On: “Euler’s differential equation and the identification of the magnetic point‐pole and point‐dipole sources” by J. O. Barongo (GEOPHYSICS, 49, 1549–1553, September 1984).

Geophysics ◽  
1987 ◽  
Vol 52 (7) ◽  
pp. 1013-1014
Author(s):  
Ronald Green
Keyword(s):  
Differential Equation ◽  
Detailed Analysis ◽  
Point Dipole ◽  
Contour Maps ◽  
Meridional Profile ◽  
Dipole Sources

In the article by Barongo, the problem of distinguishing between the anomaly patterns arising from an isolated pole and a point dipole was examined. The method the author recommended concentrated on a detailed analysis of the shape of the principal meridional profile. I suggest that a better method is to use the isogam map, rather than the profile. From the relevant expressions for contour maps of an isolated pole and a point dipole, the salient differences between the two cases become apparent.

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 On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative

2018 ◽  
Vol 22 ◽  
pp. 01045 ◽  
Author(s):  
Mehmet Yavuz ◽  
Necati Özdemir
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Exact Solutions ◽  
Detailed Analysis ◽  
Analytical Solutions ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Conformable Derivative ◽  
Homotopy Analysis ◽  
Fractional Cauchy Problem

In this study, we have obtained analytical solutions of fractional Cauchy problem by using q-Homotopy Analysis Method (q-HAM) featuring conformable derivative. We have considered different situations according to the homogeneity and linearity of the fractional Cauchy differential equation. A detailed analysis of the results obtained in the study has been reported. According to the results, we have found out that our obtained solutions approach very speedily to the exact solutions.

Heat Transfer From a Small Isothermal Spanwise Strip on an Insulated Boundary

1963 ◽  
Vol 85 (3) ◽  
pp. 230-235 ◽  
Author(s):  
S. C. Ling
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Heat Conduction ◽  
Detailed Analysis ◽  
Similarity Solution ◽  
Leading Edge ◽  
Trailing Edge ◽  
Shear Field ◽  
Uniform Shear

Detailed analysis of heat transfer of an isothermal spanwise strip in a uniform shear field is presented. Solutions for the leading edge and the trailing edge are obtained by method of relaxation. These solutions are exact in that the streamwise heat conduction term, in the differential equation of energy, is not neglected. The results are compared with the Le´veˆque similarity solution, and the ranges where the solution is valid are defined. A similarity solution for the trailing wake is also presented.

scholarly journals Folding during soft-sediment deformation

2019 ◽  
Vol 487 (1) ◽  
pp. 81-104 ◽  
Author(s):  
G. I. Alsop ◽  
R. Weinberger ◽  
S. Marco ◽  
T. Levi
Keyword(s):  
Detailed Analysis ◽  
Dead Sea ◽  
Metamorphic Rocks ◽  
Soft Sediment ◽  
Contour Maps ◽  
Sediment Deformation ◽  
Soft Sediment Deformation ◽  
Original Class ◽  
Mass Transport Deposits ◽  
Geometry Analysis

AbstractThe detailed analysis of folding in rocks was in part pioneered by John Ramsay, and resulted in a range of techniques and criteria to define folds. Although folding of unlithified or ‘soft’ sediments is typically assumed to produce similar geometries to those in ‘hard rocks’, there has to date been little detailed analysis of such folds. The aim of this paper is therefore to investigate folds developed during soft-sediment deformation (SSD) by applying techniques established for the analysis of tectonic folds during hard-rock deformation (HRD). We use the Late Pleistocene Lisan Formation exposed around the Dead Sea as our case study, as the laminated lake sediments record intricacies of fold detail generated during seismically triggered slumping of mass transport deposits (MTDs) towards the depocentre of the basin. While it is frequently assumed that folds created during SSD are chaotic and form disharmonic structures, we provide analyses that show harmonic fold trains may form during slumping, although larger upright folds cannot be traced for significant distances and are more typically disharmonic. Our analysis also reveals a range of fold styles, with more competent detrital-rich layers displaying buckles (Class 1B), as well as upright Class 1A folds marked by thickened limbs. Class 1A buckle folds are generally considered to be created by flattening that overprints folds with an original Class 1B geometry. As thickened fold limbs are truncated by overlying erosive surfaces, the vertical flattening is considered to have occurred during the slump event. Different fold shapes may partially reflect variable flattening, depending on the original orientation of upright or recumbent folds, together with continued downslope-directed simple-shear deformation that modifies the fold geometry. Analysis of fold wavelength, amplitude and bed thickness allows us to plot strain contour maps, and indicates that beds defining slump folds display viscosity contrasts in the range of 50–250, which are similar to values estimated from folds created during HRD in metamorphic rocks. A range of refold patterns, similar to those established by John Ramsay in metamorphic rocks, are observed within slumps, and are truncated by the overlying sediments, indicating that they formed during a single progressive slump event rather than distinct ‘episodes’ of superimposed deformation. This study confirms that techniques developed for the analysis of folds created during HRD are equally applicable to those formed during SSD, and that resulting folds are generally indistinguishable from one another. Extreme caution should therefore be exercised when interpreting the origin of folds in the rock record where the palaeogeographical and tectonic contexts become increasingly uncertain, thereby leading to potential misidentification of folds created during SSD.

