Gravity interpretation using the Mellin transform

Geophysics ◽  
1986 ◽  
Vol 51 (1) ◽  
pp. 114-122 ◽  
Author(s):  
N. L. Mohan ◽  
L. Anandababu ◽  
S. V. Seshagiri Rao
Keyword(s):  
Circular Cylinder ◽  
Gravity Anomaly ◽  
Mellin Transform ◽  
The Body ◽  
Two Dimensional ◽  
Gravity Effect ◽  
Horizontal Derivative ◽  
Gravity Interpretation ◽  
Body Parameters ◽  
Horizontal Circular Cylinder

The Mellin transform of the gravity effect of a buried sphere and two‐dimensional horizontal circular cylinder, and the first horizontal derivative of the gravity effect of a two‐dimensional thin fault layer are derived. The transformed functions are bounded by two asymptotes. They are analyzed and procedures are formulated excluding the asymptotic regions for the extraction of the body parameters. The application of the Mellin transform is tested on simulated models as well as on two field examples: (1) the Humble Dome gravity anomaly near Houston, USA; and (2) the Louga gravity anomaly, USA.

A comparative study of the relation figures of magnetic anomalies due to two‐dimensional dike and vertical step models

Geophysics ◽  
1982 ◽  
Vol 47 (6) ◽  
pp. 926-931 ◽  
Author(s):  
H. V. Ram Babu ◽  
A. S. Subrahmanyam ◽  
D. Atchuta Rao
Keyword(s):  
Comparative Study ◽  
Major Axis ◽  
Magnetic Anomalies ◽  
The Body ◽  
Two Dimensional ◽  
Depth Ratio ◽  
Characteristic Points ◽  
Vertical Step ◽  
Bottom To Top ◽  
Body Parameters

Magnetic anomalies in vertical and horizontal components, when plotted one against the other in polar form, result in a curve called the relation figure (Werner, 1953). In this paper, a comparative study of the relation figures of magnetic anomalies due to two‐dimensional (2-D) dike and vertical step models is made. The relation figures for these two models are found to be ellipses with different properties. The tangent at the origin to the ellipse is parallel to the major axis of the ellipse for the dike model, whereas it is perpendicular to the major axis for the vertical step. This property may be used to distinguish whether the source is a dike or a vertical step. For both of the models, the angle made by the axis of symmetry of the ellipse with the coordinate axis is equal to θ, the combined magnetic angle. The ratio between the lengths of the major and minor axes of the ellipse is directly related to the width‐to‐depth ratio of the dike or the bottom‐to‐top depth ratio of the vertical step. A few characteristic points defined on the ellipse are used to evaluate the body parameters. The major portion of the ellipse is obtained in the close vicinity of the source. Because of symmetry, the ellipse may be extrapolated easily outside the data length, and hence the effect of noise caused by adjacent objects is kept at a minimum.

A LEAST‐SQUARES PROCEDURE FOR GRAVITY INTERPRETATION

Geophysics ◽  
1965 ◽  
Vol 30 (2) ◽  
pp. 228-233 ◽  
Author(s):  
Charles E. Corbató
Keyword(s):  
Least Squares ◽  
High Speed ◽  
Gravity Anomalies ◽  
The Body ◽  
Two Dimensional ◽  
Partial Derivatives ◽  
Dimensional Gravity ◽  
Gravity Interpretation ◽  
Relationship Of ◽  
Derivatives Of

A procedure suitable for use on high‐speed digital computers is presented for interpreting two‐dimensional gravity anomalies. In order to determine the shape of a disturbing mass with known density contrast, an initial model is assumed and gravity anomalies are calculated and compared with observed values at n points, where n is greater than the number of unknown variables (e.g. depths) of the model. Adjustments are then made to the model by a least‐squares approximation which uses the partial derivatives of the anomalies so that the residuals are reduced to a minimum. In comparison with other iterative techniques, convergence is very rapid. A convenient method to use for both the calculation of the anomalies and the adjustments is the two‐dimensional method of Talwani, Worzel, and Landisman, (1959) in which the outline of the body is polygonized and the anomalies and the partial derivatives of the anomaly with respect to the depth of a vertex on the body can be expressed as functions of the coordinates of the vertex. Not only depths but under certain circumstances regional gravity values may be evaluated; however, the relationship of the disturbing body to the gravity information may impose certain limitations on the application of the procedure.

