Measuring and testing – Gravitational determination
Reexamination Certificate
2001-11-15
2003-12-09
Chapman, John E. (Department: 2856)
Measuring and testing
Gravitational determination
C073S001380
Reexamination Certificate
active
06658935
ABSTRACT:
BACKGROUND OF THE INVENTION
The earth's gravitation field varies between a low of about 880 mgals at the equator to about 1,100 mgals at the poles with gradients characterized in Eotvos units, where one Eotvos unit equals 10
−9
sec
−2
. For an idealized homogeneous sphere, an equipotential surface outside of the sphere is also spherical, and, for any relatively small volume unit in free space, an idealized gravity field can be viewed as a set of unidirectional field lines aligned along the local vertical and having zero magnitude in the x,y directions. In the context of a geoshpere such as the earth, density inhomogeneities in the geosphere give rise to an equipotential surface that is not spherical, i.e., the curvature of any point is different in different directions. In the context of the earth, local variations in gravity are caused by deviations in the surface of the earth from a geometric sphere, surface geology, water tides, atmospheric tides, and the change in relative position of the earth, the moon, and the sun.
For any observation point within an arbitrary volume unit, the gravity field at that observation point can be resolved into x,y,z components of which the z vector will have the largest magnitude and the x,y vectors will have respective magnitudes that are a function of the location of that observation point relative to any mass inhomogenieties.
FIG. 1
illustrates a conventional coordinate system in which the X axis corresponds to the north-south alignment, the Y axis corresponds to the east-west alignment, and the Z axis corresponds to the up-down alignment. Using this coordinate system convention and for any observation point, the gravity gradient is a second order derivative of the gravity potential scaler &Ggr; and is represented by a second-order nine-component symmetric tensor &Ggr;
ij
as shown in FIG.
2
.
The components &Ggr;
x,x
and &Ggr;
y,y
are approximately equal to the variation of the force of gravity along the x and y directions, respectively, and are known as the horizontal gradient components, and &Ggr;
z,z
is known as the vertical gradient of gravity. Three pairs of the nine elements are symmetrically equal, i.e., &Ggr;
x,z
=&Ggr;
z,x
, &Ggr;
y,z
=&Ggr;
z,y
, and, lastly, &Ggr;
x,y
=&Ggr;
y,x
so that the tensor is characterized by five independent components. Additionally, the diagonal elements are scalar invariant and conform to the Laplacian relationship:
0=&Ggr;
x,x
+&Ggr;
y,y
+&Ggr;
z,z
EQ. 1
from which it follows that:
&Ggr;
z,z
=−(&Ggr;
x,x
+&Ggr;
y,y
) EQ. 2
Two general types of instruments, characterized in a generic sense as “absolute” and “relative” instruments, have been developed for measuring, directly or indirectly, the various components within the gravity tensor.
In general, the gravity field along the z axis can be measured by uniaxis gravimeters of which a common type uses lasers and a high-precision clock to time a mass falling between two vertically spaced points in an evacuated space. Gradiometers, as distinguished from gravimeters, measure the curvature gradients (or differential curvature or ellipticity of the gravity equipotential surfaces), horizontal gradients (or the rate of change of the increase of gravity in the horizontal direction), or vertical gradients (or the rate of increase of gravity in the vertical direction).
An absolute gravity instrument that relies on the direct measurement of a mass whose movement is a function the of gravity field is disclosed in U.S. Pat. No. 5,351,122 issued Sep. 27, 1994 to T. Niebauer et al. As disclosed therein, the instrument utilizes a reflective mass that is dropped under the influence of gravity. The motion of the free-falling reflective mass is measured using a split-beam laser interferometer by which light from a laser is split into two paths with light from one of the paths reflected from the free-falling reflective mass and the reflected light compared with light from the other path. Since the instrument is relatively simple and the falling mass is influenced directly by the gravity field, the value of gravity can be accurately calculated using Newtonian principles.
A more sophisticated absolute gravity measuring instrument is disclosed in U.S. Pat. No. 5,892,151 issued Apr. 6, 1999 to T. Niebauer et al. which discloses the use of two physically spaced-apart falling body sensors to obtain a differential measurement of gravity. Where two of the sensors are spaced apart from one another along the vertical axis, differences in the measured output of sensors represents the component &Ggr;
z,z
of the gravity tensor. The differential instrument is well-suited for use in those applications in which differential gravity measurement are desired, including mineral and petroleum exploration and extraction.
In contrast to the falling-body absolute gravity instruments, one type of relative instrument utilizes plural pairs of accelerometers that are moved at a constant velocity along an orbital path about a spin axis. Information from each accelerometer at any angular position in the orbit provides information as to the lateral acceleration, including the gravity field, sensed by the accelerometers. A representative relative instrument is disclosed in U.S. Pat. No. 5,357,802 issued Oct. 25, 1994 to Hofmeyer and Affleck and entitled “Rotating Accelerometer Gradiometer” and sold in various forms by the Lockheed Martin corporation (Buffalo N.Y. USA). The Lockheed Martin instrument is designed to measure the local gravity gradient and includes plural pairs of accelerometers mounted at a common radius and equi-spaced about the periphery of a rotor assembly that is rotated at a constant and controlled angular velocity about a spin axis.
Each accelerometer provides a sinusoidally varying analog output that is a function of the acceleration experienced by each accelerometer as the accelerometer orbits the spin axis. For a gradiometer having its spin axis aligned along the field lines in an ideally uniform and unperturbed gravity field, each accelerometer experiences the same acceleration forces as its proceeds along its orbital path. However, where the local gravity field is perturbed by the presence of one or more masses and/or the spin axis is tilted relative to the local vertical field lines, each accelerometer will experience different accelerations throughout its orbit. The quantitative output of each accelerometer, coupled with its rotary position, provides information related to the local gravity gradients.
Gradiometers of the type that employ orbiting accelerometers must use accelerometers with precisely matched physical properties, matched scale factors, various servo loops that are linear and stable, and numerous other control and feedback loops that must remain uniformly stable with time. Various signal processing techniques, principally common mode rejection techniques, have been used to reduce and minimize errors sources to improve measurement accuracy. Errors sources include mis-matched scale factors, motor and bearing vibration, stray electromagnetic fields, and the usual array of electronic noise sources. Because of the complexity of accelerometer-type gradiometers, the accuracy and repeatability of the devices are strongly influenced by temperature, pressures, and duration of service requiring periodic instrument calibrations and monitoring of time-dependent drift errors. Additionally, the overall instrument transfer function is frequency dependent and includes specific frequencies for which the instrument is maximally sensitive. At these frequencies, it can be difficult to separate information in the output power spectrum that represents the desired gravity information and non-information noise. Since the accelerometers in these types of gradiometers do not directly measure gravity in the same direct manner as a falling-body instrument, the output can only be characterized in the context of a relative difference.
SUMMARY OF THE INVENTION
In view of the above, it is an ob
Chapman John E.
Lockheed Martin Corporation
Walter Wallace G.
LandOfFree
Complemented absolute/relative full-tensor gravity... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Complemented absolute/relative full-tensor gravity..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complemented absolute/relative full-tensor gravity... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3128892