A gravity data inversion method, system and medium

Abstract

The present invention relates to a gravity data inversion method, system and medium, a gravity data inversion method, comprising: generating tens of thousands of random single anomaly training sample pairs; based on all the random single anomaly training sample pairs, selecting a part of the preset amount of data as a training data set, and selecting another part of the preset amount of data as a verification data set; using the training data set to train a series of width learning networks with different network complexities, the goal of the gravity inversion is to estimate the optimal density model; using the verification data set to identify the width learning network with the most appropriate network complexity; inputting the measured gravity data vector into the width learning network with the most appropriate network complexity to obtain the optimal density model. The present invention uses the width learning network and the single anomaly training samples to improve the accuracy and efficiency of density structure modeling.

Description

Technical Field

[0001] The present invention relates to the field of geophysical gravity data inversion technology, and in particular to a gravity data inversion method, system and medium. Background Art

[0002] Gravity inversion plays a vital role in geophysics, enabling the determination of subsurface density structures for various practical applications, including mineral resource exploration, oil and gas exploration, geological structure identification, and groundwater resource detection. Due to the complexity of the subsurface material, a two-dimensional perspective often leads to a simplified and distorted representation of the density structure, which may overlook important structural features. Therefore, it has become crucial and increasingly popular to use three-dimensional (3-D) inversion to obtain the subsurface density structure with high spatial resolution and accuracy in gravity data inversion. However, due to the increase in higher dimensional scales, higher requirements are placed on the computational efficiency and global optimization capabilities of the algorithms applied in the inversion process. The use of single anomaly training samples for 3D width learning gravity data inversion algorithms is essential to effectively obtain accurate, effective, and realistic inversion results. The development and introduction of global inversion algorithms has always been a key research direction in 3D gravity data inversion, which generally includes traditional global optimization algorithms (such as genetic algorithms, simulated annealing algorithms, particle swarm optimization algorithms, etc.) and emerging machine learning algorithms. In the past 20 years, traditional inversion algorithms have been widely used in 3D gravity data inversion. Traditional inversion algorithms are still used to identify the optimal solution for 3D gravity data inversion due to their global optimization capabilities. In contrast, machine learning algorithms have emerged and developed rapidly in geophysical inversion in recent years. They have been widely welcomed due to their real-time processing, powerful global optimization, and generalization capabilities, which improve the efficiency and accuracy of the 3D gravity inversion process. As a representative of machine learning, deep learning networks have been introduced to address the optimization challenges of 3D gravity data inversion. For example, Zhang et al., Celaya et al., Zhou et al., Hu et al. used deep learning networks to perform 3D gravity data inversion and achieved satisfactory results in simulating underground density structures. Currently, the application of machine learning in gravity inversion is constantly evolving to meet the growing demand for enhanced inversion performance.

[0003] Compared with traditional global optimization algorithms, deep learning has received more attention from researchers in recent years for various modeling problems due to its real-time nature and optimization capabilities. Once the network training is completed, the inversion results can be determined immediately. In addition, compared with traditional algorithms, deep learning is widely regarded as having superior functional modeling capabilities. However, in most 3D deep learning gravity inversion studies, there are two major challenges that need to be addressed, namely the time-consuming problem of network training and the problem of representing the number of anomalies in the training samples. The first challenge limits the inversion efficiency, especially in some cases where it is difficult to avoid retraining the network. Regarding the second challenge, most studies implicitly assume that the maximum number of anomalies in the training samples is larger than the actual number. These two shortcomings hinder the wider application of machine learning in 3D gravity data inversion and are urgent problems that need to be solved. Summary of the invention

[0004] The present invention provides a gravity data inversion method, system and medium to solve the problems of time-consuming network training in deep learning gravity inversion and the problem of representing abnormal numbers in training samples.

[0005] To achieve the above-mentioned object, in a first aspect, the present invention provides a gravity data inversion method, comprising: generating tens of thousands of random single anomaly training sample pairs, each of the random single anomaly training sample pairs comprising input gravity training data and output density model training data;

[0006] Based on all the random single-abnormal training sample pairs, a part of the preset amount of data is selected as a training data set, and another part of the preset amount of data is selected as a verification data set;

[0007] Using the training data set to train a series of width learning networks with different network complexities, specifically: using the width learning network to perform gravity inversion modeling training on the functional relationship between measured gravity data and underground density model to obtain a trained width learning network, the goal of the gravity inversion is to estimate the optimal density model, wherein the optimal density model is an approximation of the actual density model, the training sample includes input gravity training, and the network complexity index includes the number of neurons for each group of mapping features, the number of groups of mapping features, and the number of groups of enhanced nodes;

[0008] Applying the validation data set to identify a width learning network with the most appropriate network complexity;

[0009] The measured gravity data vector is input into the width learning network of the most suitable network complexity to obtain the optimal density model.

