# 3D Gravity Inversion on Unstructured Grids
## 4 Results
### Field Data Inversion  
The survey area Vinton Dome is located in southwestern Louisiana, USA. We used a subset of the survey area for this study that covers approximately 16 km\({}^{2}\) in the middle of the survey area, which was acquired and processed by Bell Geospace in 2008 [29]. Before we inverted the data, a second-order trend surface was removed to get rid of background, and an upward continuation of 100 m was done to eliminate the shallow local anomalies. The processed gravity data is displayed in Figure 8.  
Inversion area is 4 km \(\times\) 4 km \(\times\) 1 km with 169,949 cells and 1681 survey stations. The station interval was 100 m. The upper-lower limit of density was assumed to be [0 g/cm\({}^{3}\), 0.55 g/cm\({}^{3}\)] and clusters **C** = {0 g/cm\({}^{3}\), 0.55 g/cm\({}^{3}\)} was used in our inversions. Smooth inversion, conventional and improved FCM clustering inversion are implemented with a gradient-based strategy. We specifically point the \(x\)-, \(y\)-and \(z\)-axis to the East, North, and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Result** & **Inversion Method** & **Strategy** & **Trade-Off Parameter** \\ \hline Figure 4a & NaN & Conventional strategy & 0 \\ Figure 4b & NaN & Gradient-based strategy & 0 \\ Figure 5a & Smooth inversion & Conventional strategy & \(1\times 10^{-2}\) \\ Figure 5b & Smooth inversion & Conventional strategy & \(5\times 10^{-2}\) \\ Figure 5c & Smooth inversion & Gradient-based strategy & \(1\times 10^{1}\) \\ Figure 5d & Smooth inversion & Gradient-based strategy & \(5\times 10^{1}\) \\ Figure 6a & New FCM inversion & Conventional strategy & \(1\times 10^{-3}\) \\ Figure 6b & New FCM inversion & Conventional strategy & \(3\times 10^{-3}\) \\ Figure 6c & New FCM inversion & Gradient-based strategy & \(3\times 10^{0}\) \\ Figure 6d & New FCM inversion & Gradient-based strategy & \(5\times 10^{0}\) \\ Figure 7a & Focusing inversion & Gradient-based strategy & method of [PERSON] et al. [17] \\ Figure 7b & Conventional FCM inversion & Gradient-based strategy & method of [PERSON] et al. [17] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Inversion result list with different methods, strategies, and parameters. Figure 8: Field data subset from Vinton Dome area after trend surface removing and upward continuation (data courtesy of [PERSON] from Bell Geospace). vertically downwards. Figures 9-11 show the slices of the recovered model on \(x\)-\(y\)-, \(x\)-\(z\)-, and \(y\)-\(z\)-planes of different inversion methods. Many surveys and researches have been done at the Vinton Dome. According to [PERSON] et al. [30], the Vinton salt dome is composed of a well-defined massive cap rock extending above the salt rock. This cap rock is formed by gypsum and anhydrite that is embedded in sediments characterized by intercalated layers of sandstone and shale. These researches indicate that the cap rock has a top depth of 160 m and a density of 2.75 g/cm\({}^{3}\), while the underlying media have a density of 2.20 g/cm\({}^{3}\)[31]. Besides, the sediment around slat dome has a density of about 2.0 g/cm\({}^{3}\)-2.37 g/cm\({}^{3}\). Thus, we assumed the relative density of cap rock to be 0.55 g/cm\({}^{3}\), and the observed gravity data were predominantly caused by the cap rock. From previous work in this area [30; 31; 32; 33], it is known that the extension of the anomalous body is about 1200 m in the west-east direction, 900 m in the north-south direction, 200 m in \(z\)-direction, and the top depth is about 175 m.  
The result of smooth inversion is blur and fuzzy in Figure 9, and the 3D extension size of the cap rock is much larger than the real geological model. In both Figures 10 and 11, the maximum relative density is 0.55 g/cm\({}^{3}\), and a more compact model is yielded. The extensions of the anomalous body are well consistent with the known information.