Seafloor topography inversion method based on terrain relief constraint neural network

Abstract

The present application relates to the technical field of ocean surveying and mapping, in particular to a seabed terrain inversion method based on terrain relief constraint neural network, comprising: constructing a terrain relief constraint neural network model, selecting a local standard deviation method and selecting a 9*9 moving window to calculate terrain relief information at the center point of the grid, and training the terrain relief constraint neural network model; the RANN method proposed in the present application introduces terrain relief information into the neural network as input, which weakens the influence of terrain relief difference on the model, especially in complex sea areas with terrain relief greater than 400 m, effectively improving the model inversion accuracy in the area with large terrain relief.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of marine surveying and artificial intelligence, specifically a method for seabed topography inversion based on a topographic relief constrained neural network. Background Technology

[0002] Seafloor topography reflects the undulations and changes of the seabed, and seafloor topography data provides crucial foundational information for the development of marine physics, marine biology, chemistry, and geology. Seafloor mapping and topographic models are of significant value in studying geological and oceanographic processes, ensuring navigational safety, delineating continental shelf boundaries, disaster research, seafloor infrastructure construction, and marine conservation. Ocean sounding methods include airborne lidar measurement technology, shipborne sonar detection technology, and satellite altimetry. Airborne lidar can rapidly acquire topographic data for large areas of shallow waters and nearshore regions, making it the most effective sounding method in shallow waters; however, its equipment and flight costs are high, and it cannot be used for deep-sea exploration. Shipborne sonar sounding technology is the most direct method for seafloor topographic exploration, but it suffers from limitations such as limited coverage, sparse data, and high cost, making it difficult to meet the needs of large-scale ocean exploration, and early data showed significant errors.

[0003] Satellite altimetry technology can acquire information quickly and comprehensively, overcoming the limitations of traditional measurement methods that cannot acquire large areas of sea topography in a short time, thus becoming a key technology for ocean depth measurement. Altimetry satellite data can be used to effectively invert seabed topography, such as gravity geology, the Sandwell method, and the admittance function method. However, most traditional seabed topography inversion methods only consider the relationship between sea surface gravity and seabed topography, neglecting the influence of other nonlinear terms on the inversion results. With the continuous development of computer processing and storage capabilities, artificial intelligence (AI) has made breakthroughs in image processing, speech recognition, and natural language processing. In recent years, researchers have also begun to use AI for seabed topography inversion. AI methods can naturally capture nonlinear relationships in data through the combination and mapping of features from nonlinear activation functions and multi-layer network structures. Using AI methods to fuse gravity data for seabed topography inversion can effectively improve inversion accuracy. However, existing research has not considered the impact of complex changes in seabed topography on inversion accuracy. Summary of the Invention

[0004] This invention addresses the shortcomings and deficiencies of existing technologies by proposing a seabed topography inversion method based on topographic relief constrained by a neural network. This method fully considers the influence of topographic relief on gravity information in seabed topography inversion, constructs a seabed topographic relief model, and introduces topographic relief information as input to the neural network. It fully considers the impact of complex topographic features on inversion accuracy and improves the inversion accuracy of areas with large topographic relief.

[0005] This invention achieves its purpose through the following measures: A method for seafloor topography inversion based on a topographic relief-constrained neural network is characterized by, firstly, constructing a topographic relief-constrained neural network model, using the local standard deviation method, and selecting a 9×9 moving window to calculate the grid center point (…). h 41 Topographic relief information at location ) is calculated using the following formula: (1), (2), where, This represents the number of grid points within the moving window; The average water depth of the model; We chose to use an MLP neural network to build the seabed topography model. MLPs are feedforward artificial neural networks, consisting of an input layer, hidden layers, and an output layer. Each neuron is connected to all neurons in the next layer, and the neuron output is: (3), among which, x and y Represents the input and output data of neurons. W and b Represents weights and biases. f Represents the activation function; Topographic relief information is introduced as input to the MLP neural network. The input data includes: the difference between the longitude and the longitude of the shipborne sounding point at each point on the 6′×6′ grid around the shipborne sounding point (ΔLON), the difference between the latitude and the latitude of the shipborne sounding point (ΔLAT), the difference between the gravity anomaly and the gravity anomaly of the shipborne sounding point (ΔG), the difference between the vertical gravity gradient and the vertical gravity gradient of the shipborne sounding point (ΔVGG), the difference between the ramusoidal component of the vertical deviation and the ramusoidal component of the vertical deviation of the shipborne sounding point (Δη), the difference between the meridional component of the vertical deviation and the meridional component of the vertical deviation of the shipborne sounding point (Δξ), the difference between the model water depth and the water depth of the shipborne sounding point (ΔH), and the difference between the topographic relief and the topographic relief of the shipborne sounding point (ΔRA). There are a total of 8 input data. The neural network input calculation formula is as follows: (4), of which, Indicates the first Individual grid points; and They represent the first Longitude and latitude at each grid point; and These represent the longitude and latitude of the shipborne sounding point or prediction point, respectively. , , and They represent the first Gravity anomaly, vertical gravity gradient, vertical deviation (Mao-You component) and vertical deviation (Zi-Meridian component) at each grid point; , , and These represent the gravity anomaly, vertical gravity gradient, and the ramus component and meridional component of the vertical deviation at the shipborne sounding point or prediction point, respectively. and They represent the first The water depth and terrain undulation of the Topo_25.1 model at each grid point; and These represent the water depth and topographic relief of the Topo_25.1 model at the shipborne sounding point or prediction point, respectively. The neural network output is the difference between the Topo_25.1 model and the shipborne sounding at that point: (5), among which, This represents the output of the neural network. This indicates the water depth in the Topo_25.1 model at the shipborne sounding point. This indicates shipboard depth sounding.

