a/ (10 marks) Give the surface elevation h of the deformed lithosphere as a function of the densities and thicknesses of the crust and lithospheric mantle of the reference lithosphere, f_c the thickening/thinning factor of the crust, f_l the thickening/thinning factor of the entire lithosphere, and any other relevant parameters. Please note that the surface elevation h for thickening (fc and fl >1) and thinning (fc and fl <1) must be considered separately.
NB: The thickening/thinning factor of the crust is defined by f_c the ratio between the thickness of the crust after deformation over z_c the thickness of the crust before deformation. The thickening/thinning factor of the entire lithosphere is defined by f_l and follows a similar definition.

b/ (12 marks) Numerical applications (Use the parameter values given below): Calculate h, GPE, Δ GPE (ie, the gravitational force Fg) for the three following cases:
1- f_c = f_l =2; (Homogeneous thickness doubling the thickness of the crust and that of the entire lithosphere)
2- f_c = 2; f_l =1; (Here only the thickness of the crust is changed)
3- f_c = f_l =0.5. (Homogeneous thinning).

c/ (3 marks) The gravitational force acts on a vertical lithospheric section down to the compensation level. The gravitational stress is given by the ratio between the gravitational force and the surface area on which the force is applied. Assuming lithospheric rocks have a depth independent strength of 70MPa, would the gravitational forces determined in b/ produce any lithospheric deformation?

nb: We assume here that densities are temperature independent.