Study on the stable and high-precision downward extension method of airborne gravity anomaly data

The essence of the downward continuation of airborne gravity anomalies is to solve the first kind of Fredholm integral equation, which is an ill-posed problem. Stable and high-precision downward continuation methods have always been a research hotspot in this field. This research has been conducted on data expansion to suppress edge effects and enhance computational efficiency through the use of the fast Fourier transform. To increase the depth of downward continuation, improve stability, and enhance continuation accuracy, six downward continuation methods—the integral iterative method, Tikhonov regularization iterative method, Barzilai–Borwein (BB) method, iterative least squares method, semi-iterative method, and conjugate gradient normal residual (CGNR) method—were comparatively analyzed using simulated and actual airborne gravity anomaly data. The results indicated that the BB method has the fastest convergence rate under the ideal condition of no noise in the data, with a low initial mean square error of continuation and high accuracy, thus showing a clear advantage. The iterative least squares method is insufficiently stable. The Tikhonov regularization iterative method produces an increase in error before reaching a stable continuation state, and it has a relatively high initial mean square error with a continuation effect that is generally similar to that of the other methods. After adding noise to the simulated data, the improved CGNR method showed the best noise suppression effect. Moreover, this method is capable of achieving stable downward continuation in the process of actual data continuation, with a continuation accuracy that is superior to that of the other five methods.