# Three-Dimensional Broad Learning Gravity Data Inversion Using Single-Anomaly Training Samples
## 3 Results and Evaluation of Performance
### Field Data Application  
This section further examines the inversion capability of the proposed 3D gravity data inversion method through a real-world application. The field data were obtained from a gravity survey conducted by Bell Geospace over the Vinton salt dome, located in southwest Louisiana, USA. The salt dome lies within the onshore Gulf of Mexico region, which has served as a major oil and gas production area for over a century [47,48]. Most reservoirs in this region are predominantly found along the flanks of salt domes, as structural traps are formed by the upward movement of the salt. The ability to accurately detect the size and shape of the salt dome significantly affects the analysis of these structural traps, which is critical for identifying and locating oil and gas reservoirs. In particular, the proposed inversion method was applied for the detection of the size and shape of the salt dome. Figure 10 presents the surface gravity anomaly map of the Vinton salt dome, where the observation area is limited to 4 km \(\times\) 4 km. As shown in the figure, a density anomaly with a radius of approximately 1 km is clearly visible. Figure 8: Numerical density model with varied shapes, densities, and positions and corresponding surface gravity anomaly observations. **(a)** Three-dimensional representation of the actual density model. **(b)** Surface gravity anomaly observations. Figure 9: Inversion results of the numerical density model with varied shapes, densities, and positions. **(a)** Three-dimensional representation of the inverted density model. **(b)** Gravity anomaly data forwarded from the inversion result. **(c)** Residuals between inverted and observed surface gravity anomaly data. Like the numerical simulations, the inverted density model of the subsurface was instantly obtained by inputting the surface gravity anomaly data into the trained network. Figure 11 presents the inversion results of the field data over the Vinton salt dome. As illustrated in Figure 11a, a density anomaly ranging from 0. to 0.45 g/cm\({}^{3}\) was identified. Furthermore, the inverted model was visualized in 2D through both a horizontal slice (Figure 11b) and two vertical slices (Figure 11c), offering further insights into the model. It is evident that the depths to the top and bottom of the density anomaly are 150 m and 400 m, respectively. To further evaluate the inverted model, theoretical surface gravity data (Figure 11d) were generated by inputting the inverted density model into the forward modeling function. This allowed for the calculation of the residual map (Figure 11e) and the coefficient of determination (R\({}^{2}\)) between the inverted and observed surface gravity anomaly data. The inversion residuals primarily range from \(-0.1\) to 0.1 mGal, and the R\({}^{2}\) value is 0.9931. The inverted gravity anomaly ranges from \(-1.0\) to 2.5 mGal, indicating strong consistency with the gravity anomalies shown in Figure 10. To validate the accuracy of the inverted results in this study, a comparison was made between the inversion results for the field data over the Vinton salt dome and those from previous works, as shown in Table 1. It can be observed that the top depths of the salt dome obtained by different methods are generally consistent, while there are significant differences in the bottom depths. This discrepancy occurs because the gravity field decreases quadratically with increasing source depth, which leads to reduced depth resolution in gravity inversion [46]. In particular, the bottom boundary obtained from our results is closer to the geological data [49]. This comparison confirms the reasonableness of the inverted results. The application of field data reinforces the effectiveness of the proposed 3D gravity inversion method.