A method and system for real-time regional gravity field modeling based on deep neural networks

Abstract

This invention relates to the field of deep learning technology and discloses a real-time regional gravity field modeling method and system based on deep neural networks. The method includes the following steps: acquiring ground gravity measurement data and calculating the original ground gravity anomaly at discrete ground points; introducing a global gravity field model to obtain the long-wave gravity anomaly component of the discrete ground points in real time; introducing a deep fully connected neural network (FC-DNN); calculating the short-wave gravity anomaly component of the discrete ground points in real time; introducing a convolutional neural network (CNN); predicting the residual gravity anomaly component of the discrete ground points in real time; and fusing the residual gravity anomaly component, short-wave gravity anomaly component, and long-wave gravity anomaly component of the discrete ground points to complete the modeling of the regional ground gravity field. This invention features high training efficiency and fast inference speed, solving the problem of insufficient computational efficiency in existing gravity field modeling methods.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of deep learning, and more particularly, to a real-time regional gravity field modeling method and system based on a deep neural network. BACKGROUND

[0002] High-precision local gravity field is the basis and basis for regional geoid refinement, engineering surveying, navigation positioning, geophysical exploration and geological structure analysis. Based on this, it is of great significance to study how to establish a more accurate and reliable local gravity field model to serve the needs of national economic construction and scientific research. The improvement of the multi-source data preprocessing method and the improvement of the gravity field modeling technology are all research hotspots in the field of gravity field modeling in recent years.

[0003] Modern local gravity field modeling mainly takes the remove-restore theory as the framework, combined with high-precision ground gravity data, digital terrain model and GPS leveling, etc. The specific process includes: 1) preprocessing the original gravity anomaly data obtained by gravity meter or satellite equipment, such as correction, filtering and other steps; 2) removing the long-wave gravity effect and the terrain gravity effect from the observed gravity anomaly; 3) refining the residual gravity anomaly by mathematical method; 4) restoring the long-wave gravity effect and the terrain gravity effect on the basis of the refined residual gravity anomaly, and completing the modeling of the local gravity field.

[0004] Under the remove-restore framework, the terrain gravity effect is usually calculated based on high-precision terrain data using the universal gravitation formula, but the commonly used calculation methods have their own limitations. The spectral domain method has the problem of series divergence, and the spatial domain method has the problem of low calculation efficiency. Among the methods for refining residual gravity anomaly, the most widely used are radial basis function method and least squares method, both of which involve the fusion of multi-source data for calculation, causing the problems of data weighting difficulty and large amount of calculation. The massive calculation accumulated in these two steps results in low efficiency and poor maneuverability of regional gravity field modeling, which hinders the further role of gravity field model. For example, in space science, the movement process of near-regional flying objects is affected by gravity, and the earth's gravity field parameters are important mechanical parameters in the orbit dynamics model. If the gravity field parameters can be calculated quickly and in real time, the gravity field model will play a greater role.

[0005] In view of the calculation efficiency problem existing in the current gravity field modeling, how to invent a real-time regional gravity field modeling method with flexible input and strong nonlinear fitting capability is a technical problem that needs to be solved in this technical field. SUMMARY

[0006] To address the problem of insufficient computational efficiency in gravity field modeling, this invention provides a real-time regional gravity field modeling method and system based on deep neural networks, which features high training efficiency and fast inference speed.

[0007] To achieve the above-mentioned objectives of this invention, the technical solution adopted is as follows:

[0008] A real-time regional gravity field modeling method based on deep neural networks includes the following specific steps:

[0009] Obtain ground gravity measurement data and calculate the original ground gravity anomaly at discrete ground points;

[0010] By introducing a global gravity field model, the long-wave gravity anomaly components at discrete points on the ground are calculated in real time. The specific steps are as follows:

[0011] Choosing a global gravity field model, the gravitational potential at point P outside the Earth is... Due to its distance from the Earth's center Earth's core latitude and longitude definition:

[0012]

[0013] in, It is the Earth's gravitational constant. It is related to the fully normalized spherical harmonic coefficients Related scaling factors, in addition:

[0014]

[0015] in, It is a fully normalized Legendre function of the first kind, with order . The number of times First-order term in spherical harmonic expansion Indicates the offset of the center of gravity;

[0016] point Disturbance position at Defined as the difference between the Earth's actual gravitational potential and the normal gravitational potential;

[0017] The perturbation potential is represented by spherical harmonic expansion:

[0018]

[0019] The zeroth-order term in the formula reflects the gravitational effect produced by the total mass of the Earth. If the mass of the reference ellipsoid is equal to the actual mass of the Earth, then this term is zero.

[0020] Surface free air gravity anomaly Defined as a point The actual magnitude of gravitational acceleration at the location minus the corresponding geoid point The magnitude of normal gravitational acceleration at that location:

[0021]

[0022] Assuming the gravitational potential on the geoid is equal to the normal gravitational potential on the reference ellipsoid, we obtain the basic relationship between gravity anomalies and disturbance potentials:

[0023]

[0024] in The radial derivative of the perturbation potential is represented by . These are distance-related correction terms, 3 in total. The terms represent three types of error correction;

[0025] set up This indicates the gravity anomaly after applying all systematic corrections:

[0026]

[0027] get:

[0028]

[0029] Further, the long-wavelength gravity anomaly components were obtained:

[0030]

[0031] in

[0032]

[0033] Therefore, we obtain The spherical harmonic expansion expression of has convergence in the infinite series in the outer space of the Brillouin sphere;

[0034] A terrain data sample set is obtained; a deep fully connected neural network FC-DNN is introduced; the sample location and terrain features in the terrain data sample set are used as inputs, and the shortwave gravity anomaly is used as the supervision target to train the FC-DNN to learn the mapping relationship between terrain features and shortwave gravity anomaly; the trained FC-DNN is used as a fast shortwave gravity field solution model, and the shortwave gravity anomaly component is obtained in real time based on the terrain features of discrete ground points.

