Some remarks on static field thin sheet models

Eskola, L.; Jokinen, T.; Soininen, H.; Tervo, Timo

doi:10.1016/0926-9851(93)90029-x

Cited by 7 publications

(7 citation statements)

References 6 publications

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“…Related work has been described by Sarabandi (1992). Thin-sheet models for the static case have been considered recently by Eskola, Soininen & Oksama (1989) and by Eskola et al (1993).…”

Section: Introductionmentioning

confidence: 99%

B-polarization induction in two thin half-sheets coupled to the mantle by a conducting crust-I. Solution by the Wiener-Hopf technique, with limiting forms

Dawson

1996

Geophysical Journal International

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S U M M A R YThe Wiener-Hopf technique is used to obtain an exact analytical solution to the problem of B-polarization induction in two adjacent thin half-sheets lying on a conducting layer, which is terminated at finite depth by a perfect conductor. The model may be viewed as an idealized local approximation to the Earth, with the half-sheets representing conducting layers (including the oceans) at the surface of the Earth, the conducting layer representing the crust, and the perfect conductor approximating the mantle. The solution may be used to study the behaviour of currents and electromagnetic fields induced in the Earth by ionospheric sheet-current sources flowing perpendicular to the thin-sheet junction. The solution allows for analytical investigation of the behavior of the field components near the thin-sheet junction. It also leads to some additional insight into the adjustment distance question.The model is a generalization of ones considered in three earlier publications by various authors. It is demonstrated that the field solutions for the present model contain those for the three earlier models as limiting cases, when one or more of the thin-sheet integrated conductivities become zero or infinite, or when the mantle depth becomes infinite. Also under appropriate limits, the model may also be viewed as a generalized thin sheet lying on a perfect conductor.

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“…Related work has been described by Sarabandi (1992). Thin-sheet models for the static case have been considered recently by Eskola, Soininen & Oksama (1989) and by Eskola et al (1993).…”

Section: Introductionmentioning

confidence: 99%

B-polarization induction in two thin half-sheets coupled to the mantle by a conducting crust-I. Solution by the Wiener-Hopf technique, with limiting forms

Dawson

1996

Geophysical Journal International

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“…Further, the amount of magnetic material in the large pieces can be estimated from the anomalies only if the magnetic properties are known. Smaller pieces of such steel (edge < 5 cm) are magnetically saturated and their anomalies can be 600 L. Eskola, R. Puranen and H. Soininen ᭧ 1999 European Association of Geoscientists & Engineers, Geophysical Prospecting, 47, 593-602 alternatively modelled by assuming that the sheet is at a constant potential (Eskola et al 1993). The amount of magnetic material in the saturated pieces cannot be estimated from the anomaly even if the magnetic properties of the steel piece are known.…”

Section: Discussionmentioning

confidence: 99%

“…The integral equation solutions of a magnetized thin-sheet model have been considered by Eskola (1992, pp. 107-110), and Eskola et al (1993). The thickness of the sheet is regarded as so small that the magnetic field of the sheet is inseparably dependent on the product kt of the susceptibility k and the sheet thickness t. The scalar potential U of the secondary magnetic field H, defined by the relation H ¼ ¹ٌU, can be presented in the form (Stratton 1941, p. 229),…”

Section: Appendixmentioning

confidence: 99%

Measurement of magnetic properties of steel sheets

Eskola

Puranen

Soininen

1999

Geophysical Prospecting

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Magnetic methods are used in detection of environmental, engineering and military objects fabricated of thin ferromagnetic sheets having volume susceptibilities higher than 100 SI units. Magnetic modelling of such objects would be advantageous, but it requires knowledge of the susceptibility and remanence values of sheet materials, which is scarce. We introduce a magnetometer method for the determination of susceptibility and remanence on thin steel samples. The area of the sample must be so large that its within‐sheet magnetization remains below the saturation state. The measurements are made in normal office surroundings in the Earth's magnetic field with an ordinary fluxgate magnetometer. The square‐shaped sheet samples measured in this work have an edge length of 17.5 cm and a thickness in the range 0.5–1.0 mm. During the measuring procedure the sample is placed in four positions on a subvertical measurement board. For each position, the magnetic field in the dip direction of the board plane is measured on the opposite sides of the sample. The secondary field values are averaged for each sample position in order to reduce the effect of sample inhomogeneities. With these data, the susceptibility and remanence of the sample in its edge directions are then determined, based on a model curve which is calculated numerically using thin‐sheet integral equations. The susceptibilities measured for different steel types (cold rolled and hot‐dip zinc‐coated steel sheets) varied in the range 200–500 SI units, and the remanence varied in the range 1000–20 000 A/m. No systematic differences were observed between the magnetic properties of various steel types. The repeatability of the susceptibility measurements was good (variations < 5%) but the remanence could be changed by 50% between repeated determinations. The measured susceptibility range signifies that pieces of steel with a typical thickness of 0.5 mm remain below magnetic saturation when their edge dimension is larger than 5 cm. Therefore magnetic modelling of larger steel pieces must be made using the thin‐sheet theory with known magnetic properties, whereas smaller saturated pieces can be alternatively modelled as an equipotential system.

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“…This appears to be particularly so for those integral equation formulations in which the field is represented in terms of a simple source distribution with density related to the normal component of the field over the surface of the body. Eskola et al (1993) illustrate this type of numerical instability in computing the magnetic field due to relatively thin tabular bodies in a static magnetic field. It can reasonably be expected that the approach proposed by Oksama and Suppala (1993) will display the same type of problem.…”

Section: The General Problemmentioning

confidence: 99%

An integral equation for the homogeneous Neumann condition¹

Furness

1996

Geophysical Prospecting

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Modelling the theoretical response of several important geophysical systems involves the solution of Poisson's equation with homogeneous Neumann boundary conditions (i.e. a zero normal gradient) imposed over either open or closed surfaces.A simple integral equation solution to this problem is derived from first principles. It is applicable to both types of surface and in this respect represents an improvement on existing integral equation techniques. However, the present surface integral equation displays a strong singularity of order 1/R3 which requires an appropriate interpretation for its implementation.A comparison of some numerical results with analytical data taken from the literature demonstrates that the proposed integral equation technique is suitably robust, accurate and efficient for practical application in geophysical interpretation.

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Some remarks on static field thin sheet models

Cited by 7 publications

References 6 publications

B-polarization induction in two thin half-sheets coupled to the mantle by a conducting crust-I. Solution by the Wiener-Hopf technique, with limiting forms

B-polarization induction in two thin half-sheets coupled to the mantle by a conducting crust-I. Solution by the Wiener-Hopf technique, with limiting forms

Measurement of magnetic properties of steel sheets

An integral equation for the homogeneous Neumann condition¹

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Some remarks on static field thin sheet models

Cited by 7 publications

References 6 publications

B-polarization induction in two thin half-sheets coupled to the mantle by a conducting crust-I. Solution by the Wiener-Hopf technique, with limiting forms

B-polarization induction in two thin half-sheets coupled to the mantle by a conducting crust-I. Solution by the Wiener-Hopf technique, with limiting forms

Measurement of magnetic properties of steel sheets

An integral equation for the homogeneous Neumann condition1

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An integral equation for the homogeneous Neumann condition¹