[0010] Preferably, the use of the width learning network to perform gravity inversion modeling training on the functional relationship between the measured gravity data and the underground density model to obtain a trained width learning network specifically includes:

[0011] The function mapping between the input gravity training data set and the output density model training data set constructed by the width learning network is approximately the function F(.), where the function F(.) represents the functional relationship between the measured gravity data and the underground density model, which is expressed as:

[0012]

[0013] Among them, M t represents the output density model training data set, F NF =[F 1 , F 2 , …, F NF ] represents the mapping feature, E NE represents the enhanced node, W B Represents the network weight matrix, which is the only unknown parameter that needs to be determined in the width learning network training. The mapping characteristics of each group of width learning networks are expressed as:

[0014]

[0015] Where Dt is the measured gravity data vector, φ is the feature mapping function of the sparse autoencoder for data dimension reduction, and W Fi is the i-th weight matrix with random values, β Fi is the ith bias with a random value, N F is the number of groups of mapping features, according to the mapped features F NF , each group of enhanced nodes is calculated as:

[0016]

[0017] Where ξ is a nonlinear activation function, W Ej For W Fi Similar j-th random weight matrix, β Ej For Fi Similar j-th random bias matrix, N E To increase the number of node groups, the following formula is used to calculate the only unknown parameter W of the width learning network: B :

[0018] W B =A + M t

[0019] Where A=[F NF , E NE ], where the pseudo-inverse A+ is calculated through ridge regression to obtain the weight matrix W B , the training process is completed.

[0020] Preferably, the step of inputting the measured gravity data vector into the width learning network of the most suitable network complexity to obtain the optimal density model specifically includes:

[0021] The measured gravity data vector d is input into the network to obtain the optimal density model

[0022] in,

[0023]

[0024] Preferably, the generating of tens of thousands of random single-abnormal training sample pairs specifically includes:

[0025] An input-output training sample pair is generated by forward modeling of measured gravity data. The underground density model is constructed by embedding a single, colored, cube-shaped anomaly block in a uniform background. The underground density model is discretized into different numbers of grid cells in the x-axis, y-axis and z-axis directions. The size and spatial position of the anomaly block in each underground density model vary randomly, and the anomaly density value is between -2 and 2 g / cm 3 The samples are randomly selected within the range and coordinatedly rotated around the center point of the density model to generate single samples in different directions.

[0026] Preferably, the method for generating a single sample in different directions by performing coordinated rotation around the center point of the density model is as follows:

[0027]

[0028] Where [x, y, z]T is the density model coordinate, [x′, y′, z′]T is the corresponding coordinate after rotation, angle α is the result of rotation along the z-axis, angle β is the result of rotation along the z-axis, and angle γ is the result of rotation along the x-axis.

[0029] Preferably, the applying the verification data set to identify the width learning network with the most appropriate network complexity specifically includes:

[0030] The objective function is used to quantify the inversion performance of each sample in the validation dataset, and the number of neurons N for each set of mapping features is selected. C , the number of groups of mapping features N F and the number of groups of enhanced nodes N E The most appropriate hyperparameter value is determined to optimize the network complexity of three-dimensional gravity inversion, wherein the most appropriate hyperparameter value is determined as the hyperparameter value of the width learning network that produces the minimum average objective function value among all samples in the validation data set.

[0031] Preferably, 30,000 randomly generated single-anomaly training sample pairs are selected to form a training data set, 30,000 samples in the training data set are used to train the width learning network, and 3,000 samples in the verification data set are used to optimize the network complexity of three-dimensional gravity inversion.

[0032] To achieve the above object, in a second aspect, the present invention relates to a gravity data inversion system, characterized in that it comprises:

[0033] A training sample pair generation module, used to generate tens of thousands of random single-anomaly training sample pairs, each of which includes input gravity training data and output density model training data;

[0034] A data set selection module is used to select a part of the preset amount of data as a training data set and another part of the preset amount of data as a verification data set based on all the random single abnormal training sample pairs;

[0035] A network training module, used to train a series of width learning networks with different network complexities using the training data set, specifically: using the width learning network to perform gravity inversion modeling training on the functional relationship between the measured gravity data and the underground density model to obtain a trained width learning network, the goal of the gravity inversion is to estimate the optimal density model, wherein the optimal density model is an approximation of the actual density model, the training sample includes input gravity training, and the network complexity index includes the number of neurons for each group of mapping features, the number of groups of mapping features, and the number of groups of enhanced nodes;

[0036] A network complexity determination module, for applying the validation data set to identify a width learning network with the most appropriate network complexity;

[0037] The optimal density model acquisition module is used to input the measured gravity data vector into the width learning network of the most suitable network complexity to obtain the optimal density model.

