Calculation of true thickness of the bed

Q) The oceanic depth at a distance of 1000 km from the pacific Ridge is 3500 m. calculate the age of the crust at this location and  the mean spreading rate represented by this age is?

(Thanks to Chandrasekhar, ANU)

 Solution:

 Given that     

Ocean depth (d) = 3500 m

Distnace(D) = 1000 km

Age of the crust (or) lithosphere (t) =?

Spreading rate (v) =?

We know that the relation between the mean oceanic depth (d) and the lithospheric age (t in Ma) is as follows

$d= 2500+ 350 t^{\frac{1}{2}}$

(or)

$t=(\frac{d-2500}{350}^{2})$

By substituting the Given values in the above formula we get

$t=(\frac{d-2500}{350})^{2}$

$t=(\frac{3500-2500}{350})^{2}$

$t=(\frac{1000}{350})^{2}$

$t=(2.85)^{2}$

$t=8.125 Ma$

The Spreading rate (v) = $\frac{distance}{time}$

=$\frac{1000 Km}{8.125 Ma}$

=$\frac{1000\times 10^{3} m}{8.125\times10^{6}years }$

=$\frac{1}{8.125}m/year$

=$0.123 m/year$