STANDARD CURVES FOR INTERPRETATION OF MAGNETIC ANOMALIES OVER LONG TABULAR BODIES

Geophysics ◽  
1963 ◽  
Vol 28 (2) ◽  
pp. 161-200 ◽  
Author(s):  
S. Parker Gay
Keyword(s):  
Finite Depth ◽  
Magnetic Anomalies ◽  
The Body ◽  
Profile Curve ◽  
Similar Form ◽  
Model Studies ◽  
Family Of Curves ◽  
Isolated Points ◽  
Depth Extent ◽  
Magnetizing Field

The magnetic anomalies in vertical, horizontal, and total intensity for the thin infinite dike are shown to belong to a single mathematical family of curves for all values of dip and strike of the dike and all values of inclination of the magnetizing field. The complete family of standard curves has been constructed and is incorporated into an interpretational scheme based on superposition with observed magnetic profiles. This technique should give more reliable interpretations than methods based on only a few isolated points of a profile curve. By integration of the general thin‐dike response a general expression of similar form has been derived for thick dikes, and ten sheets of curves for dikes of varying width indices have been constructed. By employing the method of subtraction of curves these serve for constructing anomaly profiles over bodies of finite depth extent. Additionally, for thin dikes the much‐neglected demagnetization corrections have been incorporated in the interpretational method following verification by model studies. One important disclosure of this work is that the depth and location of the apex of an infinite tabular body may be determined without knowing the intensity or direction of magnetization within the body, assuming only that these quantities are constant throughout.

STANDARD CURVES FOR MAGNETIC ANOMALIES OVER LONG HORIZONTAL CYLINDERS

Geophysics ◽  
1965 ◽  
Vol 30 (5) ◽  
pp. 818-828 ◽  
Author(s):  
S. Parker Gay
Keyword(s):  
Circular Cylinder ◽  
Magnetic Anomalies ◽  
Curve Matching ◽  
Profile Curve ◽  
Complete Family ◽  
Family Of Curves ◽  
Isolated Points ◽  
Horizontal Cylinders ◽  
Magnetizing Field ◽  
Horizontal Circular Cylinder

The magnetic anomalies in Z, H, and [Formula: see text] for the long horizontal circular cylinder are shown to belong to a single mathematical family of curves for all values of strike and all values of inclination of the magnetizing field, a characteristic that was previously shown to hold for long tabular bodies, or dikes (Gay, 1963). The complete family of standard curves has been constructed and is incorporated into an interpretational scheme based on superposition with observed magnetic profiles. Comparison of cylinder anomalies with dike anomalies shows only slight differences in the two types of curves, which would be very difficult, if not impossible, to detect using interpretational methods based on a few isolated points of a profile curve, such as half‐width, distance between maximum and minimum, etc. Curve‐matching, or superposition, appears to be mandatory for reliable quantitative interpretations.

A DIRECT COMPUTATION OF GRAVITY AND MAGNETIC ANOMALIES CAUSED BY 2- AND 3-DIMENSIONAL BODIES OF ARBITRARY SHAPE AND ARBITRARY MAGNETIC POLARIZATION BY EQUIVALENT‐POINT METHOD AND A SIMPLIFIED CUBIC SPLINE

Geophysics ◽  
1977 ◽  
Vol 42 (3) ◽  
pp. 610-622 ◽  
Author(s):  
Chao C. Ku
Keyword(s):  
Arbitrary Shape ◽  
Gaussian Quadrature ◽  
Magnetic Anomalies ◽  
Cubic Spline ◽  
The Body ◽  
Point Method ◽  
Magnetic Polarization ◽  
3 Dimensional ◽  
Equivalent Point ◽  
Gravity And Magnetic