[0006] The present invention also includes training a neural network model constrained by the terrain relief, including removing early shipborne sounding data to reduce data uncertainty; then, dividing the processed shipborne sounding data into training points, validation points, and test points, with the input data and target data corresponding to the shipborne sounding points serving as the training set, validation set, and test set, respectively. The training set is used only for training the neural network, the validation set is used only for early stopping and model selection during neural network model training, and the test set is used only for testing the training effect of the neural network and the accuracy of the final water depth model.

[0007] To reduce the differences between input data and ensure that each input data point contributes equally to the neural network, this invention processes the input data before training the neural network by standardizing it using z-score. The specific calculation formula is as follows: (6), among which, It is standardized data. It is the raw data. The mean of the data. This represents the standard deviation of the data.

[0008] This invention trains a neural network using standardized input data. The initial weights and biases are initialized using default settings, and the learning rate is set to 0.001. If the loss value does not decrease within five consecutive training epochs, the learning rate is reduced to 60% of its original value. The batch size is set to 128, the training iterations are 150, the Huber function is selected as the loss function, the tanh function as the hidden layer activation function, and the Adam algorithm as the optimizer. The number of training epochs during which the loss function is allowed not to decrease is 10. The specific training process is as follows: First, initialize the neural network weights and biases; second, input the training data set into the network to calculate the output value, and use the Huber function to calculate the loss between the output value and the target value. Use the Adam optimization algorithm to adjust the weights and biases of each neural network; third, calculate the loss value on the validation set, and determine whether to save the model based on the loss value. If the early stopping condition is not met or the number of training iterations has not reached the set value, continue the above process; otherwise, stop training; finally, after training, test the model's training effect on the test set. The Huber function calculation formula is as follows: (7), in, For the target value, These are the model's predicted values. The switching threshold for the loss function is used; the activation function is calculated as follows: (8).

[0009] After the model training of this invention is completed, the center points of all grids in the study area are used as prediction points. The output values ​​are obtained according to the best model saved above, and the actual predicted water depth is restored using the following formula to establish the RANNST model. Finally, the model accuracy is evaluated: (9), among which, This indicates that the model predicts the water depth. This represents the water depth in the Topo_25.1 model at the predicted point. This represents the output of the neural network at the prediction point.

[0010] The RANN method proposed in this invention reduces the impact of terrain undulation differences on the model by introducing terrain undulation information into the neural network as input. Especially in complex sea areas with terrain undulation greater than 400 m, it effectively improves the model inversion accuracy in areas with large terrain undulation. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the 9×9 movable window in this invention.

[0012] Figure 2 This is a schematic diagram of the RANN method in this invention.

[0013] Figure 3 This refers to the distribution of shipborne sounding points in the research area of ​​this invention.

[0014] Figure 4 This is the topographic relief model of the research area in this invention.

[0015] Figure 5 These are the results of different seabed topography models in the embodiments of the present invention, wherein Figure 5 (a) is the RANNST model; (b) is the Topo_25.1 model; and (c) is the GEBCO_2024 model.

[0016] Figure 6 This is a schematic diagram showing the difference distribution between the RANNST, Topo_25.1, and GEBCO_2024 models and the shipborne depth sounding at the test points in this embodiment of the invention. Figure 6 (a) corresponds to RANNST; (b) corresponds to Topo_25.1; (c) corresponds to GEBCO_2024.