[0038] Preferably, the network complexity determination module is specifically used to: quantify the inversion performance of each sample in the validation data set using an objective function, select the number of neurons N for each group of mapping features C , the number of groups of mapping features N F and the number of groups of enhanced nodes N E The most appropriate hyperparameter value is determined to optimize the network complexity of three-dimensional gravity inversion, wherein the most appropriate hyperparameter value is determined as the hyperparameter value of the width learning network that produces the minimum average objective function value among all samples in the validation data set.

[0039] To achieve the above-mentioned purpose, in a third aspect, the present invention also relates to a computer-readable storage medium, in which instructions are stored, and when the instructions are executed, the above-mentioned gravity data inversion method is executed.

[0040] The gravity data inversion method, system and medium disclosed by the present invention have the following beneficial effects compared with the prior art:

[0041] The present invention adopts a width learning (BL) network for gravity data inversion, and the network adopts a single-layer neural structure. The width learning network increases the complexity of the width dimension rather than the depth, and provides a significant advantage in training speed while maintaining the functional mapping ability equivalent to the deep learning network. The machine learning inversion method applied by the present invention combines single anomalies at different positions in different training samples, and after being extended to three-dimensional gravity inversion, the inversion results prove the effectiveness of network training with single anomaly training samples. Therefore, the present invention uses a width learning network and a single anomaly training sample to improve the accuracy and efficiency of density structure modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a method flow chart of a gravity data inversion method in Embodiment 1 of the present invention;

[0043] Figure 2 A width learning network structure diagram of a gravity data inversion method in Embodiment 1 of the present invention;

[0044] Figure 3 It is a schematic diagram of generating training sample pairs based on gravity data forward modeling of a gravity data inversion method in Embodiment 1 of the present invention;

[0045] Figure 4 is a graph of objective function under different network complexities in Example 1 of Embodiment 1 of the present invention;

[0046] Figure 5 It is the numerical density model of the four rectangular anomalies in Example 1 of the first embodiment of the present invention and the corresponding surface gravity anomaly observation map;

[0047] Figure 6 It is a numerical inversion result diagram of the four rectangular density anomaly models in Example 1 of the first embodiment of the present invention;

[0048] Figure 7 The numerical density model of the irregular shape anomaly in Example 1 of the first embodiment of the present invention and the corresponding surface gravity anomaly observation map;

[0049] Figure 8 is a numerical density model inversion result diagram of the irregular shape anomaly in Example 1 of the first embodiment of the present invention;

[0050] Fig. 9 This is the surface gravity anomaly observation map of the Vinton salt dome in Example 2 of Example 1 of the present invention;

[0051] Fig.10 This is a diagram of the inversion result of the field data of the Vinton salt dome in Example 2 of the first embodiment of the present invention;

[0052] Fig.11 It is a structural schematic diagram of a gravity data inversion system in the second embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0054] Embodiment 1

[0055] A method for inverting gravity data, see Figure 1-Figure 10 , by utilizing gravity data to improve the efficiency of the above exploration tasks. The method establishes the mapping relationship between gravity data and underground density structure by using a wide learning network with high training efficiency and robust modeling ability. It is worth noting that the inversion method eliminates the limitation on the number of anomalies in the inversion process, which is achieved by setting a position-variable anomaly to simulate different training samples. The application of numerical simulation and real data proves the effectiveness of the proposed three-dimensional machine learning gravity data inversion method, especially in the automatic determination of the number of anomalies. The proposed inversion method can promote the construction of underground density structure based on gravity data. Its characteristics include efficient training, strong modeling performance, real-time inversion capability, and the ability to handle scenarios without a priori number of anomalies.

[0056] like Figure 1 As shown, a gravity data inversion method includes the following steps: S10 to S50.

[0057] S10: generating tens of thousands of random single-anomaly training sample pairs, each of which includes input gravity training data and output density model training data.

[0058] In terms of the anomaly number problem, 3D resistivity inversion also faces the constraint of prior information on the number of anomalies. Tao et al. proposed a machine learning inversion method that combines single anomalies at different locations in different training samples. The inversion results prove the effectiveness of network training with single anomaly training samples.

