Magnetic interpretation using the 3-D analytic signal

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 116-125 ◽  
Author(s):  
Walter R. Roest ◽  
Jacob Verhoef ◽  
Mark Pilkington
Keyword(s):  
Magnetic Field ◽  
Impact Crater ◽  
Analytic Signal ◽  
Three Dimensions ◽  
Eastern Canada ◽  
Magnetic Interpretation ◽  
Absolute Value ◽  
Cape Breton ◽  
Derivatives Of ◽  
The Magnetic Field

A new method for magnetic interpretation has been developed based on the generalization of the analytic signal concept to three dimensions. The absolute value of the analytic signal is defined as the square root of the squared sum of the vertical and the two horizontal derivatives of the magnetic field. This signal exhibits maxima over magnetization contrasts, independent of the ambient magnetic field and source magnetization directions. Locations of these maxima thus determine the outlines of magnetic sources. Under the assumption that the anomalies are caused by vertical contacts, the analytic signal is used to estimate depth using a simple amplitude half‐width rule. Two examples are shown of the application of the method. In the first example, the analytic signal highlights a circular feature beneath Lake Huron that has been identified as a possible impact crater. The second example illustrates the continuation of terranes across the Cabot Strait between Cape Breton and Newfoundland in eastern Canada.

Attributes of the magnetic field, analytic signal, and monogenic signal for gravity and magnetic interpretation

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. J79-J86 ◽  
Author(s):  
Xiong Li ◽  
Mark Pilkington
Keyword(s):  
Magnetic Field ◽  
Magnetic Anomaly ◽  
Field Vector ◽  
Analytic Signal ◽  
Horizontal Gradient ◽  
Monogenic Signal ◽  
Magnetic Interpretation ◽  
Gravity And Magnetic ◽  
Gravity And Magnetic Interpretation ◽  
The Magnetic Field

Many of the transforms and attributes used in gravity and magnetic interpretation can be expressed as a 2D or 3D vector. The horizontal gradient and the 2D analytic signal are 2D vectors. The gravity or magnetic field, the 3D analytic signal, and the monogenic signal are defined by a 3D vector. In practice, we prefer to interpret the amplitude and/or phase of a 2D or 3D vector, but we often forget that a meaningful interpretation requires a magnetic reduction-to-the-pole operation when these techniques are applied to magnetic anomaly data and the source body is 3D. Furthermore, the gravity or magnetic anomaly has an unknown constant level that may affect the amplitude and phase. The horizontal gradient, the analytic signal, and the monogenic signal can be applied to not only the gravity or magnetic anomaly but also any [Formula: see text]th-order derivative or a filtered version of the anomaly. They can be related to each other and to the magnetic field vector. We do not introduce new attributes. Instead, we have explained the relationships among different transforms (or vectors) and addressed precautions and requirements for their practical use.

Inland, Coastal, and Offshore Magnetotelluric Measurements in Eastern Canada

1971 ◽  
Vol 8 (2) ◽  
pp. 204-216 ◽  
Author(s):  
S. P. Srivastava ◽  
A. White
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
East Coast ◽  
Vertical Component ◽  
Eastern Canada ◽  
Spectral Techniques ◽  
Relative Attenuation ◽  
Field Recordings ◽  
Power Spectral ◽  
The Magnetic Field

For six weeks during the summer of 1966 simultaneous magnetic and electric field recordings were made on the east coast of Canada at Fredericton, N.B., Halifax, N.S., and Sable Island. The data from these stations have been analyzed using power spectral techniques. Comparison of the simultaneous recordings from Halifax and Sable Island with those from Fredericton and Agincourt indicate some enhancement in the intensity of the vertical component of the magnetic field for periods less than 40 min at Halifax and attenuation in its intensity for periods less than 3 h at Sable Island. The enhancement at Halifax has been interpreted in terms of the "coast effect" while the effect of the island and of differences in the subsurface conductivity under the continent and under the ocean have been shown to be possible causes of the relative attenuation in the Z variations at Sable Island.

