# A New 1′ × 1′ Global Seafloor Topography Model Predicted from Satellite Altimetric Vertical Gravity Gradient Anomaly and Ship Soundings BAT_VGG2021

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## Abstract

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## 1. Introduction

## 2. Theory and Methods

## 3. Data and Results

#### 3.1. Data Sources

#### 3.2. Data Processing Procedure

- The SIO topo_20.1.nc model was filtered to construct a reference model at wavelengths longer than 160 km, ${h}_{long}\left(x\right)$. Then, the reference depths at the ship points, ${h}_{ref\_ship}\left({x}^{\prime}\right)$, were interpolated from ${h}_{long}\left(x\right)$.
- At ship points, the residual depths, ${h}_{resi\_ship}\left({x}^{\prime}\right)$, can be calculated by subtracting ${h}_{ref\_ship}\left({x}^{\prime}\right)$ from the observed depths, ${h}_{ship}\left({x}^{\prime}\right)$.$${h}_{res{i}_{ship}}\left({x}^{\prime}\right)={h}_{ship}\left({x}^{\prime}\right)-{h}_{ref\_ship}\left({x}^{\prime}\right)$$
- The SIO curv_30.1.nc model was band-pass filtered, downward continued, and divided by k to construct VGG at 15~160 km wavelength bands, $\Delta {G}_{z\_down}\left(x\right)$, and then was used to interpolate VGG at the ship points, $\Delta {G}_{z\_ship}\left({x}^{\prime}\right)$.
- The topography-to-VGG ratios at the ship points were calculated by$$s\left({x}^{\prime}\right)={h}_{resi\_ship}\left({x}^{\prime}\right)/\Delta {G}_{z\_ship}\left({x}^{\prime}\right)$$The ratios were then gridded to a 1′ $\times $ 1′ grid, S(x).
- The gridded ratios, S(x), and band-pass filtered VGG, $\Delta {G}_{z\_down}\left(x\right)$, were used to constrain seafloor topography at 15~160 km wavelength bands,$${h}_{pre}\left(x\right)=S\left(x\right)\xb7\Delta {G}_{z\_down}\left(x\right)$$
- The final seafloor topography model becomes$$h\left(x\right)={h}_{long}\left(x\right)+{h}_{pre}\left(x\right)$$

#### 3.3. The New 1′ $\times $ 1′ Global Seafloor Topography Model

## 4. Discussion

#### 4.1. Accuracy Evaluated by Comparing with Ship Soundings and Existing Models

#### 4.2. Model Evaluated by Independent Multibeam Grids of MH370 Searching Area

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The red lines represent response functions, $\phi \left(k\right)$, with the lithospheric effective elastic thickness of 3 km, 5 km, 10 km, and 25 km, respectively, which work like high-pass filters. The thick blue line shows the exponential decay function, exp(k), which works like a low-pass filter.

**Figure 2.**The black lines represent transform functions between seafloor topography and gravity anomalies, ${Z}_{topo-grav}\left(k\right)$, with lithospheric effective elastic thickness of 0 km, 3 km, 5 km, 10 km, and 25 km, respectively. The red lines show transform functions between seafloor topography and VGG, ${Z}_{topo-grad}\left(k\right)$. The results show that the transform functions work like band-pass filters. The transform function, ${Z}_{topo-grad}\left(k\right)$, suppresses the effect of isostasy and enlarge signal at wavelengths shorter than ~100 km.

**Figure 3.**The coherence between seafloor topography and gravity anomaly (black dots) or VGG (red dots) in the northwestern Pacific (144$\xb0$~180$\xb0$E, 0$\xb0$~36$\xb0$N). This indicates that the seafloor topography and gravity anomaly or VGG show high coherence at certain wavelength bands. At long wavelengths (>500 km), the topography–VGG coherence is lower than the topography–GA coherence.

**Figure 4.**The SIO VGG model, curv_30.1.nc, from ftp://topex.ucsd.edu/pub/global_grav_1min/, released on 9 October 2020. This version includes an additional year of AltiKa, CryoSat, and Sentinel-3A/B data than the previous version.

**Figure 5.**Global distribution of the ship soundings. The black dots indicate single-beam depths from NCEI, the blue dots indicate multibeam depths from NCEI, the yellow dots indicate multibeam depths from JAMSTEC, and the purple dots indicate multibeam depths from GA.

**Figure 6.**Data processing flow chart of seafloor topography construction from ship soundings and the altimetric VGG. The latest version of SIO model, topo_20.1.nc, was used to constrain seafloor topography model at wavelengths longer than 160 km. The ship soundings were cleaned by comparing with topo_20.1.nc. About 90% of the cleaned ship points were applied to constrain topography to VGG ratios at 15~160 km wavelength bands, and 10% were used to assess the model accuracy. The VGG model, curv_30.1.nc was used to predict seafloor topography model at 15~160 km wavelength bands.