[0017] Figure 7 This is a schematic diagram showing the scatter plot distribution of the RANNST, Topo_25.1, and GEBCO_2024 models and shipborne depth sounding at the test points in this embodiment of the invention. Figure 7 (a) corresponds to RANNST; (b) corresponds to Topo_25.1; (c) corresponds to GEBCO_2024.

[0018] Figure 8 This is a schematic diagram illustrating the accuracy of the RANNST model for different terrain relief calculation methods in embodiments of the present invention, wherein... Figure 8 In the middle, (a) corresponds to MAE, and (b) corresponds to RMSE.

[0019] Figure 9 This is a schematic diagram of sub-regions 1, 2, and 3 on the research area in this embodiment of the invention. Detailed Implementation

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0021] The objective of this invention is to provide a method for improving the accuracy of seabed topography inversion based on topographic relief constrained neural networks, comprising the following: Relief amplitude is an important basis for describing terrain changes and classifying landform types. This invention uses the local standard deviation method and selects a 9×9 moving window. Figure 1 ) Calculate the center point of the grid ( h 41 Topographic relief information at location (). Specific calculation formula: (1), (2), where, This represents the number of grid points within the moving window; This represents the average water depth of the model.

[0022] A multilayer perceptron (MLP) is a fundamental artificial neural network model that models complex nonlinear relationships by simulating the connections between neurons in the human brain. Because there is a nonlinear relationship between seabed topography and gravity data, this invention chooses to use an MLP neural network to build the seabed topography model. Figure 2 As shown, MLP is a feedforward artificial neural network, consisting of an input layer, hidden layers, and an output layer. Each neuron is connected to all neurons in the next layer, and the neuron output is: (3), among which, x and y Represents the input and output data of neurons. W and b Represents weights and biases. f This represents the activation function.

[0023] Traditional MLP neural networks, in seabed topography inversion, rely solely on gravity data and shipborne bathymetry data to construct their input parameter system, neglecting the crucial influencing factor of topographic relief characteristics. The RANN method proposed in this invention introduces topographic relief information as input to the MLP neural network, improving the model's inversion accuracy. For example... Figure 2 As shown, the input data for the RANN method includes: the difference between the longitude of each point on the 6′×6′ grid around the shipborne sounding point and the longitude of the shipborne sounding point (ΔLON), the difference between the latitude of each point and the latitude of the shipborne sounding point (ΔLAT), the difference between the gravity anomaly and the gravity anomaly of the shipborne sounding point (ΔG), the difference between the vertical gravity gradient and the vertical gravity gradient of the shipborne sounding point (ΔVGG), the difference between the ramusoidal component of the vertical deviation and the ramusoidal component of the vertical deviation of the shipborne sounding point (Δη), the difference between the meridional component of the vertical deviation and the meridional component of the vertical deviation of the shipborne sounding point (Δξ), the difference between the model water depth and the water depth of the shipborne sounding point (ΔH), and the difference between the topographic relief and the topographic relief of the shipborne sounding point (ΔRA), for a total of 8 input data. The neural network input calculation formula is as follows: (4),

[0024] in, Indicates the first Individual grid points; and They represent the first Longitude and latitude at each grid point; and These represent the longitude and latitude of the shipborne sounding point or prediction point, respectively. , , and They represent the first Gravity anomaly, vertical gravity gradient, vertical deviation (Mao-You component) and vertical deviation (Zi-Meridian component) at each grid point; , , and These represent the gravity anomaly, vertical gravity gradient, and the ramus component and meridional component of the vertical deviation at the shipborne sounding point or prediction point, respectively. and They represent the first The water depth and terrain undulation of the Topo_25.1 model at each grid point; and These represent the water depth and topographic relief of the Topo_25.1 model at the shipborne sounding point or prediction point, respectively.

[0025] The neural network output is the difference between the Topo_25.1 model and the shipborne sounding at that point: (5), among which, This represents the output of the neural network. This indicates the water depth in the Topo_25.1 model at the shipborne sounding point. This indicates shipboard depth sounding.

[0026] Early shipborne sounding data contained uncertainties due to various reasons. To reduce these uncertainties, this invention employs the "3σ" principle to eliminate shipborne sounding data within a given area. The steps are as follows: First, to ensure a sufficient number of original shipborne sounding points, the study area is expanded by 1° around its perimeter, resulting in a range of 109°E–121°E and 11°N–23°N. Then, according to the "3σ" principle, data where the difference between the shipborne sounding points and the interpolated data from the GEBCO_2024 model exceeds three times the standard deviation is eliminated. Finally, to reduce edge effects and facilitate subsequent testing of the seabed topography model, an additional 0.1° is retained around the study area as an inversion region, i.e., the inversion region ranges from 109.9°E–120.1°E and 11.9°N–22.1°N, while the test area ranges from 109°E–121°E and 11°N–23°N.