A computational method, which combines the Gaussian quadrature formula for numerical integration and a cubic spline for interpolation in evaluating the limits of integration, is employed to compute directly the gravity and magnetic anomalies caused by 2-dimensional and 3-dimensional bodies of arbitrary shape and arbitrary magnetic polarization. The mathematics involved in this method is indeed old and well known. Furthermore, the physical concept of the Gaussian quadrature integration leads us back to the old concept of equivalent point masses or equivalent magnetic point dipoles: namely, the gravity or magnetic anomaly due to a body can be evaluated simply by a number of equivalent points which are distributed in the “Gaussian way” within the body. As an illustration, explicit formulas are given for dikes and prisms using 2 × 2 and 2 × 2 × 2 point Gaussian quadrature formulas. The basic limitation in the equivalent‐point method is that the distance between the point of observation and the equivalent points must be larger than the distance between the equivalent points within the body. By using a reasonable number of equivalent points or dividing the body into a number of smaller subbodies, the method might provide a useful alternative for computing in gravity and magnetic methods. The use of a simplified cubic spline enables us to compute the gravity and magnetic anomalies due to bodies of arbitrary shape and arbitrary magnetic polarization with ease and a certain degree of accuracy. This method also appears to be quite attractive for terrain corrections in gravity and possibly in magnetic surveys.

A PRELIMINARY REPORT ON MODEL STUDIES OF MAGNETIC ANOMALIES OF THREE‐DIMENSIONAL BODIES

Geophysics ◽  
1956 ◽  
Vol 21 (3) ◽  
pp. 794-814 ◽  
Author(s):  
Isidore Zietz ◽  
Roland G. Henderson
Keyword(s):  
Magnetic Fields ◽  
Rapid Method ◽  
Preliminary Report ◽  
Three Dimensional ◽  
Magnetic Anomalies ◽  
Constant Thickness ◽  
Laboratory Methods ◽  
Model Experiments ◽  
Model Studies ◽  
Different Depths

Model experiments were made to devise a rapid method for calculating magnetic anomalies of three‐dimensional structures. The magnetic fields of the models were determined using the equipment at the Naval Ordnance Laboratory, White Oaks, Md. An irregularly shaped mass was approximated by an array of prismatic rectangular slabs of constant thickness and varying horizontal dimensions. Contoured maps are being prepared for these magnetic models at different depths and for several magnetic inclinations. The fields of these three‐dimensional structures are obtained by super‐imposing the appropriate contoured maps and adding numerically the effects at each point. The equipment and laboratory methods are described. Theoretical and practical examples are given.

Theory of Short Wave Excitation

1986 ◽  
Vol 30 (03) ◽  
pp. 147-152
Author(s):  
Yong Kwun Chung
Keyword(s):  
Incident Wave ◽  
Characteristic Length ◽  
Finite Depth ◽  
Short Wave ◽  
The Body ◽  
Wave Number ◽  
Floating Body ◽  
Wave Excitation ◽  
Exciting Forces ◽  
Wave Exciting Forces

When the wavelength of the incident wave is short, the total surface potential on a floating body is found to be 2∅ i & O (m-l∅ i) on the lit surface and O (m-l∅ j) on the shadow surface where ~b i is the potential of the incident wave and m the wave number in water of finite depth. The present approximation for wave exciting forces and moments is reasonably good up to X/L ∅ 1 where h is the wavelength and L the characteristic length of the body.

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 Was the moon magnetized by impact plasmas?

2020 ◽  
Vol 6 (40) ◽  
pp. eabb1475
Author(s):  
Rona Oran ◽  
Benjamin P. Weiss ◽  
Yuri Shprits ◽  
Katarina Miljković ◽  
Gábor Tóth
Keyword(s):  
Magnetic Field ◽  
Interplanetary Magnetic Field ◽  
Magnetic Anomalies ◽  
The Moon ◽  
Crustal Field ◽  
Impact Simulations ◽  
Magnetizing Field

The crusts of the Moon, Mercury, and many meteorite parent bodies are magnetized. Although the magnetizing field is commonly attributed to that of an ancient core dynamo, a longstanding hypothesized alternative is amplification of the interplanetary magnetic field and induced crustal field by plasmas generated by meteoroid impacts. Here, we use magnetohydrodynamic and impact simulations and analytic relationships to demonstrate that although impact plasmas can transiently enhance the field inside the Moon, the resulting fields are at least three orders of magnitude too weak to explain lunar crustal magnetic anomalies. This leaves a core dynamo as the only plausible source of most magnetization on the Moon.

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.

