Gravity inversion method based on physical information neural network

Abstract

The invention discloses a gravity inversion method based on a physical information neural network, and belongs to the technical field of ocean gravity inversion, and the method specifically comprises the steps: preprocessing submarine topography, ship load and satellite height measurement data; a physical reference model is constructed based on the consideration of an inverse Vening Meinesz formula, the precision of the ship load and the physical reference model is evaluated, and hyper-parameters of fusion data and physical information are quantitatively determined; constructing a physical information neural network model, and determining a loss function; by training the model, high-precision ocean gravity anomaly inversion is finally realized; according to the method, a physical mechanism is used as constraint to be embedded into neural network training, the problems that a traditional inversion method is low in precision and an existing neural network is poor in generalization ability in a data sparse region are effectively solved, and the method is particularly suitable for high-precision gravity field construction of a marine area with sparse ship load distribution.

Description

Technical Field

[0001] This invention belongs to the field of marine gravity inversion technology, and in particular relates to a gravity inversion method based on a physical information neural network. Background Technology

[0002] With the rapid development of satellite altimetry technology, using sea surface height data acquired by altimeter satellites to deduce geoid height or along-track vertical deviation, and then inverting ocean gravity anomalies, has become a primary means of obtaining global ocean gravity fields. Traditional gravity inversion methods based on satellite altimetry data mainly rely on rigorous mathematical and physical models. Representative methods include: the inverse Stokes formula method based on geoid data, the inverse Vening-Meinesz method based on along-track vertical deviation, and the Laplace method based on along-track vertical deviation. Although these traditional methods have clear physical meanings, they typically rely on only a single satellite altimetry data source during the inversion process, failing to effectively integrate other geophysical field information such as seabed topography and ship-based gravity measurements. This results in limitations in inversion accuracy and spatial resolution over vast ocean areas.

[0003] In recent years, with the development of artificial intelligence, neural networks can incorporate more data sources such as seabed topography and shipboard gravity, improving the accuracy of gravity inversion. Theoretically, they can uncover deeper correlations between data points, potentially leading to gravity field models with higher accuracy than traditional physical methods. However, most existing neural network-based gravity inversion methods are purely data-driven models, their training process relying entirely on the data itself, lacking consideration for the physical laws of the gravity field. This neglect of physical mechanisms results in a lack of physical constraints in the model's learning process, leading to poor generalization ability, especially in areas with sparse or uncovered training data, and a significant decrease in the reliability and accuracy of the inversion results. Summary of the Invention

[0004] The purpose of this invention is to provide a gravity inversion method based on a physical information neural network. This method combines deep learning and physical modeling, incorporating physical information from the inverse Vening Meinesz formula into the loss function. Based on the actual data accuracy, appropriate weights are assigned to the data error term and the physical information error term, thereby improving the accuracy of gravity inversion, especially in regions with sparse shipboard gravity distribution. To achieve the above objective, this invention provides a gravity inversion method based on a physical information neural network, comprising the following steps: S1. Acquire and preprocess seabed topographic data, shipboard gravity data, and satellite altimetry data; S2. Based on the satellite altimetry data preprocessed in S1, a residual vertical deviation model is established using the least squares collocation method. S3. Based on the residual vertical deviation model established in S2, the ocean gravity anomaly model is calculated using the inverse Vening Meinesz formula; S4. Evaluate the mean square error of the shipborne gravity in S1 and the mean square error of the ocean gravity anomaly model in S3 to determine the hyperparameters used to construct the loss function. S5. Construct a physical information neural network model. The inputs include the vertical deviation data derived from the S2 residual vertical deviation model, the topographic information derived from the preprocessed seabed topographic data of S1, the distance from the coastline, and the location information of the calculation point. The output is the predicted residual gravity anomaly at the calculation point. S6. Based on the hyperparameters determined in S4, construct the loss function of the S5 physical information neural network model. The loss function includes data error terms and physical information error terms. S7. Use the data from S1, S2, and S3 to build a dataset, train the physical information neural network model constructed in S5, and obtain the trained physical information neural network model by minimizing the loss function in S6. S8. Using the location of the calculation point, the seabed topography model, the vertical deviation model, and the distance from the grid point to the coastline as inputs to the physical information neural network model trained in S7, high-precision ocean gravity data is derived.