[0027] The processed shipborne bathymetry points are divided into training points, validation points, and test points according to a certain ratio. The input data and target data corresponding to the shipborne bathymetry points are used as the training set, validation set, and test set, respectively. The training set is only used for training the neural network, the validation set is only used for early stopping and model selection during neural network model training, and the test set is only used for testing the training effect of the neural network and the accuracy of the final water depth model.

[0028] To reduce the differences between input data and ensure that each input data contributes equally to the neural network, the input data is processed before training the neural network. This invention uses z-score to standardize the input data, with the specific calculation formula as follows: (6), among which, It is standardized data. It is the raw data. The mean of the data. This represents the standard deviation of the data.

[0029] After standardizing the input data, the neural network is trained. The initial weights and biases are initialized using the default settings, the learning rate is set to 0.001, and if the loss value does not decrease within 5 consecutive training epochs, the learning rate is reduced to 60% of its original value. The batch size is set to 128, the number of training iterations is 150, the Huber function is selected as the loss function, the tanh function as the hidden layer activation function, and the Adam algorithm as the optimizer. The number of training epochs during which the loss function is allowed not to decrease is 10. The specific training process is as follows: First, initialize the neural network weights and biases; second, input the training data into the network, calculate the output value, and use the Huber function to calculate the loss between the output value and the target value, using the Adam optimization algorithm to adjust the weights and biases of each neural network; third, calculate the loss value on the validation set, and determine whether to save the model based on the loss value. If the early stopping condition is not met or the number of training iterations has not reached the set value, continue the above process; otherwise, stop training; finally, after training, test the model training effect on the test set. The Huber function calculation formula is as follows: (7), in, For the target value, These are the model's predicted values. The switching threshold for the loss function is used; the activation function is calculated as follows: (8); After model training, using the center points of all grids in the study area as prediction points, the output values ​​are obtained according to the saved best model, and the actual predicted water depth is reconstructed using the following formula to establish the RANNST model. Finally, the model accuracy is evaluated: (9), among which, This indicates that the model predicts the water depth. This represents the water depth in the Topo_25.1 model at the predicted point. This represents the output of the neural network at the prediction point.

[0030] This study selected the sea area (110°E, 120°E, 12°N, 22°N) as the research area. The maximum water depth in the research area is about 5221 m, and the average water depth is about 2446 m. ​​Its tectonic evolution has been influenced by the combined influence of these plates for a long time. The topography is complex and consists of continental shelf, continental slope, ocean-continent transition zone, seamount and deep-sea basin.

[0031] Using single-beam shipborne bathymetry data provided by the National Center for Environmental Information, National Oceanic and Atmospheric Administration (NOAA) (https: / / www.ncei.noaa.gov / maps / trackline-geophysics / ), spanning from 1994 to 2016, the study area contained 92 sounding lines. Following the "3σ" principle, the shipborne bathymetry data was filtered out, resulting in 216,566 sounding points, a rejection rate of approximately 1.57%. Figure 3 To study the distribution of shipborne sounding points in the region, 173,252 shipborne sounding points were selected as training points (red dots in the figure), 21,657 points were selected as verification points (black dots in the figure), and 21,657 points were selected as test points (yellow dots in the figure).

[0032] The ocean gravity data model, version 32.1, released by the Scripps Institution of Oceanography (SIO) at the University of California, San Diego, has a grid resolution of 1′. This model includes gravity anomaly data (grav_32.1), vertical gravity gradient data (curv_32.1), and vertical deviation data (east_32.1 and north_32.1) used in this invention. The gravity data model was established according to the following steps: First, satellite observation data was collected; then, through waveform retracking to correct signal deviations, land masking, slope correction to compensate for observational biases, and low-pass filtering, core parameters such as gravity anomalies, vertical gravity gradients, and vertical deviations were calculated; finally, the parameters were converted to latitude and longitude or Cartesian coordinates and output as a specific format file.

