Archive for Rational Mechanics and Analysis

, Volume 231, Issue 1, pp 153–187 | Cite as

On Identifying Magnetized Anomalies Using Geomagnetic Monitoring

  • Youjun Deng
  • Jinhong Li
  • Hongyu LiuEmail author


We propose and investigate the inverse problem of identifying magnetized anomalies beneath the Earth using geomagnetic monitoring. Suppose a collection of magnetized anomalies are presented in the shell of the Earth. The presence of the anomalies interrupts the magnetic field of the Earth, as monitored from above the Earth. Using the difference of the magnetic fields before and after the presence of the magnetized anomalies, we show that one can uniquely recover the locations as well as their material parameters of the anomalies. Our study provides a rigorous mathematical theory for the geomagnetic detection technology that has been used in practice.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

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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