The absolute magnitude of stress in the crust and the shear strength of faults are poorly known, yet fundamental quantities, in lithospheric dynamics. While stress magnitude cannot be measured directly, deviatoric stress state can be inferred indirectly from focal mechanism solutions collected before and after an earthquake. We extend a standard stress inversion for normalized stresses to invert for the 3-D spatial distribution of absolute deviatoric stress and variation of fault strength with depth using focal mechanism solutions and coseismic stress changes produced by large earthquakes. We apply the method to the 2011 M9 Tohoku-oki, Japan, earthquake. The northern Japan fore-arc crust between 5 and 15km depths appears to be weak with fault strength of 40-90MPa, consistent with a coefficient of friction of 0.2-0.5. The M9 Tohoku-oki coseismic stress change was large enough, relative to the ambient stress, to rotate the principal stress directions typically 20 degrees in the upper 20km of the crust. The data from Japan require a heterogeneous ambient deviatoric stress field with short-wavelength (20-50km) fluctuations in principal stress orientations.