[0033] The Topo_25.1 model data was used to calculate the difference between the model water depth at the grid points and the model water depth at the shipborne sounding points, as well as the difference between the topographic relief at the grid points and the topographic relief at the shipborne sounding points. These results were used as input data for training the neural network model. GEBCO_2024 model data was used as the basis for shipborne sounding data elimination. The Topo_25.1 and GEBCO_2024 models were compared in subsequent accuracy assessments. The Topo_25.1 model was released by the Scripps Institution of Oceanography (SIO) in January 2023, with a grid resolution of 1'. GEBCO_2024 is a global land and sea topography model released in July 2024, covering land, ice surfaces, and subglacial topography information in Greenland and Antarctica, with a grid resolution of 15″.

[0034] This example begins by establishing a seabed topography model: The first grid point in the study area is selected as the center point of the moving window. The water depth of the Topo_25.1 model of all grid points in the window is extracted, and the topographic relief of the point is calculated according to formulas (1) and (2). The moving window is then slid to the next grid point, and the topographic relief is calculated again. The above operation is repeated until all points to be calculated are covered. All grid points are integrated to form a complete topographic relief grid, such as... Figure 4 As shown, the topography is more undulating at seamounts, islands, reefs, and trenches, while it is less undulating at continental shelves and ocean basins.

[0035] Gravity data (gravity anomaly, vertical gravity gradient, vertical deviation), water depth, and topographic relief information are used as input data for the neural network. 80%, 10%, and 10% of the shipborne sounding points are randomly selected as training, validation, and test points, respectively. A 6′×6′ grid is expanded outward from the shipborne sounding points, and the grid points are sequentially numbered 1, 2, 3…36. The aforementioned eight input data points at each point on the 6′×6′ grid surrounding the training point are combined sequentially to form a vector of size 288. This vector is used as input data for the neural network, and the prediction point vector obtained using the same method is used for the prediction model.

[0036] The input data was fed into the neural network for training. The early stopping condition was met at training epoch 145, and the iteration was stopped. At training epoch 135, the mean absolute error (MAE) on the validation set reached 23.12 m, and the mean squared error (MSE) reached 3778.26. This model was saved as the best network model for this training. The network model was tested on the test set, and the test results showed an MAE of 22.72 m and an MSE of 3498.16.

[0037] For each predicted point, data from its surrounding points are input into the network model to obtain the output value and reconstruct it as water depth to build the model. To study the relationship between the RANNST, Topo_25.1, and GEBCO_2024 models, a correlation coefficient is introduced. As an evaluation indicator, the specific formula is: (10) in, and Representing the first and second models respectively A water depth value, and These represent the average water depths of Model 1 and Model 2, respectively. It is typically used to represent the correlation between two models, with a value range of [-1, 1]. The closer the value is to 1, the higher the positive linear correlation. The closer the value is to -1, the higher the negative linear correlation.

[0038] Figure 5 The model diagrams for RANNST, Topo_25.1, and GEBCO_2024 are shown. The correlation coefficients between RANNST and Topo_25.1 and GEBCO_2024 are all close to 1, indicating that RANNST has a high positive linear correlation with Topo_25.1 and GEBCO_2024.

[0039] To evaluate the accuracy of the RANNST model, this example compares and analyzes its accuracy using shipboard bathymetry data and internationally recognized seabed topography models Topo_25.1 and GEBCO_2024. Cubic spline interpolation was used to interpolate the RANNST model data to each test point to obtain the inverted water depth. The same method was used to obtain the inverted water depths at the test points for the Topo_25.1 and GEBCO_2024 models. Finally, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) were used as evaluation metrics. The specific calculation formulas are as follows: (11), (12) (13) in, Indicates the first One predicted water depth value, Indicates the first Each shipborne depth sounding value, This indicates the number of points involved in the calculation.

[0040] The inverted water depths of the RANNST, Topo_25.1, and GEBCO_2024 models at the test points were compared with shipborne soundings. The RMSE (Recovery Mean Squared Estimate) of the differences between the inverted water depths of the RANNST, Topo_25.1, and GEBCO_2024 models and the shipborne soundings at the test points were 62.80 m, 88.81 m, and 87.54 m, respectively. The RMSE of the RANNST model decreased by 29.29% and 28.26% compared to the Topo_25.1 and GEBCO_2024 models, respectively. Furthermore, the MAE (Modal Equivalence) of the differences between the inverted water depths of the RANNST, Topo_25.1, and GEBCO_2024 models and the shipborne soundings at the test points were 26.95 m, 41.64 m, and 32.07 m, respectively, with MAPEs of 1.40%, 2.21%, and 1.55%, respectively. This indicates that the RANNST model outperforms the Topo_25.1 and GEBCO_2024 models in all three metrics: MAE, MAPE, and RMSE.

