Eotvos Torsion Balance Research Articles

Effect of the starting azimuth uncertainty in Eötvös-torsion balance measurements

The magnitude of the impact of the incorrect setting of the starting azimuth on the gradients established by the Eotvos torsion balance was tested at two different kind of area. According to the results, gradients measured by the Eotvos torsion balance are extremely sensitive regarding the precise adjustment of the starting azimuth if the vectors of gradients are high. Furthermore, the worst deviances were experienced in the case of curvature gradients i.e. the most important gradients for geodetic use.

Determination of the vertical gradients based on Eötvös torsion balance measurements

The value of the vertical gradient in any given point can be determined using Haalck’s method. The vertical gradient is the sole element of the Eotvos-tensor, which cannot be measured by the Eotvos torsion balance; however, the Haalck-method enables its calculation through interpolation. Eotvos-tensor measurement fluctuation between two adjacent points must be linear in order for the Haalck-method to work. This paper sought to analyze this assumption of linearity.

Too old for Modern Exploration? Old Torsion Balance Observations Revisited

Although gravity gradiometry was among the first geophysical methods used successfully in applied geophysics (Eotvos torsion balance), the technology fell from favour after the 1930s. Here we present a new analysis of torsion balance measurements that were made at this time to detect salt domes in the Northwest German Basin.The study was aimed at assessing methods for interpretation of torsion balance observations. The approach is to synthesize classical procedures with computer based numerical methods, taking horizontal gradients Wxz and Wyz as input parameters. First we give an overview of torsion balance operational details and then discuss the interpretation of torsion balance data.A total of 39 maps at 1:25,000 scale covering the Northwest German Basin have been digitised. These maps provide some 40,000 torsion balance measurements, but no field books or field forms are available. The gradients were digitised from old paper maps, then reprocessed and recalculated. 3D modelling of Wxz, Wyz and other components of the Eotvos tensor provides detailed insight into the geometry of salt domes and provides additional constraints for modelling the Bouguer gravity field.3D forward modelling is conducted using the IGMAS program package. This package allows the calculation of potential, gravity and its components, and the Eotvos tensor components. Results show that knowledge of the second derivatives of the potential could fundamentally change the role of gravity field measurements in underground investigations, not only for resource exploration, but also for investigations of large fault systems like the Dead Sea Transform.

Geodesy and the Torsion Balance

In the past the Eotvos torsion balance has been used only in commercial geophysical explorations and not for geodetic purposes. Even in geophysics, after approximately 30 yrs of use, it was superseded by the faster, and handier gravimeters. The lack of interest in the geodetic applications can be explained partly by the fact that geodesists of the past did not need very detailed information about the shape of the earth. The torsion balance offers several possibilities in geodetic applications, of which the most important are: The interpolation of deflections of the vertical and of geoid undulations between reference stations, where gravity material is not sufficient; the determination of the geopotential values in a given area for the purpose of leveling reductions; the determination of the radius of curvature of the plumb line for reducing astronomical coordinates to the geoid; and the investigation of curvature properties of the equipotential surface for more accurate baseline reductions to the ellipsoid of reference.

Eötvös torsion balance model E-54

The automatically rotating and photographically recording Eotvos torsion balance, model E-54, is supplied with excellent torsion wires, built into a balance housing of quadruple wall with layers of air and carefully adjusted so that exterior temperature fluctuations do not influence the positions of equilibrium of the balances. The instrument is photographing upon the plate the scale and the reticle so that the positions of equilibrium of the balances may be read simply by means of a magnifying glass, without any measuring. The instrument is simultaneously photographing the numbers of the instrument and station upon the plate, thus the troubles caused by mistakes or faulty notes are eliminated. — A mechanical device accomplishes the exposure and sets aftewards the instrument in rotation. Actual sensitivity of the balances as to the gradient is 0.255×10−9 CGS=0.255 Eotvos-unit, as to the curvature=0.724 Eotvos-unit referred to one tenth of the scale division, Relaxation time of the balance is 40 minutes. This study proving with original photographs and the interpretation of the same the sensitivity and high reliability of the instrument.

