The torsion balance as a tool for geophysical prospecting

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 527-534 ◽  
Author(s):  
Clive C. Speake ◽  
G. D. Hammond ◽  
C. Trenkel
Keyword(s):  
Mass Range ◽  
Torsion Balance ◽  
Gravity Gradient ◽  
Geophysical Prospecting ◽  
Balance Beam ◽  
Horizontal Gradients ◽  
Moving Platforms ◽  
Local Anomalies ◽  
Derivatives Of ◽  
Double Torsion

We discuss whether the torsion balance can again become a key tool for geophysical prospecting. We outline the acknowledged disadvantages of the Eötvös torsion balance and seek designs of a torsion balance beam that would enable the torsion balance to be used on moving platforms. A key result is that torsion balance beams designed to be insensitive to the curvature and horizontal gradients of the gravity field are insensitive to the angular motion of the platform about horizontal axes. We suggest that a double torsion balance using these balance beam designs could be used on moving platforms. We point out that second gradients of the gravitational field (third derivatives of the potential) can be determined with reasonable sensitivity with current technology. We describe double torsion balance schemes where the mass, range, and azimuth of localized mass anomalies could be estimated or where local anomalies could be rejected using information from the second gravity gradient.

Tensor Invariants for Gravitational Curvatures

2021 ◽  
Author(s):  
Xiao-Le Deng ◽  
Wen-Bin Shen ◽  
Meng Yang ◽  
Jiangjun Ran
Keyword(s):  
Gravity Field ◽  
Gravity Gradient ◽  
Additional Information ◽  
Tensor Invariants ◽  
Global Gravity ◽  
Potential Applications ◽  
Gravitational Curvatures ◽  
Definition Of ◽  
Elemental Mass ◽  
Derivatives Of

<p>The tensor invariants (or invariants of tensors) for gravity gradient tensors (GGT, the second-order derivatives of the gravitational potential (GP)) have the advantage of not changing with the rotation of the corresponding coordinate system, which were widely applied in the study of gravity field (e.g., recovery of global gravity field, geophysical exploration, and gravity matching for navigation and positioning). With the advent of gravitational curvatures (GC, the third-order derivatives of the GP), the new definition of tensor invariants for gravitational curvatures can be proposed. In this contribution, the general expressions for the principal and main invariants of gravitational curvatures (PIGC and MIGC denoted as I and J systems) are presented. Taking the tesseroid, rectangular prism, sphere, and spherical shell as examples, the detailed expressions for the PIGC and MIGC are derived for these elemental mass bodies. Simulated numerical experiments based on these new expressions are performed compared to other gravity field parameters (e.g., GP, gravity vector (GV), GGT, GC, and tensor invariants for the GGT). Numerical results show that the PIGC and MIGC can provide additional information for the GC. Furthermore, the potential applications for the PIGC and MIGC are discussed both in spatial and spectral domains for the gravity field.</p>

THE GROWTH OF COMPANY OWNED OPERATIONS IN GULF COAST GEOPHYSICAL PROSPECTING SINCE JULY 1930

Geophysics ◽  
1936 ◽  
Vol 1 (3) ◽  
pp. 306-312 ◽  
Author(s):  
E. E. Rosaire ◽  
K. Ransone
Keyword(s):  
Crude Oil ◽  
Gulf Coast ◽  
Torsion Balance ◽  
Steady Increase ◽  
Geophysical Prospecting ◽  
Saturation Point ◽  
Graphical Data

Graphical data are presented for the refraction seismograph, torsion balance, and reflection seismograph in the Gulf Coast over the period July 1930 to February 1936. For comparison, the variations in the price of 30° Baumé crude oil at Houston are presented for the same period. The results indicate that: (1) The refraction seismograph was discarded before the 1931 minimum in the price of oil. (2) During this 1931 minimum, exploration of any kind was practically non‐existent. (3) The 1933 minimum, on the contrary, seems to have effected contract operations more than company owned operations. (4) Company owned torsion balance operations seem to have reached a saturation point while contract torsion balance operations are rapidly decreasing from their 1934 peak. (5) Company owned reflection operations have shown a steady increase of ten crews per year while contract operations have shown a very irregular increase, averaging six crews per year, since 1932. (6) New contract reflection companies have appeared since 1930 at the rate of three per year. (7) The peak of contract reflection operations will probably be reached in 1937 or 1938, after which these operations will disappear in the same fashion as did the contract torsion balance operations.