[0035] The long-wave and short-wave gravity anomaly components of discrete ground points are removed from their original ground gravity anomalies to obtain their residual gravity anomalies; a multi-source data sample set is constructed, and a CNN is trained to model the nonlinear correlation between the multi-source data and the residual gravity anomalies; the trained CNN is used as a fast solution model for residual gravity anomalies, and the residual gravity anomaly components are predicted in real time based on the multi-source data of discrete ground points.

[0036] The residual gravity anomaly component, shortwave gravity anomaly component, and longwave gravity anomaly component at discrete points on the ground are fused to complete the modeling of the regional ground gravity field.

[0037] Preferably, the original ground gravity anomaly is calculated, and the specific steps are as follows:

[0038] For each sample, obtain ground gravity measurement data including longitude, latitude, surface elevation, ground discrete point height, and the difference between ground discrete point height and surface elevation;

[0039] Preprocessing is performed to eliminate systematic errors and outliers in the ground gravity measurement data;

[0040] Subtracting the normal gravity from the preprocessed gravity measurement data yields the original ground gravity anomaly at discrete ground points.

[0041] Further, a terrain data sample set is obtained, and the specific steps are as follows:

[0042] Define the source quality model; acquire high-resolution terrain feature data and extract terrain features including surface elevation data;

[0043] High-resolution terrain feature data is filtered to obtain reference terrain data, and the difference between the reference terrain data and the high-resolution terrain feature data is used as the residual terrain model (RTM).

[0044] Randomly select discrete points from the terrain data, record the sample location of each discrete point including longitude, latitude, and altitude, and calculate its shortwave gravity anomaly;

[0045] Based on the distance from the calculation point, the RTM mass distribution is divided into several regions, and the shortwave gravity anomaly is approximated for each region using geometry.

[0046] By integrating terrain features, shortwave gravity anomalies, and sample locations, a terrain data sample set is obtained.

[0047] Furthermore, the FC-DNN includes an input layer, L hidden layers, and an output layer. During training, the FC-DNN learns the mapping relationship between terrain features and shortwave gravity anomalies in an end-to-end manner. Specifically, assuming there are N terrain data samples, batch training is used, with the number of samples in each batch set to be N.k ,according to N / k = q Divide the data into q Each batch is processed in one iteration; the process of forward propagation to obtain the loss function for each batch, and then backpropagation to update the weights, constitutes one iteration.

[0048] The forward propagation of each layer is defined as follows:

[0049]

[0050]

[0051]

[0052] in, The input sample matrix has dimensions of . , As weight, For bias, broadcast to during computation Columns to match batch size;

[0053] The batch loss function for training is:

[0054]

[0055] in It is a real label matrix with dimensions of , It is the output matrix of the output layer, with dimension 1. , Denotes the Frobenius norm;

[0056] During backpropagation, the error term of the output layer is calculated as follows:

[0057]

[0058] in Represents element-wise matrix multiplication;

[0059] For hidden layers The recursive formula for the error term is:

[0060]

[0061] The formula for calculating the batch gradient is:

[0062]

[0063]

[0064] in for kA 1-dimensional column vector used to sum the gradients along the batch dimension;

[0065] The parameter update formula is:

[0066]

[0067]

[0068] In batch training, all batches undergo one iteration to complete one cycle, and training continues until a set threshold is reached to obtain the trained FC-DNN.

[0069] Furthermore, the training of FC-DNN also incorporates terrain regularization to further enhance the network's generalization ability and prediction accuracy; the loss function for this regularization method is:

[0070]

[0071] in, Given a trainable array with dimension 1 The mean and variance used for initialization are derived from the mean and variance of gravity anomaly and terrain ratio in the training region. To predict gravity anomalies in the training region, for The corresponding surface elevation value.

[0072] Furthermore, the structure of a CNN includes:

[0073] Feature extraction section: includes a convolutional layer, a batch normalization layer, an activation function layer, and a pooling layer;

[0074] Location information fusion part: After flattening the feature map output by the feature extraction part, it is spliced ​​with the location information of discrete points on the ground;

[0075] The regression prediction part includes at least one fully connected layer, which maps the fused feature vectors to predicted residual gravity anomalies.

[0076] Furthermore, the specific training process of CNN is as follows:

[0077] Let the feature extraction part be the first The input of each convolutional layer is The convolution kernel is , bias is The output of the convolutional layer is defined as:

[0078]

[0079] in For activation function, It is a convolution operation, defined as:

[0080]

[0081] in To output feature map at location The value, k The kernel size is [size]. b For bias terms;

[0082] Batch normalization layer processing is defined as follows:

[0083]

[0084] in, and These are the mean and variance of the batch. and These are learnable scaling and translation parameters. It is a constant;

[0085] The output of the batch normalization layer passes through the Tanh activation function layer, and then through the pooling layer, the feature map size is further reduced by downsampling.

