Gravity, Isostasy and Creep
Physics of the Solid Earth Supriyo Mitra
Figure 2: Deflection of plumbline due to Himalayas
Local Isostatic compensation
Local Isostatic compensation
Gravitational Potential and Acceleration
Gravity of the Earth
The Shape of the Earth
Gravity Measurements
Absolute Gravity measurement
Relative Gravity measurement
Gravity Corrections and Anomalies Free Air Correction
δgF = (2h/R)g
Free Air Anomaly gF = gobs – g(λ) + δgF
Bouguer Correction
SLAB APPROXIMATIOM ∆g = 2πGρt Therefore ∆g = 42ρt milligals Where ρ is the density in km/m3 and t is thickness or bathymetry in km.
Terrain Correction
(r,θ) = γρθ { ( r0 – ri ) + ( ri2 + ∆z2 )1/2 – ( r02 + ∆z2 )1/2 } Correction is small if r > 20z, where r is the average distance from the compartment to the station.
Bouguer Anomaly gB = gobs – g(λ) + δgF – δgF + δgT
Isostatic Anomaly Actual Bouguer anomaly – computed Bouguer anomaly for a proposed density model
Synthetic Examples
100% Compensation
70% Compensation
0% Compensation
Observed Gravity Anomalies Rockall, t = 2 km ∆g should be= 140 mgals
Observed anomaly = 20 mgals, So the topography must be compensated
Long wavelength topography (large scale surface features) are normally in Isostatic equlilibrium Therefore the mantle is, on a long time scale, not particularly strong.
Models of compensation and density-depth tradeoff
Geoid Height Anomalies
g∆h = -∆V
Mantle convection and geiod height anomalies
From McKenzie et al 1980
Not all topography is isostatically compensated ‌.
Not all topography is compensated. The Hawaiian Ridge, with t = 4 km, and both the observed and calculated anomalies are about 300 milligals. So the ridge is not compensated, and must be supported by elastic forces in the plate.
Wavelength of deflection will provide a measure of the elastic thickness
Creep How does compensation occur? We need to understand long term behaviour of stressed solids: Homologous Temperature τ = T / Ts Where T is the temperature of the solid and Ts is the melting temperature both in K and Homologous stress σ / μ Where σ is the stress and μ the shear modulus. Creep or long term behaviour of solids is determined by τ Only at temperatures larger than a certain homologous temperature certain types of creep can occur. Creep also depends on the stress applied.
Power-law creep / Dislocation creep
Diffusion creep
Stress
~ 60 km in oceans