WO1995005614A1

WO1995005614A1 - Laplace gravity gradiometer

Info

Publication number: WO1995005614A1
Application number: PCT/CA1994/000442
Authority: WO
Inventors: Jerry R. Panenka
Original assignee: Noranda Inc.; Canagrav Research Ltd.
Priority date: 1993-08-16
Filing date: 1994-08-16
Publication date: 1995-02-23
Also published as: CA2104180A1; CA2104180C; AU7455294A

Abstract

A gravity gradiometer capable of obtaining the vertical component Tzz of the gravity gradient tensor out of the two horizontal components Txx and Tyy based on Laplace equation: Tzz = - (Txx + Tyy) comprises a single disc, and two pairs of radially-oriented horizontal axis accelerometers oppositely-mounted on such disc along respective X and Y axes, each pair being capable of providing, respectively, Txx = Tx1 - Tx2 and Tyy = Ty1 - Ty2 where Tx1 and Tx2 are the respective outputs of the X axis accelerometers and Ty1 and Ty2 are the respective outputs of the Y axis accelerometers. The gravity gradiometer is also capable of obtaining all five independent components of the gravity gradient tensor based on the above Laplace equation and tensor symmetry as follows: one of the above pairs of horizontal axis accelerometers further comprises tangentially oriented horizontal accelerometers capable of providing by subtraction the Txy component of the gravity gradient tensor, and an accelerometer module consiting of two horizontal accelerometers aligned with the radially and tangentially oriented combination is mounted at a location on the Z axis of the disc above or below the disc to provide the Tzx and Tzy components by subtracting the values of Tx and Ty, respectively, at that location from average values of Tx and Ty at the disc plane.

Description

LAPLACE GRAVITY GRADIOMETER

This invention relates to a gravity gradiometer which obtains components of the gravity gradient tensor using the Laplace equation and tensor symmetry with horizontal accelerometers only. Background of the invention

Existing commercial gravity gradiometers depend on measurement of gravity gradients along axes inclined 45 degrees to the vertical (umbrella configuration) . Examples of these are the Bell gravity gradient survey system GGSS of Bell-Textron of Buffalo, N.Y. which operates at room temperature, and an experimental University of Maryland gradiometer which requires cryogenic temperatures. Gravity gradients at 45 degrees to the vertical are more difficult to measure since compensation for a large gravity component (G cos 45°) is required. This involves springs, which are subject to non-linearities, hysteresis, fatigue, tares, inter-atomic slippage, etc. The above Bell GGSS model uses three rotating discs, each populated with four tangentially-oriented single- axis pendulous accelerometers. Furthermore, gradiometer signals are measured in a relatively strong aircraft motion acceleration noise field, with the vertical components typically several times higher than the horizontal components. Statement of the invention

Applicant has found that there is no need to measure anomalous gradients on a background of strong aircraft sub-vertical gravity accelerations directly, since the full tensor can be derived from horizontal gradients using Laplace equation and the tensor symmetry.

Horizontal gradients can be measured more simply than gradients in the vertical directions by such means as pendulum - based accelerometers (such as Bell VII or XI models of Bell-Textron of Buffalo, N.Y.). A pendulum is stabilized by the force of gravity, and is, therefore, a reliable, sensitive and frequently used inertial element.

A first embodiment of the gravity gradiometer in accordance with the present invention comprises two pairs of radially-oriented horizontal axis accelerometers oppositely-mounted on a single disc along respective X and Y axes, each pair being capable of providing, respectively, T_xx=T_xl - T_x2 and 1^=^-_^ - T_y2 where T_xl and T_x2 are the outputs of the X axis accelerometers and T_yl and T_y2 are the outputs of the Y axis accelerometers.

A second embodiment of the gravity gradiometer in accordance with the present invention is capable of providing all five independent components of the gravity gradient tensor using the Laplace equation and tensor symmetry. In this embodiment, one of the two pairs of horizontal axis accelerometers further comprises tangentially oriented horizontal accelerometers capable of providing by substraction the ^ component of the gravity gradient tensor. In addition, an accelerometer module consisting of two horizontal accelerometers aligned with the above radial and tangential combination is mounted at a location on the Z axis of the disc above and/or below the disc to provide the T_zx and T.^ components by substracting the values of T_x and T_y at that location respectively, from average values of T_x and T_y at the disc plane.

