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.

势场的向下延续是基于某个平面的值在较低平面中计算其值的过程。该技术不仅是资源勘探的数据处理方法，而且在军事应用中起着极其重要的作用。但是，势场的向​​下连续是典型的线性逆问题，不适当地解决。广义最小残差（GMRES）是解决不适定逆问题的有效方法，但是在将GMRES直接应用于计算过程的条件下，它是不稳定的。而且，其迭代计算的长期行为是无序的，发散的结果。因此，为了获得稳定的解，应用GMRES求解势场向下连续的正态方程。它也可以通过增加阻尼系数来预判操作过程中偶尔出现的中断，从而加强残差最小化方程的稳定性条件。最后，提出了势场方法的稳定向下延续。如理论数据和实测数据所示，该方法具有精度高，稳定性好等优点。此外，与Tikhonov迭代方法相比，该方法避免了选择正则化参数的需要。如理论数据和实测数据所示，该方法具有精度高，稳定性好等优点。此外，与Tikhonov迭代方法相比，该方法避免了选择正则化参数的需要。如理论数据和实测数据所示，该方法具有精度高，稳定性好等优点。此外，与Tikhonov迭代方法相比，该方法避免了选择正则化参数的需要。