Calculation of magnitude magnetic transforms with high centricity and low dependence on the magnetization vector direction

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. I21-I30 ◽  
Author(s):  
Daniela Gerovska ◽  
Marcos J. Araúzo-Bravo
Keyword(s):  
Magnetic Field ◽  
Magnetization Vector ◽  
Field Vector ◽  
Data Sets ◽  
Volcanic Area ◽  
Square Root ◽  
Anomalous Magnetic Field ◽  
Total Magnitude ◽  
Vector Direction ◽  
Magnitude Magnetic Transforms

We present a Matlab tool that calculates five magnitude magnetic transforms (MMTs) from an input measured anomalous magnetic field. The MMTs are all based on the total magnitude anomaly (TMA), and consist of the TMA itself, the modulus of the gradient of the TMA, the Laplacian of the TMA, half of the square root of the Laplacian of the square of the TMA, and the square root of the product of the TMA plus the Laplacian of the TMA. These MMTs produce anomalies that are closer to the magnetic source’s true horizontal position and are simpler to interpret than the measured anomalous magnetic field itself. While the conventional magnetic transforms of reduction-to-the-pole (RTP), the pseudogravity field, and the analytic signal (AS) also have these properties, these MMTs have several additional advantages. They require only first-order, horizontal derivatives for their calculation. They are also more stable at low magnetic latitudes than the RTP, and have a pattern that is independent of the geomagnetic-field vector direction, in contrast to the AS. The Matlab tool is designed to deal with big data sets and is compatible with common data formats, GS ASCII grid files, and XYZ data files. A calculation of the MMTs of the total magnetic anomaly of a synthetic example at a low magnetic latitude and with a field example from the Kuju volcanic area, Japan demonstrate the effectiveness of the program.

scholarly journals Characterization of the umbra–penumbra boundary by the vertical component of the magnetic field

2020 ◽  
Vol 638 ◽  
pp. A25
Author(s):  
P. Lindner ◽  
R. Schlichenmaier ◽  
N. Bello González
Keyword(s):  
Magnetic Field ◽  
Near Infrared ◽  
Statistical Study ◽  
Vertical Component ◽  
Fundamental Property ◽  
Field Vector ◽  
Data Sets ◽  
Data Set ◽  
Geometric Difference ◽  
The Magnetic Field

Context. The vertical component of the magnetic field was found to reach a constant value at the boundary between penumbra and umbra of stable sunspots in a recent statistical study of Hinode/SP data. This finding has profound implications as it can serve as a criterion to distinguish between fundamentally different magneto-convective modes operating in the sun. Aims. The objective of this work is to verify the existence of a constant value for the vertical component of the magnetic field (B⊥) at the boundary between umbra and penumbra from ground-based data in the near-infrared wavelengths and to determine its value for the GREGOR Infrared Spectrograph (GRIS@GREGOR) data. This is the first statistical study on the Jurčák criterion with ground-based data, and we compare it with the results from space-based data (Hinode/SP and SDO/HMI). Methods. Eleven spectropolarimetric data sets from the GRIS@GREGOR slit-spectograph containing fully-fledged stable sunspots were selected from the GRIS archive. SIR inversions including a polarimetric straylight correction are used to produce maps of the magnetic field vector using the Fe I 15648 Å and 15662 Å lines. Averages of B⊥ along the contours between penumbra and umbra are analyzed for the 11 data sets. In addition, contours at the resulting B⊥const are drawn onto maps and compared to intensity contours. The geometric difference between these contours, ΔP, is calculated for each data set. Results. Averaged over the 11 sunspots, we find a value of B⊥const = (1787 ± 100) gauss. The difference from the values previously derived from Hinode/SP and SDO/HMI data is explained by instrumental differences and by the formation characteristics of the respective lines that were used. Contours at B⊥ = B⊥const and contours calculated in intensity maps match from a visual inspection and the geometric distance ΔP was found to be on the order of 2 pixels. Furthermore, the standard deviation between different data sets of averages along umbra–penumbra contours is smaller for B⊥ than for B∥ by a factor of 2.4. Conclusions. Our results provide further support to the Jurčák criterion with the existence of an invariable value B⊥const at the umbra–penumbra boundary. This fundamental property of sunspots can act as a constraining parameter in the calibration of analysis techniques that calculate magnetic fields. It also serves as a requirement for numerical simulations to be realistic. Furthermore, it is found that the geometric difference, ΔP, between intensity contours and contours at B⊥ = B⊥const acts as an index of stability for sunspots.