[0005] Preferably, S1 includes: We acquire seabed topography models, global gravity field models, shipborne gravity data, and satellite altimetry data published on internationally available websites. Based on the global gravity field model, we correct the shipborne gravity data using quadratic polynomials and resample the seabed topography model to a preset grid using cubic spline interpolation. We also perform error correction on the satellite altimetry data, Gaussian filtering on the geodetic task data, collinear adjustment for repetitive periodic tasks, and gross error removal based on the reference field.

[0006] Preferably, the method for establishing the residual perpendicular deviation model in S2 using the least squares collocation method is as follows: The residual vertical deviation model is established using the removal-restoration method. The geoid corresponding to the reference gravity field model is removed to obtain the residual geoid. Based on the gravity covariance of the region, the preset residual vertical deviation model is obtained by using the least squares collocation method.

[0007] Preferably, S4 includes: assessing the mean error of the ship's load capacity using the discrepancy in the ship's load capacity at the intersection of the ship's navigation routes. The expression is as follows: ; in, This represents the standard deviation of the gravity anomaly discrepancies at the intersection point. It is the mean error of the ship's load capacity; The standard deviation of the difference between the ocean gravity anomaly model and the shipborne gravity is calculated according to different distances from the coastline. The mean square error of the ocean gravity anomaly model was obtained. The expression is as follows: ; according to and Determine the hyperparameters that weigh the importance of the data error term. Hyperparameters related to the importance of physical information error terms The specific expression is as follows: ; .

[0008] Preferably, in S5: The vertical deviation data includes: the north-south component grid data and the east-west component grid data of the remaining vertical deviation around the calculation point; The location information of the calculation point includes: the longitude of the calculation point, the latitude of the calculation point, and the difference in longitude and latitude between the calculation point and the nearest southwest grid point; After convolution and pooling operations are performed on the grid data of vertical deviation data and grid data of seabed topography information, they are fused with the data output by the fully connected layer through the location information of the calculation point, and finally the predicted value of residual gravity anomaly at the calculation point is output.

[0009] Preferably, in S6, the loss function The expression is as follows: ; in, This is the data error term in the loss function, determined by the difference between the predicted residual gravity anomaly and the ship's loaded gravity. It is the physical information error term of the loss function, which is determined by the difference between the predicted residual gravity anomaly and the ocean gravity anomaly model established using the inverse VeningMeinesz formula.

[0010] Preferably, in S7: The dataset includes vertical deviation data around the calculation point, ocean gravity anomaly model, seabed topography data, latitude and longitude data of the calculation point, and shipborne gravity anomaly data at the calculation point. The dataset is divided into training set, validation set, and test set, and the shipborne gravity data in the test set is ensured to be independent of the shipborne gravity data in the training set and validation set. The training termination condition is determined by monitoring the changes in the loss values ​​on the training and validation sets, thus obtaining the completed physical information neural network model.

[0011] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention establishes a physical benchmark model and constructs a loss function containing error terms with physical information, embedding the physical mechanism as a hard constraint into the neural network training process, effectively overcoming the accuracy limitation caused by the traditional inverse Vening Meinesz method relying on only a single data source.

[0012] 2. This invention, through a defined hyperparameter determination method, enables the strength of physical constraints to be adaptively adjusted based on data quality. This allows the model to maintain superior performance in regions with sparse shipboard gravity distribution, even when the test set data is independent, thus solving the problem of poor generalization ability of purely data-driven neural networks in such regions.

[0013] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0014] Figure 1 This is an overall flowchart of a gravity inversion method based on a physical information neural network provided in an embodiment of the present invention; Figure 2 This is an overall flowchart of the physical information neural network method that takes into account the inverse Vening Meinesz formula provided in this embodiment of the invention; Figure 3 This is a flowchart of the physical information neural network model provided in the embodiments of the present invention; Figure 4 This is a shipborne data distribution map provided in an embodiment of the present invention. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments in this application without creative effort are within the scope of protection of this application. Examples of embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0016] It should be noted that the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, such that a process, method, system, product, or server that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products, or devices.