[0086]

[0087] in As a pooling window, features are extracted layer by layer by stacking multiple convolutional and pooling layers;

[0088] In the location information fusion part, the extracted feature map is flattened and then spliced ​​with the location of discrete points on the ground to form a complete feature vector;

[0089] The complete feature vector is flattened into a one-dimensional vector, and the fully connected layer is connected to the output layer to perform the regression task;

[0090] Introducing a weighted loss function:

[0091] Constructing a gradient descent method to minimize the loss function :

[0092]

[0093] in, As the error weight, according to The distribution definition, When the distribution is uneven, values ​​in intervals with fewer numerical values ​​are assigned greater weight;

[0094] Reshape the error into the shape of the feature map:

[0095]

[0096] For max pooling layers, gradients are only passed to the location of the maximum value within the pooling window:

[0097]

[0098] in This is the size of the pooling window;

[0099] The gradient calculation for the batch normalization layer is as follows:

[0100]

[0101] Loss function for convolutional layers The gradient of the output gradient with respect to the convolution kernel is:

[0102]

[0103] The gradient with respect to the bias is:

[0104]

[0105] The gradient of the input feature map is:

[0106]

[0107] Calculated As the error input of the previous layer, it continues to backpropagate for training;

[0108] Update network parameters using gradient descent:

[0109]

[0110]

[0111] The input multi-source data sample set is divided into a training set and a test set. The training set is divided into multiple batches and trained for several cycles. A portion of the samples in the training set are selected as a validation set. After each training cycle, the network accuracy is validated, and the hyperparameters are adjusted to ensure that the accuracy meets expectations and there is no overfitting. The trained CNN is then obtained.

[0112] Furthermore, to address the gradient vanishing and network degradation issues faced by CNNs, at least one residual block is introduced in the feature extraction part, with the following structure:

[0113]

[0114] in This represents a nonlinear transformation consisting of a convolutional layer, a batch normalization layer, and an activation function; x is the feature map extracted by the feature extraction part, and y is the complete feature map output by the residual block.

[0115] For the residual block, the error backpropagation is expressed as:

[0116]

[0117] .

[0118] A real-time regional gravity field modeling system based on deep neural networks is used to implement the method described above, including a gravity measurement module, a long-wave gravity anomaly extraction module, a short-wave gravity anomaly extraction module, a residual gravity anomaly extraction module, and a fusion reconstruction module.

[0119] The gravity measurement module is used to acquire ground gravity measurement data and calculate the original ground gravity anomaly at discrete ground points.

[0120] The long-wave gravity anomaly extraction module is used to introduce a global gravity field model and calculate the long-wave gravity anomaly components of discrete points on the ground in real time.

[0121] The shortwave gravity anomaly extraction module is used to acquire a terrain data sample set; a deep fully connected neural network FC-DNN is introduced; the sample location and terrain features in the terrain data sample set are used as input, and the shortwave gravity anomaly is used as the supervised target to train the FC-DNN to learn the mapping relationship between terrain features and shortwave gravity anomalies; the trained FC-DNN is used as a fast shortwave gravity field solution model, and the shortwave gravity anomaly components are obtained in real time based on the terrain features of discrete ground points.

[0122] The residual gravity anomaly extraction module is used to remove the long-wave and short-wave gravity anomaly components of discrete ground points from their original ground gravity anomalies to obtain their residual gravity anomalies; construct a multi-source data sample set, train a CNN to model the nonlinear correlation between the multi-source data and the residual gravity anomaly; and use the trained CNN as a fast residual gravity anomaly solution model to predict the residual gravity anomaly components in real time based on the multi-source data of discrete ground points.

[0123] The fusion reconstruction module is used to fuse the residual gravity anomaly component, shortwave gravity anomaly component, and longwave gravity anomaly component of discrete ground points to complete the modeling of the regional ground gravity field.

[0124] The beneficial effects of this invention are as follows:

[0125] This invention discloses a real-time regional gravity field modeling method based on deep neural networks. Addressing the computational efficiency issues in current gravity field modeling, it proposes a modeling method combining deep fully connected neural networks and convolutional neural networks. Through deep learning technology and the remove-restore method, it achieves effective fusion and rapid computation of multi-source data, which can be used for real-time construction of regional gravity field models, providing high-precision and high-efficiency gravity field data support for fields such as geodesy, geophysical exploration, and space science. Attached Figure Description

[0126] Figure 1 This is a flowchart illustrating a real-time regional gravity field modeling method based on deep neural networks according to the present invention.

[0127] Figure 2 This is a schematic diagram of the specific process of a real-time regional gravity field modeling method based on deep neural networks according to Embodiment 2 of the present invention.

[0128] Figure 3 This is a schematic diagram of the training process of FC-DNN, a real-time regional gravity field modeling method based on deep neural networks according to the present invention, in Example 2.

[0129] Figure 4 This is a schematic diagram of the training process of CNN, a real-time regional gravity field modeling method based on deep neural networks according to the present invention, in Example 2. Detailed Implementation

[0130] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0131] Example 1

[0132] like Figure 1 As shown, a real-time regional gravity field modeling method based on deep neural networks includes the following specific steps:

[0133] Obtain ground gravity measurement data and calculate the original ground gravity anomaly at discrete ground points;

[0134] By introducing a global gravity field model, the long-wave gravity anomaly components at discrete points on the ground are calculated in real time.

[0135] A terrain data sample set is obtained; a deep fully connected neural network FC-DNN is introduced; the sample location and terrain features in the terrain data sample set are used as inputs, and the shortwave gravity anomaly is used as the supervision target to train the FC-DNN to learn the mapping relationship between terrain features and shortwave gravity anomaly; the trained FC-DNN is used as a fast shortwave gravity field solution model, and the shortwave gravity anomaly component is obtained in real time based on the terrain features of discrete ground points.

[0136] The long-wave and short-wave gravity anomaly components of discrete ground points are removed from their original ground gravity anomalies to obtain their residual gravity anomalies; a multi-source data sample set is constructed, and a CNN is trained to model the nonlinear correlation between the multi-source data and the residual gravity anomalies; the trained CNN is used as a fast solution model for residual gravity anomalies, and the residual gravity anomaly components are predicted in real time based on the multi-source data of discrete ground points.

