多层等效源曲面磁异常转换方法

在磁异常数据处理中，利用等效源技术重构磁异常场具有较好的稳定性和较高的计算精度，因而被广泛应用.传统方法是采用设置在近地表的单层等效源拟合实测磁异常数据，尽管拟合精度很高，但向上延拓之后往往会出现较大的拟合误差，即可能存在磁异常信号的"泄漏"，尤其在原始数据中存在背景场时更容易出现此种误差.本文提出一种多层等效源技术方案，应用分布于不同深度范围内的等效源模拟实测数据，减少了等效源参数设置的盲目性.理论模型试验表明，采用多层等效源方法重构的磁异常及其梯度与分量，较单层等效源方法具有更高精度，可以吸收更完整的实测磁异常信息.论文详细地讨论了如何优化多层等效源设置、等效源参数选择以及计算方法，通过二维和三维理论模型试验，验证了在复杂条件下多层等效源方法的可行性和适应性，并且将该方法应用于广西某地的实测磁异常数据转换之中，取得了较好的应用效果.

Transformation of magnetic anomaly data on an arbitrary surface by multi-layer equivalent sources

The equivalent source technique is widely used for processing magnetic anomaly data, such as spatial continuation, derivatives and transforms. Based on the equivalence principle of potential field, this method could construct equivalent (virtual) sources through fitting the observed data, and then predict the magnetic anomaly at any point in free space, without knowing the information of actual sources. The method has good stability and high computational accuracy. Usually, it is applied by the equivalent source model with single-layer. Despite of the little misfit, it is possible to "leak" signals in this routine, especially when background anomalies exist. Theoretically, a better result can be achieved only when the equivalent sources are closer to the actual sources. However, if only acquiring magnetic anomaly data, it is inefficient to inverse the actual sources. Therefore, we propose to apply a scheme of the multi-layer equivalent sources with multi-scales, using rectangular prisms as the element cells. First, we set up equivalent layers at different depths, and their depths could be determined by power spectrum analysis or prior information. Second, we define each layer's scale based on the characteristics of anomalies. Then, utilizing preconditioned conjugate gradient (PCG) method with regularization, we obtain the equivalent magnetization intensity distribution. Finally, we can reconstruct the magnetic anomalies, using the forward calculation based on the inversed equivalent sources. This approach is able to improve the rationality of the equivalent source model, and reduce the blindness of setting parameters. Therefore, the accuracy, of transformed magnetic anomaly and its derivatives etc., could be enhanced. In this paper, we discuss the optimization issues about setting the multi-layer equivalent sources, parameters of equivalent sources and computation algorithm in details. Results of experiments of 2D and 3D synthetic models show that our approach is of better feasibility and adaptability in complex situations. Further, a real data set from Guangxi province in China has been applied to illustrate the practical effects of the proposed approach.