anomaly data, mapping the input gravity anomaly data to a subsurface three-dimensional density distribution; wherein, the loss function of the fully connected neural network includes: The data fitting term measures the difference between observed gravity anomaly data and the predicted gravity field. A smoothing constraint term is used to constrain the gradient of the underground density model in three-dimensional space based on the L1 norm. Physical boundary constraints are used to limit the density prediction value within a preset physical reasonable range; Focusing on regularization terms, including L0 norm sparse constraints based on the differentiability approximation of the Sigmoid function and depth weighting matrices, we aim to compensate for the sensitivity loss of deep gravity anomaly signals. A fully connected neural network training module is used to perform unsupervised training on the fully connected neural network using an optimizer to minimize the loss function; The gravity inversion output module is used to input actual observed gravity anomaly data into a trained fully connected neural network and output the corresponding underground three-dimensional density distribution model.
[0055] In another exemplary embodiment, based on the same inventive concept as the method embodiment, an electronic device is provided, including a memory and a processor. The memory stores computer instructions that can be executed on the processor. When the processor executes the computer instructions, it performs the gravity inversion method based on unsupervised deep learning provided in the embodiment of the present invention.
[0056] The processor may be a single-core or multi-core central processing unit or a specific integrated circuit, or one or more integrated circuits configured to implement the present invention.
[0057] The embodiments of the subject matter and functional operation described in this specification can be implemented in: tangibly embodied computer software or firmware, computer hardware including the structures disclosed in this specification and their structural equivalents, or combinations thereof. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible, non-transitory program carrier for execution by a data processing device or for controlling the operation of a data processing device. Alternatively or additionally, the program instructions may be encoded on artificially generated propagation signals, such as machine-generated electrical, optical, or electromagnetic signals, which are generated to encode information and transmit it to a suitable receiving device for execution by the data processing device.
[0058] The processing and logic flow described in this specification can be executed by one or more programmable computers that execute one or more computer programs to perform corresponding functions by operating on input data and generating output. The processing and logic flow can also be executed by dedicated logic circuitry—such as FPGAs (Field-Programmable Gate Arrays) or ASICs (Application-Specific Integrated Circuits), and the device can also be implemented as dedicated logic circuitry.
[0059] Suitable processors for executing computer programs include, for example, general-purpose and / or special-purpose microprocessors, or any other type of central processing unit. Typically, the central processing unit receives instructions and data from read-only memory and / or random access memory. The basic components of a computer include a central processing unit for implementing or executing instructions and one or more memory devices for storing instructions and data. Typically, a computer will also include one or more mass storage devices for storing data, such as disks, magneto-optical disks, or optical disks, or the computer will be operatively coupled to such mass storage devices to receive data from or transfer data to them, or both. However, a computer is not required to have such devices. Furthermore, a computer can be embedded in another device, such as a mobile phone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a global positioning system (GPS) receiver, or a portable storage device such as a universal serial bus (USB) flash drive, to name a few.
[0060] It should be understood that each block in a flowchart or block diagram can represent a module, segment, or portion of code, which contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the figures. For example, two consecutive blocks may actually be executed substantially in parallel, or they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.
[0061] The above detailed embodiments are a description of the present invention. It should not be considered that the specific embodiments of the present invention are limited to these descriptions. For those skilled in the art, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the protection scope of the present invention.
Claims
1. A gravity inversion method based on unsupervised deep learning, characterized in that, Includes the following steps: S1. Obtain gravity anomaly data from surface observations through forward modeling; S2. Construct a fully connected neural network based on the gravity anomaly data to map the input gravity anomaly data into a three-dimensional underground density distribution; wherein, the loss function of the fully connected neural network includes: The data fitting term measures the difference between observed gravity anomaly data and the predicted gravity field. A smoothing constraint term is used to constrain the gradient of the underground density model in three-dimensional space based on the L1 norm. Physical boundary constraints are used to limit the density prediction value within a preset physical reasonable range; Focusing on regularization terms, including L0 norm sparse constraints based on the differentiability approximation of the Sigmoid function and depth weighting matrices, we aim to compensate for the sensitivity loss of deep gravity anomaly signals. S3. An optimizer is used to perform unsupervised training on the fully connected neural network to minimize the loss function; S4. Input the actual observed gravity anomaly data into the trained fully connected neural network, and output the corresponding underground three-dimensional density distribution model.
