A Magnetic Potential-field Downward Continuation Method Based on Accelerated Landweber Iteration

Abstract

Abstract A high-precision geomagnetic database is the basis of geomagnetic matching navigation. In the construction of a geomagnetic database, it is necessary to use magnetic field extension technology to construct the vertical height relationship of geomagnetic data, in which downward continuation is mathematically ill-posed, and Landweber iterative method is a common solution. However, the convergence rate of the Landweber iterative method for the “non-smooth“ solution is very slow, resulting in low delay accuracy in dealing with local magnetic anomalies. Therefore, to solve the problem of slow convergence of the Landweber iterative method, a downward continuation method based on accelerated Landweber iteration is proposed in this paper. In the framework of the iterative method, stable upward continuation is used to connect the observation surface with the magnetic field values on the plane with the same height as upward continuation and downward continuation. Then the residual term is constructed by the vertical first-order derivative relation, and then the residual term is modified by using the low-pass filtering characteristic of the upward continuation operator to suppress the high-frequency noise in the residual term and finally update the iterative value. The simulation results of magnetic field models with different field source depths show that the improved method has faster convergence speed and higher extension accuracy when dealing with shallow local anomalies and deep regional anomalies, and under the condition of shallow source model, the continuation error of the improved algorithm is only 60% of that of Landweber iterative method. At the same time, the measured data also verify that the improved method can achieve fast and high-precision downward continuation of a magnetic field.