# Refining Altimeter-Derived Gravity Anomaly Model from Shipborne Gravity by Multi-Layer Perceptron Neural Network: A Case in the South China Sea

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## Abstract

**:**

## 1. Introduction

^{−5}m/s

^{2}) [8,9]. Even so, the altimetry waveforms can be contaminated by land and reefs, so the accuracy of altimeter-derived gravity decreases with the increasing proximity to the coastline [10,11]. The standard deviation (STD) of altimeter-measured sea surface heights increases with decreasing water depth [10]. Meanwhile, water depth in coastal areas is shallow, so the precision of altimeter-derived gravity is low in shallow waters. Gravity anomalies are related to submarine topographic undulation and crustal density variations [12,13,14]. Gravity anomalies change dramatically in areas with large topographic undulation. As gravity anomalies are derived from altimetric data in a calculation windows (tens of kilometers), the precision of altimeter-derived gravity is lower in areas with notable submarine topography [15,16,17]. The precision of modern shipborne gravity with higher resolution is approximately 1~3 mGal [18]. Moreover, coastlines and submarine topography have less effects on the accuracy of shipborne gravity than altimeter-derived gravity.

## 2. Materials and Methods

#### 2.1. Research Data

#### 2.1.1. Reference Gravity Model and Topography Model

#### 2.1.2. Shipborne Gravity

#### 2.1.3. Altimeter-Derived Gravity Anomaly Model

#### 2.2. Methodology

#### 2.2.1. Structure of MLP

#### 2.2.2. Refined Area Classification

#### 2.2.3. Training and Predicting

^{−4}. Taking overfitting of training and observation errors of shipborne gravity into account, the iteration threshold and maximum number of iterations should be determined through testing, so that the determination coefficient R

^{2}for training is approximately 0.7. Therefore, the MLP models are established by the MLP training.

## 3. Results

#### 3.1. Refining the Gravity Model by Classification

#### 3.2. Refining the Gravity Model as a Whole

#### 3.3. Analysis of the Refined Gravity Anomaly Model

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Shipborne gravity data tracks. (

**a**) Shipborne data measured since 1990, (

**b**) shipborne data measured before 1990. The tracks in the blue box are from Ministry of Natural Resources of P. R. China (MNR). The data in black are not in the refined area. The region in the yellow box is region A.

**Figure 2.**Tracks of altimetric data used to determine altimetric gravity anomaly model around the South China Sea (SCSGA) V1.0.

**Figure 3.**Structure of multi-layer perceptron (MLP): dh

_{x}and dh

_{y}are respectively prime vertical and meridian components of submarine topography slopes and dg

_{res}represents residual gravity anomalies.

**Figure 7.**Shipborne gravity track and surrounding submarine topography for power spectral density (PSD) analysis.

Submarine Topography Slope (m/arcmin ^{a}) | Shipborne Data before 1990 (mGal) | Shipborne Data Since 1990 (mGal) |
---|---|---|

All | 4.41 | 3.93 |

N > 50 or E > 50 ^{b} | 4.55 | 4.16 |

N > 100 or E > 100 | 4.89 | 4.17 |

N > 150 or E > 150 | 5.10 | 4.38 |

^{a}1 m/arcmin is equal to 0.54 m/km.

^{b}N: meridian component E: prime vertical component.

Satellite | Period | Inter-Track Distance at Equator (km) | Sampling Interval along Track (km) |
---|---|---|---|

ERS-1 | 94.04–95.03 | 7 | 6.6 |

Jason-1 | 12.05–13.06 | 7 | 5.8 |

Jason-2 | 17.07–19.02 | 7 | 5.8 |

HY-2A | 16.03–18.07 | 15 | 6.5 |

SARAL–AltiKa | 16.07–18.10 | 5 | 6.9 |

CryoSat-2 | 11.01–18.07 | 2.5 | 6.4 |

Bathymetry (m) | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 | 70–100 |
---|---|---|---|---|---|---|---|---|

RMS (mGal) | 10.48 | 7.80 | 6.54 | 7.63 | 6.41 | 5.59 | 4.48 | 3.89 |

STD (mGal) | 9.80 | 7.74 | 6.31 | 7.59 | 6.36 | 5.53 | 4.48 | 3.84 |

**Table 4.**Differences between SCSGA V1.0 and shipborne data since 1990 in deep waters with different submarine topography slopes.

Slopes (m/arcmin) | All | E > 50 or N > 50 | E > 100 or N > 100 | E > 150 or N > 150 |
---|---|---|---|---|

RMS (mGal) | 5.36 | 5.88 | 6.28 | 6.37 |

STD (mGal) | 5.35 | 5.85 | 6.22 | 6.30 |

Category | Bathymetry 50 m | Submarine Topography Slope | Number of Samples | Number of Predicted Grid Points | |
---|---|---|---|---|---|

