PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Earth, Climate & Energy Physics · Temperature, heat and the macroscopic behaviour of matter
The Solid Earth, Ch Plates, creep and convection: the mantle in motion
Problem
A patch of oceanic lithosphere is t=80Myr old. It formed at a ridge with mantle temperature Tm=1350∘C and has since cooled from a seafloor held at T0=0∘C. Take the thermal diffusivity κ=10−6m2s−1 and 1Myr=3.156×1013s.
((a)) Using the half-space cooling model T(z,t)=Tmerf(2κtz) for the temperature at depth z below the seafloor after time t, find the depth of the 650∘C isotherm, taken here as the crossover between frictional and olivine creep strength (olivine's brittle-ductile transition lies near 600 to 750∘C). You may use erf(0.45)=0.475 and erf(0.46)=0.485.
((b)) The outer trench slope of an old, bending oceanic plate is normally faulted (extensional). With hydrostatic pore pressure and Byerlee friction in mantle rock of density 3300kgm−3, the frictional strength for normal faulting grows at 15MPakm−1. Taking the depth found in (a) as the base of the brittle layer, find the frictional strength there, expressed as the compressive stress difference S1−S3 (S1,S3 the greatest and least principal compressive stresses). Then state the same differential stress in the tension-positive convention (σi=−Si), saying which principal stress, σ1 or σ3, is now the algebraically larger, and confirm that the magnitude of the differential stress is unchanged by the sign convention.
((c)) For a mantle viscosity ηv=1021Pas, the onset thickness and age of the thermal boundary layer beneath cooling sea floor, from the criterion Raδ=103, are δc=92km and tc=50Myr. State by how many million years the 80Myr plate of this problem has already passed that onset age, and say in one sentence what this implies for the fixed-thickness plate model used for its cooling history.