[0059] In this embodiment, the present application adopts the resistivity inversion sample generation method proposed by Tao et al., and uses single anomalies at different locations in different training samples for network training. Therefore, this method has no limit on the number of anomalies before inversion. An input-output training sample pair is generated by forward modeling of the measured gravity data. The underground density model is constructed by embedding a single, colorful, cube-shaped anomaly block in a uniform background. The underground density model is discretized into different numbers of grid units in the x-axis, y-axis and z-axis directions, respectively. The size and spatial position of each anomaly block in the underground density model vary randomly, and the anomaly density value is between -2 and 2 g / cm 3 The samples are randomly selected within the range and coordinatedly rotated around the center point of the density model to generate single samples in different directions.

[0060] The rotation method is as follows:

[0061]

[0062] Where [x, y, z]T is the density model coordinate, [x', y', z']T is the corresponding coordinate after rotation, angle α is the result of rotation along the z axis, angle β is the result of rotation along the z axis, and angle γ is the result of rotation along the x axis. Figure 3 As shown, using the single anomaly density model ( Figure 3 a) and gravimeter deployment ( Figure 3 b) Simulate surface gravity data through forward gravity modeling ( Figure 3 c), generate input training samples ( Figure 3 d).

[0063] S20: Based on all the random single-abnormal training sample pairs, a part of the preset amount of data is selected as a training data set, and another part of the preset amount of data is selected as a verification data set.

[0064] In one example, 30,000 randomly generated single-anomaly training sample pairs are selected to form a training data set, 30,000 samples in the training data set are used to train the width learning network, and 3,000 samples in the verification data set are used to optimize the network complexity of three-dimensional gravity inversion.

[0065] S30: Use the training data set to train a series of width learning networks with different network complexities, specifically: use the width learning network to perform gravity inversion modeling training on the functional relationship between the measured gravity data and the underground density model to obtain a trained width learning network, the goal of the gravity inversion is to estimate the optimal density model, wherein the optimal density model is an approximation of the actual density model, the training samples include input gravity training, and the network complexity indicators include the number of neurons for each group of mapping features, the number of groups of mapping features, and the number of groups of enhanced nodes.

[0066] The above-mentioned use of the width learning network to perform gravity inversion modeling training on the functional relationship between the measured gravity data and the underground density model to obtain a trained width learning network specifically includes:

[0067] Function F(.) represents the functional relationship between the measured gravity data and the underground density model and can be expressed as:

[0068] d=F(m)

[0069] Where d = [d1, d2, ..., dNd] T∈RNd is the measured gravity data vector, m = [m1, m2, ..., mNm] T∈RNm is the density model vector, T represents the matrix transpose, Nd is the number of data points of the measured gravity data, Nm is the number of grid points of the density model, and F(.) is the functional relationship to be modeled. The goal of gravity inversion is to estimate the optimal density model This model is an approximation of the actual density model m. In order to quantitatively evaluate the inversion effect, the following objective function is used in the inversion process:

[0070]

[0071] The function mapping F(.) in the above formula is modeled using a width learning network, such as Figure 2 The figure shows the structure of the width learning network. As a supervised learning model, the width learning network explores the function mapping between the input and output data sets to approximate the actual underlying relationship. Given the number of training samples N, using D t =[d t1 ,d t2 , …, d tN ] T ∈R N ×Nd )(d ti ∈R Nd is the input training sample) and M t =[m t1 ,m t2 ,…,m tN ] T ∈R N×Nm (m ti ∈R Nm are the output training samples) represent the input gravity training dataset and the output density model training dataset respectively. It should be noted that the training samples are generated by forward modeling of gravity data.

[0072] d ti =T(m ti ), i = 1, 2, ..., N

[0073] Where T(.) is the forward function of gravity data under any density model.

[0074] The function mapping between the input gravity training data set and the output density model training data set constructed by the width learning network is approximately the function F(.), which is expressed as:

[0075]

[0076] Among them, M t represents the output density model training data set, F NF =[F 1 , F 2 , …, F NF ] represents the mapping feature, E NE represents the enhanced node, W B Represents the network weight matrix, which is the only unknown parameter that needs to be determined in the width learning network training. The mapping characteristics of each group of width learning networks are expressed as:

[0077]

[0078] Where Dt is the measured gravity data vector, φ is the feature mapping function of the sparse autoencoder for data dimension reduction, and W Fi is the i-th weight matrix with random values, β Fi is the ith bias with a random value, N F is the number of groups of mapping features, according to the mapped features F NF , each group of enhanced nodes is calculated as:

[0079]

[0080] Where ξ is a nonlinear activation function, W Ej For W Fi Similar j-th random weight matrix, β Ej For Fi Similar to the i-th random bias matrix, N E To increase the number of node groups, the following formula is used to calculate the only unknown parameter W of the width learning network: B :

[0081] W B =A + M t

[0082] Where A=[F NF , E NE ], where the pseudo-inverse A + The calculation is done through ridge regression, and the weight matrix W is calculated. B , the training process is completed.