[0137] The residual gravity anomaly component, shortwave gravity anomaly component, and longwave gravity anomaly component at discrete points on the ground are fused to complete the modeling of the regional ground gravity field.

[0138] Example 2

[0139] like Figure 2 As shown, the specific steps of the real-time regional gravity field modeling method based on deep neural networks in this embodiment are as follows:

[0140] Obtain ground gravity measurement data within the area, set the location information of discrete ground points, perform preprocessing to eliminate systematic errors and outliers, and calculate the original ground gravity anomaly.

[0141] By selecting a suitable global gravity field model, and based on spherical harmonic analysis and spherical harmonic synthesis methods, long-wave gravity anomaly components at discrete points on the ground are constructed.

[0142] This study integrates high-resolution terrain feature data, uses Residual Terrain Modeling (RTM), and forward modeling techniques to solve shortwave gravity anomalies, and constructs a shortwave gravity anomaly sample set. A Deep Fully Connected Neural Network (FC-DNN) is introduced. Using sample location information and terrain elevation as inputs, and high-frequency terrain-induced gravity anomalies as the supervised target, the FC-DNN is trained to learn the mapping relationship between terrain features and shortwave gravity anomalies, replacing the classic integral model and achieving efficient prediction of local shortwave gravity anomalies. Furthermore, a terrain regularization method is introduced to further improve the network's generalization ability and prediction accuracy.

[0143] The long-wave and short-wave gravity anomalies of the obtained discrete ground points are removed from the ground gravity anomalies to obtain the residual gravity anomalies.

[0144] A dataset was constructed using multi-source data such as landform morphology and crustal thickness, and a convolutional neural network (CNN) was used to model the nonlinear correlation between the dataset and ground gravity anomalies. The CNN extracted key patterns from the multi-source heterogeneous information through spatial slicing, scale unification, and feature fusion to improve the model's predictive ability for local gravity anomalies. Furthermore, a weighted loss function was introduced to adjust for the uneven distribution of residual gravity anomalies, further enhancing the balance and accuracy of the network's predictions.

[0145] The residual gravity anomaly component of discrete ground points predicted by the trained CNN, the short-wave gravity anomaly calculated by the trained FC-DNN, and the long-wave gravity anomaly provided by the spherical harmonic model are fused together to complete the reconstruction of the regional ground gravity field model, achieving the goal of high-precision and high-efficiency refinement of the local gravity field.

[0146] In one specific embodiment, the original ground gravity anomaly is calculated through the following steps:

[0147] For each sample, obtain ground gravity measurement data including longitude, latitude, surface elevation, ground discrete point height, and the difference between ground discrete point height and surface elevation;

[0148] Preprocessing is performed to eliminate systematic errors and outliers in the ground gravity measurement data;

[0149] Subtracting the normal gravity from the preprocessed gravity measurement data yields the original ground gravity anomaly at discrete ground points.

[0150] In one specific embodiment, a global gravity field model is introduced to construct long-wave gravity anomaly components at discrete points on the ground. The specific steps are as follows:

[0151] Choosing a global gravity field model, the gravitational potential at point P outside the Earth is... Due to its distance from the Earth's center Earth's core latitude and longitude definition:

[0152]

[0153] in, It is the Earth's gravitational constant. It is related to the fully normalized spherical harmonic coefficients The relevant scale factor is usually taken as the equatorial radius of the mean Earth ellipsoid. Additionally:

[0154]

[0155] in, It is a fully normalized Legendre function of the first kind, with order . The number of times First-order term in spherical harmonic expansion This indicates the offset of the center of gravity. In the geocentric coordinate system, the geometric parameters of the reference ellipsoid already reflect the overall shape of the Earth, and the offset of the center of gravity in the coordinate system is zero, so the first-order term is ignored.

[0156] point Disturbance position at Defined as the difference between the actual gravitational potential and the normal gravitational potential; where the normal gravitational potential refers to the gravitational potential of the reference ellipsoid at that point, and the perturbation potential is represented by spherical harmonic expansion:

[0157]

[0158] The zeroth-order term in the formula reflects the gravitational effect produced by the total mass of the Earth. If the mass of the reference ellipsoid is equal to the actual mass of the Earth, then this term is zero.

[0159] Surface free air gravity anomaly Defined as a point The actual magnitude of gravitational acceleration at the location minus the corresponding geoid point The magnitude of normal gravitational acceleration at that location:

[0160]

[0161] Assuming the gravitational potential on the geoid is equal to the normal gravitational potential on the reference ellipsoid, we obtain the basic relationship between gravity anomalies and disturbance potentials:

[0162]

[0163] in The radial derivative of the perturbation potential is represented by . These are distance-related correction terms, 3 in total. The terms represent three types of error correction;

[0164] set up This indicates the gravity anomaly after applying all systematic corrections:

[0165]

[0166] get:

[0167]

[0168] Further, the long-wavelength gravity anomaly components were obtained:

[0169]

[0170] Gravity Anomaly It is not a harmonic function in itself, but It is harmonic in the space outside the mass body, in which

[0171]

[0172] Therefore, we obtain The spherical harmonic expansion expression of has convergence in the infinite series in the outer space of the Brillouin sphere.

[0173] In one specific embodiment, such as Figure 3 As shown, the specific steps to obtain a terrain data sample set are as follows:

[0174] The constant density is 2.67 g / cm³. 3 The terrain quality is defined as the source quality model; MERIT DEM (Multi-Error-Removed Improved-Terrain DEM) is used as high-resolution terrain feature data, and terrain features including surface elevation data are extracted;

[0175] The spatial resolution of the MERIT DEM is 3″. A filter with a window size of 100×100 is used to filter the high-resolution terrain feature data to obtain reference terrain data. The difference between the reference terrain data and the high-resolution terrain feature data is used as the residual terrain model (RTM).

