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Multi-Scale Inverse Mollifier Magnetometry

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Inverse Magnetometry

Part of the book series: Lecture Notes in Geosystems Mathematics and Computing ((LNGMC))

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Abstract

This chapter explains the origin of mollifier approximation; the mollifier philosophy is explained in more detail and new impulses are given to the theory of inverse problems by mollifier techniques. The specific role of mollifier approximation is pointed out within the multi-scale context using mollifier dipole potentials corresponding to Haar-type Dirac sequences. Haar-wavelet based decorrelation of both magnetization distribution and geomagnetic potential data is investigated. The transfer methodology is provided from geomagnetic measurements to space-limited mollifier modeling of geological structures as well as mollifier reconstruction and decomposition. Altogether, innovative ways of modeling geologic layers by mollifier techniques are developed by reducing magnetometry in a multi-scale concept to mathematically accessible and thus calculable decorrelated models.

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Authors and Affiliations

  1. Business und Management mbH, CBM - Gesellschaft für Consulting, Bexbach, Saarland, Germany

    Christian Blick & Helga Nutz

  2. Mathematics Department, University of Kaiserslautern, Kaiserslautern, Rheinland-Pfalz, Germany

    Willi Freeden

  3. Mathematics Department, University of Central Florida, Orlando, FL, USA

    M. Zuhair Nashed

  4. OST, Institute for Computational Engineering, Buchs, Switzerland

    Michael Schreiner

Authors
  1. Christian Blick
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  2. Willi Freeden
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  3. M. Zuhair Nashed
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  4. Helga Nutz
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  5. Michael Schreiner
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Blick, C., Freeden, W., Nashed, M.Z., Nutz, H., Schreiner, M. (2021). Multi-Scale Inverse Mollifier Magnetometry. In: Inverse Magnetometry. Lecture Notes in Geosystems Mathematics and Computing. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-79508-5_5

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