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On Identifying Magnetized Anomalies Using Geomagnetic Monitoring Within a Magnetohydrodynamic model

  • Youjun Deng
  • Jinhong Li
  • Hongyu LiuEmail author
Article
  • 19 Downloads

Abstract

This paper is a continuation and an extension of our recent work (Deng et al. in Arch Ration Mech Anal 231(1):153–187, 2019) on the identification of magnetized anomalies using geomagnetic monitoring, which aims to establish a rigorous mathematical theory for the geomagnetic detection technology. Suppose a collection of magnetized anomalies is present in the shell of the Earth. By monitoring the variation of the magnetic field of the Earth due to the presence of the anomalies, we establish sufficient conditions for the unique recovery of these unknown anomalies. Deng et al. (2019), the geomagnetic model was described by a linear Maxwell system. In this paper, we consider a much more sophisticated and complicated magnetohydrodynamic model, which stems from the widely accepted dynamo theory of geomagnetics.

Notes

Acknowledgements

The authors would like to express their gratitudes to the anonymous referee for many insightful and constructive comments, which have led to significant improvements on the results and presentation of the paper. The work of Y. Deng was supported by NSF Grant of China No. 11601528, NSF Grant of Hunan Nos. 2017JJ3432 and 2018JJ3622, Innovation-Driven Project of Central South University, No. 2018CX041. The work of H. Liu was supported by the FRG and startup grants from Hong Kong Baptist University, Hong Kong RGC General Research Funds 12302017, 12301218 and 12302919.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsCentral South UniversityChangshaChina
  2. 2.School of ScienceQilu University of Technology (Shandong Academy of Sciences)JinanChina
  3. 3.Department of MathematicsHong Kong Baptist UniversityKowloonChina

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