[0176] Randomly select discrete points from the reference terrain data, and record the location information of each discrete point, including longitude, latitude, surface elevation, ground discrete point height, and the difference between the ground discrete point height and the surface elevation; the terrain quality is referred to as the source quality model, and the random discrete points are... P Gravitational potential generated by a point Represented as:

[0177]

[0178] in, The gravitational constant is... and For the source mass model and the mass of a single integration unit, and They are respectively and The mass element, and Calculation points arrive and The Euclidean distance from the geometric center;

[0179] Calculation points Establish a coordinate axis with the origin, the x-axis pointing north to the Earth, the y-axis pointing east to the Earth, and the z-axis pointing to the zenith. Shortwave gravity anomaly at point :

[0180]

[0181] This yields the shortwave gravity anomalies at all discrete points;

[0182] Based on the distance from the calculation point, the RTM mass distribution was divided into three regions, and approximations were made using geometries such as polyhedra, prisms, tesseroids, and point masses. Specifically, the terrain gravity effect within a 0.03° range from the calculation point was calculated using a prism model with a source mass model spatial resolution of 3″; the range from 0.03° to 0.80° used a tesseroid model with a source mass model spatial resolution of 3″; and the range from 0.80° to 2.00° used a point mass model with a source mass model spatial resolution of 30″. Shortwave gravity anomalies were approximated for each region using geometries.

[0183] By integrating terrain features, shortwave gravity anomalies, and sample locations, a terrain data sample set is obtained.

[0184] In one specific embodiment, the FC-DNN includes an input layer, L hidden layers, and an output layer; during training, the FC-DNN learns the mapping relationship between terrain features and shortwave gravity anomalies in an end-to-end manner, specifically as follows:

[0185] In this embodiment, the input layer of the FC-DNN specifically includes 5 neurons and 6 hidden layers; each hidden layer contains 256 neurons, and all hidden layers are fully connected; the output layer contains 1 neuron, corresponding to the unique output variable—shortwave gravity anomaly; the activation function of the hidden layer is selected as Tanh, the activation function of the output layer is selected as Linear, and the optimizer is selected as Adam.

[0186] Suppose there are N terrain data samples, and batch training is used, with the number of samples in each batch set to be N. k ,according to N / k = q Divide the data into q Each batch is processed in one iteration; the process of forward propagation to obtain the loss function for each batch, and then backpropagation to update the weights, constitutes one iteration.

[0187] The forward propagation of each layer is defined as follows:

[0188]

[0189]

[0190]

[0191] in, The input sample matrix has dimensions of . , As weight, For bias, broadcast to during computation Columns to match batch size;

[0192] The batch loss function for training is:

[0193]

[0194] in It is a real label matrix with dimensions of , It is the output matrix of the output layer, with dimension 1. , Denotes the Frobenius norm;

[0195] During backpropagation, the error term of the output layer is calculated as follows:

[0196]

[0197] in Represents element-wise matrix multiplication;

[0198] For hidden layers The recursive formula for the error term is:

[0199]

[0200] The formula for calculating the batch gradient is:

[0201]

[0202]

[0203] in for k A 1-dimensional column vector used to sum the gradients along the batch dimension;

[0204] The parameter update formula is:

[0205]

[0206]

[0207] In batch training, all batches undergo one iteration to complete one cycle, and training continues until a set threshold is reached to obtain the trained FC-DNN.

[0208] Furthermore, the training of FC-DNN also incorporates terrain regularization to further enhance the network's generalization ability and prediction accuracy; the loss function for this regularization method is:

[0209]

[0210] in, Given a trainable array with dimension 1 The mean and variance used for initialization are derived from the mean and variance of gravity anomaly and terrain ratio in the training region. To predict gravity anomalies in the training region, for The corresponding surface elevation value.

[0211] In this embodiment, after training the FC-DNN, its accuracy was also verified. 80% of the training samples were selected as the training set, with a learning rate of 0.0005, a batch size of 4096, and a training epoch of 3000. 20% of the samples were randomly selected as the test set to test the network performance. The test set was not used in the parameter optimization process.

[0212] The FC-DNN with qualified accuracy was used as the fast solution model for shortwave gravity field to quickly solve the shortwave gravity anomaly at discrete points on the Earth's surface.

[0213] In this embodiment, the pseudocode for the FC-DNN training algorithm is as follows: Input: Training set D ={( x i ,y i )} i=1,…,N ;

[0214] Batch size k ;

[0215] Learning rate η

[0216] Maximum training epochs.

[0217] process:

[0218] 1: Randomly initialize network parameters W within the range (0, 1). (l) and B (l)

[0219] 2: for epoch = 1 to max_epochs do

[0220] 3: The training set D is based on... k Randomly divided into multiple batches

[0221] 4: for each batch in D do

[0222] 5: According to the formula: Input data

[0223] 6: for l = l to L

[0224] 7: Calculation: ,

[0225] 8: End for

[0226] 9: Calculation

[0227] 10: Calculation

[0228] 11: for l = L -1 to 1 do

[0229] 12: Calculation

[0230] 13: end for

[0231] 14: for l = 1 to L do

[0232] 15: Calculation ,

[0233] 16: Calculation formula ,

[0234] 17: end for

[0235] 18: end for

[0236] 19: end for

[0237] Output: Parameters of the trained neural network and .

[0238] Example 3

[0239] In this embodiment, the method for constructing the multi-source data sample set is as follows: collect multi-source data including but not limited to DEM, reference topography, land cover, crustal thickness, sediment thickness, Moho depth, land cover type, crustal thickness, etc.; perform preprocessing such as splicing and fusion and interpolation on the multi-source data; and construct a multi-source data sample set by taking the grid data with a diameter of 0.6° around each discrete point as a set of samples based on the location of the residual gravity anomaly.

