Measuring and testing – Gravitational determination
Reexamination Certificate
2003-03-06
2004-10-05
Chapman, John E. (Department: 2856)
Measuring and testing
Gravitational determination
Reexamination Certificate
active
06799459
ABSTRACT:
BACKGROUND
Geologists have discovered that one can identify certain physical characteristics of a geological formation from the gravitational potential field (denoted with the symbol G in this application) near the formation. For example, the gravitational field G can often indicate the presence and yield the identity of a mineral such as coal that is located beneath the surface of the formation. Therefore, measuring and analyzing the gravitational field G of a formation, can often yield such physical characteristics of the formation more easily and less expensively than an invasive technique such as drilling. Relevant characteristics of the field are typically determined not by measuring the gravitational potential G directly, but either by measuring components of the gravitational acceleration vector g resulting from this field or by measuring spatial derivatives of these acceleration vector components. The three components of the acceleration vector can each be spatially differentiated along three different axes providing a set of nine different signals mathematically related to the underlying gravitational potential G. These nine signals are the gravitation tensor elements (sometimes called the gravity Gradients), and much effort has gone into developing techniques for accurately measuring these tensor elements.
Referring to
FIG. 1
, one can use a gravity gradiometer
10
to measure the gravitational potential field G near a geological formation (not shown). The notation used in this patent to the refer to the nine gravitational field tensor elements in matrix form is:
Γ
=
[
Γ
xx
Γ
xy
Γ
xz
Γ
yx
Γ
yy
Γ
yz
Γ
zx
Γ
zy
Γ
zz
]
(
1
)
where the matrix members represent the respective gravity tensors along each of the three X, Y, and Z “body” axes, which typically intersect at the centroid
12
of the gradiometer
10
. For example, the tensor element &Ggr;
xx
(which can be expressed in equivalent units of (meters/seconds
2
)/meter, 1/seconds
2
, or Eötvös units where 10
9
Eötvös=1/seconds
2
) is the spatial partial derivative along the X axis of the X component of the gravitational acceleration vector g, &Ggr;
xy
is the spatial partial derivative along the Y axis of the X component of g, &Ggr;
xz
is the spatial partial derivative along the Z axis of the X component of g, &Ggr;
yx
is the spatial partial derivative along the X axis of the Y component of g, etc. Furthermore, although the tensors elements &Ggr; may vary over time, for many formations the tensor elements &Ggr;are constant over time, or vary so slowly that they can be treated as being constant over time. Moreover, in some applications the gradiometer
10
may make measurements sufficient to calculate only the desired elements of the full tensor &Ggr;. To measure the gravitational potential field G of a geological formation (not shown in FIG.
1
), one mounts the gradiometer
10
in a vehicle (not shown) such as a helicopter that sweeps the gradiometer over the formation. For maximum accuracy, it is desired that the gradiometer
10
not rotate at a high rate about any of the X, Y, and Z body axes as it sweeps over the formation. But unfortunately, the vehicle often generates vibrations (e.g., engine) or is subject to vibrations (e.g., wind) that causes such rotations about the body axes. Therefore, the gradiometer
10
is often rotationally isolated from the vehicle by a gimballing system (not shown) which allows the gradiometer to remain non-rotating even as the vehicle experiences varying orientations typical of its operation. The gimballing system carrying the gradiometer
10
typically includes a rotational sensor assembly
18
, such as a gyroscope assembly for measuring rotational activity (typically rotational rate &ohgr; or rotational displacement) about the X, Y, and Z body axes. Control signals derived form these measurements are fed back to the motors attached to the gimbal axes to reduce the rotations experienced by the gradiometer
10
. But although the gimballing system typically reduces the magnitude of the vibration-induced rotations of the gradiometer
10
about the body axes, it is typically impossible to eliminate such rotations altogether. Even with an ideal gradiometer, the tensor measurement would, of physical necessity, be additively corrupted by the presence of gradient signals caused by these rotations. These additional non-gravitational gradients are simple deterministic functions of the rotational rates (e.g. rotational &Ggr;=&ohgr;
x
, &ohgr;
y
where &ohgr;
j
refers to the rotational rate around the j body axis in radians/sec). Consequently, the measurements from the gradiometer
10
typically have these corrupting signals subtracted by a processor
20
to increase the accuracy of the gradiometer's measurement of the gravitational field G as discussed below in conjunction with FIG.
3
. Although shown as being disposed within the housing
16
, the processor
20
may be disposed outside of the housing for processing of the measurement data from the gradiometer
10
in real time or after the gradiometer measures the gravitational field G. In the latter case, the gradiometer
10
typically includes a memory
22
for storage of the measurement data for later download to the external processor
20
. Alternatively, the gradiometer
10
may include a transmitter (not shown) for transmitting the measurement data to the external processor
20
and/or an external memory
22
. Moreover, the processor
20
or memory
22
includes a sample-and-hold circuit (not shown) and an analog-to-digital converter (ADC) (not shown) to digitize the gradiometer measurement data and any other measured signals required for optimal operation.
Referring to
FIG. 2
, the gravity gradiometer
10
of
FIG. 1
includes one or more disc assemblies—here three disc assemblies
24
,
26
, and
28
—each for measuring a subset of the full set of tensors F for the gravitational field G of a geological formation
36
.
Each disc assembly
24
,
26
, and
28
includes a respective disc
30
,
32
, and
34
that is mounted in a respective plane that is coincident or parallel with one of the three body-axis planes such that the spin axis of the disc is either coincident with or parallel to the body axis that is normal to the mounting plane. Furthermore, each disc includes orthogonal disc axes that lie in but rotate relative to the mounting plane. For example, the disc
30
lies in the X-Y body-axis plane, has a spin axis Zs that is parallel to the Z body axis—that is, the X-Y coordinates of Z
S
are (X=C
1
, Y=C
2
) where C
1
and C
2
are constants—and includes orthogonal disc axes X
D
and Y
D
. As the disc
30
rotates—here in a counterclockwise direction—the X
D
and Y
D
, disc axes rotate relative to the non-rotating X and Y body axes. At the instant of time represented in
FIG. 2
, the X
D
and Y
D
disc axes of the disc
30
are respectively parallel and coincident with the X and Y body axes. In addition, the disc
32
lies in a plane that is parallel to the Y-Z body-axis plane and has a spin axis X
S
that is parallel to the X body axis. At the instant of time represented in
FIG. 2
, the Y
D
and Z
D
disc axes of the disc
32
are respectively parallel with the Y and Z body axes.
To measure the gravitational field G, the disc assemblies
24
,
26
, and
28
each include at least one respective pair of accelerometers that are mounted &pgr; radians apart on the discs
30
,
32
, and
34
, respectively. For clarity of explanation, only the disc assembly
24
is discussed, it being understood that the other disc assemblies
26
and
28
are similar. Here, the disc assembly
28
includes two pairs of accelerometers
38
a
,
38
b
and
38
c
,
38
d
. Each accelerometer
38
a
,
38
b
,
38
c
, and
38
d
includes a respective input axis
40
a
,
40
b
,
40
c
, and
40
d
along which the accelerometer measures a respective acceleration magnitude Aa, Ab, Ac, and Ad, and each accelerometer is mounted to the disc
30
such that its input axi
Dosch Daniel E.
Sieracki David L.
Chapman John E.
Graybeal Jackson Haley LLP
Lockheed Martin Corporation
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