全球地磁感应测深数据三维反演

全球地磁感应测深能获得地幔转换带及下地幔上部的导电结构.但目前稀疏的地磁台站分布及部分台站的观测数据稳定性较差,影响了三维反演对地下电性结构的分辨力和反演可靠性.为此,区别于传统的L2-范数反演方法,本文提出并实现了基于L1-范数的地磁测深响应三维反演技术.在反演中,利用L1-范数度量数据预测误差,降低"飞点"数据的影响,将相关系数较小的C-响应估计也纳入反演数据中.三维正演模拟采用球坐标系下的交错网格有限差分法,反演采用有限内存拟牛顿法.文中利用指数概率密度分布函数构造非高斯噪声的合成数据,并采用棋盘模型对反演方法的可靠性进行了验证.之后,我们将本文提出的三维反演方法用于全球129个地磁观测台站的C-响应数据反演,结果表明在地幔转换带深部,中国东北地区为高导电异常,南欧和北非则均为高阻;夏威夷在900km以下为高导;菲律宾海及以东地区在转换带表现为明显的高阻,这些结果与前人研究结果一致.由于采用了更多的台站数据,我们的反演结果还发现一些新的异常:南美洲南端,转换带表现为明显的高导;澳大利亚东南部,地幔转换带深部,也存在一个明显的高导异常,这些异常分布和地震层析成像的低速区一致.因此,L1-范数三维反演能够充分利用全球C-响应数据信息,提高地磁测深对地球深部电性结构的分辨能力,更好的研究全球地幔电性结构.

3-D inversion for global geomagnetic depth sounding

Global geomagnetic depth sounding (GDS) permits to detect the electrical structure of mantle transition zone and the upper part of lower mantle. However, the resolution and reliability of 3-D GDS inversion are restricted by sparse distribution of observatories and rejection caused by records' poor stability. In this paper, a 3-D GDS inversion method based on L₁-norm has been developed to solve the problem, which differs from the traditional L₂-norm inversion. The algorithm uses L₁-norm in the measure of data misfit when outliers occur in the data, so during inversion process we could take C-responses with low coherency into account at a certain observatory. The L-BFGS inversion method is used and the forward solver is based on a staggered-grid finite difference method in frequency domain for spherical geometry. Non-Gaussian noise of synthetic data are generated by using an exponential probability density function, then a checkerboard model inversion test is performed to ensure the valid of our method. This 3-D inversion method is applied to C-responses of 129 selected observatories around the world. Results show high conductivity beneath Northeast of China and high resistivity in lower mantle transition beneath South Europe and North Africa, while high conductivity also exists below 900 km in Hawaii and high resistivity is registered beneath Philippine Sea and the East. These features are coincident with previous studies. Due to more observatories are used, our results present more anomalies, such as the high conductivity in the mantle transition zone beneath southern South America, and the high conductivity in the lower part of mantle transition zone of southeastern Australia. These anomalies coincide with the low velocity areas derived from seismic tomography. This work demonstrates that the L₁-norm inversion method can make full use of observatories' records and improve exploratory resolution of deep electrical distribution of the Earth, contributing to further study of the global mantle structure.