On: “Gravity Interpretation Using the Fourier Integral”, by M. E. Odegard and J. W. Berg, Jr. (GEOPHYSICS, June 1965, p. 127–138)

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 356-357
Author(s):  
Jay Gopal Saha
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
Fourier Integral ◽  
Two Dimensional ◽  
Transform Method ◽  
Reverse Problem ◽  
Vertical Fault ◽  
Vertical Step ◽  
The Fourier Transform ◽  
Gravity Interpretation

In their paper, Odegard and Berg claim that from the gravity anomaly due to a two‐dimensional vertical fault the density, the throw, and the depth can be determined uniquely by a Fourier transform method. It is true that the solution of the reverse problem for a two‐dimensional vertical step is theoretically unique. The derivation of the Fourier transform by the authors, however, is erroneous.

Transient Growth of Three-Dimensional Vortex Perturbations During Near-Parallel Collision With a Circular Cylinder

2006 ◽  
Author(s):  
X. Liu ◽  
J. S. Marshall
Keyword(s):  
Circular Cylinder ◽  
Vortex Core ◽  
Computational Study ◽  
Three Dimensional ◽  
The Body ◽  
Transient Growth ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Flow Features

A computational study is reported that examines the transient growth of three-dimensional flow features for nominally parallel vortex-cylinder interaction problems. We consider a helical vortex with small-amplitude perturbations that is advected onto a circular cylinder whose axis is parallel to the nominal vortex axis. The study assesses the applicability of the two-dimensional flow assumption for parallel vortex-body interaction problems in which the body impinges on the vortex core. The computations are performed using an unstructured finite-volume method for an incompressible flow, with periodic boundary conditions along the cylinder axis. Growth of three-dimensional flow features is quantified by use of a proper-orthogonal decomposition of the Fourier-transformed velocity and vorticity fields in the cylinder azimuthal and axial directions. The interaction is examined for different axial wavelengths and amplitudes of the initial helical waves on the vortex core, and the results for cylinder force are compared to the two-dimensional results. The degree of perturbation amplification as the vortex approaches the cylinder is quantified and shown to be mostly dependent on the dominant axial wavenumber of the perturbation. The perturbation amplification is observed to be greatest for perturbations with axial wavelength of about 1.5 times the cylinder diameter.

scholarly journals The vertical force on a cylinder submerged in a uniform stream

1929 ◽  
Vol 122 (790) ◽  
pp. 387-393 ◽  
Keyword(s):  
Circular Cylinder ◽  
Wave Resistance ◽  
Point Sources ◽  
The Body ◽  
Resultant Force ◽  
Dimensional Case ◽  
Vertical Force ◽  
Horizontal Force ◽  
Two Dimensional ◽  
Sources And Sinks

1. The horizontal force on a circular cylinder immersed in a stream is familiar as an example of wave resistance. The following note supplies a similar calculation for the resultant vertical force. The problem was sug­gested in a consideration of the forces on a floating body in motion, the hori­zontal and vertical forces and the turning moment; but the case of a partially immersed body presents great difficulties. It seemed, however, of sufficient interest to compare the resultant horizontal and vertical forces for a simple case of complete immersion for which the calculations can be carried out. The horizontal force, or wave resistance, has usually been obtained indirectly from considerations of energy, but a different method is adopted here for both components of force and the turning moment. In a former paper the method of successive images was applied to the problem of the circular cylinder, taking images alternately in the surface of the cylinder and in the free surface of the stream. Using these results to the required stage of approximation, the com­plete force on the cylinder is now obtained as the resultant of forces between the sources and sinks within the cylinder and those external to it. The same method can be applied to any submerged body for which the image sytems are known, and the resultant force and couple calculated in the same manner. The proposition used in this method is that for a body in a fluid, the motion of which is due to given sources and sinks, the resultant force and couple on the body are the same as if the sources and their images attract in pairs accord­ing to a simple law of force, inverse distance for the two-dimensional case and inverse square of the distance for point sources. This fairly obvious proposition follows directly from a contour integration in the two-dimensional case; and, in view of the application, the extension is given in 2 when the flow is due to a distribution of doublets. In 3 the horizontal and vertical force on a circular cylinder are obtained by this method, the former agreeing with the usual expression for the wave resistance. The different variation of the two components with velocity is of interest, and the expressions are graphed on the same scale. The additional vertical force due to velocity changes direction at a certain speed, and is clearly associated more with the surface elevation immediately over the centre of the cylinder. In 4 reference is made to the couple on the cylinder. This should, of course, be zero for a complete solution; it is verified that the method used here gives zero moment up to the stage of approximation in terms of the ratio of the radius of the cylinder to the depth of its centre.