2. The gravity inversion method based on unsupervised deep learning according to claim 1, characterized in that, The loss function is as follows: ,in, Represents the total loss function. Represents the data fitting term. Represents the smoothing constraint term. Represents physical boundary constraint terms. This indicates focusing on the regularization term. , , Weighting parameters to balance the contributions of each loss term.
3. The gravity inversion method based on unsupervised deep learning according to claim 2, characterized in that, The data fitting term is calculated using the following formula: ,in, Let A be a weighted matrix of data, and A be a forward operator. The output of the network shows the underground three-dimensional density distribution. To observe gravity anomaly data, This represents the L2 norm.
4. The gravity inversion method based on unsupervised deep learning according to claim 2, characterized in that, The smoothness constraint term is calculated using the following formula: ,in, These are the first-order spatial derivative operators of the underground density model in the x, y, and z directions, respectively. A three-dimensional magnetization model. 1 represents the L1 norm.
5. The gravity inversion method based on unsupervised deep learning according to claim 3, characterized in that, The physical boundary constraint terms are calculated using the following formula: ,in, Indicates the lower limit of density. Indicates the upper limit of density, This represents the total number of three-dimensional mesh cells corresponding to the underground density model. Indicates the index of the grid cell.
6. The gravity inversion method based on unsupervised deep learning according to claim 5, characterized in that, The focus regularization term is calculated using the following formula: Where mean(⋅) is the mean operation, which normalizes the loss to [0,1]. The Sigmoid activation function is used. Steepness coefficient, The threshold for determining non-zero values. is a depth-weighted matrix, where m represents density.
7. The gravity inversion method based on unsupervised deep learning according to claim 6, characterized in that, The depth-weighted matrix is calculated using the following formula: ,in, This represents the depth of the grid corresponding to the underground density model; For reference depth, The parameter is used to control the rate of change of weights with depth. This represents a diagonal matrix.
8. The gravity inversion method based on unsupervised deep learning according to claim 1, characterized in that, The fully connected neural network takes a one-dimensional vector flattened from two-dimensional gravity anomaly data as input and outputs a one-dimensional vector of underground three-dimensional density distribution. The fully connected neural network is trained using the Adam optimizer and employs a learning rate decay strategy.
9. A gravity inversion system based on unsupervised deep learning, characterized in that, include: The gravity anomaly data acquisition module is used to acquire gravity anomaly data observed on the Earth's surface through forward modeling. A fully connected neural network construction module is used to construct a fully connected neural network based on the gravity anomaly data, mapping the input gravity anomaly data to a subsurface three-dimensional density distribution; wherein, the loss function of the fully connected neural network includes: The data fitting term measures the difference between observed gravity anomaly data and the predicted gravity field. A smoothing constraint term is used to constrain the gradient of the underground density model in three-dimensional space based on the L1 norm. Physical boundary constraints are used to limit the density prediction value within a preset physical reasonable range; Focusing on regularization terms, including L0 norm sparse constraints based on the differentiability approximation of the Sigmoid function and depth weighting matrices, we aim to compensate for the sensitivity loss of deep gravity anomaly signals. A fully connected neural network training module is used to perform unsupervised training on the fully connected neural network using an optimizer to minimize the loss function; The gravity inversion output module is used to input actual observed gravity anomaly data into a trained fully connected neural network and output the corresponding underground three-dimensional density distribution model.
10. An electronic device comprising a memory and a processor, wherein the memory stores computer instructions executable by the processor, characterized in that, When the processor executes computer instructions, it performs the gravity inversion method based on unsupervised deep learning as described in any one of claims 1-8.