[0017] Similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0018] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of this invention is usually placed when in use. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0019] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," and "connect" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0020] This invention proposes a gravity inversion method based on a physical information neural network, which can be implemented through the following embodiment. This embodiment uses the sea area at the junction of the Philippine Plate and the Pacific Plate (125°E-140°E, 10°N-20°N) as the research area for illustration: refer to Figures 1-2 Specifically, it includes the following steps: S1, acquiring and preprocessing seabed topographic data, shipborne gravity data, and satellite altimetry data.

[0021] Seafloor topography models, global gravity field models, shipborne gravity data, and satellite altimetry data for the study area were obtained from publicly available international websites. Based on the global gravity field model, systematic error corrections were applied to the shipborne gravity data using quadratic polynomials. The seafloor topography model was resampled to a 1′×1′ regular grid using cubic spline interpolation. Error corrections for instrumentation and atmospheric delay were applied to the satellite altimetry data. Gaussian filtering was performed on the geodetic data, collinearity adjustment was performed on the repetitive periodic data, and gross errors were removed based on a reference gravity field.

[0022] S2. Based on the preprocessed satellite altimetry data from S1, a residual vertical deviation model is established using the least squares collocation method. The specific process is as follows: Based on the preprocessed satellite altimetry data in S1, a removal-restoration method is adopted: first, the geoid corresponding to the reference gravity field model is removed to obtain the remaining geoid; then, based on the gravity covariance function of this region, the 1′×1′ remaining vertical deviation model is obtained by using the least squares collocation method.

[0023] S3. Based on the residual vertical deviation model established in S2, the ocean gravity anomaly model is calculated using the inverse Vening Meinesz formula. The specific process is as follows: Based on the 1′×1′ residual vertical deviation model obtained in S2, the residual gravity anomaly of 1′×1′ is calculated using the inverse Vening Meinesz formula, and then the gravity anomaly corresponding to the reference gravity field model is recovered to obtain the final 1′×1′ ocean gravity anomaly model.

[0024] S4. Evaluate the mean square error of the shipborne gravity in S1 and the mean square error of the ocean gravity anomaly model in S3 to determine the hyperparameters used to construct the loss function. The specific process is as follows: Assess the standard error of ship load capacity by using discrepancies in ship load capacity at intersections of ship routes. The expression is as follows: ; in, This represents the standard deviation of the gravity anomaly discrepancies at the intersection point. It is the mean error of the ship's load weight.

[0025] Based on different distances from the coastline, the regions are divided into different areas: 0-10km, 10-20km, 20-30km, 30-40km, 40-50km, 50-100km, 100-200km, and >200km from the coastline. The standard deviation of the difference between the ocean gravity anomaly model and the shipborne gravity is calculated and denoted as . The mean square error of the ocean gravity anomaly model was obtained. The expression is as follows: ; according to and Determine the hyperparameters that weigh the importance of the data error term. Hyperparameters related to the importance of physical information error terms The specific expression is as follows: ; .

[0026] S5. Construct a physical information neural network model. Inputs include vertical deviation data derived from the residual vertical deviation model in S2, topographic information derived from the preprocessed seabed topography data in S1, distance from the coastline, and location information of the calculation point. Output: predicted residual gravity anomaly at the calculation point, such as... Figure 3 As shown, the details are as follows: The input layer contains four channels and four nodes. Two channels represent the north-south and east-west components of the 1′×1′ residual vertical deviation around the calculation point. The third channel represents the resampled 1′×1′ seabed topography model around the calculation point. The fourth channel represents the distance of the 1′×1′ grid points around the calculation point from the coastline. The four nodes represent the longitude, latitude, longitude difference between the calculation point and the nearest southwest grid point, and latitude difference between the calculation point and the nearest southwest grid point, respectively. The three channels undergo two convolution and pooling operations, and after unpacking, they are added to the four nodes of the input layer. These nodes are then processed by a fully connected layer to output the residual gravity anomaly at the calculation point.

[0027] S6. Based on the hyperparameters determined in S4, construct the loss function for the S5 physical information neural network model. The loss function includes a data error term and a physical information error term. The expression is as follows: ; in, The data error term of the loss function is determined by the difference between the predicted residual gravity anomaly and the ship's onboard gravity. The physical information error term of the loss function is determined by the difference between the predicted residual gravity anomaly and the ocean gravity anomaly model established using the inverse VeningMeinesz formula.

