# A Scalable and Consistent Method for Multi-Component Gravity-Gradient Data Processing
## 4 Real Data Applications
### Kauring  
With funding from the Western Australian government's Exploration Incentive Scheme, a matching industry contribution, and support from the Geological Survey of Western Australia and Geoscience Australia, the Kauring test site situated near York in  
Figure 10: Synthetic FTG data. The transformation results: (**a**) the predicted \(\mathbf{g}_{zz}\) component and (**b**) the predicted \(\|\
abla\mathbf{g}_{\mathbf{z}}\|\).  
Western Australia, was established to support coordinated geophysical data collection [42]. The site is located in a farming region characterized by gently undulating granitic terrain, featuring occasional incised valleys, with a maximum topographic relief of about 75 m. According to [43], the gravity anomaly at the Kauring test site is attributed to iron-rich rocks underlying a small topographic rise near the center of the map. Ref. [44] interpreted that the amplitude of the complete Bouguer gravity anomaly field in the Kauring test site gradually decreases from west to east. Higher anomaly values are concentrated in the southwestern part of the study area, while lower values are found in the northeast. Although it remains uncertain whether the linear gravity ridge is produced by similar rocks beneath the soil cover, airborne geophysical surveys support this interpretation.  
The observed Falcon AGG components \(\mathbf{g}_{xy}\) and \(\mathbf{g}_{uv}\) (Figure 11a,b) over the Kauring test site, Australia, consists of 114 northwest-southeast oriented lines with line spacing of 50 m, totaling 164,624 observed points at the \(z\)-coordinates shown in Figure 4. We have transformed the gravity-gradient data from the north-east system to the data system (step 1 of Algorithm 1) by using \(\psi=-30^{\circ}\) (Equation (12)). The observed Falcon AGG data, transformed to the data system, is available in the Supplementary Materials (see Figure S3). We then interpolated the dataset in the data system (step 2 of Algorithm 1) to obtain 1275 points in each of the 114 flight lines, which corresponds to 145,350 reduced points. We placed one equivalent source directly beneath each interpolated point, at a constant depth of \(z_{c}=23.54\) m.  
After approximately 120 iterations and just a few seconds of computation (Figure 12c), we estimated a mass distribution that fits the \(\mathbf{g}_{xy}\) and \(\mathbf{g}_{uv}\) components. Using this model, we calculated the predicted data and the corresponding residuals (Figure 12a,b) for the two AGG components in the north-east coordinate system. The insets in these figures show the histograms of the residuals, which have means of 0.11 and \(-\)1.22 eotvos, and standard deviations of 3.88 and 3.40 eotvos, for the \(\mathbf{g}_{xy}\) and \(\mathbf{g}_{uv}\) components, respectively. Combining the RMSE curve (Figure 12c), which stabilizes below 4 evotos, with the residual distributions (insets in Figure 12a,b) supports the conclusion that the data are well-fitted within the expected noise level.  
Figure 11: Real data over Kauring test site, Australia. Observed Falcon AGG components (**a**) \(\mathbf{g}_{xy}\) and (**b**) \(\mathbf{g}_{uv}\) obtained with the Falcon AGG system at 164,624 observation points.  
The predicted \(\mathbf{g}_{zz}\) and \(\|\
abla\mathbf{g}_{z}\|\), shown in Figures 7b and 13a, respectively, reveal strong linear anomalies in the southwestern part and a set of isolated anomalies in the northeastern part. These results are consistent with those reported in [44].