isostasy answers - Myweb @ CW Post

V.J. DiVenere - 2/13/12
D) Now imagine that millions of years of weathering and erosion have removed 20 km from
the top of the thickened crust.
- How much will the crust rise up? (Consider how deep into the mantle the root of the mountain
will be, r in the figure, for 65 km - 20 km = 45 km thick crust, compared to in part C)
( 2700 kg/m 3
) ( 45 km) = ( 2700 kg/m 3
) ( 35 km) + ( 3300 kg/m 3
) i r
( 2700 kg/m 3
) 45 km
( ) − ( 2700 kg/m 3
) ( 35 km)
( 3300 kg/m 3
)
= r
r = 8.2 km below bottom of normal crust
so, mountain crust (bottom) isostatically rose up from 24.5 below to 8.2 km below
24.5 km - 8.2 km = 16.3 km
20 km erosion yielded 16.3 km uplift (or 0.82 * 20 km)
- How high above the top of normal crust, e, in the figure, will the mountain now be?
e = 45 km - 35 km - 8.2 km = 1.8 km above top of normal crust
- How much lower are the mountains after the 20 km of erosion?
old elevation - new elevation = 5.5 km - 1.8 km = 3.7 km
so, 20 km of erosion only resulted in 3.7 km lowering of the mountains!
(3.7 km lower = 0.18 * 20 km, complement of the 0.82 * 20 km uplift)
- Surprised?
Wow!