Variation of G with latitude gp =983.2 Gal ge = 978.0 Gal Radius gprad-gerad = 6.6 Gal Excess mass gpem-geem = -4.8 Gal Rotation gprot-gerot = 3,4 Gal
Variation of G with latitude In the long-term, the earth behaves like a fluid Reference ellipsoid (approximation to geoid) The scalar potential verifies the Laplace equation and the solution can be expanded on Legendre polynomials degree 0 degree 2 rotation
Variation of G with latitude We then get for the normal gravity (uniform density) due to position only We are interested in the gravity anomaly gobs -gn
Variation of G with latitude
Free air correction At the Earth’s surface z is the elevation from sea level. The gravity anomaly is then (brings gravity to sea level) Units: mGal, m
Bouguer correction We also need to correct for the mass between sea level and elevation z. Bouguer assumes an infinite slab of density ρ and thickness z Units: mGal, m, g/cm3
Bouguer correction The difficulty is to choose the right density ρ (average crustal rock has a density of 2.67
Terrain correction
Terrain correction (hammer)
Terrain correction (laborious)
other corrections and precautions Isostatic correction: due to deeper sources regional trend correct or filter Tidal correction correct or drift if short time sales Elevation Latitude Drift Base
Gravity of simple shapes
Gravity of simple shapes
Gravity of simple shapes Bedrock density 2.3, ore density 3.0, half cylinder at depth 100m radius for precision 0.1 mGal?
Gravity of simple shapes
Regionals and residuals
Regionals and residuals
Regionals and residuals geological knowledge and experience
Regionals and residuals trend surfaces
Regionals and residuals trend surfaces
Regionals and residuals trend surfaces
Regionals and residuals upward continuation
Regionals and residuals second derivatives
Regionals and residuals second derivatives
Gravity interpretation half-maximum technique
Gravity interpretation half-maximum technique
Gravity interpretation 2nd derivatives technique
Gravity interpretation 2nd derivatives technique
Gravity interpretation 2nd derivatives technique
Detection of cavities
Bedrock depths