**Figure 7.**Seafloor topography construction example in the northwestern Pacific (144$\xb0$~180$\xb0$E, 0$\xb0$~36$\xb0$N). The seafloor topography at wavelengths longer than 160 km, ${h}_{long}\left(x\right)$ (

**a**), the VGG grid at 15~160 km wavelength bands, $\Delta {G}_{z\_down}\left(x\right)$ (

**b**), the topography-to-VGG ratios at ship points $s\left({x}^{\prime}\right)$ (

**c**), and the predicted 1′ $\times $ 1′ seafloor topography model, $h\left(x\right)$ (

**d**).

**Figure 8.**The new 1′ × 1′ global seafloor topography model predicted from VGG and ship soundings, BAT_VGG2021.

**Figure 9.**Global distribution of the differences between BAT_VGG2021 and ship soundings. The standard deviation of model–ship differences is 45.464 m, and ~93% of the differences are within 100 m. The result indicated that the predicted model fits ship measurements very well.

**Figure 10.**The differences between BAT_VGG2021 and the SIO topo_20.1.nc model. The standard deviation difference of these two models is 80.732 m, ~84% of the differences are within 100 m, and ~95.8% of the differences are within 200 m.

**Figure 11.**The frequency distribution histogram of the differences between BAT_VGG2021 and ship soundings (

**a**), and differences between BAT_VGG2021 and SIO topo_20.1.nc model (

**b**).

**Figure 12.**The frequency distribution histogram of the differences between BAT_VGG2021 and ship soundings in north Pacific (

**a**), south Pacific (

**b**), north Atlantic (

**c**), south Atlantic (

**d**), and Indian Ocean (

**e**).

**Figure 13.**Distribution of ship soundings in the northeastern Indian Ocean. The black lines indicate ship soundings used to construct seafloor model with satellite data, noted as BAT_Pre. The colored depths were multibeam grids of MH370 searching area, and were used to assess the predicted model as independent data.

**Figure 14.**A 1′ $\times $ 1′ seafloor topography model (BAT_Pre) predicted from sparse ship soundings and satellite VGG model. The thinblack lines indicate sparsely distributed ship depths used to construct BAT_Pre model. The model reveals seamounts’ details and “troughs” along southeast Indian Ridge very well.

**Figure 15.**A 1′ $\times $ 1′ seafloor topography model gridded from ship-alone data using GMT tools. The thinblack lines indicate all ship soundings used to build BAT_Ship model. The model shows seafloor topography of large scales but loses many details.

**Table 1.**Theoretical crustal model for calculating admittance ${Z}_{topo-grav}\left(k\right)$ and ${Z}_{topo-grad}\left(k\right)$.

Parameters | Notation | Value |
---|---|---|

Density of water | ${\rho}_{w}$ | 1030 kg/m³ |

Density of crust | ${\rho}_{c}$ | 2800 kg/m³ |

Density of mantle | ${\rho}_{m}$ | 3350 kg/m³ |

Mean crustal thickness | T | 7 km |

Mean water depth | D | 4 km |

Effective elastic thickness | T_{e} | 3, 5, 10, 25 km |

Young’s modulus | E | ${10}^{11}$N/m² |

Poisson’s ratio | $\upsilon $ | 0.25 |

Data Sources | Descriptions | Processes | Data Provider |
---|---|---|---|

Topography modelSIO topo_20.1.nc | Seafloor topography at 1 arc-minute resolution derived from altimetric gravity anomalies. | Low-pass filtered to construct model at wavelengths longer than 160 km. | SIO, UCSD |

Altimetric VGGSIO curv_30.1.nc | Model derived from satellite altimetric missions at 1 arc-minute resolution. | Band-pass filtered and downward continued to constrain seafloor topography at 15–160 km wavelength bands | |

Multibeam grids | Shipboard multibeam grid. | Re-sampled at each 15 arc-second grid | JAMSTEC |

Multibeam grids | AusSeabed-2018 at 50 m resolution; MH370 searching seafloor topography at 150 m resolution; Kerguelen seafloor topography model at 100 m resolution; Macquarie seafloor topography model at 100 m resolution. | Re-sampled at each 15 arc-second grid | GA |

Multibeam grids | Depth grids at about 100 m ~ 2 km resolution, provided by website AutoGrid service. | Re-sampled at each 15 arc-second grid | NCEI |

Single-beam depths | ~74.66 million points | Evaluated by comparing with SIO topo_20.1.nc model | NCEI |

**Table 3.**The statistics of differences between global seafloor topography models and ship soundings.

Region | Model | Minimums (m) | Maximums (m) | Mean (m) | STD (m) |
---|---|---|---|---|---|

