CONTINUOUS SPECTRUM OF THE TOTAL‐MAGNETIC‐FIELD ANOMALY DUE TO A RECTANGULAR PRISMATIC BODY

Geophysics ◽  
1966 ◽  
Vol 31 (1) ◽  
pp. 97-121 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Magnetic Field ◽  
Magnetization Vector ◽  
High Amplitude ◽  
The Body ◽  
Two Dimensional ◽  
Near Surface ◽  
Prismatic Body ◽  
Total Magnetic Field ◽  
Dimensional Spectrum ◽  
Prismatic Bodies

The Fourier transform of the total‐magnetic‐field anomaly due to a rectangular prismatic body with arbitrary magnetization yields the two‐dimensional spectrum of the anomaly. In the expression for the spectrum the individual effects of the horizontal and vertical dimensions of the body appear as separate factors. Another factor in the expression takes into account the combined influence of the orientation of the magnetization vector and the dip and declination of the earth’s magnetic field. The expression for the two‐dimensional spectrum is used to obtain analytical formulas of the spectra for magnetic‐field values along profiles parallel to the two horizontal axes of the body. This theoretical study provides a quantitative picture of the shift of the spectrum to the low‐frequency end with increase in either depth or horizontal dimension, or in both, of the magnetized body. It has thus been possible to realize the feasibility of a method for separating the effects of near‐surface high‐amplitude components from those of deep crustal sources in total‐field aeromagnetic maps. Separation of these effects is, however, not unique because of spectral overlap between anomalies due to “shallow” and “deep” sources. A detailed discussion has been made about the characteristics of amplitude and phase spectra of anomalies due to prismatic bodies of differing dimensions. The spectra of anomalies seem to be useful in rapid estimation of the dimensions of a body under suitable conditions. The effect of demagnetization on the fields due to prismatic bodies has been ignored in this paper.

Parametric instability in the expanding solar wind

2021 ◽  
Author(s):  
Andrea Verdini ◽  
Roland Grappin ◽  
Francesco Malara ◽  
Leonardo Primavera ◽  
Luca Del Zanna
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Parametric Instability ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Total Magnetic Field ◽  
One Dimensional ◽  
Preliminary Results ◽  
Dimensional Spectrum ◽  
N Wave

<p>Recent measurments of Parker Solar Probe show that alfvenic fluctuations in the solar wind often appear in the form of swithcback with constant total magnetic field. Our aim is to understand if and how such fluctuations can contribute to the heating or acceleration of the solar wind, via the Parametric Instability. The intability of one dimensional Alfvénic fluctuations has been extensively studied in both homogenoeus plasma and in the expanding solar wind, less so for the two-dimensional case which is closer to expected three-dimensional nature of switchbacks. In this work we study under which condition an Alfvén wave with a two dimensional spectrum (as introduced in Primavera et al ApJ 2019) can decay in the expanding solar wind and we will present preliminary results.</p>

The effect of a strong magnetic field on two-dimensional flows of a conducting fluid

1963 ◽  
Vol 15 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Stephen Childress
Keyword(s):  
Magnetic Field ◽  
Perturbation Technique ◽  
The Body ◽  
Conducting Fluid ◽  
Order Effects ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Exterior Region ◽  
Electrically Conducting ◽  
Higher Order Effects

The motion of a viscous, electrically conducting fluid past a finite two-dimensional obstacle is investigated. The magnetic field is assumed to be uniform and parallel to the velocity at infinity. By means of a perturbation technique, approximations valid for large values of the Hartmann number M are derived. It is found that, over any finite region, the flow field is characterized by the presence of shear layers fore and aft of the body. The limit attained over the exterior region represents the two-dimensional counterpart of the axially symmetric solution given by Chester (1961). Attention is focused on a number of nominally ‘higher-order’ effects, including the presence of two distinct boundary layers. The results hold only when M [Gt ] Re; Re = Reynolds number. However, a generalization of the procedure, in which the last assumption is relaxed, is suggested.