[0041] Figure 6 This is a histogram showing the difference between the inverted water depth and shipborne sounding values ​​from the RANNST, Topo_25.1, and GEBCO_2024 models at the test points. The horizontal axis represents the difference, covering an equidistant interval of 25 m between -350 and 350 m. The vertical axis represents the number of data samples within the corresponding difference interval. The differences between the inverted water depth and shipborne sounding values ​​from each model are mainly distributed near 0, exhibiting a normal distribution, primarily within the range of -200 to 200 m. Statistically, the percentages of the differences between the inverted water depth and shipborne sounding values ​​from the three models within the -200 to 200 m range are 98.39%, 96.12%, and 97.37%, respectively. The percentages within the ranges less than -350 m or greater than 350 m are 0.63%, 1.34%, and 1.18%, respectively, indicating that the RANNST model has relatively few points with large errors.

[0042] Figure 7 This is a scatter plot with the shipborne depth sounding value at the test point on the horizontal axis and the model inversion depth value on the vertical axis. It combines the scatter plot distribution with R... 2 The values ​​show that the RANNST model has the best fit with the shipborne depth sounding at the test point, while the Topo_25.1 and GEBCO_2024 models have a poorer fit with the shipborne depth sounding, further indicating that the RANNST model performs better.

[0043] To analyze the accuracy differences of the RANNST, Topo_25.1, and GEBCO_2024 models under different terrain relief levels, this invention statistically analyzed the MAE, MAPE, and RMSE of the difference between the inverted water depth and the shipborne depth sounding for each model in different terrain relief intervals. The results show that the accuracy of each model group decreases with increasing terrain relief: when the terrain relief is small, all models exhibit high accuracy; when the terrain relief is large, the accuracy of each model decreases. Compared to the Topo_25.1 model, the RANNST model has a poorer MAPE in only one group, while the other indicators are better. Compared to the GEBCO_2024 model, the RANNST model has a poorer MAPE in groups 1 and 2 with lower terrain relief, while the other indicators are better. Compared with the Topo_25.1 and GEBCO_2024 models, the RANNST model has a more significant advantage in areas with large topographic relief, especially in group 5, where the RANNST model reduces the RMSE by 30.95% and 40.04% compared with the Topo_25.1 and GEBCO_2024 models, respectively.

[0044] To analyze the accuracy differences of the RANNST, Topo_25.1, and GEBCO_2024 models at different water depths, this invention statistically analyzed the MAE, MAPE, and RMSE of the difference between the inverted water depth and the shipborne depth sounding for each model in different water depth ranges. The results show that the model has higher accuracy in shallower and deeper water regions, and lower accuracy in medium-depth water regions. Compared to the Topo_25.1 and GEBCO_2024 models, the RANNST model performed poorly only in one group, outperforming in all indicators across the other groups. Compared to the Topo_25.1 and GEBCO_2024 models, the RANNST model showed a more significant advantage in medium-depth water regions, especially in the second group, where the RMSE of the RANNST model decreased by 40.73% and 33.25% respectively compared to the Topo_25.1 and GEBCO_2024 models.

[0045] The impact of terrain relief calculation methods on inversion accuracy: To select the sliding window size for terrain relief calculation, this invention uses the sliding window size as a variable and sets up 5 experimental groups: Group 1 uses a 3×3 sliding window to calculate terrain relief, Group 2 uses a 5×5 sliding window, Group 3 uses a 7×7 sliding window, Group 4 uses a 9×9 sliding window, and Group 5 uses an 11×11 sliding window. Each group uses three random initialization seeds (random=42, random=43, and random=44) for the experiment. The MAE and RMSE of the RANNST model and the shipborne depth sounding difference for different groups are statistically analyzed. Figure 8As shown in the figure. The results indicate that the average MAE and RMSE of the three experiments in the four groups were the lowest, at 27.02 m and 63.06 m respectively, and the 9×9 sliding window method was the most effective for calculating the terrain relief.

[0046] The impact of different landform types on inversion accuracy: To further analyze the impact of landform types on inversion accuracy, this invention selects three areas with significant differences in topographic relief within the study area for investigation, such as... Figure 9 As shown, Area 1, ranging from 113°E to 116°E and from 18°N to 20°N, is mainly composed of continental slopes, with the lowest average water depth and average topographic relief among the three areas, at 1985.11 m and 91.11 m respectively; Area 2, ranging from 112°E to 113.5°E and from 13°N to 15°N, is mainly composed of islands and reefs, with the highest average topographic relief among the three areas, at 237.63 m; Area 3, ranging from 118.5°E to 119.5°E and from 13.5°N to 19°N, is mainly composed of trenches, with the highest average water depth among the three areas, at 3751.74 m.

