High-precision downward continuation of potential fields algorithm utilizing adaptive damping coefficient of generalized minimal residuals

Abstract

The downward continuation of potential fields is a process of calculating their values in a lower plane based on those of a certain plane. This technology is not only a data processing method for resource exploration but also plays an extremely important role in military applications. However, the downward continuation of potential fields is a typical linear inverse problem that is ill-posed. Generalized minimal residuals (GMRES) is an effective solution to ill-posed inverse problems, but it is unstable under the condition wherein the GMRES is directly applied in the calculation process. Moreover, the long-term behavior of its iterative computation is a disordered, divergent result. Therefore, to obtain stable solutions, GMRES is applied to solve the normal equations of the downward continuation of potential fields; it is also used to prequalify for occasional interruptions in the operation process by adding the damping coefficient, thus strengthening the stability conditions of the equations of residual minimization. Finally, the stable downward continuation of the potential fields method is proposed. As indicated by the theoretical data and the measured testing data, the method proposed in this paper has the advantages of high-precision and excellent stability. Furthermore, compared with the Tikhonov iteration method, the proposed method avoids the need to choose regularization parameters.