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
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
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 Bedrock density 2.3, ore density 3.0, half cylinder at depth 100m radius for precision 0.1 mGal?