Study of Enhanced Self Mixing in Ferrofluid Flow in an Elbow Channel Under the Influence of Non-Uniform Magnetic Field

2019 ◽  
Author(s):  
Nadish Anand ◽  
Richard Gould
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Magnetization Vector ◽  
Field Vector ◽  
Mixing Efficiency ◽  
Mixing Enhancement ◽  
Initial Flow ◽  
Viscosity Term ◽  
Flow Mixing ◽  
The Magnetic Field

Abstract This paper investigates numerically the various parameters dictating the vortical (self)-mixing induced by a non-uniform magnetic field in a ferrofluid flow in an elbow channel. The elbow bend region of the channel has two current carrying conductors placed symmetrically and parametrically from the channel and are used to generate a non-uniform magnetic field. The ferrofluid is assumed to be pre-magnetized, isothermal and electrically non-conductive as it enters the channel and has a prescribed inlet magnetization and temperature. The mixing efficiency is characterized by introducing different mixing scalars based on velocity of the fluid and are compared in order to determine the overall suitability of each scalar to quantify the flow vortical (self)-mixing. Parametric studies were performed by varying parameters influencing the magnetic field and the initial flow field. This resulted in variations in non-dimensional groups which control different aspects of the flow and helped establish their relationship with mixing efficiency. It was found that at higher Reynolds numbers the flow mixing induced by the lateral gradient in the Kelvin Body Force (KBF) dissipates and higher electrical inputs are required to sustain mixing in the flow. The effects of mixing enhancement on the pressure gradient across the channel was also established, along with the introduction of an enhanced viscosity term which is due to the non-collinearity of the magnetization vector and the magnetic field vector.

A generalized multibody model for inversion of magnetic anomalies

Geophysics ◽  
1980 ◽  
Vol 45 (2) ◽  
pp. 255-270 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Magnetization Vector ◽  
Critical Dimension ◽  
Magnetic Anomalies ◽  
Field Vector ◽  
Magnetic Survey ◽  
Multibody Model ◽  
Anomalous Field ◽  
Rectangular Block

The height of the observation surface above a magnetized region primarily determines the critical dimension of the smallest inhomogeneity in magnetization that can be resolved from magnetic survey data. When a rectangular block is smaller in size than this critical dimension, it appears homogeneously magnetized in the observed magnetic field. This consideration leads to the selection of a unit rectangular block of suitable dimensions with homogeneous magnetization. The magnetized region creating the anomalous field values in the area of observation can, therefore, be broken up into several blocks having different magnetizations, each block being equal in size and uniformly magnetized. The iterative method described here assumes initially that the anomalous field values are caused by a three‐dimensional (3-D) distribution of magnetized rectangular blocks. The optimum orientation of these blocks with respect to geographic north is then determined. This orientation is particularly insensitive to adjustments in the dimensions of the blocks. The top and bottom surfaces of each of the blocks in one or more layers are adjusted in a least‐squares sense to minimize the difference between observed and calculated field values. A method is also described for constraining the magnetization vector of each block to lie within a specified angle of the normal or reversed direction of the geomagnetic field vector. The procedure for analysis of data can also be extended to the case of anomalies over a draped surface. At the conclusion of the iterations, a 3-D distribution of magnetization is generated to delineate the magnetized region responsible for the observed anomalous magnetic field. Examples including model and aeromagnetic data are provided to demonstrate the usefulness of a generalized multibody model for inversion of magnetic anomalies.

Reducing the dependence of the analytic signal amplitude of aeromagnetic data on the source vector direction

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. J55-J60 ◽  
Author(s):  
Gordon R. J. Cooper
Keyword(s):  
Synthetic Data ◽  
Magnetization Vector ◽  
Signal Amplitude ◽  
Analytic Signal ◽  
Data Sets ◽  
Aeromagnetic Data ◽  
3D Data ◽  
Vector Direction ◽  
2D Data ◽  
Derivatives Of

The analytic signal amplitude (As) is commonly used as an edge-detection filter for aeromagnetic data. For profile (2D) data, its shape is independent of the source magnetization vector direction, but this is not the case for map (3D) data. A modified analytic signal amplitude ([Formula: see text]) is introduced here which has a much reduced dependence on this vector for both contact and dike models. When the modified analytic signal amplitude was applied to synthetic data sets, it was more effective in enhancing the edges of the bodies than the standard As. Because it uses second-order derivatives of the magnetic field, the method is sensitive to noise and so an additional formulation was developed for noisy data sets that only use first-order derivatives.

scholarly journals How to make the Sun look less like the Sun and more like a star?

2016 ◽  
Vol 12 (S328) ◽  
pp. 237-239
Author(s):  
A. A. Vidotto
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Vector Fields ◽  
Radial Component ◽  
Field Vector ◽  
Small Scale ◽  
General Context ◽  
The Sun ◽  
Flux Transport ◽  
Large Scale Magnetic Field

AbstractSynoptic maps of the vector magnetic field have routinely been made available from stellar observations and recently have started to be obtained for the solar photospheric field. Although solar magnetic maps show a multitude of details, stellar maps are limited to imaging large-scale fields only. In spite of their lower resolution, magnetic field imaging of solar-type stars allow us to put the Sun in a much more general context. However, direct comparison between stellar and solar magnetic maps are hampered by their dramatic differences in resolution. Here, I present the results of a method to filter out the small-scale component of vector fields, in such a way that comparison between solar and stellar (large-scale) magnetic field vector maps can be directly made. This approach extends the technique widely used to decompose the radial component of the solar magnetic field to the azimuthal and meridional components as well, and is entirely consistent with the description adopted in several stellar studies. This method can also be used to confront synoptic maps synthesised in numerical simulations of dynamo and magnetic flux transport studies to those derived from stellar observations.

