Solving the magnetostatic field problem (a case of high susceptibility) by means of the method of subsections

S U M M A R YThe field and frequency dependences of the initial susceptibility of pyrrhotite have been analysed as a function of grain size, motivated by a strong field dependence recently observed for large (mm-sized) pyrrhotite crystals (Worm 1991) and smaller field dependences determined on smaller grain sizes by Clark (1984). In the present study, the frequency ranged from 30 Hz to 27 kHz. At 2 kHz, a field range from 0.05 to 1500 p T was investigated. Separate determinations of in-phase ( k ' ) and quadrature (k") susceptibility components allow for the analysis of eddy current effects.Up to 4 kHz the in-phase susceptibility of a pyrrhotite-ore specimen is practically independent of frequency whereafter it decreases while the quadrature component increases linearly with frequency to a valuc on the order of k' at 20 kHz for large grains. k" is proportional to d2p.af where d is grain diameter, p the intrinsic permeability, u the electrical conductivity and f the frequency. The frequency response of magnetite is essentially flat up to frequencies >20 kHz. Both frequency dependences agree well with calculations based on the theory by Wait (1 951). The conductivity of the pyrrhotite ore has been determined to be u = 1.40 (+0.05) * 1 O S E ' m -' .The susceptibility of pyrrhotite and its field dependence increase strongly with grain size. While the susceptibility of grains smaller than 30 p m is field independent (up to 1.5 mT) it may increase as k cx H025 for mm-sized crystals in fields >10pT. For most samples the Rayleigh law is inadequate to characterize induced magnetizations in weak alternating fields. When susceptibilities are measured for geomagnetic anomaly modelling, laboratory fields should be of similar intensity as the Earth's field and of frequency 5 1 kHz.

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“…Thc demagnetization factor N decreases with increasing k,(Eskola & Tervo 1980). Dashed line indicates limit for k, + 30.…”

mentioning

confidence: 94%

Magnetic Susceptibility of Pyrrhotite: Grain Size, Field and Frequency Dependence

Worm

Clark

Dekkers

1993

Geophysical Journal International

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“…We give a brief theoretical description of demagnetization below. Refer to Sharma (1966Sharma ( , 1968, Eskola and Tervo (1980), Emerson et al (1985), and Clark et al (1986) for more detailed discussions on demagnetization.…”

Section: General Concept Of Demagnetizationmentioning

confidence: 99%

“…Demagnetization effects in magnetic interpretation have been noted or studied in a number of publications (Bath, 1962;Gay, 1963;Strangway, 1967;Farrar, 1979;Wang, 1983;Emerson et al, 1985;Clark et al, 1986;Eskola, 1992;Gunn and Dentith, 1997), and a few experimental and real cases related to the effects have been reported (Zietz and Henderson, 1956;Vogel, 1963;Sharma, 1966Sharma, , 1968Fang, 1978;Eskola and Tervo, 1980;Lee, 1980;Guo et al, 1998). Although all of these publications point out the presence and importance of demagnetization in regard to magnetic interpretation, little attempt has been made to systematically document these effects by analyzing the error distribution that exists between demagnetization-corrected and uncorrected magnetic properties.…”

Section: Introductionmentioning

confidence: 96%

Systematic error analysis of demagnetization and implications for magnetic interpretation

