An alternate derivation of the three‐dimensional Hilbert transform relations from first principles

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 1014-1015 ◽  
Author(s):  
J. Bradley Nelson
Keyword(s):  
Hilbert Transform ◽  
Magnetic Field Intensity ◽  
Three Dimensional ◽  
Gradient Methods ◽  
Vertical Gradient ◽  
Horizontal Gradient ◽  
Implicit Assumption ◽  
Limited Applicability ◽  
Magnetic Gradients ◽  
The Magnetic Field

Several techniques for determining the location, geometry, and strength of a source are based on a knowledge of the magnetic gradients generated by that source. Hood (1965), Bhattacharyya (1966), and Rao et al. (1981) detailed three of these gradient methods. For many years, geophysicists have used the two‐dimensional (2-D) Hilbert transform to approximate the vertical gradient from measurements of the horizontal gradient in the magnetic‐field intensity (Nabighian, 1972; Stanley and Green, 1976; Stanley, 1977; Mohan et al., 1982). This technique is of limited applicability because of the implicit assumption that the source is a linear, 2-D body oriented at right angles to the profile direction.

Relative precision of vertical and horizontal gravity gradients measured by gravimeter

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 99-101 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Survey Data ◽  
Hilbert Transform ◽  
Gravity Data ◽  
Gradient Methods ◽  
Vertical Gradient ◽  
Gravity Gradients ◽  
Relative Precision ◽  
The Hilbert Transform ◽  
Vertical Gradients ◽  
Vertical Gradient Of Gravity

Several recent publications advocate the use of the vertical gradient of gravity from gravimeter measurements at two elevations in a portable tower (Thyssen‐Bornemisza, 1976; Fajklewicz, 1976; Mortimer, 1977). Contrary opinions have also been expressed (Hammer and Anzoleaga, 1975; Stanley and Green, 1976; Thysen‐Bornemisza, 1977; Arzi, 1977). The disagreement revolves around the question of practically attainable precision of the vertical gradient tower method. Although it is possible to calculate both horizontal and vertical gradients from conventional gravity survey data by use of the Hilbert transform (Stanley and Green, 1976), it should be noted that highly precise gravity data are required. Also the need for connected elevation and location surveys, the major cost in gravity surveying, is not avoided. This is a significant advantage of the gradient methods. The purpose here is to present a brief consideration of the relative precision of the horizontal and vertical gradients, as measured in the field by special gravimeter observations.

GRAVITY GRADIENTS AND THE INTERPRETATION OF THE TRUNCATED PLATE

Geophysics ◽  
1976 ◽  
Vol 41 (6) ◽  
pp. 1370-1376 ◽  
Author(s):  
John M. Stanley ◽  
Ronald Green
Keyword(s):  
Hilbert Transform ◽  
Theoretical Data ◽  
Vertical Gradient ◽  
Density Contrast ◽  
Horizontal Gradient ◽  
Gravity Gradients ◽  
Gravity Method ◽  
Commercially Important ◽  
Dip Angle ◽  
Vertical Gradients

The truncated plate and geologic contact are commercially important structures which can be located by the gravity method. The interpretation can be improved if both the horizontal and vertical gradients are known. Vertical gradients are difficult to measure precisely, but with modern gravimeters the horizontal gradient can be measured conveniently and accurately. This paper shows how the vertical gradient can be obtained from the horizontal gradient by the use of a Hilbert transform. A procedure is then presented which easily enables the position, dip angle, depth, thickness, and density contrast of a postulated plate to be precisely and unambiguously derived from a plot of the horizontal gradient against the vertical gradient at each point measured. The procedure is demonstrated using theoretical data.

