Gravity anomalies determined from mean sea surface model data over the Gulf of Mexico
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Abstract: With the improvements in the density and quality of satellite altimetry data, a high-precision and high-resolution mean sea surface model containing abundant information regarding a marine gravity field can be calculated from long-time series multi-satellite altimeter data. Therefore, in this study, a method is proposed for determining marine gravity anomalies from a mean sea surface model. Taking the Gulf of Mexico (15°–32°N, 80°–100°W) as the study area and using a removal-recovery method, the residual gridded deflections of the vertical (DOVs) are calculated by combining the mean sea surface, mean dynamic topography, and XGM2019e_2159 geoid, and then using the inverse Vening-Meinesz method to determine the residual marine gravity anomalies from the residual gridded DOVs. Finally, residual gravity anomalies are added to the XGM2019e_2159 gravity anomalies to derive marine gravity anomaly models. In this study, the marine gravity anomalies are estimated with mean sea surface models CNES_CLS15MSS, DTU21MSS, and SDUST2020MSS and the mean dynamic topography models CNES_CLS18MDT and DTU22MDT. The accuracy of the marine gravity anomalies derived by the mean sea surface model is assessed based on ship-borne gravity data. The results show that the difference between the gravity anomalies derived by DTU21MSS and CNES_CLS18MDT and those of the ship-borne gravity data is optimal. With an increase in the distance from the coast, the difference between the gravity anomalies derived by mean sea surface models and ship-borne gravity data gradually decreases. The accuracy of the difference between the gravity anomalies derived by mean sea surface models and those from ship-borne gravity data is optimal at a depth of 3–4 km. The accuracy of the gravity anomalies derived by the mean sea surface model is high.
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Figure 1. Study area and ship-borne gravity trace distribution. The thick solid red line is ship-borne gravity trace; the light gray area is land; the dark gray area corresponds to the marine regions that have been excluded from consideration or inclusion in this study.
Figure 3. Flowchart of data processing of deriving gravity anomalies using the mean sea surface model.
Figure 4. Gravity anomalies derived from mean sea surface models: Grav-1 (a); Grav-2 (b); Grav-3 (c); Grav-4 (d); Grav-5 (e); Grav-6 (f).
Figure 5. Differences among six marine gravity anomaly models. a. Grav-1-Grav-2; b. Grav-1-Grav-3; c. Grav-1-Grav-4; d. Grav-1-Grav-5; e. Grav-1-Grav-6; f. Grav-2-Grav-3; g. Grav-2-Grav-4; h. Grav-2-Grav-5; i. Grav-2-Grav-6; j. Grav-3-Grav-4; k. Grav-3-Grav-5; l. Grav-3-Grav-6; m. Grav-4-Grav-5; n. Grav-4-Grav-6; o. Grav-5-Grav-6.
Figure 6. Histogram distribution of differences among six marine gravity anomaly models. The red line is the normal distribution curve. a. Grav-1-Grav-2; b. Grav-1-Grav-3; c. Grav-1-Grav-4; d. Grav-1-Grav-5; e. Grav-1-Grav-6; f. Grav-2-Grav-3; g. Grav-2-Grav-4; h. Grav-2-Grav-5; i. Grav-2-Grav-6; j. Grav-3-Grav-4; k. Grav-3-Grav-5; l. Grav-3-Grav-6; m. Grav-4-Grav-5; n. Grav-4-Grav-6; o. Grav-5-Grav-6.
Figure 7. Histogram distribution of difference between marine gravity anomaly models and the ship-borne gravity data. The red line is the normal distribution curve. a. Grav-1-NCEI; b. Grav-2-NCEI; c. Grav-3-NCEI; d. Grav-4-NCEI; e. Grav-5 -NCEI; f. Grav-6-NCEI.
Figure 8. Distribution of differences between Grav-3 and the ship-borne gravity data at depth >4 km
and seafloor topography in this area. The light gray area is land; the dark gray area represents the marine region.
Table 1. Basic information of global mean sea surface models
Mean sea surface model Grid size Coverage area Altimeter data CNES_CLS15MSS 1'×1' 80°S–84°N T/P+J1+J2+E2+En+GFO+C2 DTU21MSS 1'×1' 90°S–90°N T/P+J1+J2+E1+E2+En+Ic+Ge+GFO+C2+S3A SDUST2020MSS 1'×1' 80°S–84°N T/P+J1+J2+J3+E1+E2+GFO+En+H2+C2+Al+S3A Note: T/P, Topex/Poseidon; J1, Jason-1; J2, Jason-2; J3, Jason-3; E1, ERS-1; E2, ERS-2; En, Envisat; Ic, Icesat; Ge, Geosat; H2, HY-2A; C2, Cryosat-2; Al, Saral/Altika; S3A, Sentinel-3A. 