[0047] Using shipboard measured data, the accuracy of the RANNST, Topo_25.1, and GEBCO_2024 models was evaluated in regions with different terrain relief. In region 1, where the average terrain relief was relatively small, the RMSE of the RANNST, Topo_25.1, and GEBCO_2024 models were the lowest, at 56.58 m, 75.75 m, and 66.27 m, respectively. In region 2, where the average terrain relief was the largest, the RMSE of the RANNST, Topo_25.1, and GEBCO_2024 models were the highest, at 96.42 m, 101.78 m, and 97.01 m, respectively. In region 3, where the terrain relief was between that of regions 1 and 2, the RMSE of the RANNST, Topo_25.1, and GEBCO_2024 models were also between those regions, at 73.57 m, 93.38 m, and 89.47 m, respectively. This indicates that the accuracy of the model inversion is affected by topographic relief. In areas with less topographic relief, the model inversion accuracy is relatively high; in areas with greater topographic relief, the model inversion accuracy is relatively low.

[0048] The impact of different input data on inversion accuracy: To evaluate the impact of input data on the inversion accuracy of the neural network model, different combinations of gravity or terrain data were fused as neural network inputs, and shipborne bathymetry data were used to evaluate the model accuracy of inversion with different input data.

[0049] When the neural network input only includes η and ξ, the MAE, MAPE, and RMSE are 30.59 m, 1.73%, and 68.07 m, respectively, indicating the lowest model inversion accuracy. After adding VGG data, MAE and RMSE decrease by 0.23 m and 1.04 m, respectively, while MAPE remains essentially unchanged. Adding ΔG information further reduces MAE, MAPE, and RMSE by 0.37 m, 0.06%, and 0.13 m, respectively. Adding H information further reduces MAE, MAPE, and RMSE by 2.47 m, 0.27%, and 2.87 m, respectively. Finally, adding RA data results in MAE, MAPE, and RMSE values ​​of 26.95 m, 1.40%, and 62.80 m, respectively, with MAE, MAPE, and RMSE decreasing by 0.57 m, 0.04%, and 1.23 m, respectively. Compared to the model constructed by fusing only gravity data (NNST), the MAE, MAPE, and RMSE of RANNST are reduced by 3.04m, 0.31%, and 4.10m, respectively, indicating that the RANNST model that incorporates all data has the highest inversion accuracy.

[0050] To address the insufficient accuracy of seafloor topography inversion based on traditional geophysical methods, this invention proposes a novel Relief Amplitude Neural Network (RANN) method. The effectiveness of the RANN method is verified by constructing the seafloor topography of the study area. By combining gravity data (gravity anomaly, vertical gravity gradient, vertical deviation), topographic relief, and shipborne bathymetry data, the RANN method is used to invert and construct the RANNST (Relief Amplitude Neural Network Seafloor Topography, RANNST) model. (1) Based on shipborne bathymetry data and international seafloor topography models Topo_25.1 and GEBCO_2024, the accuracy of the seafloor topography is evaluated. The results show that the root mean square error of the RANNST model inverted by the method proposed in this invention is 62.80 m, which is an improvement of approximately 29.29% and 28.26% in accuracy compared to the Topo_25.1 and GEBCO_2024 models, respectively. (2) The inversion accuracy of the seabed topography model is greatly affected by topographic relief. The model inversion accuracy is significantly better in areas with less topographic relief than in areas with greater topographic relief. (3) The RANN method proposed in this invention reduces the impact of topographic relief differences on the model by introducing topographic relief information into the neural network as input. Especially in complex sea areas with topographic relief greater than 400m, the RANNST model reduces the RMSE by 30.95% and 40.04% compared with the Topo_25.1 and GEBCO_2024 models, respectively, effectively improving the model inversion accuracy in areas with greater topographic relief.

