# American Institute of Mathematical Sciences

August  2019, 13(4): 745-754. doi: 10.3934/ipi.2019034

## Magnetic parameters inversion method with full tensor gradient data

 1 Key Laboratory of Petroleum Resources Research, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China 2 University of the Chinese Academy of Sciences, Beijing 100049, China 3 Institutions of Earth Science, Chinese Academy of Sciences, Beijing 100029, China 4 Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia

* Corresponding author: Yanfei Wang

Received  April 2018 Revised  January 2019 Published  May 2019

Retrieval of magnetization parameters using magnetic tensor gradient measurements receives attention in recent years. Determination of subsurface properties from the observed potential field measurements is referred to as inversion. Little regularizing inversion results using full tensor magnetic gradient modeling so far has been reported in the literature. Traditional magnetic inversion is based on the total magnetic intensity (TMI) data and solving the corresponding mathematical physical model. In recent years, with the development of the advanced technology, acquisition of the full tensor gradient magnetic data becomes available. In this paper, we study invert the magnetic parameters using the full tensor magnetic gradient data. A sparse Tikhonov regularization model is established. In solving the minimization model, the conjugate gradient method is addressed. Numerical and field data experiments are performed to show feasibility of our algorithm.

Citation: Yanfei Wang, Dmitry Lukyanenko, Anatoly Yagola. Magnetic parameters inversion method with full tensor gradient data. Inverse Problems & Imaging, 2019, 13 (4) : 745-754. doi: 10.3934/ipi.2019034
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Results of testing calculations: a) model solution (the normalized value of the magnitude of the magnetic moment density ${\mathit{\boldsymbol{M}}}$), b) retrieved solution for the TMI-model, c) retrieved solution for the MGT-model, d) retrieved solution for the TMI+MGT-model. The MGT-model produces the better reconstruction for the magnitude of the small details of the model solution. The use of the combined TMI+MGT-data does not give any advantages in reconstruction quality comparing with the using of TMI-data only
Results of calculation for Real Field Example 1. The main figure shows the result of preliminary allocation of the magnetic sources using quite large area as integral domain for calculations. The mini-figure shows more accurate results of second calculations for the integral domain with specified dimensions
Results of calculation for Real Field Example 2. The main figure shows the result of preliminary allocation of the magnetic sources using quite large area as integral domain for calculations. The mini-figure shows more accurate results of second calculations for the integral domain with specified dimensions
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