[0240] In one specific embodiment, such as Figure 4 As shown, the structure of a CNN includes:

[0241] Feature extraction section: includes one convolutional layer, batch normalization layer, activation function layer, pooling layer, and two residual blocks;

[0242] In this embodiment, the input features of a multi-source data sample set, including DEM, reference topography, land cover, crustal thickness, sediment thickness, and Moho depth, are extracted through a 3×3 convolutional layer, outputting 16 feature maps. These feature maps are then subjected to a nonlinear transformation using a batch normalization layer and a Tanh activation function, and finally reduced in size using a max-pooling layer. The resulting feature maps are then used for deep feature extraction through two residual blocks. Each residual block contains two 3×3 convolutional layers, coupled with a batch normalization layer and a Tanh activation function, expanding the number of channels to 32 and 64, respectively. A random deactivation dropout layer is added during feature extraction, with a dropout rate of 0.2.

[0243] In this embodiment, when the number of input and output channels of the residual block is mismatched, 1×1 convolution is used to adjust the channels to ensure that the residual connection is correctly implemented;

[0244] Location information fusion part: The feature map obtained from the two residual blocks is flattened and then concatenated with the location code including longitude, latitude and elevation to form a complete feature vector;

[0245] The regression prediction part consists of a three-layer fully connected network. The first layer reduces the concatenated feature vector to 256 dimensions, the second layer further reduces it to 128 dimensions, and finally outputs a single predicted value—residual gravity anomaly.

[0246] In this embodiment, the CNN training process is as follows:

[0247] Let the feature extraction part be the first The input of each convolutional layer is The convolution kernel is , bias is The output of the convolutional layer is defined as:

[0248]

[0249] in For activation function, It is a convolution operation, defined as:

[0250]

[0251] in To output feature map at location The value, k The kernel size is [size]. b For bias terms;

[0252] Batch normalization layer processing is defined as follows:

[0253]

[0254] in, and These are the mean and variance of the batch. and These are learnable scaling and translation parameters. It is a constant;

[0255] The output of the batch normalization layer passes through the Tanh activation function layer, and then through the pooling layer, the feature map size is further reduced by downsampling.

[0256]

[0257] in As a pooling window, features are extracted layer by layer by stacking multiple convolutional and pooling layers;

[0258] In the location information fusion part, the extracted feature map is flattened and then spliced ​​with the location of discrete points on the ground to form a complete feature vector;

[0259] The complete feature vector is flattened into a one-dimensional vector, and the fully connected layer is connected to the output layer to perform the regression task;

[0260] Introducing a weighted loss function:

[0261] Constructing a gradient descent method to minimize the loss function :

[0262]

[0263] in, As the error weight, according to The distribution definition, When the distribution is uneven, values ​​in intervals with fewer numerical values ​​are assigned greater weight;

[0264] Reshape the error into the shape of the feature map:

[0265]

[0266] For max pooling layers, gradients are only passed to the location of the maximum value within the pooling window:

[0267]

[0268] in This is the size of the pooling window;

[0269] The gradient calculation for the batch normalization layer is as follows:

[0270]

[0271] Loss function for convolutional layers The gradient of the output gradient with respect to the convolution kernel is:

[0272]

[0273] The gradient with respect to the bias is:

[0274]

[0275] The gradient of the input feature map is:

[0276]

[0277] Calculated As the error input of the previous layer, it continues to backpropagate for training;

[0278] Update network parameters using gradient descent:

[0279]

[0280]

[0281] The input multi-source data sample set is divided into a training set and a test set. The training set is divided into multiple batches and trained for several cycles. A portion of the samples in the training set are selected as a validation set. After each training cycle, the network accuracy is validated, and the hyperparameters are adjusted to ensure that the accuracy meets expectations and there is no overfitting. The trained CNN is then obtained.

[0282] In this embodiment, hyperparameters are selected to train the network. Preferably, the input data is divided into a training set and a test set in an 8:2 ratio. The training set is divided into multiple batches (Batch Size) and trained over multiple epochs. A subset of samples from the training set is selected as a validation set. After each training epoch, the network accuracy is validated, and the hyperparameters are adjusted to ensure that the accuracy meets expectations and there is no overfitting. Specifically, the Batch Size is set to 128 and the Epoch is set to 30.

[0283] In one specific embodiment, to address the gradient vanishing and network degradation problems faced by CNNs, at least one residual block is introduced in the feature extraction part, with the following structure:

[0284]

[0285] in This represents a nonlinear transformation consisting of a convolutional layer, a batch normalization layer, and an activation function; x is the feature map extracted by the feature extraction part, and y is the complete feature map output by the residual block.

[0286] For the residual block, the error backpropagation is expressed as:

[0287]

[0288] .

[0289] Example 4

[0290] A real-time regional gravity field modeling system based on deep neural networks includes a gravity measurement module, a long-wave gravity anomaly extraction module, a short-wave gravity anomaly extraction module, a residual gravity anomaly extraction module, and a fusion reconstruction module.

[0291] The gravity measurement module is used to acquire ground gravity measurement data and calculate the original ground gravity anomaly at discrete ground points.

[0292] The long-wave gravity anomaly extraction module is used to introduce a global gravity field model and calculate the long-wave gravity anomaly components of discrete points on the ground in real time.