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Table 2. Statistics of the difference between the ship-borne gravity data and XGM2019e_2159 gravity anomaly model
State Data number Max/ mGal Min/ mGal Mean/ mGal STD/ mGal RMS/ mGal Before correction 266 361 181.11 -90.51 0.53 7.10 7.12 After correction 251 023 43.63 -40.73 0.04 3.98 3.98 After excluding routes1) 249 908 38.34 -36.31 0.04 3.91 3.91 Note: 1) Excluded routes are routes v2103 and u271gm.
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Table 3. Statistical information of abnormal ship-borne routes
Route Data number Time STD before correction /mGal STD after correction /mGal v2103 680 1965/03/01–1965/03/10 15.76 15.03 u271gm 443 1971/06/27–1971/07/08 21.95 21.95
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Table 4. Statistics of the difference between marine gravity field model and the ship-borne gravity data
Model Max/mGal Min/mGal Mean/mGal STD/mGal RMS/mGal Grav-1 38.53 –36.17 0.07 3.71 3.71 Grav-2 38.49 –37.64 0.09 3.72 3.72 Grav-3 39.31 –35.81 0.07 3.66 3.66 Grav-4 39.30 –35.79 0.08 3.67 3.67 Grav-5 38.19 –35.97 0.07 3.77 3.77 Grav-6 38.20 –35.94 0.10 3.76 3.76 XGM2019e_2159 38.34 –36.31 0.04 3.91 3.91
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Table 5. Statistics of the difference between marine gravity anomaly models and the ship-borne gravity data at different distances from coastline
Model Distance from coastline /km Data number Max /mGal Min /mGal Mean /mGal STD /mGal RMS /mGal Grav-1 >0 249908 38.53 -36.17 0.07 3.71 3.71 >10 247401 38.53 -36.17 0.07 3.67 3.67 >20 241044 38.53 -36.17 0.07 3.59 3.59 >30 232606 38.53 -36.17 0.08 3.53 3.54 >40 223320 38.53 -36.17 0.09 3.50 3.50 >50 214231 37.81 -36.17 0.11 3.48 3.48 Grav-2 >0 249908 38.49 -37.64 0.09 3.72 3.72 >10 247401 38.49 -36.16 0.08 3.67 3.67 >20 241044 38.49 -36.16 0.07 3.59 3.59 >30 232606 38.49 -36.16 0.08 3.54 3.54 >40 223320 38.49 -36.16 0.09 3.50 3.51 >50 214231 37.88 -36.16 0.11 3.48 3.49 Grav-3 >0 249908 39.31 -35.81 0.07 3.66 3.66 >10 247401 39.31 -35.81 0.07 3.63 3.63 >20 241044 39.31 -35.81 0.07 3.56 3.56 >30 232606 39.31 -35.81 0.07 3.50 3.50 >40 223320 39.31 -35.81 0.09 3.47 3.47 >50 214231 37.91 -35.81 0.10 3.45 3.45 Grav-4 >0 249908 39.30 -35.79 0.08 3.67 3.67 >10 247401 39.30 -35.79 0.07 3.63 3.63 >20 241044 39.30 -35.79 0.07 3.56 3.56 >30 232606 39.30 -35.79 0.07 3.51 3.51 >40 223320 39.30 -35.79 0.09 3.48 3.48 >50 214231 37.99 -35.79 0.10 3.46 3.46 Grav-5 >0 249908 38.19 -35.97 0.07 3.77 3.77 >10 247401 38.19 -35.97 0.06 3.74 3.74 >20 241044 38.19 -35.97 0.07 3.66 3.66 >30 232606 38.19 -35.97 0.08 3.60 3.60 >40 223320 38.19 -35.97 0.09 3.57 3.57 >50 214231 38.19 -35.97 0.10 3.55 3.55 Grav-6 >0 249908 38.20 -35.94 0.10 3.76 3.76 >10 247401 38.20 -35.94 0.09 3.74 3.74 >20 241044 38.20 -35.94 0.08 3.66 3.66 >30 232606 38.20 -35.94 0.09 3.60 3.61 >40 223320 38.20 -35.94 0.10 3.57 3.57 >50 214231 38.20 -35.94 0.11 3.55 3.55
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Table 6. Statistics of differences between marine gravity anomaly models and the ship-borne gravity data measured values at different depths
