Using a dual-layer gradient-boosted equivalent sources method to grid large magnetic datasets.

Towards the construction of a new magnetic map of Antarctica, we investigate the use of gradient-boosted equivalent sources to model data from aeromagnetic surveys. Airborne surveys have larger spacing between adjacent lines compared with along-line spacing. By using the equivalent source technique, gravity and magnetic data can be interpolated onto a regular grid at constant height. This method is particularly useful to prepare the data for further use, such as modelling crustal structures and geological interpretation. The equivalent source technique uses a finite layer of sources to generate the same field as the observed data. These sources are then used to predict the field in unobserved locations. However, estimating the source coefficients that best fit the observed data is computationally demanding. To overcome this problem, the source coefficients are estimated in overlapping windows and carried out iteratively, similar to the gradient boosting method used in machine learning. At each iteration, the sources are fit to the field residuals from the previous iteration. Here we apply the gradient-boosted equivalent sources method to interpolate total-field anomaly observations and convert them to the norm of the anomalous field. We use two layers of equivalent sources at different depths to fit both the regional field and the field due to the shallower sources. We demonstrate using synthetic surveys and an Antarctic magnetic dataset that our dual-layer gradient-boosted equivalent sources are able to produce grids of both the total-field anomaly and the norm of the anomalous field accurately and with a low computational cost.