Presentation on theme: "Instruments used in gravity prospecting Fundamental design of almost all gravity instruments uses a mass on a spring: A change in gravity should cause."— Presentation transcript:
Instruments used in gravity prospecting Fundamental design of almost all gravity instruments uses a mass on a spring: A change in gravity should cause a change in length given by Problems: measurement must be accurate to one part in 10 8. restoring force overcompensates, mass overshoots equilibrium point, system oscillates Solution: a system with no effective restoring force, an “unstable gravimeter” such a system has infinite periodicity, and mechanical amplification
Lacoste-Romberg gravimeter At equilibrium, zero torque implies: Sine rule for triangles: Substituting: Solving for g:
Lacoste-Romberg gravimeter At equilibrium, zero torque implies: Sine rule for triangles: Substituting: If the beam is stable in the horizontal position, it is stable in any position! IF z=0 :
Zero length spring Sketch a graph of spring force k(s − z) vs spring length, s for a real “zero length spring”. Force, f Spring length, s
Zero length spring Sketch a graph of spring force k(s − z) vs spring length, s for a real “zero length spring”.
Equation for g: Sensitivity: Minimize the amount that g has to change, before the spring length, s will change a given amount: Minimize Thus, the instrument sensitivity is maximized if z, the unstretched spring length is as small as possible. This re-enforces the importance of the “zero length spring”
Field operations for gravity surveys We may divide gravity surveys into: land operations marine operations sea bed measurements ship-borne surveys airborne gravity satellite altimetry (This is arranged in order of decreasing accuracy and precision, and increasing costs, and spatial dimensions of the target)
Land operations Desired gravity precision ±0.01mgal. Elevation precision ±3 cm Latitude precisions ±10 m Typical station spacing: Very large scale regional survey 20 km Oil and gas exploration 1 km Mineral exploration 15 - 30 m Geotechnical 1-5 m Archaeological < 1 m. Drift - small change in the instrument response with time, caused by spring inelasticity and thermal dependencies in the system. Earth tides - changes in Earth gravity due to the relative movement of the Sun and Moon. These cause changes of the order of ±0.3 mgal over a 24 hour period.
Land gravity survey plan
Marine operations An underwater gravimeter system
Marine operations An air/sea gravity meter, showing the gyro-stabilized platform
Airborne gravity only widely available for the last decade depends on dramatic improvements in GPS estimation of acceleration requires: Gyro-stabilized platforms, see Figure 2.8 GPS-derived acceleration corrections Use of gravity “gradiometry” to minimize effects of sensor movement
Eötvös correction (required for seaborne, airborne measurements) Apparent gravity is affected by motion of moving platforms Eastward ship (aircraft) travel: adds to the earth's rotation, increases centrifugal forces and decreases the gravity readings. Westward travel: increases the gravity reading. North-south travel: is independent of rotation, and decreases the gravity reading in either case. Correction required:
Next lecture: Gravity Data Reduction In decreasing order, gravity is affected by 1.Latitude (due to shape and rotation 2.Elevation 3.Local topography 4.Lunar and solar tidal forces 5.Local density variations The first four must be corrected for before we can “see” the local density variations in the gravity data