Euler’s differential equation and the identification of the magnetic point‐pole and point‐dipole sources

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1549-1553 ◽  
Author(s):  
J. O. Barongo
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Magnetic Anomalies ◽  
Field Vector ◽  
Magnetic Data ◽  
Dipole Source ◽  
Point Dipole ◽  
Main Subject ◽  
Depth Extent ◽  
Dipole Sources

The concept of point‐pole and point‐dipole in interpretation of magnetic data is often employed in the analysis of magnetic anomalies (or their derivatives) caused by geologic bodies whose geometric shapes approach those of (1) narrow prisms of infinite depth extent aligned, more or less, in the direction of the inducing earth’s magnetic field, and (2) spheres, respectively. The two geologic bodies are assumed to be magnetically polarized in the direction of the Earth’s total magnetic field vector (Figure 1). One problem that perhaps is not realized when interpretations are carried out on such anomalies, especially in regions of high magnetic latitudes (45–90 degrees), is that of being unable to differentiate an anomaly due to a point‐pole from that due to a point‐dipole source. The two anomalies look more or less alike at those latitudes (Figure 2). Hood (1971) presented a graphical procedure of determining depth to the top/center of the point pole/dipole in which he assumed prior knowledge of the anomaly type. While it is essential and mandatory to make an assumption such as this, it is very important to go a step further and carry out a test on the anomaly to check whether the assumption made is correct. The procedure to do this is the main subject of this note. I start off by first using some method that does not involve Euler’s differential equation to determine depth to the top/center of the suspected causative body. Then I employ the determined depth to identify the causative body from the graphical diagram of Hood (1971, Figure 26).

scholarly journals THE VECTOR DIRECTION OF THE INTERSTELLAR MAGNETIC FIELD OUTSIDE THE HELIOSPHERE

2010 ◽  
Vol 710 (2) ◽  
pp. 1769-1775 ◽  
Author(s):  
M. Swisdak ◽  
M. Opher ◽  
J. F. Drake ◽  
F. Alouani Bibi
Keyword(s):  
Magnetic Field ◽  
Vector Direction

DIPOLE-FIELD TYPE MAGNETIC DISTURBANCES AND AURORAL ACTIVITIES

1961 ◽  
Vol 39 (2) ◽  
pp. 350-366 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Magnetic Field ◽  
Current System ◽  
Field Vector ◽  
Maximum Magnitude ◽  
Horizontal Magnetic Field ◽  
Auroral Activity ◽  
The North ◽  
Initial Location ◽  
Sequence Relationship ◽  
Direction Of Movement

The characteristics of the magnetic field components at Agincourt have been calculated for a current system produced by an electric dipole located in the region of auroral activity near Ottawa. It is noted that, irrespective of the orientation of the dipole, the horizontal magnetic field component rotates in the clockwise and anticlockwise senses for motion of the dipole towards the east and the west respectively, when the dipole is situated in the north half of the sky as seen from the observing station.Next, the magnetograms obtained at Agincourt have been studied at those times of the night when auroral activity was recorded in the all-sky camera photographs at Springhill near Ottawa. It is noted that the horizontal magnetic field describes a loop during a particular phase of auroral activity because of its gradual growth and decay. The distributions of clockwise and anticlockwise rotations with respect to local time are found to be very similar in many respects to those of auroral motions to the east and west respectively. The sense of rotation of the loop is predominantly anticlockwise in the early part of the night and clockwise in the late hours of the night.It is found that eastward and westward orientations of the dipole are the most probable ones. The direction of movement and the initial location of the predominant auroral form in the sky are found to tally well with those of the dipole deduced from a study of the magnetograms.It seems that there is a time sequence relationship between successive phases of auroral activity and changes of characteristics of the loops described by the horizontal magnetic field vector. The area of a loop and the maximum magnitude of the field vector in the loop appear to be related to the brightness and horizontal extent of the auroral forms.

scholarly journals Properties of the inner penumbral boundary and temporal evolution of a decaying sunspot

2018 ◽  
Vol 620 ◽  
pp. A191 ◽  
Author(s):  
M. Benko ◽  
S. J. González Manrique ◽  
H. Balthasar ◽  
P. Gömöry ◽  
C. Kuckein ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Temporal Evolution ◽  
Vertical Component ◽  
Field Vector ◽  
Linear Increase ◽  
Vertical Magnetic Field ◽  
Magnetic Diffusion ◽  
The Magnetic Field ◽  
Linear Decay

Context. It has been empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field. Aims. We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28–September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to prove the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots. Methods. A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits. Results. We find a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the sunspot decay shown, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what is seen in stable sunspots. Conclusions. During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field is found for the inner penumbral boundary.

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