Heat Flow Paradox

Paradox-The seismogenic zone extends from the surface to a depth of about 10 km. According to Byerlee's law, the shear stress on the fault should be some large fraction of the hydrostatic stress. f static coefficient of friction ~ 0.60 ρ c crustal density 2600 kg m-3 ρ w water density 1000 kg m-3 g acceleration of gravity 9.8 m s-2 D depth of seismogenic zone 12 km This assumes that water percolates to 12 km depths to lower friction on the fault. We can compute the average shear stress on the fault. The observed stress drop during an earthquake ranges from 0.1 to 10 MPa with a typical value of 5 MPa which is about 10 times smaller than the average stress from Byerlee's Law. This implies that only a fraction of the total stress is released during an earthquake. The average stress during the earthquake times the earthquake displacement produces energy both as seismic radiation (small fraction) and as heat (large fraction). If this heat energy is averaged over many earthquake cycles, then this average heat/area generated on the fault plane will appear as a heat flow anomaly on the surface having a similar heat/area as along the fault. To calculate this heat anomaly for a variety of frictional heating models, first consider a line source of heat. τ ρ ρ () z f gz c w = − () (1) τ ρ ρ ρ ρ = − () − () ∫ 1 1 2 D f gzdz f gD c w o D c w = = 56 MPa (2)