An integral-equation method for determining the fluid motion due to a cylinder heaving on water of finite depth

1980 ◽  
Vol 372 (1748) ◽  
pp. 93-110 ◽  
Keyword(s):  
Integral Equation ◽  
Fundamental Solution ◽  
Integral Equations ◽  
Fluid Motion ◽  
Integral Equation Method ◽  
Finite Depth ◽  
The Body ◽  
Wave Source ◽  
Method Of Integral Equations ◽  
Infinite Set

The method of integral equations is used here to calculate the virtual mass of a half-immersed cylinder heaving periodically on water of finite constant depth. For general sections this method is more appropriate than the method of multipoles; particular sections that are considered are the circle and the ellipse. Green’s theorem is applied to the potential and to a fundamental solution (wave source) satisfying the conditions at the free surface, at the bottom and at infinity, but not necessarily on the body. An integral equation for the potential on the body only is thus obtained. For the simplest choice of fundamental solution the method breaks down at a discrete infinite set of frequencies, as is well known. When the fundamental solution was modified, however, a different integral equation could be obtained for the same unknown function and this was found not to break down for the circle and ellipse. The present numerical results are in good agreement with those obtained by the method of multipoles which for the circle is more efficient than the method of integral equations but which is not readily applicable to other sections. Much effort now goes into such calculations.

Radiation of waves by a cylinder submerged in water with ice floe or polynya

2015 ◽  
Vol 784 ◽  
pp. 373-395 ◽  
Author(s):  
Izolda V. Sturova
Keyword(s):  
Elastic Plate ◽  
Diffraction Problem ◽  
Open Water ◽  
Finite Depth ◽  
The Body ◽  
Elastic Plates ◽  
Radiation Problem ◽  
Radiation Load ◽  
Body Contour ◽  
Damping Coefficients

The problems of radiation (sway, heave and roll) of surface and flexural-gravity waves by a submerged cylinder are investigated for two configurations, concerning; (i) a freely floating finite elastic plate modelling an ice floe, and (ii) two semi-infinite elastic plates separated by a region of open water (polynya). The fluid of finite depth is assumed to be inviscid, incompressible and homogeneous. The linear two-dimensional problems are formulated within the framework of potential-flow theory. The method of mass sources distributed along the body contour is applied. The corresponding Green’s function is obtained by using matched eigenfunction expansions. The radiation load (added mass and damping coefficients) and the amplitudes of vertical displacements of the free surface and elastic plates are calculated. Reciprocity relations which demonstrate both symmetry of the radiation load coefficients and the relation of damping coefficients with the far-field form of the radiation potentials are found. It is shown that wave motion essentially depends on the position of the submerged body relative to the elastic plate edges. The results of solving the radiation problem are compared with the solution of the diffraction problem. It is noted that resonant frequencies in the radiation problem correlate with those frequencies at which the reflection coefficient in the diffraction problem has a local minimum.

Interpretation of three‐component borehole magnetometer data

Geophysics ◽  
1981 ◽  
Vol 46 (12) ◽  
pp. 1721-1731 ◽  
Author(s):  
João B. C. Silva ◽  
Gerald W. Hohmann
Keyword(s):  
Magnetization Vector ◽  
The Body ◽  
Sensitivity Matrix ◽  
Value Analysis ◽  
Data Density ◽  
Magnetometer Data ◽  
Length Width ◽  
Scaling Matrix ◽  
Probe Orientation ◽  
Depth Extent

We have made a theoretical study of the problem of locating and defining a magnetized prism in the vicinity of a drillhole. The study shows that a three‐component borehole magnetometer can be very useful in exploration for deep magnetic targets, which are difficult to intersect by drilling. There are nine parameters to be estimated from the data: the x, y, and z positions of the center of the prism; length, width and depth extent; and the three parameters defining the magnetization vector. The parameters are estimated by minimizing the sum of squared differences between the predicted and observed data. Since the problem is nonlinear, it must be solved iteratively. At each iteration a singular value analysis of the sensitivity matrix is performed, and a particular solution is chosen from a set of minimal length solutions; each solution corresponds to a different rank of the sensitivity matrix. The main difficulty is an ambiguity involving the position parameters and the parameters defining the magnetization vector. In order to minimize this obstacle, a parameter scaling matrix is introduced. The effects of noise, wrong model, probe orientation errors, borehole length, and data density are analyzed. We have found that the position and depth extent of the body can be estimated with reasonable accuracy.

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