[0028] S7. Using the data from S1, S2, and S3, construct a dataset to train the physical information neural network model built in S5. By minimizing the loss function in S6, the trained physical information neural network model is obtained, as follows: A dataset was constructed by selecting a subset of data, including vertical deviation data around the calculation point, a marine gravity anomaly model calculated using the inverse VeningMeinesz formula, seabed topography data, longitude and latitude data of the calculation point, and shipborne gravity anomaly data at the calculation point. A portion of this dataset was selected as the training set, a portion as the validation set, and the remainder as the test set. The shipborne data in the test set was independent of the shipborne data in the other two datasets. The number of training iterations and the learning rate were determined based on the changes in the loss values ​​of the data error term and the physical information error term in the training and validation sets, resulting in a trained physical information neural network model.

[0029] S8. Using the location of the calculation point, the seabed topography model, the vertical deviation model, and the distance from the grid point to the coastline as inputs to the physical information neural network model trained in S7, high-precision ocean gravity data is derived.

[0030] This embodiment utilizes the inverse Vening Meinesz method, convolutional neural networks, and the marine gravity anomaly models of the study area as described in this invention, which are respectively denoted as Model 1, Model 2, and Model 3.

[0031] This embodiment uses shipboard gravity data published by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) for the study area. For example... Figure 4 As shown, using 47 of them, namely Figure 4 The thin lines in the diagram are used as the training and validation sets to train the neural network model; four independent flight paths are utilized, namely... Figure 4 The thick lines in the table represent test data used to evaluate the accuracy of gravity measurements obtained by different methods. Since the test shipboard data was not used in the training of the neural network model, the test shipboard data is independent of the ocean gravity anomaly model and can be used to evaluate the accuracy of the ocean gravity anomaly model. The results are shown in Table 1.

[0032] Table 1. Statistical Table of Differences between Ocean Gravity Anomaly Model and Test Ship Onboard Data

[0033] As shown in Table 1, the models obtained by the Physical Information Neural Network (PIN) exhibit higher accuracy compared to the traditional inverse Vening Meinesz method, with the mean squared error of the difference between the model and the test shipboard data reduced by approximately 10%. Furthermore, the PIN model shows a slight improvement in accuracy compared to the convolutional neural network method. Given that the shipboard data calibration accuracy is 1 mGal, the PIN model achieves approximately 14% and 3% higher accuracy compared to the inverse Vening Meinesz method and the convolutional neural network method, respectively.

[0034] Depend on Figure 4 It can be seen that there is a lack of training shipborne data in the southwest of this study area. To investigate the advantages of physical information neural networks in regions with sparse training data, test shipborne data from the southwest was selected. Figure 4The thick line in the diagram, denoted as segment 1, is used for further analysis of the marine gravity anomaly model. Compared to the traditional inverse Vening Meinesz method, the model obtained by the Physical Information Neural Network (PIN) shows a significant improvement in accuracy, reducing the mean square error of the difference between the model and the test shipborne data by approximately 17%; compared to the convolutional neural network method, the mean square error is reduced by approximately 6%. Since the shipborne data calibration accuracy is 1 mGal, the model accuracy obtained by the PIN is improved by approximately 25% and 11% compared to the inverse Vening Meinesz method and the convolutional neural network method, respectively.

[0035] Based on the inverse Vening Meinesz formula, a novel physical information neural network method for gravity anomaly inversion is proposed. Compared with traditional inverse Vening Meinesz methods and convolutional neural network methods, it can improve the accuracy of gravity inversion, especially in regions with sparse training data.

[0036] In summary, this invention provides a gravity inversion method based on a physical information neural network. By embedding physical mechanisms as constraints into the neural network training, it effectively solves the problems of low accuracy in traditional inversion methods and poor generalization ability of existing neural networks in sparse data regions. It is particularly suitable for constructing high-precision gravity fields in sea areas with sparse shipborne gravity distribution.

