Imagine a sedimentary basin on some planetary body that is confined on all sides and filled to a depth of 1 km. The horizontal strains, ε_xx and ε_yy are both zero, and the vertical stress at any depth z in the basin is given by σ_zz = ρzg. Use the constitutive relations in Equation 8.4 to find expressions for the strain in the vertical direction (ε_zz) and the stresses in the horizontal directions (σ_xx and σ_yy). Compute these quantities at depths of 0.1, 0.5, and 1.0 km for a sedimentary basin on Earth, assuming ρ = 2100 kg/m³, E = 50 GPa, and ν = 0.2. Now compute the same quantities for an icy sedimentary basin on Titan, where g = 1.3 m/s², ρ = 917 kg/m³, E= 10 GPa, and ν = 0.3. Compare the results for the two bodies.

 Equation 8.4 

Exx Eyy Ezz 1 XX E - V E V E V E 5 xx yy 1 Oxx + Oyy V yy V E - 0 zz V 2012 0 zz E 1 + 20 E zz