Automated interpretation of horizontal magnetic gradient profile data

Geophysics ◽  
1992 ◽  
Vol 57 (2) ◽  
pp. 288-295 ◽  
Author(s):  
D. L. Marcotte ◽  
C. D. Hardwick ◽  
J. B. Nelson
Keyword(s):  
Vertical Gradient ◽  
Horizontal Gradient ◽  
Two Dimensional ◽  
Total Field ◽  
Profile Data ◽  
Magnetic Gradient ◽  
Inversion Methods ◽  
Automated Interpretation ◽  
A New Technique ◽  
Magnetic Gradients

A new technique has been developed to estimate the vertical magnetic gradient [Formula: see text] along a profile from measurements of the two orthogonal horizontal magnetic gradients [Formula: see text]. In addition, a means of identifying two‐dimensional anomaly sources and the angle of the structure relative to the profile direction is shown to be a function of [Formula: see text]. This angle can be used to correct interpretations from vertical gradient or total field inversion methods which assume source structures oriented perpendicular to the profile direction. A modified Werner deconvolution algorithm for vertical gradient data incorporating these features has been applied to both real and simulated horizontal gradient data.

scholarly journals Reconciliating the Vertical and Horizontal Gradients of the Sunspot Magnetic Field

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Véronique Bommier
Keyword(s):  
Magnetic Field ◽  
Aspect Ratio ◽  
Vertical Gradient ◽  
Spectral Lines ◽  
Horizontal Gradient ◽  
Plasma Anisotropy ◽  
Different Depths ◽  
Mhd Modeling ◽  
Horizontal Flux ◽  
The Magnetic Field

In the literature, we found 15 references showing that the sunspot photospheric magnetic field vertical gradient is on the order of 3-4 G/km, with field strength decreasing with height, whereas the horizontal gradient is nine times weaker on the order of 0.4-0.5 G/km. This is confirmed by our recent THEMIS observations. As a consequence, the vanishing of divB→ is not realized. In other words, a loss of magnetic flux is observed with increasing height, which is not compensated for by an increase of the horizontal flux. We show that the lack of spatial resolution, vertical as well as horizontal, cannot be held responsible for the nonvanishing observed divB→. The present paper is devoted to the investigation of this problem. We investigate how the magnetic field is influenced by the plasma anisotropy due to the stratification, which is responsible for an “aspect ratio” between horizontal and vertical typical lengths. On the example of our THEMIS observations, made of two spectral lines formed at two different depths, which enables the retrieval of the three components entering divB→, it is shown that once this aspect ratio is applied, the rescaled divB→ vanishes, which suggests a new methodology for MHD modeling in the photosphere.

scholarly journals Magnetic Field Structure of Star Forming Regions: VLBI Spectral Line Results

1984 ◽  
Vol 110 ◽  
pp. 333-334
Author(s):  
J.A. Garcia-Barreto ◽  
B. F. Burke ◽  
M. J. Reid ◽  
J. M. Moran ◽  
A. D. Haschick
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Aperture Synthesis ◽  
Stokes Parameters ◽  
Hii Region ◽  
Star Forming ◽  
Star Forming Regions ◽  
Vlbi Observations ◽  
The Magnetic Field ◽  
Synthesis Experiment

Magnetic fields play a major role in the general dynamics of astronomical phenomena and particularly in the process of star formation. The magnetic field strength in galactic molecular clouds is of the order of few tens of μG. On a smaller scale, OH masers exhibit fields of the order of mG and these can probably be taken as representative of the magnetic field in the dense regions surrounding protostars. The OH molecule has been shown to emit highly circular and linearly polarized radiation. That it was indeed the action of the magnetic field that would give rise to the highly polarized spectrum of OH has been shown by the VLBI observations of Zeeman pairs of the 1720 and 6035 MHz by Lo et. al. and Moran et. al. VLBI observations of W3 (OH) revealed that the OH emission was coming from numerous discrete locations and that all spots fell within the continuum contours of the compact HII region. The most detailed VLBI aperture synthesis experiment of the 1665 MHz emission from W3 (OH) was carried out by Reid et. al. who found several Zeeman pairs and a characteristic maser clump size of 30 mas. In this work, we report the results of a 5 station VLBI aperture synthesis experiment of the 1665 MHz OH emission from W3 (OH) with full polarization information. We produced VLBI synthesis maps of all Stokes parameters of 16 spectral features that showed elliptical polarization. The magnitude and direction of the magnetic field have been obtained by the detection of 7 Zeeman pairs. The three dimensional orientation of the magnetic field can be obtained, following the theoretical arguments of Goldreich et. al., from the observation of π and σ components.