[0037] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A gravity inversion method based on physical information neural network, characterized in that, The method comprises the following steps: S1, acquiring and preprocessing seafloor topography data, shipborne gravity data and satellite altimetry data; S2, based on the satellite altimetry data preprocessed in S1, a residual vertical deflection model is established by using a least square collocation method; S3, based on the residual vertical deflection model established in S2, a marine gravity anomaly model is calculated by using an inverse Vening Meinesz formula; S4, the mean error of the shipborne gravity in S1 and the mean error of the marine gravity anomaly model in S3 are evaluated to determine hyperparameters for constructing a loss function; S5, a physical information neural network model is constructed, input data includes vertical deflection data derived from the residual vertical deflection model in S2, topographic information derived from the seafloor topography data preprocessed in S1, distance from the coastline and position information of the calculation point, and output data is the predicted residual gravity anomaly at the calculation point; S6, based on the hyperparameters determined in S4, a loss function of the physical information neural network model in S5 is constructed, the loss function includes a data error term and a physical information error term; S7, a dataset is constructed by using the data obtained in S1, S2 and S3, the physical information neural network model constructed in S5 is trained by minimizing the loss function in S6, and a trained physical information neural network model is obtained; S8, the position of the calculation point, the seafloor topography model, the vertical deflection model and the distance from the grid point to the coastline are input into the trained physical information neural network model in S7, and high-precision marine gravity data is inverted.

2. The gravity inversion method based on physical information neural network according to claim 1, characterized in that, S1 comprises: The seafloor topography model, the global gravity field model, the shipborne gravity and the satellite altimetry data published on an international public website are acquired, the shipborne gravity data is corrected by using a quadratic polynomial based on the global gravity field model, the seafloor topography model is resampled to a preset grid by using a cubic spline interpolation method, and the satellite altimetry data is error-corrected, geodetic survey task data is Gauss-filtered, repeated period task is collinearly adjusted, and reference field-based gross error is removed.

3. A gravity inversion method based on a physical information neural network according to claim 2, characterized in that, In S2, the residual vertical deflection model is established by using the least square collocation method as follows: The residual vertical deflection model is established by using a remove-restore method, the geoid corresponding to the reference gravity field model is removed to obtain a residual geoid, and the residual vertical deflection model of the preset grid is solved by using the least square collocation method based on the regional gravity covariance.

4. The gravity inversion method based on physical information neural network according to claim 3, characterized in that, S4 comprises evaluating the mean error of the ship gravity using the ship gravity discrepancy values at the intersection points of the ship route The expression is as follows: ； in, This represents the standard deviation of the gravity anomaly discrepancies at the intersection point. It is the mean error of the ship's load capacity; According to the distance from the coastline, the standard deviation of the marine gravity anomaly model and the shipborne gravity difference value is calculated , the mean error of the marine gravity anomaly model is obtained , the expression is as follows: ； According to and , the super parameter of the importance of the data error term and the super parameter of the importance of the physical information error term , the specific expression is as follows: ； 。 5. The gravity inversion method based on physical information neural network according to claim 4, characterized in that, In S5, The vertical deflection data includes residual vertical deflection grid data of north-south and east-west components around the calculation point; The position information of the calculation point includes the calculation point longitude, the calculation point latitude, the longitude difference and the latitude difference between the calculation point and the nearest southwest grid point; After convolution and pooling operations are performed on the grid data of the vertical deflection data and the grid data of the seafloor topography information, the data output by the fully connected layer of the position information of the calculation point is fused, and finally the residual gravity anomaly prediction value at the calculation point is output.

6. The gravity inversion method based on physical information neural network according to claim 5, characterized in that: In S6, the loss function is expressed as follows: ； wherein, is a data error term of the loss function determined by the difference between the predicted residual gravity anomaly and the shipborne gravity, is a physical information error term of the loss function determined by the difference between the predicted residual gravity anomaly and the marine gravity anomaly model established using the inverse Vening Meinesz formula.

7. The gravity inversion method based on physical information neural network according to claim 6, characterized in that, In S7, the data set formed includes the perpendicular deviation data of the periphery of the calculation point, the marine gravity anomaly model, the seafloor topography data, the latitude and longitude data of the calculation point, and the shipborne gravity anomaly data at the calculation point, and the data set is divided into a training set, a validation set and a test set, and it is ensured that the shipborne gravity data in the test set is independent of the shipborne gravity data in the training set and the validation set; The training termination condition is determined by monitoring the loss value change on the training set and the validation set, and a trained physical information neural network model is obtained.

Images