[0083] S40: Using the verification data set to identify a width learning network with the most appropriate network complexity.

[0084] Selecting the appropriate mapping complexity (i.e., the appropriate hyperparameter combination) is crucial for BL gravity data inversion. In this embodiment, a grid search is used to select N in the range of [20:20:200]×[20:20:200]×[50:50:500]. C 、N F and N E The most appropriate hyperparameter value ([s:i:e] means the range starting from s and ending at e with an interval of i). This application uses 30,000 samples in the training dataset to train the width learning network and uses 3,000 samples in the validation dataset to optimize the network complexity of 3D gravity inversion.

[0085] The objective function defined in the above formula is used to quantify the inversion performance of each sample in the validation dataset, and the number of neurons N for each set of mapping features is selected. C , the number of groups of mapping features N F and the number of groups of enhanced nodes N E The most appropriate hyperparameter value is determined to optimize the network complexity of three-dimensional gravity inversion, wherein the most appropriate hyperparameter value is determined as the hyperparameter value of the width learning network that produces the minimum average objective function value among all samples in the validation data set.

[0086] S50: Inputting the measured gravity data vector into the width learning network of the most suitable network complexity to obtain the optimal density model.

[0087] Among them, the measured gravity data vector d is input into the network to obtain the optimal density model

[0088] in,

[0089] Preferably, the computer configuration used for the inversion task in this embodiment is Intel Core i7-11700KF@3.60GHz and 64.00GB (3200MHz) RAM.

[0090] Two examples are given below to further illustrate the present invention:

[0091] Example 1

[0092] Figure 4 The objective function curves under different network complexities are shown, and by following the implementation steps S10-S40, candidate width learning networks with different complexities are trained for network complexity selection. Figure 4The objective function values ​​for these width learning networks on the validation dataset are shown. This process determines the optimal hyperparameters: N C =160,N F =100,N E = 100. Using these hyperparameters, two numerical examples and one real data application are carried out to evaluate the effectiveness of the proposed inversion method.

[0093] Figure 5 Numerical density models with four rectangular anomalies and the corresponding surface gravity anomaly observations. Two numerical density models are used to validate the proposed inversion method. The first model consists of multiple rectangular-shaped anomalies and aims to evaluate the ability of the proposed method to accurately identify the number of anomalies. The second part focuses on evaluating the ability to recover irregular shapes of anomalies. Figure 5 In the figure, (a) is the three-dimensional representation of the actual density model and (b) is the surface gravity anomaly observation.

[0094] First, we apply an anomaly with multiple regular shapes ( Figure 5 a) The simulated gravity data of the density model ( Figure 5 b) to test the proposed inversion method. The surface gravity data generated by forward simulations of the numerical model are used as input to a training network built using a single anomaly training sample. The network then produces the corresponding inverse density model. Figure 6 a is a 3D view of the inverted density model. The results clearly show that the trained width learning network successfully identified four density anomalies without any prior assumptions about the number of anomalies. It also shows that the anomaly shapes are well identified in the inversion results compared to the actual model. The actual model and the inverted model have a difference of 0.0249 in the objective function value, which performs better in inverting gravity anomaly values. In order to evaluate the inversion results more comprehensively, the residuals between the inverted gravity anomaly data and the observed gravity anomaly data are calculated, as shown in Figure 6 b. The inversion residuals are mainly concentrated in the range of -1.0 to 1.0 mGal, which is consistent with Figure 5 b is relatively small. Undoubtedly, the function mapping established by the width learning network trained with single anomaly training samples effectively captures the relationship between the multi-anomaly density model and the actual measured gravity data. It can be reasonably analyzed that the success of this method lies in the variation of anomaly size and position in the training samples, and more importantly, in the generalization ability of the width learning network to different numbers of anomalies. Numerical examples verify the effectiveness of this method in underground density models with multiple regular-shaped anomalies.