scholarly journals Hilbert transform for the three-dimensional Vekua equation

2018 ◽  
Vol 64 (11) ◽  
pp. 1797-1824 ◽  
Author(s):  
Briceyda B. Delgado ◽  
R. Michael Porter
Keyword(s):  
Hilbert Transform ◽  
Three Dimensional ◽  
Vekua Equation

scholarly journals Magnetotaxis as a Means for Nanofabrication

2014 ◽  
Vol 23 (01n02) ◽  
pp. 1450008
Author(s):  
Isaac Macwan ◽  
Zihe Zhao ◽  
Omar Sobh ◽  
Jinnque Rho ◽  
Ausif Mahmood ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Geomagnetic Field ◽  
Semiconductor Manufacturing ◽  
Magnetic Field Intensity ◽  
Magnetotactic Bacteria ◽  
Semiconductor Substrate ◽  
Field Lines ◽  
A Chain ◽  
Magnetospirillum Magneticum ◽  
The Magnetic Field

Magnetotactic bacteria (MTB), discovered in early 1970s contain single-domain crystals of magnetite ( Fe 3 O 4) called magnetosomes that tend to form a chain like structure from the proximal to the distal pole along the long axis of the cell. The ability of these bacteria to sense the magnetic field for displacement, also called magnetotaxis, arises from the magnetic dipole moment of this chain of magnetosomes. In aquatic habitats, these organisms sense the geomagnetic field and traverse the oxic-anoxic interface for optimal oxygen concentration along the field lines. Here we report an elegant use of MTB where magnetotaxis of Magnetospirillum magneticum (classified as AMB-1) could be utilized for controlled navigation over a semiconductor substrate for selective deposition. We examined 50mm long coils made out of 18AWG and 20AWG copper conductors having diameters of 5mm, 10mm and 20mm for magnetic field intensity and heat generation. Based on the COMSOL simulations and experimental data, it is recognized that a compound semiconductor manufacturing technology involving bacterial carriers and carbon-based materials such as graphene and carbon nanotubes would be a desirable choice in the future.

scholarly journals INCREASING THE EFFICIENCY OF MULTY-VARIANT CALCULATIONS OF ELECTROMAGNETIC FIELD DISTRIBUTION IN MATRIX OF A POLYGRADIENT SEPARATOR

2021 ◽  
Author(s):  
Jasim Mohmed Jasim Jasim ◽  
Iryna Shvedchykova ◽  
Igor Panasiuk ◽  
Julia Romanchenko ◽  
Inna Melkonova
Keyword(s):  
Magnetic Field ◽  
Field Distribution ◽  
Three Dimensional ◽  
Magnetic Potential ◽  
Geometric Parameters ◽  
Two Dimensional ◽  
Air Gaps ◽  
Vector Magnetic Potential ◽  
Electromagnetic Separator ◽  
The Magnetic Field

An approach is proposed to carry out multivariate calculations of the magnetic field distribution in the working gaps of a plate polygradient matrix of an electromagnetic separator, based on a combination of the advantages of two- and three-dimensional computer modeling. Two-dimensional geometric models of computational domains are developed, which differ in the geometric dimensions of the plate matrix elements and working air gaps. To determine the vector magnetic potential at the boundaries of two-dimensional computational domains, a computational 3D experiment is carried out. For this, three variants of the electromagnetic separator are selected, which differ in the size of the working air gaps of the polygradient matrices. For them, three-dimensional computer models are built, the spatial distribution of the magnetic field in the working intervals of the electromagnetic separator matrix and the obtained numerical values of the vector magnetic potential at the boundaries of the computational domains are investigated. The determination of the values of the vector magnetic potential for all other models is carried out by interpolation. The obtained values of the vector magnetic potential are used to set the boundary conditions in a computational 2D experiment. An approach to the choice of a rational version of a lamellar matrix is substantiated, which provides a solution to the problem according to the criterion of the effective area of the working area. Using the method of simple enumeration, a variant of the structure of a polygradient matrix with rational geometric parameters is selected. The productivity of the electromagnetic separator with rational geometric parameters of the matrix increased by 3–5 % with the same efficiency of extraction of ferromagnetic inclusions in comparison with the basic version of the device