Model depth/km Data number Max /mGal Min /mGal Mean /mGal STD /mGal RMS /mGal Grav–1 <1 93723 24.69 –34.73 –0.29 3.33 3.34 1–2 48005 37.81 –36.17 0.07 4.31 4.31 2–3 37387 38.53 –33.80 –0.44 3.87 3.89 3–4 56472 34.80 –35.78 –0.35 3.22 3.23 >4 14321 37.72 –33.56 0.43 4.92 4.94 Grav–2 <1 93723 24.71 –37.64 –0.26 3.35 3.36 1–2 48005 37.88 –36.16 0.09 4.31 4.31 2–3 37387 38.49 –33.86 0.43 3.87 3.90 3–4 56472 34.74 –35.77 0.35 3.22 3.24 >4 14321 37.73 –33.59 0.42 4.92 4.94 Grav–3 <1 93723 25.76 –33.05 –0.29 3.25 3.26 1–2 48005 37.91 –35.81 0.08 4.24 4.24 2–3 37387 39.31 –33.36 0.43 3.83 3.86 3–4 56472 35.85 –35.62 0.35 3.20 3.22 >4 14321 37.33 –33.82 0.42 4.91 4.93 Grav–4 <1 93723 25.80 –33.07 –0.26 3.25 3.26 1–2 48005 37.99 –35.79 0.09 4.25 4.25 2–3 37387 39.30 –33.46 0.41 3.84 3.86 3–4 56472 35.80 –35.61 0.35 3.21 3.23 >4 14321 37.37 –33.86 0.41 4.91 4.92 Grav–5 <1 93723 23.99 –35.74 –0.30 3.30 3.32 1–2 48005 38.12 –35.97 0.06 4.47 4.47 2–3 37387 38.19 –34.07 0.44 3.95 3.97 3–4 56472 36.29 –35.31 0.35 3.25 3.27 >4 14321 37.69 –34.41 0.48 5.02 5.04 Grav–6 <1 93723 24.04 –35.51 –0.25 3.29 3.30 1–2 48005 38.17 –35.94 0.11 4.47 4.47 2–3 37387 38.20 –34.09 0.43 3.95 3.97 3–4 56472 36.22 –35.31 0.35 3.25 3.27 >4 14321 37.70 –34.44 0.48 5.02 5.04
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Table 7. Statistics of differences between marine gravity anomaly models and the ship-borne gravity data at different submarine topography gradients
Model Seafloor topographic gradient (m/arcmin*) Data number Max /mGal Min /mGal Mean /mGal STD /mGal RMS /mGal Grav-1 <50 182668 37.81 –35.78 0.07 3.25 3.25 50–100 28246 37.29 –31.79 –0.03 4.14 4.14 100–150 14099 34.07 –33.25 0.07 4.57 4.57 150–200 7893 37.72 –33.56 0.18 4.74 4.74 200–250 5060 35.58 –30.24 0.06 4.93 4.93 >250 11925 38.53 –36.17 0.30 6.01 6.01 Grav-2 <50 182668 37.88 –35.77 0.09 3.25 3.25 50–100 28246 37.29 –37.60 –0.03 4.15 4.15 100–150 14099 34.01 –37.64 0.04 4.66 4.66 150–200 7893 37.73 –33.59 0.19 4.75 4.75 200–250 5060 35.54 –30.61 0.04 4.99 4.99 >250 11925 38.49 –36.16 0.32 6.01 6.02 Grav-3 <50 182668 37.91 –35.62 0.06 3.22 3.22 50–100 28246 36.85 –31.76 –0.02 4.06 4.06 100–150 14099 34.82 –34.04 0.11 4.40 4.40 150–200 7893 37.33 ––33.82 0.18 4.67 4.67 200–250 5060 35.55 –30.20 0.05 4.93 4.93 >250 11925 39.31 –35.81 0.32 5.93 5.93 Grav-4 <50 182668 37.99 –35.61 0.08 3.22 3.22 50–100 28246 36.88 –31.98 –0.03 4.07 4.07 100–150 14099 34.79 –34.06 0.07 4.45 4.45 150–200 7893 37.37 –33.86 0.18 4.68 4.68 200–250 5060 35.58 –30.24 0.06 4.93 4.93 >250 11925 39.30 –35.79 0.33 5.93 5.94 Grav-5 <50 182668 38.12 –35.74 0.06 3.27 3.28 50–100 28246 36.99 –31.05 –0.02 4.24 4.24 100–150 14099 33.17 –33.38 0.14 4.58 4.59 150–200 7893 37.69 –34.41 0.18 4.89 4.89 200–250 5060 35.95 –30.33 0.04 5.14 5.14 >250 11925 38.19 –35.97 0.30 6.20 6.21 Grav-6 <50 182668 38.17 –35.51 0.09 3.27 3.27 50–100 28246 36.98 –31.32 –0.01 4.24 4.24 100–150 14099 33.17 –33.48 0.13 4.59 4.59 150–200 7893 37.70 –34.44 0.21 4.90 4.90 200–250 5060 36.04 –30.34 0.07 5.14 5.14 >250 11925 38.20 –35.94 0.33 6.20 6.21
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