Two‐dimensional transient electromagnetic responses

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2849-2861 ◽  
Author(s):  
Jopie I. Adhidjaja ◽  
Gerald W. Hohmann ◽  
Michael L. Oristaglio
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Time Domain ◽  
The Body ◽  
Two Dimensional ◽  
Total Field ◽  
Secondary Field ◽  
Field Solution ◽  
Transient Electromagnetic ◽  
Simple Boundary

The time‐domain electromagnetic (TEM) modeling method of Oristaglio and Hohmann is reformulated here in terms of the secondary field. This finite‐difference method gives a direct, explicit time‐domain solution for a two‐dimensional body in a conductive earth by advancing the field in time with DuFort‐Frankel time‐differencing. As a result, solving for the secondary field, defined as the difference between the total field and field of a half‐space, is not only more efficient but is also simpler and eliminates several problems inherent in the solution for the total field. For example, because the secondary field varies slowly both in space and time, it can be modeled on a coarse grid with large time steps. In addition, for a simple body the field is local; therefore, because the field can be assumed to satisfy a simple boundary condition in the earth computation is greatly simplified. Our tests show that for the same accuracy, the secondary‐field solution is roughly five times faster than the total‐field solution. We compute and analyze the magnetic field impulse response for a suite of models, most of which consist of a thin body embedded in a conductive half‐space—with or without overburden. The results indicate the conductive half‐space will both delay and attenuate the response of the body and even obscure it if the conductivity contrast is small. The results also suggest that the conductive host can alter the decay rate of the response of the body from its free‐space counterpart. Our results for multiple bodies illustrate the importance of early‐time measurements to obtain resolution, particularly for measurements of the horizontal magnetic field. The vertical magnetic field, however, can be used to infer the dip direction of a dipping body by studying the migration of the crossover. The results for models which include overburden show that the effect of a conductive overburden, in addition to the half‐space effect, is to delay the response of the body, because the primary current initially tends to concentrate and slowly diffuse through the overburden, and does not reach the body until later time. This effect also complicates the early‐times profiles, becoming more severe as the conductivity of the overburden is increased.

IX. Lines of induction in a magnetic field

1901 ◽  
Vol 195 (262-273) ◽  
pp. 303-327 ◽  
Keyword(s):  
Magnetic Field ◽  
Circular Cylinder ◽  
Viscous Liquid ◽  
Thin Sheet ◽  
The Body ◽  
Two Dimensional ◽  
Transparent Medium ◽  
Exact Position ◽  
Stream Lines ◽  
Lines Of Force

The following paper, which is partly experimental and partly mathematical, has arisen from the discovery that two-dimensional cases of magnetic lines of force could apparently be represented by the flow of a viscous liquid.* The original experiments upon which this assumption was made, showed that the stream lines which were obtained by the method in question, gave results very similar to those which had been calculated and plotted for the cases of an elliptical and circular cylinder. In order to ascertain definitely that the stream lines under these circum­stances actually gave the exact position and direction of the corresponding magnetic lines of force, a result which, if verified, could be used for many practical investi­gations—it was necessary to undertake a long research dealing with the various points involved, a research which has proved extremely laborious, extending without intermission over a period of nearly two years. In the first place it was necessary to devise some method by which a thin sheet of transparent or semi-transparent medium could be obtained of any required thickness, and on which, when placed between two sheets of glass, the required section of the body to be investigated could be formed.

SPECTRAL ANALYSIS OF GRAVITY AND MAGNETIC ANOMALIES DUE TO RECTANGULAR PRISMATIC BODIES

Geophysics ◽  
1977 ◽  
Vol 42 (1) ◽  
pp. 41-50 ◽  
Author(s):  
B. K. Bhattacharyya ◽  
Lei‐Kuang Leu
Keyword(s):  
Spectral Analysis ◽  
Approximation Method ◽  
Magnetic Anomalies ◽  
The Body ◽  
Exponential Approximation ◽  
Prismatic Body ◽  
First Order ◽  
Gravity And Magnetic ◽  
Sums Of Exponentials ◽  
Prismatic Bodies

The spectra of gravity and magnetic anomalies due to a prismatic body can be expressed as sums of exponentials. The complex exponents of these exponentials are functions of frequency and locations of the corners of the body. An exponential approximation method is used for the analysis of the radial spectra of an anomaly and its first order moments for obtaining accurate estimates of the depths to the top and bottom of the body. A method has also been developed for determining approximately the location of the centroid of the body. When the location of the centroid and the depths to the top and bottom are known for the causative body, it is possible to calculate the horizontal dimensions with the help of the spectrum of the anomaly.

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