Two-dimensional vortex motion in the cross-flow of a wing-body configuration

1995 ◽  
Vol 305 ◽  
pp. 93-109 ◽  
Author(s):  
T. W. G. De Laat ◽  
R. Coene
Keyword(s):  
Circular Cylinder ◽  
Initial Conditions ◽  
Vortex Motion ◽  
Cross Flow ◽  
Vortex Pair ◽  
The Body ◽  
Two Dimensional ◽  
Oncoming Flow ◽  
Stagnation Flow ◽  
Closed Orbits

For a two-dimensional potential flow, Föppl obtained the equilibrium positions for a symmetric vortex pair behind a circular cylinder in a uniform oncoming flow. In this article it is shown that such an equilibrium is in general possible for a vortex in a stagnation flow (e. g. in a corner). Furthermore it is found that a vortex near such an equilibrium position will rotate with a definite frequency around this equilibrium. Expressions are derived for the frequencies associated with the closed orbits of the vortices in the case of equilibrium of a vortex in a stagnation flow and for the equilibrium of the symmetric vortex pair behind a circular cylinder in oncoming flow. For the large-amplitude case the vortex trajectories are claculated using a fifth-order Runge-Kutta integration method. The analysis is then extended to the case of a simple wing-body combination in a cross-flow such as arises for a slender aircraft at an angle of attack with vortices generated by strakes or at the front part of the body. At the wint-body junctions the motions of the vortices may be periodic, quasi-periodic or the vortices may be swept away, depending on the initial conditions.

Interpretation of some two‐dimensional magnetic bodies using Hilbert transforms

Geophysics ◽  
1982 ◽  
Vol 47 (3) ◽  
pp. 376-387 ◽  
Author(s):  
N. L. Mohan ◽  
N. Sundararajan ◽  
S. V. Seshagiri Rao
Keyword(s):  
Circular Cylinder ◽  
Andhra Pradesh ◽  
Theoretical Models ◽  
Magnetic Anomalies ◽  
Two Dimensional ◽  
Hilbert Transforms ◽  
Infinite Depth ◽  
The Hilbert Transform ◽  
Depth Extent ◽  
Horizontal Circular Cylinder

Procedures are formulated using the Hilbert transform for interpreting vertical magnetic anomalies of (1) the sheets (finite and infinite depth extent), (2) the dike, and (3) the horizontal circular cylinder. The applicability of the method is tested on theoretical models. The method is also applied on the well‐known Kursk field anomaly of a sheet (infinite‐depth extent) and the field anomaly of a dike of Karimnagar, Andhra Pradesh, India.

scholarly journals Unsteady magnetohydrodynamic mixed convection flow with heat and mass transfer over a horizontal circular cylinder embedded in a porous medium

2016 ◽  
Vol 20 (suppl. 5) ◽  
pp. 1381-1390
Author(s):  
Branko Boricic ◽  
Aleksandar Boricic
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Circular Cylinder ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Thermal Parameter ◽  
Magnetic Reynolds Number ◽  
The Body ◽  
Convection Flow ◽  
Horizontal Circular Cylinder

The objective of the present study is to investigate the effect of flow parameters on the mixed convection heat and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompressible fluid over a horizontal circular cylinder embedded in porous medium, considering effects of chemical reaction and heat source/sink, by taking into account viscous dissipation. The present magnetic field is homogenous and perpendicular to the body surface. Magnetic Reynolds number is significantly lower than one i. e. considered the problem is in approximation without induction. The governing non-linear partial differential equations and associated boundary conditions are made dimensionless using a suitable similarity transformation and similarity parameters. System of non-dimensionless equations are solved numerically by implicit finite difference three-diagonal and iteration method. Numerical results obtained for different values of porous medium, magnetic, diffusion and temperature parameters, buoyancy diffusion parameter and thermal parameter and for different values Prandtl, Echart, and Schmidt numbers. Variation of velocity, temperature and concentration and many integral and differential characteristics boundary layer are discussed and shown graphically.

The motions of a floating slender torus

1977 ◽  
Vol 83 (4) ◽  
pp. 721-735 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Circular Cylinder ◽  
Asymptotic Expansions ◽  
The Body ◽  
Ship Motions ◽  
Two Dimensional ◽  
Scattering Problems ◽  
Incident Wavelength ◽  
Strip Theory ◽  
Incident Waves ◽  
Body Section

The motions of a floating torus oscillating in response to incident waves are analysed under the assumptions that the incident wavelength is comparable with the radius of the body section and small compared with the larger radius of the torus. This problem serves to illustrate certain features of the strip theory for ship motions, but the axisymmetric geometry and absence of body ends greatly simplify the analysis. Matched asymptotic expansions are used, with the inner solution close to the body section composed of suitable radiation and scattering problems for the two-dimensional circular cylinder. Resonant standing-wave modes in the internal basin have a singular effect upon the hydrodynamic forces acting on the body, and its response to incident waves.

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.

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