et al. 2001

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Demagnetization can affect the interpretation of magnetic data significantly. However, little attempt has been made to understand its effects by analyzing systematically the differences between demagnetizationcorrected and uncorrected magnetic properties. A systematic error analysis is made in this paper using a 2-D elliptic cylinder model. Generally, demagnetization changes the effective susceptibility and remanence or the effective magnetization in both magnitude and direction. Error analyses show that demagnetization causes the magnitude of effective magnetization of a magnetic body to be less than its intrinsic magnetization. This implies that a theoretical anomaly computed without accounting for demagnetization will overestimate the amplitude of the anomaly associated with the body. The decrease in magnetization magnitude depends on the intrinsic magnetic susceptibility of a body as well as on the body's geometry (flattening ratio) and its relative orientation (magnetic dip) in the geomagnetic field. The magnitude of the effective magnetization, relative to the intrinsic magnetization, decreases with increasing intrinsic magnetic susceptibility. This factor dominates the body's effective magnetization. When intrinsic magnetic susceptibility is less than 0.1 SI, the demagnetization effects are generally insignificant and may be ignored in magnetic anomaly modeling. The magnetic dip and flattening ratio only cause minor fluctuations in the effective magnetization. Demagnetization also changes the direction of the effective magnetization vector by making it approach the plane of flattening of any flattened body. The difference between the inclinations of the effective and intrinsic magnetization changes the horizontal positions of extreme values of an anomaly, which may affect the precision of magnetic interpretations. Generally, the inclination difference is significant for magnetic dips of 30 • to 70 • and increases with increasing susceptibility and decreasing flattening ratio. In particular, for large flat-lying magnetic geological units located at middle magnetic latitudes (30 • to 70 • ), significant magnetic inclination deflections are expected because of demagnetization effects. Theoretical, experimental, and practical examples of magnetic interpretation are presented to illustrate these demagnetization effects.

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“…This is a function of the body shape and gives rise to shape anisotropy (Uyeda et al, 1963;Thompson and Oldfield, 1986;Dunlop and Özdemir, 1997;Clark and Emerson, 1999;Tauxe, 2003). It is well established in the literature that the self-demagnetization can be neglected if the body has a susceptibility lower than 0.1 SI (Emerson et al, 1985;Clark et al, 1986;Eskola and Tervo, 1980;Guo et al, 1998Guo et al, , 2001Purss and Cull, 2005;Hillan and Foss, 2012;Austin et al, 2014;Clark, 2014). On the other hand, neglecting the self-demagnetization in geological bodies with high susceptibilities (> 0.1 SI) may strongly mislead the interpretation obtained from magnetic methods.…”

Section: Introductionmentioning

confidence: 97%

“…In the absence of conduction currents, the total magnetic field H(r) at the position r (Eq. 1) of a point referred to the main coordinate system is defined as follows (Sharma, 1966;Eskola and Tervo, 1980;Reitz et al, 1992;Stratton, 2007):…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Ellipsoids (v1.0): 3-D magnetic modelling of ellipsoidal bodies

Takahashi¹,

Oliveira²

2017

Geosci. Model Dev.

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Abstract. A considerable amount of literature has been published on the magnetic modelling of uniformly magnetized ellipsoids since the second half of the nineteenth century. Ellipsoids have flexibility to represent a wide range of geometrical forms, are the only known bodies which can be uniformly magnetized in the presence of a uniform inducing field and are the only finite bodies for which the selfdemagnetization can be treated analytically. This property makes ellipsoids particularly useful for modelling compact orebodies having high susceptibility. In this case, neglecting the self-demagnetization may strongly mislead the interpretation of these bodies by using magnetic methods. A number of previous studies consider that the self-demagnetization can be neglected for the case in which the geological body has an isotropic susceptibility lower than or equal to 0.1 SI. This limiting value, however, seems to be determined empirically and there has been no discussion about how this value was determined. In addition, the geoscientific community lacks an easy-to-use tool to simulate the magnetic field produced by uniformly magnetized ellipsoids. Here, we present an integrated review of the magnetic modelling of arbitrarily oriented triaxial, prolate and oblate ellipsoids. Our review includes ellipsoids with both induced and remanent magnetization, as well as with isotropic or anisotropic susceptibility. We also discuss the ambiguity between confocal ellipsoids with the same magnetic moment and propose a way of determining the isotropic susceptibility above which the self-demagnetization must be taken into consideration. Tests with synthetic data validate our approach. Finally, we provide a set of routines to model the magnetic field produced by ellipsoids. The routines are written in Python language as part of the Fatiando a Terra, which is an open-source library for modelling and inversion in geophysics.

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Solving the magnetostatic field problem (a case of high susceptibility) by means of the method of subsections

Cited by 22 publications

References 8 publications

Magnetic Susceptibility of Pyrrhotite: Grain Size, Field and Frequency Dependence

Magnetic Susceptibility of Pyrrhotite: Grain Size, Field and Frequency Dependence

Systematic error analysis of demagnetization and implications for magnetic interpretation

Ellipsoids (v1.0): 3-D magnetic modelling of ellipsoidal bodies

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