基于奇异谱分析的重磁位场分离方法

奇异谱分析是一种近年兴起的时间序列分析方法，它利用降秩原理实现信号分离.该方法将数据空间投影到不同特征的子空间中，并用奇异值来表征这些子空间的性质，最后通过截取奇异值实现数据的重构.重磁位场分离可以看成一种多信号叠加的分离问题.不同特征的重磁异常具有不同特征的奇异谱，这是奇异谱分析用于解决位场分离问题的应用基础.本文通过建立理论模型，分析重磁异常的奇异谱特征，得出适用于重磁位场分离的最优参数选择方法，并与传统方法进行比较.对比发现，无论是横向叠加模型、垂向叠加模型还是斜向叠加模型，奇异谱分析都具有很好的分离效果.最后，将奇异谱分析用于鄂东南某矿区的重力资料处理中，实现弱异常的识别和分离.

Separation of potential field based on singular spectrum analysis

Singular spectrum analysis (SSA), which uses the rank reduction to separate signals, is a new method for time series analysis in recent years. In this method, the data space is projected into subspace of different features, which properties are represented by singular values. Then, signal can be reconstructed by hard-thresholding. The potential field separation can be considered as a separation problem of multiple signal superposition. Gravity and magnetic anomalies with different characteristics have different singular spectrum features, which is the application basis of potential field separation. In this paper, synthetic models are established to analyze singular spectrum characteristics of gravity and magnetic anomalies, and we recommend the setting of parameters. Then, we compare SSA with existing methods. It is found that the horizontal superposition model, the vertical superposition model and the diagonal superposition model separated by SSA have the best accuracies. Finally, the singular spectrum analysis is applied to process gravity data to identify and separate the weak anomalies in the mining area of southeastern Hubei.