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 L-1-norm has been developed to solve the problem, which differs from the traditional L-2-norm inversion. The algorithm uses L-1-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 L-1-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.