A seismologist studies a strike-slip earthquake on a fault that has slipped…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics

The Solid Earth, Ch The earthquake source: moment tensor, radiation and spectra

Problem

A seismologist studies a strike-slip earthquake on a fault that has slipped repeatedly since the Miocene and is known from laboratory tests to be frictionally weak. From the moment tensor she finds the pressure (P) axis trending N45∘45^\circE. She writes: "The P axis found from the moment tensor is the direction of maximum compressive stress released by the earthquake, so the regional maximum principal stress S1S_1 must also trend N45∘45^\circE." Independent borehole-breakout evidence places the true S1S_1 direction at N60∘60^\circE. ((a)) Find the error in her reasoning. ((b)) For a new fault optimally oriented under Coulomb friction with μf=0.6\mu_f = 0.6, the angle between S1S_1 and the fault plane is θ=12arctan⁡(1/μf)\theta = \tfrac12\arctan(1/\mu_f), and the P axis lies 45∘−θ45^\circ - \theta from S1S_1. Compute this angle and compare it with the 15∘15^\circ discrepancy observed above, then explain why that agreement is coincidental for this fault.

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