Brief Description of the Drawings

The invention will now be disclosed, by way of example, with reference to the accompanying drawings in which:

Figure 1 illustrates an embodiment of a gravity gradiometer capable of obtaining the vertical component T_zz of the gravity gradient from measurement of horizontal components T_xx and T_yy, and Figure 2 illustrates an embodiment of a gravity gradiometer capable of obtaining all five independent components of the gravity gradient tensor from measurement of horizontal components. Detailed Description of Preferred Embodiments

Before proceeding with the description of the preferred embodiments, let us provide the following well known definitions: Basic Formulas Gravity Gradient is a second derivative of Gravity Potential T. It is represented by the second-order nine-component symmetric tensor T .

T ^xxx T T

On and above the earth surface the value of its in-line (diagonal) components conforms to Laplace equation:

T + T J-yy + τ_zz = 0 from which follows

T — - (τ_xx + Tyy )

Thus we can obtain vertical component out of the two horizontal components. By virtue of gradient tensor symmetry

T. ■ = T-- it is clear that only five of the nine components are independent (which is a well known theorem) . Therefore, in order to describe fully the tensor it is sufficient to measure two in-line (diagonal) components and three independent cross-components. None of these has to be a vertical component. Sensor Geometry

In a first embodiment of the invention illustrated in Figure 1, the vertical gravity gradient T_zz is obtained through Laplace equation T_zz = - (T_xx + T_yy) from two horizontal gradients T_xx and T_yy using two pairs 1 and 2 of radially oriented horizontal axis accelerometers mounted on a horizontal disc 6 along X and Y axes, respectively. Accelerometer pairs 1 and 2 are, respectively, capable of providing by substraction T_xx and T^. In a second embodiment of the invention illustrated in Figure 2, all five independent components of the gravity gradient tensor can be obtained from horizontal gradients based on Laplace equation and tensor symmetry. In this embodiment, one of the pairs of radially- oriented horizontal accelerometers (pair 1) is replaced with a pair 3 of radially and tangentially oriented horizontal accelerometers 3 capable of providing by substraction the T-__y component of the gravity gradient sensor: In addition, an accelerometer module 4 consisting of two horizontal accelerometers aligned with the above radial and tangential combination is mounted at a location on the Z axis above the disc to provide the T_zx and T_zy components by substracting the values of T_x and T_y, respectively, at that location from average values of T_x and T_y at the disc plane. The accelerometer disc may be rotated around the vertical axis in order to narrow the signal bandwidth and reduce noise thus increasing signal-to-noise ratio, which is a standard industry practice, as for example in Bell GGSS gravity gradiometer. The second embodiment can obtain the full tensor using a single stationary or rotating horizontal disc configuration rather than three discs in a 45 degree umbrella orientation such as employed in Bell GGSS, or three pairs of spring accelerometers in the same configuration like in the above mentioned University of Maryland cryogenic gradiometer. This simplification results in lower noise as well as a decrease in complexity and cost.

Although the invention has been disclosed, by way of example, with reference to preferred embodiments, it is to be understood that other alternatives are also envisaged within the scope of the following claims:

Claims

1. A gravity gradiometer capable of obtaining the vertical component T_zz of the gravity gradient tensor out of the two horizontal components T_xx and T^ based on Laplace equation _zz = - (T_xx + T_yy) comprising: a) a single disc; and b) two pairs of radially-oriented horizontal axis accelerometers oppositely-mounted on said disc along respective X and Y axes, each pair being capable of providing, respectively, T_xx = T_xl - T_x2 and T_yy = T_yl - T_y2 where T_xl and T_x2 are the respective outputs of the X axis accelerometers and T_yl and T_y2 are the respective outputs of the Y axis accelerometers.

2. A gravity gradiometer as defined in claim 1, capable of obtaining all five independent components of the gravity gradient tensor based on said Laplace equation and tensor symmetry, wherein one of said pairs of horizontal axis accelerometers further comprises tangentially oriented horizontal accelerometers capable of providing by substraction the T^ component of the gravity gradient tensor, and further comprising an accelerometer module consisting of two horizontal accelerometers aligned with said radially and tangentially oriented combination mounted at a location on the Z axis of the disc above or below the disc to provide the T_zx and T_zy components by subtracting the values of T_x and T_y, respectively, at that location from average values of T_x and T_y at the disc plane.

3. A gravity gradiometer as defined in claim 1 or 2 , wherein the disc is rotatable around the Z axis.