North Pacific (120°~280°E, 0°~70°N) | BAT_VGG2021 | −204.6 | 204.5 | 0.7 | 39.6 |

SIO topo.20.1.nc | −207.3 | 207.3 | −0.2 | 45.0 | |

DTU18BAT | −315.1 | 315.1 | 5.7 | 65.8 | |

BAT_VGG2014 | −507.7 | 507.7 | 22.2 | 125.1 | |

ETOPO1 | −497.1 | 497.1 | 11.2 | 119.7 | |

GEBCO_08 | −757.9 | 757.9 | 29.6 | 184.7 | |

South Pacific (120°~300°E, −75°~0°N) | BAT_VGG2021 | −246.0 | 246.0 | 1.1 | 46.7 |

SIO topo.20.1.nc | −258.7 | 258.7 | 1.3 | 53.1 | |

DTU18BAT | −420.6 | 420.6 | 8.0 | 91.2 | |

BAT_VGG2014 | −595.0 | 595.1 | 30.6 | 156.2 | |

ETOPO1 | −612.2 | 612.2 | 11.9 | 159.5 | |

GEBCO_08 | −926.8 | 926.8 | 20.2 | 225.9 | |

North Atlantic (280°~360°E, 0°~70°N) | BAT_VGG2021 | −201.6 | 201.7 | 1.3 | 39.8 |

SIO topo.20.1.nc | −219.1 | 219.1 | 0.1 | 49.2 | |

DTU18BAT | −288.0 | 288.0 | 3.1 | 63.6 | |

BAT_VGG2014 | −451.3 | 451.3 | 14.1 | 119.0 | |

ETOPO1 | −480.5 | 480.6 | 5.2 | 116.2 | |

GEBCO_08 | −642.4 | 642.0 | 28.0 | 161.7 | |

South Atlantic (−60°~20°E, −75°~0°N) | BAT_VGG2021 | −508.0 | 508.0 | 0.8 | 77.6 |

SIO topo.20.1.nc | −319.2 | 319.3 | 1.8 | 54.5 | |

DTU18BAT | −400.5 | 400.5 | 4.3 | 71.4 | |

BAT_VGG2014 | −519.3 | 519.0 | 10.2 | 120.1 | |

ETOPO1 | −546.1 | 546.1 | 6.7 | 126.1 | |

GEBCO_08 | −753.0 | 753.0 | 24.9 | 192.9 | |

Indian Ocean (20°~120°E, −75°~26°N) | BAT_VGG2021 | −232.6 | 232.6 | 1.3 | 41.7 |

SIO topo.20.1.nc | −264.1 | 264.2 | −0.2 | 55.6 | |

DTU18BAT | −420.7 | 420.7 | 6.0 | 100.1 | |

BAT_VGG2014 | −593.9 | 593.9 | 20.9 | 160.3 | |

ETOPO1 | −581.9 | 581.9 | 7.6 | 150.5 | |

GEBCO_08 | −663.1 | 663.1 | 15.7 | 166.3 |

**Table 4.**The statistics of differences between BAT_Pre model, BAT_Ship model, and multibeam grids in MH370 searching area.

Model | Minimums (m) | Maximums (m) | Mean (m) | STD (m) |
---|---|---|---|---|

BAT_Pre | −416.1 | 416.1 | 1.9 | 106.2 |

BAT_Ship | −639.4 | 639.4 | 3.6 | 148.5 |

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## Share and Cite

**MDPI and ACS Style**

Hu, M.; Li, L.; Jin, T.; Jiang, W.; Wen, H.; Li, J.
A New 1′ × 1′ Global Seafloor Topography Model Predicted from Satellite Altimetric Vertical Gravity Gradient Anomaly and Ship Soundings BAT_VGG2021. *Remote Sens.* **2021**, *13*, 3515.
https://doi.org/10.3390/rs13173515

**AMA Style**

Hu M, Li L, Jin T, Jiang W, Wen H, Li J.
A New 1′ × 1′ Global Seafloor Topography Model Predicted from Satellite Altimetric Vertical Gravity Gradient Anomaly and Ship Soundings BAT_VGG2021. *Remote Sensing*. 2021; 13(17):3515.
https://doi.org/10.3390/rs13173515

**Chicago/Turabian Style**

Hu, Minzhang, Li Li, Taoyong Jin, Weiping Jiang, Hanjiang Wen, and Jiancheng Li.
2021. "A New 1′ × 1′ Global Seafloor Topography Model Predicted from Satellite Altimetric Vertical Gravity Gradient Anomaly and Ship Soundings BAT_VGG2021" *Remote Sensing* 13, no. 17: 3515.
https://doi.org/10.3390/rs13173515