RESPONSE OF DYKE TO OSCILLATING DIPOLE

Geophysics ◽  
1958 ◽  
Vol 23 (1) ◽  
pp. 128-133 ◽  
Author(s):  
James Paul Wesley
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Scalar Potential ◽  
Three Dimensions ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
First Approximation ◽  
Sulfide Ore ◽  
Infinite Conductivity ◽  
The Magnetic Field

A dyke of sulfide ore may be geophysically prospected by observing its electromagnetic response to a slowly oscillating magnetic dipole source. An excellent first approximation of the fields generated is obtained by considering the idealized case of a dyke of infinite conductivity and vanishing thickness in a vacuum. Surprisingly, this idealized problem can be solved exactly in terms of a newly discovered Green’s function for Laplace’s equation (in three dimensions) which is simply expressed in closed form. The magnetic scalar potential and the magnetic field are given for final results.

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

Kinetic and transport theory for a non-neutral plasma taking account of strong gyration and non-uniformities on the collisional scale

1987 ◽  
Vol 38 (3) ◽  
pp. 351-371 ◽  
Author(s):  
Alf H. Øien
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Electric Field ◽  
Strong Magnetic Field ◽  
Transport Theory ◽  
Collision Integral ◽  
Collision Term ◽  
Third Order ◽  
Derivatives Of ◽  
The Magnetic Field

From the BBGKY equations for a pure electron plasma a derivation is made of a collision integral that includes the combined effects of particle gyration in a strong magnetic field and non-uniformities of both the distribution function and the self-consistent electric field on the collisional scale. A series expansion of the collision integral through the distribution function and the electric field on the collisional scale is carried out to third order in derivatives of the distribution function and to second order in derivatives of the electric field. For the strong-magnetic-field case when collision-term contributions to only first order in 1/B are included, a particle flux transverse to the magnetic field proportional to l/B2 is derived. The importance of long-range collective collisions in this process is shown. The result is in contrast with the classical l/B4 proportionality, and is in accordance with earlier studies.

Small-scale magnetic fields in turbulence: Saffman's approximation revisited

1980 ◽  
Vol 99 (3) ◽  
pp. 481-493
Author(s):  
Ralph Baierlein
Keyword(s):  
Magnetic Field ◽  
Numerical Evaluation ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Small Scale ◽  
Fluid Element ◽  
Relative Time ◽  
Fourier Decomposition ◽  
The Subject ◽  
The Magnetic Field

The subject is the small-scale structure of a magnetic field in a turbulent conducting fluid, ‘small scale’ meaning lengths much smaller than the characteristic dissipative length of the turbulence. Philip Saffman developed an approximation to describe this structure and its evolution in time. Its usefulness invites a closer examination of the approximation itself and an attempt to place sharper limits on the numerical parameters that appear in the approximate correlation functions, topics to which the present paper is addressed.A Lagrangian approach is taken, wherein one makes a Fourier decomposition of the magnetic field in a neighbourhood that follows a fluid element. If one construes the viscous-convective range narrowly, by ignoring magnetic dissipation entirely, then results for a magnetic field in two dimensions are consistent with Saffman's approximation, but in three dimensions no steady state could be found. Thus, in three dimensions, turbulent amplification seems to be more effective than Saffman's approximation implies. The cause seems to be a matter of geometry, not of correlation times or relative time scales.Strictly-outward spectral transfer is a characteristic of Saffman's approximation, and this may be an accurate description only when dissipation suppresses the contributions from inwardly directed spectral transfer. In the spectral region where dominance passes from convection to dissipation, one can generate expressions for the parameters that arise in Saffman's approximation. Their numerical evaluation by computer simulation may enable one to sharpen the limits that Saffman had already set for those parameters.

