The equivalent source method offers a potential means for continuing and manipulating magnetic data between arbitrary surfaces. However, it ultimately suffers from a limited continuation distance and significant errors, which restrict its applicability in practice. To address this problem, we reformulate the equivalent source method with a partial differential equation framework. A multilayer equivalent susceptibility method is innovatively derived based on this approach. The location of equivalent sources is designed for adaptive estimation through the inverse procedure. We introduce nonlinear optimization, regularization, and constraining technologies in inversion to improve the stability and accuracy of the solution. Synthetic, real airborne, and ground data are tested in experiments. The results show that the new method significantly improves the capability and accuracy of the downward continuation and transformation of irregularly located data between arbitrary undulating surfaces.

中文翻译：

---

使用多层等效源向下将任意磁场之间的全场磁异常向下延续和转换为磁梯度张量

等效源方法提供了一种在任意表面之间连续和操纵磁数据的潜在手段。然而，它最终遭受有限的连续距离和明显的误差，这限制了其在实践中的适用性。为了解决这个问题，我们用偏微分方程框架重新构造了等效源方法。基于这种方法，创新地推导了一种多层等效磁化率方法。等效源的位置旨在通过逆过程进行自适应估计。我们引入了非线性优化，正则化和反演约束技术，以提高解的稳定性和准确性。综合，真实的机载和地面数据在实验中进行了测试。