Case Histories and Quantitative Calculations in Gravimetric Prospecting

Of the four papers that comprise this TECHNICAL PUBLICATION, three are casehistories of individual geophysical prospects, subsequently tested bydrilling. The bibliography of Dr. Barton's published scientific papers includesinvestigations in physiography and surface geological mapping, as well as hisgeophysical papers, and from this list it is to be observed that he earlyrecognized the place of different types of geophysical prospecting methods inthe search for geological structures of economic importance. Moreover, hisviewpoint was not merely that the structures should be found, but that thegeophysical data should be examined quantitatively to determine the geometry ofthe structures. In other words, that although these data are insufficient todeduce a unique form for the structure that caused the effects measured in thedata, the engineering computations should be carried out to give as much of adefinite configuration to the structure as the data permitted, in order thatthe testing of the structures could be conducted in the most economical mannerand with the idea that the experience so gained could be later incorporated inthe study of structures subsequently found. Dr. Barton continually emphasized the quantitative use of geophysicalobservations, whereas at the time that he began his specialization ingeophysics it was considered sufficient to use observations only qualitatively.He, more than anyone else, was responsible for the first volume on geophysicalprospecting issued by the Institute in 1929, and his three articles in thatvolume stressed the quantitative use of geophysical prospecting. The fourth article in this present TECHNICAL PUBLICATION is a furthercontribution to this branch of geophysical interpretation, and is a supplementto the paper in the 1929 volume, "Calculations in the Interpretation ofObservations with the Eotvos Torsion Balance." T.P. 1760

A simple method of demonstrating the paramagnetism and diamagnetism of substances in magnetic fields of low intensity

The instrument described is the result of an attempt to construct a magnetic gradiometer capable of measuring small distortions of the earth's magnetic field in the same way as the Eotvos torsion balance measures non-uniformities of gravity. Although this purpose has not yet been achieved the first model of the instrument has revealed itself as a means of demonstrating in a convincing manner the paramagnetism or diamagnetism of substances of small susceptibility, for example, the diamagnetism of a few cubic centimetres of water. Moreover, the magnetizing fields employed are much smaller than has hitherto been customary, being of the order of 50 gauss or less. This first model of the instrument is imperfect in certain respects, mainly on account of the use of some brass in the construction. The objections to this material, on account of its ferromagnetic content, were not at first realized, and it will be necessary to construct a new apparatus, employing carefully chosen materials, before full advantage can be taken of the sensitivity available, and demonstration refined to precise measurement. It seems certain that gases also may be brought within the scope of accurate determination, particularly if access can be had to a suitable laboratory. The present apparatus, however, behaves well enough to warrant description, which is made pending the projected modifications. The system used also provides a basis for the construction of a new form of very sensitive galvanometer, and this matter is discussed briefly.

Societies and Academies

LONDON Royal Society, January 18. B. F. J. SCHONLAND and H. COLLENS: Progressive lightning. Eleven lightning flashes, comprising fifty separate strokes from two separate thunderstorms, have been photographed with a rotating lens camera based upon the design of C. V. Boys. The speed was fast enough to permit the study of the propagation of the discharge. The majority of the strokes were double and consisted of a dart-like downward-moving leader stroke, followed immediately upon arrival at the ground by a more intense flame-like upward-moving main stroke. The mean velocity of the leader strokes was 1-1×109 cm./sec. along the tortuous track in two dimensions and 7-0×108 cm./sec. in the vertical direction. The dart was less than 54 metres long. Corresponding mean velocities for the main strokes were 6-0×109 cm./sec. and 3-8×109 cm./sec. The leader strokes are identifiable with electron avalanches and the main strokes with thermally ionised channels. The cloud base was negative and the earth positive. A. O. RANKINE: A simple method of demonstrating the paramagnetism and diamagnetism of substances in magnetic fields of low intensity. The instrument described is the result of an attempt to construct a magnetic gradiometer capable of measuring small distortions of the earth's magnetic field in the same way that the Eotvos torsion balance measures non-uniformities of gravity. Although this purpose has not yet been achieved, the first model of the instrument has revealed itself as a means of demonstrating the paramagnetism or diamagnetism of substances of small susceptibility. Moreover, the magnetising fields employed are much smaller than has hitherto been customary, being of the order of 50 gauss or less. The system used also provides a basis for the construction of a new form of very sensitive galvanometer. C. W. GILBERT: The production of showers by cosmic radiation. Experiments made with triple coincidence counters showed that the frequency of showers produced in lead by the passage of cosmic radiation is proportional to the general cosmic radiation. The transition curves for air to lead were obtained at 3,500 m., and it was found that there the energy of the shower particles was greater than at sea-level. To explain the curves obtained, three types of radiation are needed, a primary radiation, a shower-producing radiation and the shower particles.

