谱矩方法在磁源体深度反演中的应用研究

谱矩方法可以对数据的表面形貌做较为细致的描述.它以随机过程为理论基础，用各阶谱矩及统计不变量等具体的参数表征表面的几何形态，算术平均顶点曲率是一种基于四阶谱矩的统计不变量.通常，埋深不同的场源所引起的磁异常尺度不同，从曲率的角度来理解即为磁异常曲面的弯曲程度不同.因此，本文应用算术平均顶点曲率提取磁异常的几何信息，并将所提取的信息用于场源深度的反演.理论上推导了基于谱矩的球状磁源体和板状磁源体的反演公式，得到了场源深度与磁异常、曲率之间的关系式.结合理论模型计算验证了方法的有效性，并与欧拉反褶积方法进行对比.与传统的方法相比，该方法快速简单，无需调节参数，且有较好的反演精度.最后，将该方法用于塔里木盆地航磁异常的反演和解释中，反演出的磁源体深度可满足区域磁异常数据分析和解释的要求，为克拉通沉积盆地磁异常源的深度划分提供丰富的信息.

Depth evaluation of magnetic sources by spectral moment analysis

The spectrum moments based approach can precisely describe the characteristics of surface geometry. Based on the theory of stochastic processes, different order spectrums and their statistical invariants can describe the geometries of each area. Arithmetical mean vertex curvature is one of the statistical invariants based on the fourth-order spectral moments. Usually, different scales of magnetic anomalies are caused by different depth sources, which can be explained as different degree of bending of the magnetic anomaly curve. This paper detects the geometry information of magnetic anomalies by using the fourth-order spectrum moments, and then the magnetic depth estimation is achieved from the extracted information. First, depth inversion of spherical globular and tabula magnetic body is deduced theoretically, the relation among the source depth, the magnetic anomaly and the curvature is obtained. And then, the simulation results were compared with that from Euler deconvolution method and validated the effectiveness of the proposed method. The results indicate that the new method is simple but efficient. Finally, the method is applied to the magnetic depth estimation in Tarim Basin. And the depth estimation results can meet the requirement of regional magnetic anomaly data analysis and interpretation, and provide sufficient information of source depths for cratonic sedimentary basin.