The stress tensor orientation was calculated by inversion of 81 fault plane solutions of M=3.5¿0.6 earthquakes located in an area 6 by 16 km at depths of 7¿2 km. This crustal volume is situated on a straight line between the summits of the active volcanoes Kilauea and Mauna Loa. The orientation of the greatest principal stress was found to be near horizontal and in the line connecting the two volcanoes. This is further evidence supporting the model that magmatic expansion within the feeding conduits of these volcanoes is the source of stress that causes earthquakes in southern Hawaii. These earthquakes are tectonic earthquakes in the sense that they occur in a brittle elastic crust at distances of a few to several tens of kilometers from the volcanoes, and that they are not directly associated with the opening of cracks by intrusions. We propose that this model leads to the corollary that the shear stress (gt) responsible for earthquake failure in the shallow Hawaiian crust are approximately 3¿2 MPa, and that the pore pressure of ground-water (p) in the hypocentral volume must be under near lithostatic pressure. This result is obtained by arguing that the greatest principal stress (&sgr;1) is equal to the magma pressure in the volcanic feeder pipe, but cannot exceed the least principal stress (&sgr;3) by more than the tensile strength of the crust, because otherwise hydrofracture would occur, opening a crack against the least principal stress.

Given the difference between the greatest and least principal stress, the fact that the overburden at the 7 km hypocentral depth equals the intermediate principal stress and the ratio R=(&sgr;1-&sgr;2)/(&sgr;1-&sgr;3)=0.4, which is obtained in the inversion of fault plane solutions, we estimate that &sgr;1=202 MPa, &sgr;2=200 MPa, &sgr;3=196 MPa, &tgr;=3 MPa, and &sgr;n=199 MPa, with uncertainties on the order of several MPa. It follows that for any coefficients of friction larger than 0.15, the pore fluid pressure necessary for faulting on the observed fault planes has to be larger than 90% of the lithostatic pressure. These considerations suggest that many earthquakes represent fault ruptures under low ambient shear stresses in the order of the average observed stress drop of 3 MPa. ¿ American Geophysical Union 1992