A review of methods for determining stress fields from earthquakes focal mechanisms; Application to the Sierentz 1980 seismic crisis (Upper Rhine graben)

The inversion of earthquake focal mechanisms is one of the few tools available for determining principal stress directions at seismogenic depths. Various methods have been proposed for performing such inversions. For three of the most commonly used methods, including one that has been proposed by Jacques Angelier, we discuss the physical assumptions and the error determination and then we propose an extension for one of the methods. All four methods are then applied for evaluating the stress field in the Upper Rhine graben. They are applied to seismic data recorded with a temporary monitoring network that was deployed 12 hours after the magnitude Mw = 4.4 Sierentz earthquake, which occurred on July 15, 1980. While differences in principal stress directions can be as much as 28° depending on the method used for the principal stress direction determination (orientation of the minimum principal stress has been found to range from N051°E with a 27° plunge to N090° E with a 20° plunge), the 90% confidence level associated with each method varies from 11° to 27°. Moreover, these various methods yield fairly diverse values for the R factor that characterizes relative differences between principal stress magnitudes (from R = 0.7 with a 0.2 90% confidence level to R = 0.3 with a 0.2 90% confidence level). Furthermore all three methods leave some focal mechanisms unexplained. These are then declared to be the result of heterogeneity and are not considered for the inversion. It is concluded that earthquake focal mechanisms inversions lack resolution for stress field evaluation at depth if no proper attention is given to the event independence hypothesis. When proper attention is given to this hypothesis, a resolution of the order of 15° may be achieved. The minimum principal stress orientation derived with these various focal mechanisms inversions differs by 4 to 36° from the orientation determined from borehole breakouts observed in Basel, in a 5 km deep well (N054°E ± 14°), located some 20 km from Sierentz. The solution that fits best borehole breakout observations is that which satisfies the minimum number (three) of prerequisite physical assumptions.