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

Abstract

International audienceThe 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

Tectonic stress regime in the 2003–2004 and 2012–2015 earthquake swarms in the Ubaye Valley, French Alps

“…If we know focal mechanisms for a set of earthquakes that occurred in the focal zone, we can invert them for tectonic stress (e.g., Michael 1984Michael , 1987Angelier 1984;Gephart and Forsyth 1984;Zoback 1992). The stress inversion is based on several assumptions (Maury et al 2013;Vavryčuk 2015): (1) the stress is uniform in the region, (2) the earthquakes occur on faults with varying orientations, (3) the slip vector points in the direction of the shear traction on the fault (the socalled Wallace-Bott hypothesis; see, Wallace 1951;Bott 1959) and (4) the earthquakes do not interact with each other and do not disturb the background tectonic stress. Under these conditions the stress inversion allows us to estimate the orientation of the principal stress axes and the shape (stress) ratio…”

“…In this case, the area should be studied by subdividing into cells of similar stress regime and by inverting for stress in individual cells (Hardebeck and Michael 2006;Vavryčuk 2006;Townend et al 2012). As regards the stress variation with depth, it is also possible to invert for a vertical stress gradient if the activity samples a large depth range (Maury et al 2013). Besides, if seismic sequences include strong earthquakes with magnitude greater than 5, the effects of the Coulomb stress produced by earthquakes cannot be neglected and some selection criteria for independent earthquakes should be applied to the input dataset (Maury et al 2013;Martinez-Garzón et al 2016a).…”

Present‐Day Deformations of the Jura Arc Inferred by GPS Surveying and Earthquake Focal Mechanisms

“…Only six events have a magnitude higher than 4 in the period 1971–2012. The three biggest events were the M l 5.2–5.3 Vuache earthquake in 1996 (Thouvenot et al, ), the M l 4.8–5.1 Besançon earthquake in 2004 (Baer et al, ), and the M l 4.7–4.8 Sierentz earthquake in 1980 (Maury et al, ; Rouland et al, ), respectively, A, B and C on Figure .…”

Present‐day crustal stress field in Greece inferred from regional‐scale damped inversion of earthquake focal mechanisms

“…In reality, prefracturing in the Earth's crust and friction along the fault surfaces makes this correspondence for a single focal mechanism less reliable. Thus, many methodologies have been proposed to derive the stress tensor from a set of focal mechanisms through inversion algorithms [Gephart and Forsyth, 1984;Michael, 1984Michael, , 1987Angelier, 2002]; a review of which can be found in Hardebeck and Hauksson [2001] and in Maury et al [2013]. The basic assumption of these methodologies is that the set of inverted focal mechanisms can be explained by one stress tensor or in other words that stress is homogeneous.…”