Fast inversion of magnetic field maps of unidirectional planar geological magnetization

Lima, Eduardo A.; Weiss, B. P.; Baratchart, Laurent; Hardin, Douglas P.; Saff, Edward B.

doi:10.1002/jgrb.50229

Cited by 45 publications

(75 citation statements)

References 38 publications

(60 reference statements)

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“…Techniques for elimination of inaccuracies of magnetic meteorite scans, such as inversion of magnetic maps (Lima et al. ), provide more details about the magnetic minerals.…”

Section: Methodsmentioning

confidence: 99%

Magnetic, in situ, mineral characterization of Chelyabinsk meteorite thin section

Nabelek

Mazanec

Kdýr

et al. 2015

Meteorit & Planetary Scien

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Abstract-Magnetic images of Chelyabinsk meteorite's (fragment F1 removed from Chebarkul lake) thin section have been unraveled by a magnetic scanning system from Youngwood Science and Engineering (YSE) capable of resolving magnetic anomalies down to 10 À3 mT range from about 0.3 mm distance between the probe and meteorite surface (resolution about 0.15 mm). Anomalies were produced repeatedly, each time after application of magnetic field pulse of varying amplitude and constant, normal or reversed, direction. This process resulted in both magnetizing and demagnetizing of the meteorite thin section, while keeping the magnetization vector in the plane of the thin section. Analysis of the magnetic data allows determination of coercivity of remanence (B cr ) for the magnetic sources in situ. Value of B cr is critical for calculating magnetic forces applicable during missions to asteroids where gravity is compromised. B cr was estimated by two methods. First method measured varying dipole magnetic field strength produced by each anomaly in the direction of magnetic pulses. Second method measured deflections of the dipole direction from the direction of magnetic pulses. B cr of magnetic sources in Chelyabinsk meteorite ranges between 4 and 7 mT. These magnetic sources enter their saturation states when applying 40 mT external magnetic field pulse.

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“…Techniques for elimination of inaccuracies of magnetic meteorite scans, such as inversion of magnetic maps (Lima et al. ), provide more details about the magnetic minerals.…”

Section: Methodsmentioning

confidence: 99%

Magnetic, in situ, mineral characterization of Chelyabinsk meteorite thin section

Nabelek

Mazanec

Kdýr

et al. 2015

Meteorit & Planetary Scien

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“…If we make the additional assumption that Q is locally supported in some subregion ⊂ S r , then the susceptibility is actually determined uniquely (cf. [2], based on results from [3,4] in a Euclidean set-up). Therefore, in the latter scenario, but under the condition that the dipole direction is not known, our goal is to find suitable candidates for the dipole direction d. If the magnetization m was known, then a standard procedure such as described in [5,Chapter 7] can be used to derive d from the direction of m or to see that m cannot be of the form (1.1).…”

Section: M(x) = Q(x)mentioning

confidence: 99%

“…Therefore, the relations (2.10)-(2.12) can be quite helpful. Some related applications and information on such a decomposition on the Euclidean plane instead of a sphere can be found in [3,4,18].…”

Section: Theorem 22 (Spherical Hardy-hodge Decompositionmentioning

confidence: 99%

On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere

Gerhards

2018

Inverse Problems in Science and Engineering

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Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to those induced by an ambient magnetic dipole field (i.e. the magnetization is described by a scalar susceptibility and the dipole direction). Here, we investigate the situation under the additional constraint that the susceptibility is either spatially localized in a subregion of the sphere or that it is band-limited. If the dipole direction is known, then the susceptibility is uniquely determined under the spatial localization constraint while it is only determined up to a constant under the assumption of bandlimitedness. If the dipole direction is not known, uniqueness is lost again. However, we show that all dipole directions that could possibly generate the measured magnetic potential need to be zeros of a certain polynomial which can be computed from the given potential. We provide examples of non-uniqueness of the dipole direction and examples on how to find admissible candidates for the dipole direction under the spatial localization constraint. ARTICLE HISTORY

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“…By following a similar approach in the wavenumber domain, Lima et al . [] presented an efficient method attempted to estimate the magnetization intensity distribution within a planar rock sample having a previously defined constant magnetization direction. The method developed by Lima et al .…”

Section: Introductionmentioning

confidence: 99%

“…The method developed by Lima et al . [] also uses two‐dimensional signal processing methods to regularize the inverse problem, tame noise amplification, and improve nonnegativity.…”

Section: Introductionmentioning

confidence: 99%

Estimating the magnetization distribution within rectangular rock samples

Reis

Oliveira

Yokoyama

et al. 2016

Geochem Geophys Geosyst

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Over the last decades, scanning magnetic microscopy techniques have been increasingly used in paleomagnetism and rock magnetism. Different from standard paleomagnetic magnetometers, scanning magnetic microscopes produce high‐resolution maps of the vertical component of the magnetic induction field (flux density) on a plane located over the sample. These high‐resolution magnetic maps can be used for estimating the magnetization distribution within a rock sample by inversion. Previous studies have estimated the magnetization distribution within rock samples by inverting the magnetic data measured on a single plane above the sample. Here we present a new spatial domain method for inverting the magnetic induction measured on four planes around the sample in order to retrieve its internal magnetization distribution. We have presumed that the internal magnetization distribution of the sample varies along one of its axes. Our method approximates the sample geometry by an interpretation model composed of a one‐dimensional array of juxtaposed rectangular prisms with uniform magnetization. The Cartesian components of the magnetization vector within each rectangular prism are the parameters to be estimated by solving a linear inverse problem. Our method automatically deals with the averaging of the measured magnetic data due to the finite size of the magnetic sensor, preventing the application of a deconvolution before the inversion. Tests with synthetic data show the performance of our method in retrieving complex magnetization distributions even in the presence of magnetization heterogeneities. Moreover, they show the advantage of inverting the magnetic data on four planes around the sample and how this new acquisition scheme improves the estimated magnetization distribution within the rock sample. We have also applied our method to invert experimentally measured magnetic data produced by a highly magnetized synthetic sample that was manufactured in the laboratory. The results show that even in the presence of apparent position noise, our method was able to retrieve the magnetization distribution consistent with the isothermal remanent magnetization induced in the sample.

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Fast inversion of magnetic field maps of unidirectional planar geological magnetization

Cited by 45 publications

References 38 publications

Magnetic, in situ, mineral characterization of Chelyabinsk meteorite thin section

Magnetic, in situ, mineral characterization of Chelyabinsk meteorite thin section

On the reconstruction of inducing dipole directions and susceptibilities from knowledge of the magnetic field on a sphere

Estimating the magnetization distribution within rectangular rock samples

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