Claims

1. A method for seafloor topography inversion based on a topographic relief-constrained neural network, characterized in that, First, a neural network model constrained by terrain relief is constructed, and the local standard deviation method is selected, with a 9×9 moving window used to calculate the grid center point. h 41 The topographic relief information at point ) is calculated using the following formula: (1), (2), where, This represents the number of grid points within the moving window; The average water depth of the model; We chose to use an MLP neural network to build the seabed topography model. MLPs are feedforward artificial neural networks, consisting of an input layer, hidden layers, and an output layer. Each neuron is connected to all neurons in the next layer, and the neuron output is: (3), among which, x and y Represents the input and output data of neurons. W and b Represents weights and biases. f Represents the activation function; Topographic relief information is introduced as input to the MLP neural network. The input data includes: the difference between the longitude and the longitude of the shipborne sounding point at each point on the 6′×6′ grid around the shipborne sounding point (ΔLON), the difference between the latitude and the latitude of the shipborne sounding point (ΔLAT), the difference between the gravity anomaly and the gravity anomaly of the shipborne sounding point (ΔG), the difference between the vertical gravity gradient and the vertical gravity gradient of the shipborne sounding point (ΔVGG), the difference between the ramusoidal component of the vertical deviation and the ramusoidal component of the vertical deviation of the shipborne sounding point (Δη), the difference between the meridional component of the vertical deviation and the meridional component of the vertical deviation of the shipborne sounding point (Δξ), the difference between the model water depth and the water depth of the shipborne sounding point (ΔH), and the difference between the topographic relief and the topographic relief of the shipborne sounding point (ΔRA). There are a total of 8 input data. The neural network input calculation formula is as follows: （4）， in, Indicates the first Individual grid points; and They represent the first Longitude and latitude at each grid point; and These represent the longitude and latitude of the shipborne sounding point or prediction point, respectively. , , and They represent the first Gravity anomaly, vertical gravity gradient, vertical deviation (Mao-You component) and vertical deviation (Zi-Meridian component) at each grid point; , , and These represent the gravity anomaly, vertical gravity gradient, and the ramus component and meridional component of the vertical deviation at the shipborne sounding point or prediction point, respectively. and They represent the first The water depth and terrain undulation of the Topo_25.1 model at each grid point; and These represent the water depth and topographic relief of the Topo_25.1 model at the shipborne sounding point or prediction point, respectively. The neural network output is the difference between the Topo_25.1 model and the shipborne sounding at that point: (5), among which, This represents the output of the neural network. This indicates the water depth in the Topo_25.1 model at the shipborne sounding point. This indicates shipboard depth sounding.

2. The seabed topography inversion method based on topographic relief constrained neural network according to claim 1, characterized in that, It also includes training a neural network model constrained by the terrain relief, including removing early shipborne sounding data to reduce data uncertainty; then, the processed shipborne sounding data is divided into training points, validation points, and test points. The input data and target data corresponding to the shipborne sounding points are used as training sets, validation sets, and test sets, respectively. The training set is only used for training the neural network, the validation set is only used for early stopping and model selection during neural network model training, and the test set is only used for testing the training effect of the neural network and the accuracy of the final water depth model.

3. The seabed topography inversion method based on topographic relief constrained neural network according to claim 2, characterized in that, To reduce the differences between input data and ensure that each input data point contributes equally to the neural network, the input data is first processed before training the neural network. The z-score is used to standardize the input data, and the specific calculation formula is as follows: (6), among which, It is standardized data. It is the raw data. The mean of the data. This represents the standard deviation of the data.

4. The seabed topography inversion method based on topographic relief constrained neural network according to claim 3, characterized in that, After standardizing the input data, the neural network is trained. The initial weights and biases are initialized using the default settings, and the learning rate is set to 0.

001. If the loss value does not decrease within five consecutive training epochs, the learning rate is reduced to 60% of its original value. The batch size is set to 128, the training iterations are 150, the Huber function is selected as the loss function, the tanh function as the hidden layer activation function, and the Adam algorithm as the optimizer. The number of training epochs during which the loss function is allowed not to decrease is 10. The specific training process is as follows: First, initialize the neural network weights and biases; second, input the training data into the network, calculate the output value, and use the Huber function to calculate the loss between the output value and the target value. Use the Adam optimization algorithm to adjust the weights and biases of each neural network; third, calculate the loss value on the validation set, and determine whether to save the model based on the loss value. If the early stopping condition is not met or the number of training iterations has not reached the set value, continue the above process; otherwise, stop training; finally, after training, test the model's training effect on the test set. The Huber function calculation formula is as follows: （7）， in, For the target value, These are the model's predicted values. The switching threshold for the loss function is used; the activation function is calculated as follows: （8）。 5. The seabed topography inversion method based on topographic relief constrained neural network according to claim 1, characterized in that, After model training, using the center points of all grids in the study area as prediction points, the output values ​​obtained from the optimal model are used to reconstruct the actual predicted water depth using the following formula, thus establishing the RANNST model. Finally, the model accuracy is evaluated: (9), among which, This indicates that the model predicts the water depth. This represents the water depth in the Topo_25.1 model at the predicted point. This represents the output of the neural network at the prediction point.

Images