Measuring and testing – Gravitational determination
Patent
1997-06-13
1999-10-05
Chapman, John E.
Measuring and testing
Gravitational determination
G01V 700
Patent
active
059627816
DESCRIPTION:
BRIEF SUMMARY
This invention relates to the measurement of gravitational fields, particularly to gravity gradiometry, and more particularly to a method for measuring absolutely off-diagonal components of the gravity gradient tensor.
The gravity gradient tensor is a two-dimensional matrix of the second partial derivatives of a gravitational potential, V, with respect to the Cartesian co-ordinates, x, y, z, of some arbitrary reference frame. It represents how the gravity vector itself in each of these directions varies along the axes.
Accurate absolute measurements of the components of the gravity gradient tensor .GAMMA..sub.ij =.differential..sup.2.sub.ij V (ij=x,y,z), taken at some local coordinate frame OXYZ are very important to progress in the fields of geological prospecting, mapping of the Earth's gravitational field, and space, sea and underwater navigation.
A method of absolute measurement of gravity gradient tensor components was invented first by Baron Roland von Eotvos as early as 1890, utilising a torsion balance with proof masses hung at different heights from a horizontal beam suspended by a fine filament. The gravity gradients give rise to differential forces being applied to the masses which result in a torque being exerted on the beam, and thus to angular deflection of the masses which can be detected with an appropriate sensor. A sensitivity of about 1 E (1 E=1 Eotvos=10.sup.-9 s.sup.-2) can be reached but measurement requires several hours at a single position due to the necessity to recalculate the gravity gradient components from at least 5 independent measurements of an angular deflection each with a different azimuth angle.
Practical devices, which have been built in accordance with this basic principle, are large in size and have low environmental noise immunity, thus requiring specially prepared conditions for measurements which excludes any possibility of using them on a moving carrier.
A method for absolute measurement of gravity gradient tensor components which enhances the above method was invented by Forward in the middle of the sixties (see U.S. Pat. No. 3,722,284 (Forward et al) and U.S. Pat. No. 3,769,840 (Hansen). The method comprises mounting both a dumbbell oscillator and a displacement sensor on a platform which is in uniform horizontal rotation with some frequency .OMEGA. about the axis of the torsional filament. The dumbbell then moves in forced oscillation with double the rotational frequency, whilst many of the error sources and noise sources are modulated at the rotation frequency or not modulated (particularly 1/f noise). The forced oscillation amplitude is at a maximum when the rotation frequency satisfies the resonance condition 2.OMEGA.=.omega..sub.0, where .omega..sub.0 is the angular resonant frequency, and the oscillator quality factor Q tends to infinity. Unlike the non-rotating method, this method enables one to determine rapidly the quantities .GAMMA..sub.yy -.GAMMA..sub.xx and .GAMMA..sub.xy by separating the quadrature components of the response using synchronous detection with a reference signal of frequency 2.OMEGA..
The same principles can be directly used, as proposed by Metzger (see U.S. Pat. No. 3,564,921), if one replaces the dumbbell oscillator with two or more single accelerometers properly oriented on such a moving platform. There are no new features of principle in this solution to compare with the previous one except that the outputs of the pairs of accelerometers require additional balancing.
Devices have been built according to this method, but they have met more problems than advantages, principally because of the need to maintain precisely uniform rotation and the small displacement measurement with respect to the rotating frame of reference. The devices have reached a maximum working accuracy of about a few tens of Eotvos for a one second measuring interval, and they are extremely sensitive to environmental vibrational noise due to their relatively low resonant frequencies. The technological problems arising in this case are so difficult to overcome t
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A. Nicolaidis et al., "String as a Gravitational Antenna," Il Nuovo Cimento, vol. 107 B, N.11, Nov. 1992, pp. 1261-1266.
Chapman John E.
Gravitec Instruments Limited
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