[0293] The shortwave gravity anomaly extraction module is used to acquire a terrain data sample set; a deep fully connected neural network FC-DNN is introduced; the sample location and terrain features in the terrain data sample set are used as input, and the shortwave gravity anomaly is used as the supervised target to train the FC-DNN to learn the mapping relationship between terrain features and shortwave gravity anomalies; the trained FC-DNN is used as a fast shortwave gravity field solution model, and the shortwave gravity anomaly components are obtained in real time based on the terrain features of discrete ground points.

[0294] The residual gravity anomaly extraction module is used to remove the long-wave and short-wave gravity anomaly components of discrete ground points from their original ground gravity anomalies to obtain their residual gravity anomalies; construct a multi-source data sample set, train a CNN to model the nonlinear correlation between the multi-source data and the residual gravity anomaly; and use the trained CNN as a fast residual gravity anomaly solution model to predict the residual gravity anomaly components in real time based on the multi-source data of discrete ground points.

[0295] The fusion reconstruction module is used to fuse the residual gravity anomaly component, shortwave gravity anomaly component, and longwave gravity anomaly component of discrete ground points to complete the modeling of the regional ground gravity field.

[0296] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A real-time regional gravity field modeling method based on deep neural networks, characterized in that: The specific steps include the following: Obtain ground gravity measurement data and calculate the original ground gravity anomaly at discrete ground points; By introducing a global gravity field model, the long-wave gravity anomaly components at discrete points on the ground are calculated in real time. The specific steps are as follows: Choosing a global gravity field model, the gravitational potential at point P outside the Earth is... Due to its distance from the Earth's center Earth's core latitude and longitude definition: in, It is the Earth's gravitational constant. It is related to the fully normalized spherical harmonic coefficients Related scaling factors, in addition: in, It is a fully normalized Legendre function of the first kind, with order . The number of times First-order term in spherical harmonic expansion Indicates the offset of the center of gravity; point Disturbance position at Defined as the difference between the Earth's actual gravitational potential and the normal gravitational potential; The perturbation potential is represented by spherical harmonic expansion: The zeroth-order term in the formula reflects the gravitational effect produced by the total mass of the Earth. If the mass of the reference ellipsoid is equal to the actual mass of the Earth, then this term is zero. Surface free air gravity anomaly Defined as a point The actual magnitude of gravitational acceleration at the location minus the corresponding geoid point The magnitude of normal gravitational acceleration at that location: Assuming the gravitational potential on the geoid is equal to the normal gravitational potential on the reference ellipsoid, we obtain the basic relationship between gravity anomalies and disturbance potentials: in The radial derivative of the perturbation potential is represented by . These are distance-related correction terms, 3 in total. The terms represent three types of error correction; set up This indicates the gravity anomaly after applying all systematic corrections: get: Further, the long-wavelength gravity anomaly components were obtained: in Therefore, we obtain The spherical harmonic expansion expression of has convergence in the infinite series in the outer space of the Brillouin sphere; A terrain data sample set is obtained; a deep fully connected neural network FC-DNN is introduced; the sample location and terrain features in the terrain data sample set are used as inputs, and the shortwave gravity anomaly is used as the supervision target to train the FC-DNN to learn the mapping relationship between terrain features and shortwave gravity anomaly; the trained FC-DNN is used as a fast shortwave gravity field solution model, and the shortwave gravity anomaly component is obtained in real time based on the terrain features of discrete ground points. The long-wave and short-wave gravity anomaly components of discrete ground points are removed from their original ground gravity anomalies to obtain their residual gravity anomalies; a multi-source data sample set is constructed, and a CNN is trained to model the nonlinear correlation between the multi-source data and the residual gravity anomalies; the trained CNN is used as a fast solution model for residual gravity anomalies, and the residual gravity anomaly components are predicted in real time based on the multi-source data of discrete ground points. The residual gravity anomaly component, shortwave gravity anomaly component, and longwave gravity anomaly component at discrete points on the ground are fused to complete the modeling of the regional ground gravity field.

2. The real-time regional gravity field modeling method based on deep neural networks according to claim 1, characterized in that: The original ground gravity anomaly was calculated using the following steps: For each sample, obtain ground gravity measurement data including longitude, latitude, surface elevation, ground discrete point height, and the difference between ground discrete point height and surface elevation; Preprocessing is performed to eliminate systematic errors and outliers in the ground gravity measurement data; Subtracting the normal gravity from the preprocessed gravity measurement data yields the original ground gravity anomaly at discrete ground points.

3. The real-time regional gravity field modeling method based on deep neural networks according to claim 1, characterized in that: The specific steps to obtain a terrain data sample set are as follows: Define the source quality model; acquire high-resolution terrain feature data and extract terrain features including surface elevation data; High-resolution terrain feature data is filtered to obtain reference terrain data, and the difference between the reference terrain data and the high-resolution terrain feature data is used as the residual terrain model (RTM). Randomly select discrete points from the terrain data, record the sample location of each discrete point including longitude, latitude, and altitude, and calculate its shortwave gravity anomaly; Based on the distance from the calculation point, the RTM mass distribution is divided into several regions, and the shortwave gravity anomaly is approximated for each region using geometry. By integrating terrain features, shortwave gravity anomalies, and sample locations, a terrain data sample set is obtained.