[0095] Furthermore, the effectiveness of the inversion method is verified using a numerical model of irregular-shaped anomalies. Figure 7is the actual density model and the corresponding theoretical surface gravity anomaly data. Unlike the first numerical model, this model contains irregularly shaped anomalies. This numerical example aims to explore the performance of inversion prediction of irregularly shaped anomalies. Using gravity data as the input of the training network, the inverted density model can be quickly obtained, such as Figure 8 As shown in a. Compared with the actual density anomaly, while accurately estimating the number of anomalies, the shape of the anomaly is also well predicted. For the inverted density value, the objective function value of the inverted density model and the actual density model is 0.0198, indicating that the density value has a strong recovery in the anomaly area. In particular, each training sample used for network training contains only one anomaly. It can be seen that the generalization ability of the gravity inversion method of the present invention is not only limited to the recognition of the number of anomalies, but can also be extended to the shape prediction of irregular shaped anomalies. In order to evaluate the inversion accuracy in more detail, the difference between the inverted gravity anomaly data and the observed gravity anomaly data was quantified, as shown in Figure 8 b. The inversion residual is mainly limited to the range of -1.0 to 1.5 mGal, which is consistent with Figure 7 Compared with the gravity anomaly shown in (a), the difference is relatively small. The proposed inversion method is trained on only a single anomaly sample and can produce accurate results even when applied to anomalies with irregular shapes. The example further verifies the effectiveness of the method.

[0096] Example 2

[0097] The inversion capability of the proposed three-dimensional gravity data inversion method was further verified through practical applications. The field data came from the gravity survey of the Vinton Salt Dome in southwestern Louisiana, USA, conducted by Bell Geospace. The observation area was limited to 4 km × 4 km. Fig. 9 As shown, a density anomaly with a radius of about 1 km can be clearly seen.

[0098] As with numerical simulation, by inputting surface gravity anomaly data into the trained network, the subsurface density inversion results can be quickly obtained. Fig.10 This is the inversion result of Vinton salt dome field data. Fig.10 As shown in a, a density anomaly was found, which is very close to the observed gravity anomaly. In order to further evaluate the inversion model, the inverted density model was input into the forward function to generate theoretical surface gravity data, and the residual map between the inverted surface gravity anomaly data and the measured surface gravity anomaly data was calculated ( Fig.10 b). The inversion residuals are mainly limited to the range of -0.1 to 0.1 mGal, which is relatively small compared to gravity anomalies. In addition, the inversion results are sliced ​​horizontally ( Fig.10 c is a horizontal slice with a depth of Z = 400m) and two vertical slices ( Fig.10d is a vertical slice at X = 2000m and Y = 1600m) visualized in 2D, providing an additional perspective for the inverted model. It can be seen that the upper and lower depths of the density anomaly are 150m and 400m, respectively. To verify the accuracy of the inversion results of this study, the inversion results of the Vinton Salt Dome field data are compared with the results of previous work, as shown in Table 1. This comparison confirms the rationality of the inversion results. The application of measured data also further verifies the effectiveness of the proposed three-dimensional gravity inversion method.

[0099] Table 1 Comparison of inversion results of this study and previous Wenton salt dome field data

[0100]

[0101]

[0102] The width learning network improves its mapping ability by expanding the number of neurons in the width direction instead of increasing the depth, which helps to minimize the training time. Using the width learning network, the inversion method proposed in this paper effectively simulates the relationship between the measured gravity data and the underground three-dimensional density structure. In addition, the inversion method eliminates the need for prior knowledge of the number of anomalies by using a single anomaly training sample. The variability of the anomaly positions in different training samples stimulates the generalization ability of the network, enabling it to automatically detect the number of anomalies and further construct an accurate three-dimensional density model. Numerical simulations and actual data inversions verify the effectiveness of the proposed three-dimensional BL gravity data inversion method in accurately estimating the underground density structure. The method has the characteristics of high training time efficiency, strong functional mapping modeling capability, strong real-time performance, and strong adaptability to scenarios where the number of anomalies is unknown before inversion. This study helps to promote better estimation of density structure in gravity data inversion.

[0103] Embodiment 2

[0104] A gravity data inversion system, such as Fig.11 As shown, it includes a training sample pair generation module 71, a data set selection module 72, a network training module 73, a network complexity determination module 74 and an optimal density model acquisition module 75.