Evolution Solutions for the Ostrovsky Equation: A Perspective from an Auxiliary Elliptic Equation

2012 ◽  
Vol 538-541 ◽  
pp. 621-624
Author(s):  
Chun Huan Xiang
Keyword(s):  
Differential Equation ◽  
Elliptic Equation ◽  
Detailed Analysis ◽  
Periodic Solutions ◽  
Elliptic Function ◽  
Earth Rotation ◽  
Direct Method ◽  
Jacobi Elliptic Function ◽  
Ostrovsky Equation ◽  
A Direct Method

The Ostrovsky equation is used to describe the oceanic waves affected by Earth rotation. The auxiliary elliptic equation was employed as a direct method to construct the evolution solutions for the Ostrovsky equation in this manuscript. Detailed analysis of evolution solutions of the Ostrovsky equation is presented. The periodic solutions, which read Jacobi elliptic function solutions, hyperbolic solutions and trigonal solutions, are obtained. More parameters are included in the evolution solutions, the parameter space is enlarged. This method adds a new route to explore evolution solutions of nonlinear differential equation in a perspective from auxiliary elliptic equation.

Analysis of the 9th November 1990 flare

2000 ◽  
Vol 179 ◽  
pp. 229-232
Author(s):  
Anita Joshi ◽  
Wahab Uddin
Keyword(s):  
Image Processing ◽  
Two Dimensional ◽  
Temporal Behaviour ◽  
Contour Maps ◽  
Dimensional Measurements ◽  
Processing Software ◽  
Image Processing Software

AbstractIn this paper we present complete two-dimensional measurements of the observed brightness of the 9th November 1990Hαflare, using a PDS microdensitometer scanner and image processing software MIDAS. The resulting isophotal contour maps, were used to describe morphological-cum-temporal behaviour of the flare and also the kernels of the flare. Correlation of theHαflare with SXR and MW radiations were also studied.

Small Computer System for Micrograph Analysis

1981 ◽  
Vol 39 ◽  
pp. 270-271
Author(s):  
J. F. Hainfeld ◽  
J. S. Wall
Keyword(s):  
Large Range ◽  
Small Computer ◽  
Black And White ◽  
Contour Maps ◽  
Points Of Interest ◽  
Computer Aided Analysis ◽  
Specialized Hardware ◽  
Additional Memory ◽  
Selection Of ◽  
Publication Quality

Cost reduction and availability of specialized hardware for image processing have made it reasonable to purchase a stand-alone interactive work station for computer aided analysis of micrographs. Some features of such a system are: 1) Ease of selection of points of interest on the micrograph. A cursor can be quickly positioned and coordinates entered with a switch. 2) The image can be nondestructively zoomed to a higher magnification for closer examination and roaming (panning) can be done around the picture. 3) Contrast and brightness of the picture can be varied over a very large range by changing the display look-up tables. 4) Marking items of interest can be done by drawing circles, vectors or alphanumerics on an additional memory plane so that the picture data remains intact. 5) Color pictures can easily be produced. Since the human eye can detect many more colors than gray levels, often a color encoded micrograph reveals many features not readily apparent with a black and white display. Colors can be used to construct contour maps of objects of interest. 6) Publication quality prints can easily be produced by taking pictures with a standard camera of the T.V. monitor screen.

Two structural states of the Z-band in cardiac and skeletal muscle

1989 ◽  
Vol 47 ◽  
pp. 1022-1023
Author(s):  
J.P. Schroeter ◽  
M.A. Goldstein ◽  
J.P. Bretaudiere ◽  
L.H. Michael ◽  
R.L. Sass
Keyword(s):  
Skeletal Muscle ◽  
Cross Section ◽  
Real Space ◽  
Contractile State ◽  
Contour Maps ◽  
False Color ◽  
Grey Scale ◽  
Fourier Filtering ◽  
Cardiac Muscles ◽  
Enhancement Algorithm

We have recently established the existence of two structural states of the Z band lattice in cross section in cardiac as well as in skeletal muscle. The two structural states are related to the contractile state of the muscle. In skeletal muscle at rest, the Z band is in the small square (ss) lattice form, but tetanized muscle exhibits the basket weave (bw) form. In contrast, unstimu- lated cardiac muscle exhibits the bw form, but cardiac muscles exposed to EGTA show the ss form.We have used two-dimensional computer enhancement techniques on digitized electron micrographs to compare each lattice form as it appears in both cardiac and skeletal muscle. Both real space averaging and fourier filtering methods were used. Enhanced images were displayed as grey-scale projections, as contour maps, and in false color.There is only a slight difference between the lattices produced by the two different enhancement techniques. Thus the information presented in these images is not likely to be an artifact of the enhancement algorithm.

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