A VGGNet-based correction for satellite altimetry-derived gravity anomalies to improve the accuracy of bathymetry to depths of 6 500 m
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Abstract: Understanding the topographic patterns of the seafloor is a very important part of understanding our planet. Although the science involved in bathymetric surveying has advanced much over the decades, less than 20% of the seafloor has been precisely modeled to date, and there is an urgent need to improve the accuracy and reduce the uncertainty of underwater survey data. In this study, we introduce a pretrained visual geometry group network (VGGNet) method based on deep learning. To apply this method, we input gravity anomaly data derived from ship measurements and satellite altimetry into the model and correct the latter, which has a larger spatial coverage, based on the former, which is considered the true value and is more accurate. After obtaining the corrected high-precision gravity model, it is inverted to the corresponding bathymetric model by applying the gravity-depth correlation. We choose four data pairs collected from different environments, i.e., the Southern Ocean, Pacific Ocean, Atlantic Ocean and Caribbean Sea, to evaluate the topographic correction results of the model. The experiments show that the coefficient of determination (R2) reaches 0.834 among the results of the four experimental groups, signifying a high correlation. The standard deviation and normalized root mean square error are also evaluated, and the accuracy of their performance improved by up to 24.2% compared with similar research done in recent years. The evaluation of the R2 values at different water depths shows that our model can achieve performance results above 0.90 at certain water depths and can also significantly improve results from mid-water depths when compared to previous research. Finally, the bathymetry corrected by our model is able to show an accuracy improvement level of more than 21% within 1% of the total water depths, which is sufficient to prove that the VGGNet-based method has the ability to perform a gravity-bathymetry correction and achieve outstanding results.
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Key words:
- gravity anomaly /
- bathymetry inversion /
- VGGNet /
- multibeam sonar /
- satellite altimetry
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Figure 2. Architecture of the VGG-19 model. The boxes represent the size of each layer.
Figure 4. The training and validation loss from the experiments in the Southern Ocean, Pacific Ocean, Atlantic Ocean, and Caribbean Sea.
Figure 5. Comparison of local details of gravity anomalies before and after correction from the Southern Ocean, Pacific Ocean, Atlantic Ocean, and Caribbean Sea. Each subfigure shows three visualizations of randomly selected locations.
Figure 6. R2 values at different water depths compared with the bathymetry-only correction methos in the Southern Ocean (a), Pacific Ocean (b), Atlantic Ocean (c), and Caribbean Sea (d).
Figure 7. Percentage distributions of NRMSE performance in datasets from the Southern Ocean, Pacific Ocean, Atlantic Ocean, and Caribbean Sea.
Table 1. The default hyperparameters of the training model
Hyperparameter Setting Content layer “conv4_2” Style layer “conv1_1”, “conv2_1”, “conv3_1”, “conv4_1”, “conv5_1” Weight of loss at content layer 1 Weight of loss at style layer 1, 1, 1, 1 Weights among content, style, and total variation loss 1 × 10−4, 1, 1 × 10−5
Learning rate starts at 10 and linear decays over 100 iterations to 1 
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Table 2. The parameters of the datasets
Location Center point coordinate Spatial resolution/m Data size Area/km2 Bathymetry/m Southern Ocean 71°S, 173°E 93 5 097 104 43 700 211−4077 Pacific Ocean 9°S, 140°W 93 33 048 000 283 337 113−4992 Atlantic Ocean 32°N, 65°W 93 3 240 000 27 778 58−4920 Caribbean Sea 18°N, 82°W 123 10 614 363 150 310 1−6580
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Table 3. Overall accuracy of the gravity correction
Location R2 SD/mGal RMSE/mGal NRMSE Southern Ocean 0.902 18.333 13.630 0.113 Pacific Ocean 0.955 17.892 10.050 0.118 Atlantic Ocean 0.930 19.567 21.549 0.114 Caribbean Sea 0.919 21.051 16.485 0.113
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Table 4. The overall accuracy of the bathymetry correction
Location R2 SD/m RMSE/m NRMSE Southern Ocean 0.822 104.790 107.024 0.027 Pacific Ocean 0.834 117.630 126.366 0.026 Atlantic Ocean 0.833 124.847 136.622 0.028 Caribbean Sea 0.783 139.583 164.475 0.025
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Table 5. Proportion of corrected errors from true values within 2% and 1% of the depth range
Location Proportion of corrected errors/% 1% of depth 2% of depth Southern Ocean 68.05 75.69 Pacific Ocean 61.53 77.52 Atlantic Ocean 57.58 68.69 Caribbean Sea 51.03 64.58
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