Gravity 3

Gravity Corrections/Anomalies Gravity survey flow chart: 1. Measurements of the gravity (absolute or relative)  2. Calculation of the theoretical gravity (reference formula)  3. Gravity corrections 4. Gravity anomalies 5. Interpretation of the results

Theoretical Gravity Gravity is a function of: Latitute of observation () Elevation of the station (R – the difference for R) Mass distribution in the subsurface (M)

Theoretical Gravity For a Reference Oblate Spheroid: – latitude of observation (sometime you can see  instead of )

Free Air Gravity Anomaly/Correction Accounts for the elevation For g  980,625 MGal, and R  6,367 km = 6,367,000 m Average value for the change in gravity with elevation

Free Air Gravity Anomaly/Correction FAC – Free Air Correction (mGal); h – elevation above sea level (m) gfa = g – gt + FAC

Free Air Gravity Anomaly/Correction Example of free air gravity anomaly across areas of mass excess and mass deficiency

Bouguer Gravity Anomaly/Correction Accounts for the gravitational attraction of the mass above sea level datum Attraction of a infinite slab with thickness h = elevation of the station: BC = 2Gh BC = 0.0418 h BC – Bouguer Correction (mGal); h – elevation above sea level (m)  - density (g/cm3)

Bouguer Gravity Anomaly/Correction For land gB = gfa – BC in BC must be assumed (reduction density) For a typical  = 2.67 g/cm3 (density of granite): BC = 0.0419 x 2.67 x h = = (0.112 mGal/m) x h gB = gfa – (0.112 mGal/m) x h

Bouguer Gravity Anomaly/Correction For sea For a typical w = 1.03 g/cm3 (water) and c = 2.67 g/cm3 (crust): BCs = 0.0419 x (w - c) x hw = 0.0419 x (-1.64) x hw = -0.0687 (mGal/m) x hw gB = gfa – BCs gB = gfa – 0.0419h h = 0  gB = gfa gB = gfa + (0.0687 mGal/m) x hw

Bouguer Gravity Anomaly/Correction FAC vs. BC: BC < FAC (always for stations above sea level) Mass excesses result in “+” anomalies, and deficiencies in “-” anomalies for both Short-wavelength changes in FAC due to abrupt topographic changes are removed by BC.

Terrain Correction For rugged areas – additional correction For low relief the BC is okay but for rugged terrain it is not gBc = gB + TC

Free Air and Bouguer Gravity Anomalies (summary) 3. Bouguer Gravity Anomaly gB = gfa – BC = gfa – 0.0419h On land: gB = gfa – (0.112 mGal/m) h for  = +2.67 At sea: gB = gfa + (0.0687 mGal/m) h for  = - 1.64 In rugged terrain: gBc = gB + TC Theoretical Gravity Free Air Gravity Anomaly gfa = g – gt + (0.308 mGal/m) h Bs – Bouguer – simple; Bc – Bouguer – complete

Free Air and Bouguer Gravity Anomalies (summary) 3. Bouguer Gravity Anomaly gB = gfa – BC = gfa – 0.0419h On land: gB = gfa – (0.112 mGal/m) h for  = +2.67 At sea: gB = gfa + (0.0687 mGal/m) h for  = - 1.64 In rugged terrain: gBc = gB + TC Theoretical Gravity Free Air Gravity Anomaly gfa = g – gt + (0.308 mGal/m) h Bs – Bouguer – simple; Bc – Bouguer – complete

Gravity Corrections/Anomalies 1. Measurements of the gravity (absolute or relative)  2. Calculation of the theoretical gravity (reference formula)  3. Gravity corrections  4. Gravity anomalies 5. Interpretation of the results

Gravity modelling - 2-D approach Developed by Talwani et al. (1959): Gravity anomaly can be computed as a sum of contribution of individual bodies, each with given density and volume. The 2-D bodies are approximated , in cross-section as polygons.

Gravity anomaly of sphere Analogy with the gravitational attraction of the Earth: g  g (change in gravity) M  m (change in mass relative to the surrounding material) R  r

Gravity anomaly of sphere Total attraction at the observation point due to m

Gravity anomaly of sphere - Total attraction (vector) Horizontal component of the total attraction (vector) Vertical component of the total attraction (vector) Horizontal component Vertical component Angle between a vertical component and g direction

Gravity anomaly of sphere a gravimeter measures only this component R – radius of a sphere  - difference in density

Gravity anomaly of sphere