scholarly journals Vertical Vortex Development in Hurricane Michael (2018) during Rapid Intensification

2021 ◽  
Author(s):  
Alexander J. DesRosiers ◽  
Michael M. Bell ◽  
Ting-Yu Cha
Keyword(s):  
Inner Core ◽  
Doppler Radar ◽  
Three Dimensional ◽  
Vertical Gradient ◽  
Machine Learning Techniques ◽  
Rapid Intensification ◽  
Wind Retrieval ◽  
Retrieval Technique ◽  
Budget Analysis ◽  
Tangential Wind

AbstractThe landfall of Hurricane Michael (2018) at category 5 intensity occurred after rapid intensification (RI) spanning much of the storm’s lifetime. Four Hurricane Hunter aircraft missions observed the RI period with tail Doppler radar (TDR). Data from each of the 14 aircraft passes through the storm were quality controlled via a combination of interactive and machine learning techniques. TDR data from each pass were synthesized using the SAMURAI variational wind retrieval technique to yield three-dimensional kinematic fields of the storm to examine inner core processes during RI. Vorticity and angular momentum increased and concentrated in the eyewall region. A vorticity budget analysis indicates the tendencies became more axisymmetric over time. In this study we focus in particular on how the eyewall vorticity tower builds vertically into the upper levels. Horizontal vorticity associated with the vertical gradient of tangential wind was tilted into the vertical by the eyewall updraft to yield a positive vertical vorticity tendency inward atop the existing vorticity tower, that is further developed locally upward and outward along the sloped eyewall through advection and stretching. Observed maintenance of thermal wind balance from a thermodynamic retrieval shows evidence of a strengthening warm core, which aided in lowering surface pressure and further contributed to the efficient intensification in the latter stages of this RI event.

scholarly journals A Three-Dimensional Semianalytical Model for Elastic-Plastic Sliding Contacts

2007 ◽  
Vol 129 (4) ◽  
pp. 761-771 ◽  
Author(s):  
Daniel Nélias ◽  
Eduard Antaluca ◽  
Vincent Boucly ◽  
Spiridon Cretu
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Computing Time ◽  
Three Dimensional ◽  
Gradient Methods ◽  
Reciprocal Theorem ◽  
Contact Pressure Distribution ◽  
Sliding Contacts ◽  
Elastic Plastic ◽  
Residual Strains

A three-dimensional numerical model based on a semianalytical method in the framework of small strains and small displacements is presented for solving an elastic-plastic contact with surface traction. A Coulomb’s law is assumed for the friction, as commonly used for sliding contacts. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces are derived from Betti’s reciprocal theorem with initial strain. The main advantage of this approach over the classical finite element method (FEM) is the computing time, which is reduced by several orders of magnitude. The contact problem, which is one of the most time-consuming procedures in the elastic-plastic algorithm, is obtained using a method based on the variational principle and accelerated by means of the discrete convolution fast Fourier transform (FFT) and conjugate gradient methods. The FFT technique is also involved in the calculation of internal strains and stresses. A return-mapping algorithm with an elastic predictor∕plastic corrector scheme and a von Mises criterion is used in the plasticity loop. The model is first validated by comparison with results obtained by the FEM. The effect of the friction coefficient on the contact pressure distribution, subsurface stress field, and residual strains is also presented and discussed.

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