[0105] A training sample pair generation module 71 is used to generate tens of thousands of random single-anomaly training sample pairs, each of which includes input gravity training data and output density model training data;

[0106] A data set selection module 72 is used to select a part of a preset amount of data as a training data set and another part of a preset amount of data as a verification data set based on all the random single abnormal training sample pairs;

[0107] A network training module 73 is used to train a series of width learning networks with different network complexities using the training data set, specifically: using the width learning network to perform gravity inversion modeling training on the functional relationship between the measured gravity data and the underground density model to obtain a trained width learning network, wherein the goal of the gravity inversion is to estimate the optimal density model, wherein the optimal density model is an approximation of the actual density model, the training sample includes input gravity training, and the network complexity index includes the number of neurons for each group of mapping features, the number of groups of mapping features, and the number of groups of enhanced nodes;

[0108] A network complexity determination module 74, for applying the validation data set to identify a width learning network with the most appropriate network complexity;

[0109] The optimal density model acquisition module 75 is used to input the measured gravity data vector into the width learning network of the most suitable network complexity to obtain the optimal density model.

[0110] In some embodiments, the network complexity determination module 74 is specifically used to: quantify the inversion performance of each sample in the validation data set using an objective function, select the number of neurons N for each group of mapping features C , the number of groups of mapping features N F and the number of groups of enhanced nodes N E The most appropriate hyperparameter value is determined to optimize the network complexity of three-dimensional gravity inversion, wherein the most appropriate hyperparameter value is determined as the hyperparameter value of the width learning network that produces the minimum average objective function value among all samples in the validation data set.

[0111] The implementation process, method and effect of a gravity data inversion system in this embodiment are the same as those of a gravity data inversion method described in the first embodiment, and will not be described in detail here.

[0112] Embodiment 3

[0113] The present invention relates to a computer-readable storage medium, in which instructions are stored. When the instructions are executed, a gravity data inversion method of embodiment 1 is executed. The execution process method and effect of the execution process method are the same as those of the gravity data inversion method described in embodiment 1, and will not be repeated here.

[0114] It should be noted that, in the present invention, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0115] The above are only preferred 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 gravity data inversion method, characterized in that: include: Generate tens of thousands of random single anomaly training sample pairs: Generate an input-output training sample pair through forward modeling of measured gravity data. The underground density model is constructed with a single, colored, cube-shaped anomaly block embedded in a uniform background. The underground density model is discretized into different numbers of grid cells in the x-axis, y-axis and z-axis directions. The size and spatial position of the anomaly block in each underground density model vary randomly, and the anomaly density value is between -2 and 2 g / cm 3 Randomly select within the range, coordinately rotate around the center point of the density model, and generate single samples in different directions as random single anomaly training sample pairs, wherein each of the random single anomaly training sample pairs includes input gravity training data and output density model training data; Based on all the random single-abnormal training sample pairs, a part of the preset amount of data is selected as a training data set, and another part of the preset amount of data is selected as a verification data set; The training data set is used to train a series of width learning networks with different network complexities, specifically: the width learning network constructs a function mapping between the input gravity training data set and the output density model training data set that is approximately the function F(.), where the function F(.) represents the functional relationship between the measured gravity data and the underground density model, expressed as: Among them, M t represents the output density model training data set, F NF =[F1,F2,…,F NF ] represents the mapping feature, E NE represents the enhanced node, W B Represents the network weight matrix, which is the only unknown parameter that needs to be determined in the width learning network training. The mapping characteristics of each group of width learning networks are expressed as: Among them, D t is the measured gravity data vector, φ is the feature mapping function of the sparse autoencoder for data dimension reduction, W Fi is the i-th weight matrix with random values, β Fi is the ith bias with a random value, N F is the number of groups of mapping features, according to the mapped features F NF , each group of enhanced nodes is calculated as: Where ξ is a nonlinear activation function, W Ej For W Fi Similar j-th random weight matrix, β Ej For Fi Similar j-th random bias matrix, N E To increase the number of node groups, the following formula is used to calculate the only unknown parameter W of the width learning network: B : W B =A + M t Where A=[F NF , E NE ], where the pseudo-inverse A + The calculation is done through ridge regression, and the weight matrix W is calculated. B , the training process is completed and a trained width learning network is obtained; The goal of gravity inversion is to estimate an optimal density model, wherein the optimal density model is an approximation of an actual density model, the training sample includes input gravity training, and the network complexity index includes the number of neurons per group of mapping features, the number of groups of mapping features, and the number of groups of enhanced nodes; Applying the validation data set to identify a width learning network with the most appropriate network complexity; The measured gravity data vector is input into the width learning network of the most suitable network complexity to obtain the optimal density model.

2. A gravity data inversion method according to claim 1, characterized in that: The step of inputting the measured gravity data vector into the width learning network of the most suitable network complexity to obtain the optimal density model specifically includes: The measured gravity data vector d is input into the network to obtain the optimal density model in, 3. A gravity data inversion method according to claim 1, characterized in that: The method for generating a rotation of a single sample in different directions by performing coordinated rotation around the center point of the density model is as follows: Where [x, y, z]T is the density model coordinate, [x', y', z']T is the corresponding coordinate after rotation, angle α is the result of rotation along the z-axis, angle β is the result of rotation along the z-axis, and angle γ is the result of rotation along the x-axis.