4. The real-time regional gravity field modeling method based on deep neural networks according to claim 1, characterized in that: The FC-DNN includes an input layer, L hidden layers, and an output layer. During training, the FC-DNN learns the mapping relationship between terrain features and shortwave gravity anomalies in an end-to-end manner. Specifically, assuming there are N terrain data samples, batch training is used, with each batch containing a set number of samples. k ,according to N / k=q Divide the data into q Each batch is processed in one iteration; the process of forward propagation to obtain the loss function for each batch, and then backpropagation to update the weights, constitutes one iteration. The forward propagation of each layer is defined as follows: in, The input sample matrix has dimensions of . , As weight, For bias, broadcast to during computation Columns to match batch size; The batch loss function for training is: in It is a real label matrix with dimensions of , It is the output matrix of the output layer, with dimension 1. , Denotes the Frobenius norm; During backpropagation, the error term of the output layer is calculated as follows: in Represents element-wise matrix multiplication; For hidden layers The recursive formula for the error term is: The formula for calculating the batch gradient is: in for k A 1-dimensional column vector used to sum the gradients along the batch dimension; The parameter update formula is: In batch training, all batches undergo one iteration to complete one cycle, and training continues until a set threshold is reached to obtain the trained FC-DNN.

5. The real-time regional gravity field modeling method based on deep neural networks according to claim 4, characterized in that: The training of FC-DNN also incorporates terrain regularization to further enhance the network's generalization ability and prediction accuracy; the loss function for this regularization method is: in, Given a trainable array with dimension 1 The mean and variance used for initialization are derived from the mean and variance of gravity anomaly and terrain ratio in the training region. To predict gravity anomalies in the training region, for The corresponding surface elevation value.

6. The real-time regional gravity field modeling method based on deep neural networks according to claim 1, characterized in that: The structure of a CNN includes: Feature extraction section: includes a convolutional layer, a batch normalization layer, an activation function layer, and a pooling layer; Location information fusion part: After flattening the feature map output by the feature extraction part, it is spliced ​​with the location information of discrete points on the ground; The regression prediction part includes at least one fully connected layer, which maps the fused feature vectors to predicted residual gravity anomalies.

7. The real-time regional gravity field modeling method based on deep neural networks according to claim 6, characterized in that: The specific training process for CNN is as follows: Let the feature extraction part be the first The input of each convolutional layer is The convolution kernel is , bias is The output of the convolutional layer is defined as: in For activation function, It is a convolution operation, defined as: in To output feature map at location The value, k The kernel size is [size]. b For bias terms; Batch normalization layer processing is defined as follows: in, and These are the mean and variance of the batch. and These are learnable scaling and translation parameters. It is a constant; The output of the batch normalization layer passes through the Tanh activation function layer, and then through the pooling layer, the feature map size is further reduced by downsampling. in As a pooling window, features are extracted layer by layer by stacking multiple convolutional and pooling layers; In the location information fusion part, the extracted feature map is flattened and then spliced ​​with the location of discrete points on the ground to form a complete feature vector; The complete feature vector is flattened into a one-dimensional vector, and the fully connected layer is connected to the output layer to perform the regression task; Introducing a weighted loss function: Constructing a gradient descent method to minimize the loss function : in, As the error weight, according to The distribution definition, When the distribution is uneven, values ​​in intervals with fewer numerical values ​​are assigned greater weight; Reshape the error into the shape of the feature map: For max pooling layers, gradients are only passed to the location of the maximum value within the pooling window: in This is the size of the pooling window; The gradient calculation for the batch normalization layer is as follows: Loss function for convolutional layers The gradient of the output gradient with respect to the convolution kernel is: The gradient with respect to the bias is: The gradient of the input feature map is: Calculated As the error input of the previous layer, it continues to backpropagate for training; Update network parameters using gradient descent: The input multi-source data sample set is divided into a training set and a test set. The training set is divided into multiple batches and trained for several cycles. A portion of the samples in the training set are selected as a validation set. After each training cycle, the network accuracy is validated, and the hyperparameters are adjusted to ensure that the accuracy meets expectations and there is no overfitting. The trained CNN is then obtained.

8. The real-time regional gravity field modeling method based on deep neural networks according to claim 7, characterized in that: To address the gradient vanishing and network degradation issues faced by CNNs, at least one residual block is introduced in the feature extraction part, with the following structure: in This represents a nonlinear transformation consisting of a convolutional layer, a batch normalization layer, and an activation function; x is the feature map extracted by the feature extraction part, and y is the complete feature map output by the residual block. For the residual block, the error backpropagation is expressed as: 。 9. A real-time regional gravity field modeling system based on deep neural networks, characterized in that: The method for implementing the method as described in claims 1 to 8 includes a gravity measurement module, a long-wave gravity anomaly extraction module, a short-wave gravity anomaly extraction module, a residual gravity anomaly extraction module, and a fusion reconstruction module. The gravity measurement module is used to acquire ground gravity measurement data and calculate the original ground gravity anomaly at discrete ground points. The long-wave gravity anomaly extraction module is used to introduce a global gravity field model and calculate the long-wave gravity anomaly components of discrete points on the ground in real time. The shortwave gravity anomaly extraction module is used to acquire a terrain data sample set; a deep fully connected neural network FC-DNN is introduced; the sample location and terrain features in the terrain data sample set are used as input, and the shortwave gravity anomaly is used as the supervised target to train the FC-DNN to learn the mapping relationship between terrain features and shortwave gravity anomalies; the trained FC-DNN is used as a fast shortwave gravity field solution model, and the shortwave gravity anomaly components are obtained in real time based on the terrain features of discrete ground points. The residual gravity anomaly extraction module is used to remove the long-wave and short-wave gravity anomaly components of discrete ground points from their original ground gravity anomalies to obtain their residual gravity anomalies. A multi-source data sample set is constructed, and a CNN is trained to model the nonlinear correlation between the multi-source data and residual gravity anomalies; A trained CNN was used as a fast solution model for residual gravity anomalies, and its residual gravity anomaly components were predicted in real time based on multi-source data from discrete ground points. The fusion reconstruction module is used to fuse the residual gravity anomaly component, shortwave gravity anomaly component, and longwave gravity anomaly component of discrete ground points to complete the modeling of the regional ground gravity field.

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