Numerical modelling of MHD waves in the solar chromosphere

2005 ◽  
Vol 364 (1839) ◽  
pp. 395-404 ◽  
Author(s):  
Mats Carlsson ◽  
Thomas J Bogdan
Keyword(s):  
Magnetic Field ◽  
Acoustic Waves ◽  
Mode Conversion ◽  
Three Dimensions ◽  
Mhd Waves ◽  
Solar Chromosphere ◽  
Fast Mode ◽  
Reflected Waves ◽  
The Waves ◽  
The Magnetic Field

Acoustic waves are generated by the convective motions in the solar convection zone. When propagating upwards into the chromosphere they reach the height where the sound speed equals the Alfvén speed and they undergo mode conversion, refraction and reflection. We use numerical simulations to study these processes in realistic configurations where the wavelength of the waves is similar to the length scales of the magnetic field. Even though this regime is outside the validity of previous analytic studies or studies using ray-tracing theory, we show that some of their basic results remain valid: the critical quantity for mode conversion is the angle between the magnetic field and the k-vector: the attack angle. At angles smaller than 30° much of the acoustic, fast mode from the photosphere is transmitted as an acoustic, slow mode propagating along the field lines. At larger angles, most of the energy is refracted/reflected and returns as a fast mode creating an interference pattern between the upward and downward propagating waves. In three-dimensions, this interference between waves at small angles creates patterns with large horizontal phase speeds, especially close to magnetic field concentrations. When damping from shock dissipation and radiation is taken into account, the waves in the low–mid chromosphere have mostly the character of upward propagating acoustic waves and it is only close to the reflecting layer we get similar amplitudes for the upward propagating and refracted/reflected waves. The oscillatory power is suppressed in magnetic field concentrations and enhanced in ring-formed patterns around them. The complex interference patterns caused by mode-conversion, refraction and reflection, even with simple incident waves and in simple magnetic field geometries, make direct inversion of observables exceedingly difficult. In a dynamic chromosphere it is doubtful if the determination of mean quantities is even meaningful.

Effect of Elongation on the Proton Magnetic Resonance of Natural Rubber

1957 ◽  
Vol 30 (2) ◽  
pp. 528-530
Author(s):  
Keichi Oshima ◽  
Hazime Kusumoto
Keyword(s):  
Magnetic Field ◽  
Magnetic Resonance ◽  
Natural Rubber ◽  
Proton Magnetic Resonance ◽  
Room Temperature ◽  
Resonance Absorption ◽  
Field Inhomogeneity ◽  
Fixed Frequency ◽  
Derivatives Of ◽  
The Magnetic Field

Abstract Several authors have already reported their studies on natural rubber by the method of proton magnetic resonance. However, since there has been little work on the effect of elongation on proton magnetic resonance absorption, we present our investigation on the proton magnetic resonance absorption of stretched samples of vulcanized natural rubber. For this experiment a large permanent magnet shown in Figure 1 was constructed. The magnetic field strength was 6090 gauss at the center of the gap at 18° C. The magnet had a field inhomogeneity of about 0.01 gauss in a 0.2 cc. sample. The derivatives of the resonance line were recorded at fixed frequency, changing the magnetic field linearly in time with an automatic electronic bias control. Control of the temperature from liquid nitrogen to room temperature was performed by a cryostat similar to that described by Gutowsky.

Potential fields and their partial derivatives produced by a 2D homogeneous polygonal source: A summary with some revisions

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. L29-L34 ◽  
Author(s):  
Zhen Jia ◽  
Shiguo Wu
Keyword(s):  
Magnetic Field ◽  
Cross Section ◽  
Observation Point ◽  
Potential Fields ◽  
Data Sets ◽  
Partial Derivatives ◽  
First Order ◽  
Gravity And Magnetic ◽  
Derivatives Of ◽  
The Magnetic Field

We summarized and revised the present forward modeling methods for calculating the gravity- and magnetic-field components and their partial derivatives of a 2D homogeneous source with a polygonal cross section. The responses of interest include the gravity-field components and their first- and second-order partial derivatives and the magnetic-field components and their first-order partial derivatives. The revised formulas consist of several basic quantities that are common in all the formulations. A singularity appears when the observation point coincides with a polygon vertex. This singularity is removable for the gravity formulas but not for the others. The compact forms of the revised formulas make them easy to implement. We compare the gravity- and magnetic-field components and their partial derivatives produced by a 2D prism whose polygonal cross section approximates a cylinder with the corresponding analytical fields and partial derivatives of the cylinder. The perfect fittings presented by both data sets confirm the reliability of the updated formulas.

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