Conjugate complex variables method for the computation of gravity anomalies

Geophysics ◽  
1989 ◽  
Vol 54 (12) ◽  
pp. 1629-1637 ◽  
Author(s):  
Yue‐Kuen Kwok
Keyword(s):  
Gravity Anomalies ◽  
Higher Order ◽  
Complex Variables ◽  
Gravity Potential ◽  
Gravity Gradient ◽  
Horizontal Distance ◽  
Contour Integrals ◽  
Vertical Gravity ◽  
Analytical Expressions ◽  
Derivatives Of

Using conjugate complex variables, a generalized method is presented to derive formulas to calculate first‐ and higher‐order derivatives of the gravity potential due to selected mass models. Double integrals in the computation of gravity‐gradient anomalies are transformed into complex contour integrals. Analytical expressions for higher‐order derivatives of the gravitational potential in arbitrary directions due to two‐dimensional (2‐D) polygonal mass models are derived. The method is extended to 2‐D polygonal bodies whose density contrasts vary with depth and horizontal distance and can be generalized to deal with 2‐D bodies of any shape. The vertical gravity field and its first derivatives due to a homogeneous radially symmetric body are also computed using conjugate complex variables. Derivation of gravity and gravity gradient formulas generally is greatly simplified by the use of complex variables.

scholarly journals Geometric Interpretation of the Derivatives of Parallel Robots’ Jacobian Matrix With Application to Stiffness Control

2003 ◽  
Vol 125 (1) ◽  
pp. 33-42 ◽  
Author(s):  
N. Simaan ◽  
M. Shoham
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Geometric Interpretation ◽  
Parallel Robots ◽  
Redundant Robot ◽  
Moving Platforms ◽  
Stiffness Control ◽  
Derivatives Of ◽  
Direct Kinematics

This paper presents a closed-form formulation and geometrical interpretation of the derivatives of the Jacobian matrix of fully parallel robots with respect to the moving platforms’ position/orientation variables. Similar to the Jacobian matrix, these derivatives are proven to be also groups of lines that together with the lines of the instantaneous direct kinematics matrix govern the singularities of the active stiffness control. This geometric interpretation is utilized in an example of a planar 3 degrees-of-freedom redundant robot to determine its active stiffness control singularity.

CANADIAN AERIAL MAGNETIC SURVEYS (M.A.D.)

1948 ◽  
Vol 26f (12) ◽  
pp. 523-539 ◽  
Author(s):  
Ralph Bailey
Keyword(s):  
Geophysical Prospecting ◽  
Total Field ◽  
Magnetic Detector ◽  
High Degree ◽  
Local Anomalies ◽  
Airborne Magnetic

Tests concluded with an airborne magnetic detector measuring the earth's total field indicate a high degree of accuracy and speed for reconnaissance work over large areas. Cheapness of operation and freedom from small local anomalies make this a valuable tool for geophysical prospecting.

scholarly journals A torsion balance device for measuring the gravity gradient

2018 ◽  
Vol 1065 ◽  
pp. 042058 ◽  
Author(s):  
Xiang Hu ◽  
Ye Yu ◽  
Jun Liu ◽  
Rong Jiang
Keyword(s):  
Torsion Balance ◽  
Gravity Gradient

RECONNAISSANCE SURVEY USING AVERAGE HORIZONTAL GRADIENTS OF GRAVITY

Geophysics ◽  
1965 ◽  
Vol 30 (4) ◽  
pp. 661-664
Author(s):  
Stephen Thyssen‐Bornemisza
Keyword(s):  
Gravity Gradient ◽  
Gravity Gradients ◽  
The South ◽  
Horizontal Gradients ◽  
Experimental Profile ◽  
Reconnaissance Survey ◽  
Gradient Technique ◽  
Vertical Gradients ◽  
Reconnaissance Surveys

Some time ago, Romberg (1956/57) pointed out the advantage of reading horizontal gravity gradients rather than vertical gradients with the gravity meter. Several years later, in March, 1960, an experimental profile of gravity‐meter‐determined horizontal gradients was run for the author in the South Houston field by courtesy of Texas Instruments Incorporated. Since then, this gradient technique was repeatedly discussed but only very few results could be published (Thyssen‐Bornemisza et al., 1960, 1962a, 1962b). Stackler (1963) more recently pointed out again the value of the average gravity gradient for reconnaissance surveys predominantly in inaccessible areas.

Integrated Structural and Control Optimization

2004 ◽  
Vol 10 (10) ◽  
pp. 1377-1391 ◽  
Author(s):  
Ijar M. Fonseca ◽  
Peter M. Bainum
Keyword(s):  
Analytical Approach ◽  
Minimum Weight ◽  
Space Structure ◽  
Design Parameters ◽  
Gravity Gradient ◽  
Control Optimization ◽  
Design Variables ◽  
Analytical Derivatives ◽  
And Control ◽  
Derivatives Of

This paper focuses on the integrated structural/control optimization of a large space structure with a robot arm subject to the gravity-gradient torque through a semi-analytical approach. It is well known that the computer effort to compute numerically derivatives of the constraints with respect to design variables makes the process expensive and time-consuming. In this sense, a semi-analytical approach may represent a good alternative when optimizing systems that require sensitivity calculations with respect to design parameters. In this study, constraints from the structure and control disciplines are imposed on the optimization process with the aim of obtaining the structure’s minimum weight and the optimum control performance. In the process optimization, the sensitivity of the constraints is computed by a semi-analytical approach. This approach combines the use of analytical derivatives of the mass and stiffness matrices with the numerical solution of the eigenvalue problem to obtain the eigenvalue derivative with respect to the design variables. The analytical derivatives are easy to obtain since our space structure is a long one-dimensional beam-like spacecraft.

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