Measuring Gravity

Relative instruments

• pendulum measurements once used
  
  for point mass on massless string,
  
  where I is moment of inertia about point of suspension; h is distance from point of suspension to center of mass.  But, since K doesn't vary, can measure change in g:
   
  • Used by Gulf R&D in 1930s; 1-second period (how long), thermostat, vacuum
  • used in late 50s, early 60s by George Woolard at airports, seaports, large cities, to establish worldwide gravity network

mass on spring

• static mass-spring system; k is spring constant:

   
  for 0.1 mgal (10^-6 m/s²) accuracy:
  interferometer, wavelength of light about 5x10^-7 m!

  N.B.  A 1^oC change in T would change length of quartz spring 5.5 microns! (How much of a change in gravity would this appear to be?)

• consider system as SHO: or ,
  but from above, , so
• thus, increasing the period increases sensitivity (but slows readings)
• for ordinary mass-spring system, 20-s period requires 100 m spring/mass system!

For this reason, modern relative gravity meters cannot use a linear spring system:

• use an unstable, non-linear mass-on-a-spring system
• the extension of the main spring is NOT proportional to gravity
• fine restoring spring (or electrostatic charge, or whatever) is used to bring the mass back to the same position each time
• referred to as a null-reading instrument

Device on left is linear; device on right is not

LaCoste & Romberg Zero-Length Spring

• History of the LaCoste & Romberg meter(s)

• 

• moment balance about pivot gives
  

• solving for g:
  

• we want to be small, and so a spring with an unstretched length of zero gives (theoretically) infinite sensitivity.

Worden Gravimeter

Scintrex CG-3 Automated Gravity Meter

• "microgal" meter
• manual levelling
• automatic reading
• automatic long-term drift correction
• automatic tide correction
• stores data

Underwater Gravimeters [From L&R web site]

• underwater meters operate on ocean bottom; no averaging as with shipboard meters
• usually shallow; can be modified for use at almost any depth (deep water operations slow, $$$)
• useful in swamps, on muskegs, frozen lakes, ice islands
• if tranpsorted by helicopter, can hover over the gravity station while taking reading
• accuracy decreases with depth due to errors in measuring water depth and position of meter
• inherent precision meter about 0.01 mgal
• in actual sea operation, base station checks => about 0.1 mgal
• water depth usually measured with pressure gauges; accuracy ~1/2% (0.6 meter error in depth => ~0.1 mgal)
• overall accuracy of about 0.2 mgal is considered good in a survey in water 160 meters deep

Our Meters

Data Acquisition