4. A gravity data inversion method according to claim 1, characterized in that: The applying the verification data set to identify the most suitable width learning network of network complexity specifically includes: The objective function is used to quantify the inversion performance of each sample in the validation dataset, and the number of neurons N for each set of mapping features is selected. C , the number of groups of mapping features N F and the number of groups of enhanced nodes N E The most appropriate hyperparameter value is determined to optimize the network complexity of three-dimensional gravity inversion, wherein the most appropriate hyperparameter value is determined as the hyperparameter value of the width learning network that produces the minimum average objective function value among all samples in the validation data set.

5. A gravity data inversion method according to claim 1 or 4, characterized in that: 30,000 randomly generated single-anomaly training sample pairs are selected to form a training data set, 30,000 samples in the training data set are used to train the width learning network, and 3,000 samples in the verification data set are used to optimize the network complexity of three-dimensional gravity inversion.

6. A gravity data inversion system, characterized in that: include: The training sample pair generation module is used to generate tens of thousands of random single anomaly training sample pairs: an input-output training sample pair is generated by forward modeling of measured gravity data. The underground density model is constructed by embedding a single, colored, cube-shaped anomaly block in a uniform background. The underground density model is discretized into different numbers of grid cells in the x-axis, y-axis and z-axis directions. The size and spatial position of each anomaly block in the underground density model vary randomly, and the anomaly density value is between -2 and 2 g / cm 3 Randomly select within the range, coordinately rotate around the center point of the density model, and generate single samples in different directions as random single anomaly training sample pairs, wherein each of the random single anomaly training sample pairs includes input gravity training data and output density model training data; A data set selection module is used to select a part of the preset amount of data as a training data set and another part of the preset amount of data as a verification data set based on all the random single abnormal training sample pairs; The network training module is used to train a series of width learning networks with different network complexities using the training data set, specifically: the width learning network constructs a function mapping between the input gravity training data set and the output density model training data set that is approximate to the function F(.), where the function F(.) represents the functional relationship between the measured gravity data and the underground density model, expressed as: Among them, M t represents the output density model training data set, F NF =[F1,F2,…,F NF ] represents the mapping feature, E NE represents the enhanced node, W B Represents the network weight matrix, which is the only unknown parameter that needs to be determined in the width learning network training. The mapping characteristics of each group of width learning networks are expressed as: Among them, D t is the measured gravity data vector, φ is the feature mapping function of the sparse autoencoder for data dimension reduction, W Fi is the i-th weight matrix with random values, β Fi is the ith bias with a random value, N F is the number of groups of mapping features, according to the mapped features F NF , each group of enhanced nodes is calculated as: Where ξ is a nonlinear activation function, W Ej For W Fi Similar j-th random weight matrix, β Ej For Fi Similar j-th random bias matrix, N E To increase the number of node groups, the following formula is used to calculate the only unknown parameter W of the width learning network: B : W B =A + M t Where A=[F NF , E NE ], where the pseudo-inverse A + The calculation is done through ridge regression, and the weight matrix W is calculated. B , the training process is completed and a trained width learning network is obtained; The goal of gravity inversion is to estimate an optimal density model, wherein the optimal density model is an approximation of an actual density model, the training sample includes input gravity training, and the network complexity index includes the number of neurons per group of mapping features, the number of groups of mapping features, and the number of groups of enhanced nodes; A network complexity determination module, for applying the validation data set to identify a width learning network with the most appropriate network complexity; The optimal density model acquisition module is used to input the measured gravity data vector into the width learning network of the most suitable network complexity to obtain the optimal density model.

7. A gravity data inversion system according to claim 6, characterized in that: The network complexity determination module is specifically used to: quantify the inversion performance of each sample in the validation data set using an objective function, select the number of neurons N for each group of mapping features C , the number of groups of mapping features N F and the number of groups of enhanced nodes N E The most appropriate hyperparameter value is determined to optimize the network complexity of three-dimensional gravity inversion, wherein the most appropriate hyperparameter value is determined as the hyperparameter value of the width learning network that produces the minimum average objective function value among all samples in the validation data set.

8. A computer-readable storage medium, characterized in that: The storage medium stores instructions, which, when executed, execute a gravity data inversion method according to any one of claims 1 to 5.

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