Accuracy of Determination of Relative Gravity by Torsion Balance

Determination of relative gravity by the Eotvos torsion balance has been shown by Oltay and others to be as accurate as the determination by the invariable pendulum. In the present paper, the probable error of the torsion balance determination of relative gravity is calculated from the error of closure of 45 traverses comprising 2,800 stations, most of them in the Gulf Coast region. The probable error of each individual observation in those surveys is calculated to have been ±2.2 Eotvos units for the traverses taken together, or from ±1.9 E for the traverses with the larger station interval to ±5 E for the traverses for the small station interval. But the greater error of the individual observations in the traverses which have the shorter station interval h s been compensated, intentionally, by that shorter interval, and the probable error of the determination of relative gravity by those 45 traverses is approximately 0.4 milledyne per 10 kilometers of traverse without regard to the magnitude of the probable error of the individual observations or of the station interval. The probable error of the determination of relative gravity between key points in good torsion balance surveys presumably is approximately ±2.5 to ±3.5 E per 10 kilometers airline distance between the two places. If pendulum determinations of relative gravity are used to supplement and to increase the accuracy of torsion balance surveys, there is a minimum interval at which the pendulum stations should be placed, for at lesser intervals the determination of relat ve gravity by the torsion balance is more accurate than that by the pendulum. That minimum interval ranges from 100 to 200 kilometers for the pendulum observations of the first quarter of the century to 8 to 50 kilometers for first class modern pendulum observations.

On the proportionality of mass and weight

In a previous paper* the writer has described some experiments carried out under the direction of Prof. 0. W. Richardson on the gravitational acceleration of substances rich in hydrogen. It was pointed out that the nuclei of all elements are probably built up of hydrogen and helium nuclei, and that the substances on which gravitational experiments have been performed might in nearly all cases be considered as consisting almost entirely oi the latter. By use of the pendulum method the gravitational accelerations of ammonium fluoride and paraffin wax were compared with that of brass. According to the suggestions put forward in the paper referred to, these two substances would contain 24 per cent, and 15 per cent, of hydrogen respectively, whereas brass would consist almost entirely of helium. A small effect, amounting to about one part in 70,000, which made substances rich in hydrogen appear to have an acceleration greater than the normal value was obtained. This was attributed to experimental error, but further tests appeared desirable. The experiments have recently been repeated using an Eotvos torsion balance. This instrument, which compares for different substance the ratio of the force due to the earth’s rotation and that due to its attraction, is capable of an accuracy far greater than that obtainable with the pendulum.

Book Reviews

As the title indicates, this book is largely influenced by the economic aspect of geophysics. Prominence is given to the discovery of ores and salt deposits by means of the Eotvos torsion balance, and by seismological and magnetic methods. Most of the book deals, however, with the purely scientific parts of the subject. It contains a bibliography of about 1700 references, but unfortunately there are signs that they have not all been verified, and the author seldom gives much information himself, referring the reader instead to original sources, with little indication of what is to be found there.

Torsion-Balance Principles as Applied by the Original Eotvos Torsion Balance

With the original type of torsion balance three to four stations a day can be taken with a crew of three men and two light trucks with a large instrument, or two men and one truck with the new smaller instrument. The distance between stations depends upon the type of the survey and the conditions of terrain and structure. The observed gradient must be corrected for terrain effects. The principle of interpretation of torsion-balance results is that the gravity gradient is toward the heavier mass and is the greater the heavier the mass, the nearer the heavy mass is to the surface, and the steeper its flank. In the case of a dome such as a salt dome, heavier than the country rock, the gradient is toward the center of the dome, is zero on top of the dome, and is opposite in d rection on opposite sides of the dome. If the dome is lighter than the country rock, the gradient is away from the dome. The gradient existing above such a dome is illustrated by the results of the surveys of two salt domes in the Gulf Coast. In the case of an anticline the gradient is toward the axis. In the case of a fault, the gradient reverses across the fault, but differs in intensity on the up- and down-throw sides of the fault. The gradient relations above a series of hypothetical faults and folds are illustrated by the results of a torsion-balance survey in Texas. The irregular gradient conditions caused by irregular subsurface structure are illustrated by a torsion-balance survey in the vicinity of the Kellum lease in the Powell field, Texas.

The Tendency of Elongated Bodies to Set in the East and West Direction

PERHAPS readers of NATURE will recognise the principle of the Eotvos torsion balance in the communication of Sir Arthur Schuster published in NATURE of October 20 (p. 240) entitled “The Tendency of Elongated Bodies to Set in the North and South Direction.” The calculation there given is, however, incomplete, and this causes the sign of the effect to be reversed. For the hypothetical “normal case” a complete calculation shows that the tendency is rather for an elongated body to set itself in an east and west direction. The missing element in the calculation is the difference in the directions of the centrifugal force on the different portions of the rod. If we call λ the longitude, reckoned from the meridian of the centre of the rod, of an element ds of the rod at distance s from the centre, then approximately λ = s sin o/a sin θ, where a is the radius of the earth and the remaining notation is the same as in the original communication. Since λ is small, we may write for the horizontal force perpendicular to the meridian of the centre of the rod σρω2λds; its moment is (σρω2λds)(s cos o), or, finally, since ρ = a sinθ, the moment of an element of length ds is σω2S2 sin o cos o ds.