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As shown below, the Southern Rockies have an average elevation around 3000 meter

ID: 232286 • Letter: A

Question

As shown below, the Southern Rockies have an average elevation around 3000 meters.

(a) Estimate the crust root needed beneath the Rockies to establish isostatic equilibrium. You can assume a two-layer model with 2700 kg/m^3 crustal denisty and 3380 kg/m^3 upper mantle density.

(b) Calculate the free air correction and Bouguer correction if you are measuring gravity on top of the Rockies.

the Rockies and eastern Colorado based on your mo Elevation (meters) 245 250 255 3600 3200 45 45 2800 2400 2200 2000 1200 800 400 40 40 FR Jemez neamern 35 400 1000 1950 35" 255 245 250

Explanation / Answer

given that, height h= 3000 m

and density of crust pc= 2700 Kg/m^3

density of mantle pm=3300 Kg/m^3

the crust root needed beneath the Rockies to establish isostatic equilibrium or the depth of the mountain belt is b1= h1*pc/(pm-pc) = 3000*2700/(3300*2700) = 13500 mts

in case of a negative topography(marine basin), the balence of lithospheric column gives b2= ((pc-pw)/(pm-pc))*h2

b2 = ((2700-1000)/(3300-2700))*1950 = 5524 mts.

b) free air correction formula in case of earth is given by = 0.3086 mgals/m*h = 0.3086*5524 = 1704 mgals

bougher correction = 0.1967*5524 = 1086 mgals

the difference in gravity on top of rockies and eastern colorado is given as = 1704-1086 = 617 mgals.

The reason Bouguer anomalies are too low in regions of high elevation is isostasy; topography is high because the crust is thick and floating in the mantle.