Prime Vertical 100 m/arcmin | Meridian 100 m/arcmin | ||||

Case1 | < | ≤ | ≤ | 795 | 245,314 |

< | > | ≤ | |||

< | ≤ | > | |||

< | > | > | |||

Case2 | ≥ | > | > | 3431 | 52,692 |

Case3 | ≥ | > | ≤ | 7612 | 74,093 |

Case4 | ≥ | ≤ | > | 5260 | 76,225 |

Layer | Variable | Vector Size | |
---|---|---|---|

Input layer | Input | (256,146) | |

Output | (256,146) | ||

Hidden layer | 1 | Input | (256,146) |

Output | (256,512) | ||

2 | Input | (256,512) | |

Output | (256,256) | ||

Output layer | Input | (256,256) | |

Output | (256,1) |

Refined Area | Case1 | Case2 | Case3 | Case4 | ||
---|---|---|---|---|---|---|

Number | 99,048 | 11,343 | 24,222 | 30,815 | 32,668 | |

V1.0- NCEI | MEAN | −0.59 | −0.06 | −0.77 | −0.80 | −0.44 |

STD | 5.78 | 5.80 | 6.16 | 5.70 | 5.54 | |

RMS | 5.81 | 5.80 | 6.21 | 5.75 | 5.55 | |

V1.1- NCEI | MEAN | −0.36 | 0.04 | −0.58 | −0.30 | −0.40 |

STD | 5.66 | 5.65 | 6.06 | 5.54 | 5.45 | |

RMS | 5.67 | 5.65 | 6.09 | 5.55 | 5.46 |

Refined Area | Case1 | Case2 | Case3 | Case4 | ||
---|---|---|---|---|---|---|

Number | 99,048 | 11,343 | 24,222 | 30,815 | 32,668 | |

V1.2- NCEI | MEAN | −0.40 | −0.38 | −0.55 | −0.40 | −0.30 |

STD | 5.65 | 5.68 | 6.04 | 5.58 | 5.40 | |

RMS | 5.67 | 5.69 | 6.06 | 5.57 | 5.41 |

**Table 9.**Differences between SCSGAV1.2 and the testing shipborne data in different regions (in mGal).

Refined Area | Case1 | Case2 | Case3 | Case4 | |||
---|---|---|---|---|---|---|---|

Region A | Number | 7626 | 189 | 1682 | 2421 | 3334 | |

V1.0- NCEI | MEAN | 0.14 | −0.85 | 0.78 | −0.44 | 0.28 | |

STD | 5.91 | 5.75 | 6.36 | 6.15 | 5.45 | ||

RMS | 5.91 | 5.81 | 6.41 | 6.16 | 5.46 | ||

V1.2- NCEI | MEAN | 0.18 | −1.50 | 0.70 | −0.22 | 0.30 | |

STD | 5.65 | 5.49 | 6.03 | 5.95 | 5.18 | ||

RMS | 5.65 | 5.69 | 6.07 | 5.95 | 5.19 | ||

Region B | Number | 91,422 | 11,154 | 22,540 | 28,394 | 29,334 | |

V1.0- NCEI | MEAN | −0.65 | −0.05 | −0.88 | −0.83 | −0.52 | |

STD | 5.76 | 5.80 | 6.13 | 5.65 | 5.54 | ||

RMS | 5.80 | 5.80 | 6.19 | 5.71 | 5.56 | ||

V1.2- NCEI | MEAN | −0.45 | −0.36 | −0.65 | −0.42 | −0.36 | |

STD | 5.65 | 5.68 | 6.03 | 5.55 | 5.43 | ||

RMS | 5.67 | 5.69 | 6.06 | 5.57 | 5.44 |

Gravity Model | Refined Area | Case1 | Case2 | Case3 | Case4 |
---|---|---|---|---|---|

SCSGA V1.0 | 5.81 | 5.80 | 6.21 | 5.75 | 5.55 |

SCSGA V1.2 | 5.67 | 5.69 | 6.06 | 5.57 | 5.41 |

M1 | 5.75 | 5.77 | 6.13 | 5.66 | 5.53 |

M2 | 5.71 | 5.73 | 6.08 | 5.64 | 5.49 |

M3 | 5.70 | 5.83 | 6.05 | 5.62 | 5.46 |

Depth (m) | MAX | MIN | MEAN | STD | RMS |

0–10 | 17.55 | −23.55 | 0.36 | 1.85 | 1.89 |

10–20 | 15.74 | −15.43 | 0.40 | 1.64 | 1.69 |

20–30 | 19.25 | −18.53 | 0.46 | 1.43 | 1.50 |

30–40 | 12.67 | −14.42 | 0.40 | 1.25 | 1.31 |

40–50 | 13.80 | −16.20 | 0.35 | 1.10 | 1.15 |

Slopes (m/arcmin) | MAX | MIN | MEAN | STD | RMS |

N > 100 or E > 100 | 20.05 | −23.78 | −0.18 | 2.01 | 2.02 |

N > 150 or E > 150 | 19.94 | −23.78 | −0.14 | 2.23 | 2.23 |

N > 200 or E > 200 | 17.52 | −23.78 | −0.11 | 2.44 | 2.44 |

N > 300 or E > 300 | 17.52 | −21.98 | −0.05 | 2.86 | 2.86 |

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**MDPI and ACS Style**

Zhu, C.; Guo, J.; Yuan, J.; Jin, X.; Gao, J.; Li, C.
Refining Altimeter-Derived Gravity Anomaly Model from Shipborne Gravity by Multi-Layer Perceptron Neural Network: A Case in the South China Sea. *Remote Sens.* **2021**, *13*, 607.
https://doi.org/10.3390/rs13040607

**AMA Style**

Zhu C, Guo J, Yuan J, Jin X, Gao J, Li C.
Refining Altimeter-Derived Gravity Anomaly Model from Shipborne Gravity by Multi-Layer Perceptron Neural Network: A Case in the South China Sea. *Remote Sensing*. 2021; 13(4):607.
https://doi.org/10.3390/rs13040607

**Chicago/Turabian Style**

Zhu, Chengcheng, Jinyun Guo, Jiajia Yuan, Xin Jin, Jinyao Gao, and Chengming Li.
2021. "Refining Altimeter-Derived Gravity Anomaly Model from Shipborne Gravity by Multi-Layer Perceptron Neural Network: A Case in the South China Sea" *Remote Sensing* 13, no. 4: 607.
https://doi.org/10.3390/rs13040607