Gravity, Isostasy and Creep

Physics of the Solid EarthSupriyo 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 – ( r0

2 + ∆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

Long wavelength topography (large scale surface features) are normally in Isostatic equlilibrium

Therefore the mantle is, on a long time scale, not particularly strong.

Observed anomaly = 20 mgals, So the topography must be compensated

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 notcompensated, and must be supported by elastic forces in the plate.

Wavelength of deflection will provide a measure of the elastic thickness

CreepHow 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.

Diffusion creepPower-law creep / Dislocation creep

Stre

ss

~ 60 km in oceans