Gravity Gradient Field Transformation by Enhanced Physics-Guided Multitask Network

The transformation of the gravity field into the gravity gradient data is an important topic in geophysical research, playing a key role in mineral boundary delineation and geological structure interpretation. However, traditional wavenumber-domain and spatial-domain transformation methods are often susceptible to noise and boundary effects, thereby limiting the accuracy, stability, and adaptability of the transformed gravity gradient data in complex geological settings. In this study, we introduce a new approach to the solution of this problem based on multi-task learning U-Net deep Neural Network. First, we propose an innovative approach to construct geological density model datasets using probabilistic constraints. Next, we utilize the Physics-Guided Multi-Task (PGMT) Network, a multi-layer CNN module, to enable the transition from single-task to multi-task outputs, capturing interdependencies among gravity gradient components. Finally, we incorporate the Laplace equation into the network architecture as a physical constraint, ensuring the three gravity gradient components adhere to the solid physical relationships. Numerical studies show that this network effectively alleviates noise and boundary effects. The determination coefficient (R²) is above 0.98, significantly reducing the root mean square error (RMSE), thereby greatly improving the prediction accuracy and robustness. After verification using the total tensor gradient gravity data of the Nordkapp Basin in Norway, the average error between the predicted gravity gradient data and the on-site measurement results is less than about 1%. These results demonstrate that the PGMT Network provides high precision and reliability in transforming low-order gravity data into high-order gravity gradient data, confirming its effectiveness for gravity field transformations.