On: “Interpretation of some two‐dimensional magnetic bodies using Hilbert transforms, by N. L. Mohan, N. Sundararajan, and S. V. Seshagiri (GEOPHYSICS, 47, 376–387, March, 1982)

Geophysics ◽  
1987 ◽  
Vol 52 (2) ◽  
pp. 239-240
Author(s):  
R. Nagendra ◽  
H. V. Ram Babu
Keyword(s):  
Magnetic Anomalies ◽  
Two Dimensional ◽  
Hilbert Transforms ◽  
The Subject

We read Mohan et al.’s paper on interpretation of magnetic anomalies using Hilbert transforms and the discussion raised on it by Pauls (1985) and the authors’ reply (Mohan et al., 1985). While critically going through the authors’ reply (Mohan et al., 1985), we noticed a serious error in the subject paper related to the incompatibility of its equations (1) and (2).

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.

Two-dimensional buoyant plumes in a uniform co-flow

2021 ◽  
Vol 932 ◽  
Author(s):  
Gary R. Hunt ◽  
Jamie P. Webb
Keyword(s):  
Theoretical Investigation ◽  
Analytical Solutions ◽  
Richardson Number ◽  
Relative Magnitude ◽  
Dynamical Behaviour ◽  
Finite Width ◽  
Two Dimensional ◽  
Buoyant Plumes ◽  
The Subject ◽  
Flow Case

The behaviour of turbulent, buoyant, planar plumes is fundamentally coupled to the environment within which they develop. The effect of a background stratification directly influences a plumes buoyancy and has been the subject of numerous studies. Conversely, the effect of an ambient co-flow, which directly influences the vertical momentum of a plume, has not previously been the subject of theoretical investigation. The governing conservation equations for the case of a uniform co-flow are derived and the local dynamical behaviour of the plume is shown to be characterised by the scaled source Richardson number and the relative magnitude of the co-flow and plume source velocities. For forced, pure and lazy plume release conditions the co-flow acts to narrow the plume and reduce both the dilution and the asymptotic Richardson number relative to the classic zero co-flow case. Analytical solutions are developed for pure plumes from line sources, and for highly forced and highly lazy releases from sources of finite width in a weak co-flow. Contrary to releases in quiescent surroundings, our solutions show that all classes of release can exhibit plume contraction and the associated necking. For entraining plumes, a dynamical invariance spatially only occurs for pure and forced releases and we derive the co-flow strengths that lead to this invariance.

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.

COMMENTS ON “INTERRELATIONSHIPS BETWEEN MAGNETIC ANOMALY COMPONENTS”

Geophysics ◽  
1959 ◽  
Vol 24 (2) ◽  
pp. 366-369 ◽  
Author(s):  
Aivars Celmins
Keyword(s):  
Magnetic Field ◽  
Magnetic Anomaly ◽  
Simple Formula ◽  
Magnetic Anomalies ◽  
Horizontal Component ◽  
Two Dimensional ◽  
Interesting Behavior ◽  
Normal Magnetic Field

On page 748 of the above named paper, Affleck (1958) mentions an interesting behavior of magnetic anomalies which are caused by homogeneous magnetized two‐dimensional bodies. He states that in these cases the airborne magnetometer anomaly can be treated as either the vertical or horizontal component anomaly if the true magnetization is replaced by a pseudo‐magnetization of other direction and intensity. It may be of some interest to formulate this behavior more precisely, so much the more as the interdependence between the magnetization directions and the direction of a normal magnetic field can be expressed by a rather simple formula.

On: “Simulating true amplitude reflections by stacking shot records,” by P. Hubral (GEOPHYSICS, v. 49, p. 303–306, 1984).

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1806-1807
Author(s):  
Th. Krey
Keyword(s):  
Short Note ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Precise Result ◽  
Normal Waves ◽  
Analytical Derivation ◽  
The Subject ◽  
Line Survey ◽  
Zero Offset

Quite recently Peter Hubral published a short note in which he described a special, very perspicuous stacking method which, starting from the records of a line survey, produces true amplitude reflections for “normal waves,” as defined in his Introduction. In the following I want to supplement Hubral’s note by showing the analytical connection with Hubral’s earlier paper (Hubral, 1983) and the additional short note by Krey (Krey, 1983). My present investigation will be two‐dimensional (2-D) as is that in the subject paper; an extension to the three‐dimensional (3-D) case is conceptionally easy for the following analytical derivation as well as for Hubral’s note. Besides a basic confirmation of Hubral’s findings, I shall show that the result of Hubral’s method has still to be multiplied by [Formula: see text] in the 2-D case and by [Formula: see text] in the 3-D case in order to obtain the precise result. Here ω is the frequency. Moreover the angle of emergence α of the zero‐offset raypath has to be taken into account.

Reply by the authors to R. Pauls

Geophysics ◽  
1985 ◽  
Vol 50 (1) ◽  
pp. 168-169
Author(s):  
N. L. Mohan ◽  
N. Sundararajan ◽  
S. V. Seshagiri Rao
Keyword(s):  
Two Dimensional ◽  
Hilbert Transforms ◽  
Keen Interest

We appreciate the keen interest evinced by Mr. Rob Pauls on our article “Interpretation of some two‐dimensional magnetic bodies using Hilbert transforms.” We are very sorry to note that Mr. Pauls has made hasty comments without going through our article critically.

scholarly journals Analytic materials

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160613 ◽  
Author(s):  
Graeme W. Milton
Keyword(s):  
Connected Domain ◽  
Free Field ◽  
Exact Results ◽  
Two Dimensional ◽  
Simply Connected Domain ◽  
Maximum Value ◽  
Two Dimensional Materials ◽  
The Subject ◽  
Simply Connected ◽  
Made In

The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer p . If p takes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rank p . For two-dimensional materials, further progress can be made in the identification of analytic materials by using the well-known fact that a 90 ° rotation applied to a divergence-free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.

Binary model for two-dimensional magnetic anomalies

1971 ◽  
Vol 12 (1) ◽  
pp. 108-118 ◽  
Author(s):  
Richard J. Blakely ◽  
Allan Cox
Keyword(s):  
Magnetic Anomalies ◽  
Two Dimensional ◽  
Binary Model
Sign in / Sign up

Export Citation Format

Share Document