Nucleation Depth Research Articles

Rheological Models for Continental Seismicity and Maximum Seismogenic Depth

Abstract In fault systems at plate boundaries, maximum seismogenic depth is likely defined by the transition with depth from unstable frictional slip to localized, high strain rate (γ̇≈1011/s) quasi-plastic shearing in trans-crustal, tabular fault zones; the transition being significantly affected by variations in regional heat flow. However, such deep driven rheological models are probably inappropriate for areas of intraplate seismicity such as the eastern United States where, despite the low cratonic heat flow, the larger earthquakes (mb≈5) seem to nucleate in the 5–10 km depth range. Similar shallow nucleation depths have also been noted for large intraplate events in the cratonic crust of Australia. A more appropriate model for such intraplate activity is to view the upper levels of cratonic crust as a remotely-loaded, flawed stress-guide, where time-dependent failure may occur through processes such as stress corrosion. A rheological criterion accounting for the depths of these cratonic events is that seismogenic failure can only occur when the loading strain rate is greater than the potential rate of flow relaxation within the focal volume, suggesting an important size effect. Loading strain rates estimated from likely earthquake recurrence intervals in such areas are extremely low (<10−16/s ). At such low strain rates, the upper crust is effectively decoupled, even though no geologically obvious strain signature will develop in the middle or lower crust over lengthy time periods. Available strain energy, and perhaps maximum earthquake size, may then be quite sensitively linked to maximum seismogenic depth. A range of intermediate mixed behavior must exist between these end-member models.

Crustal deformation in Great California earthquake cycles

Periodic crustal deformation associated with repeated strike‐slip earthquakes is computed for the following model; A depth L (≤ H) extending downward from the Earth's surface at a transform boundary between uniform elastic lithospheric plates of thickness H is locked between earthquakes. It slips an amount consistent with remote plate velocity Vpl after each lapse of earthquake cycle time Tcy. Lower portions of the fault zone at the boundary slip continuously so as to maintain constant resistive shear stress. The plates are coupled at their base to a Maxwellian viscoelastic asthenosphere through which steady deep‐seated mantle motions, compatible with plate velocity, are transmitted to the surface plates. The coupling is described approximately through a generalized Elsasser model. We argue that the model gives a more realistic physical description of tectonic loading, including the time dependence of deep slip and crustal stress buildup throughout the earthquake cycle, than do simpler kinematic models in which loading is represented as imposed uniform dislocation slip on the fault below the locked zone. Parameters of the model are chosen to fit seismic and geologic constraints and the apparent time dependence of surface strain rates along presently locked traces of the 1857 and 1906 San Andreas ruptures. We fix Vpl = 35 mm/yr, Tcy = 160 years, and L = 9–11 km based on earthquake nucleation depths. The geodetic data are then found to be described reasonably, within the context of a model that is locally uniform along strike and symmetric about a single San Andreas fault strand, by lithosphere thickness H = 20–30 km and Elsasser relaxation time tr = 10–16 years. We therefore suggest that the asthenosphere appropriate to describe crustal deformation on the earthquake cycle time scale lies in the lower crust and perhaps crust‐mantle transition zone and has an effective viscosity between about 2 × 1018 and 1019 Pa s, depending on the thickness assigned to the asthenospheric layer. Predictions based on the chosen set of parameters are also consistent with data on variations of contemporary surface strain and displacement rates as a function of distance from the 1857 and 1906 rupture traces, although the fit is degraded by asymmetry relative to the fault and by slip on adjacent fault strands.

Active normal faulting and crustal extension

Summary A world-wide review of fault-plane solutions and focal depths for large normal-faulting earthquakes on the continents shows that the overwhelming majority of such earthquakes nucleate in the depth range 6–15 km on faults dipping between 30 and 60°. In the few cases where levelling or seismic data are good enough, these normal faults are shown to be approximately planar from the surface to their nucleation depth at the base of the brittle crust. There is evidence that, in some cases, as a result of the enormous transitory increase in strain rate during large earthquakes, rupture continues into the normally ‘ductile’ lower crust on surfaces with substantially gentler dips. These low-angle surfaces may be analogous to some of the ‘detachments’ seen in metamorphic core complexes of the western USA, but the nature of the motion on them depends on strain rate as well as on rheological contrasts between the ‘detachments’ and the blocks on either side. Such contrasts, however, are unlikely to introduce substantial curvature to an originally planar shear zone. If the observed spread in active normal-fault dips is caused by rotation of the faults and the blocks they bound during extension, then a maximum β value of 1.7 can be accommodated by seismic activity on a single generation of normal faults. With continued extension, either a new generation of steeper faults, cutting the rotated first faults, is likely to form, or the deformation will continue aseismically on faults dipping at less than 30°. Large earthquakes have not been observed to nucleate on very low-angle (<20°) normal faults within the continental crust anywhere in the world. Such faults can of course move aseismically, but are unlikely to do so on a large scale within the upper crust in areas where steep normal faults are seismically active. Thus extensional models that require concentrated simple shear on large sub-horizontal faults within the brittle upper crust will also require a spatial separation between aseismic, very low-angle faulting and seismic high-angle faulting. Since seismogenic high-angle faults dominate the topography of extending regions, upper-crustal very-low-angle faulting, if it occurs on a large scale, presumably does so in areas that are relatively flat.

Crustal earthquake instability in relation to the depth variation of frictional slip properties

Recent stability studies using constitutive relations of the type found by Dieterich, Ruina, and others to describe frictional slip of rocks in the laboratory have provided a new explanation of the depth cutoff of shallow crustal earthquakes. The class of friction laws discussed has the property that the sliding stress depends on normal stress, temperature, slip rate, and slip history. For sliding at a fixed slip rate V and fixed environment (e.g., normal stress, temperature, etc.) the shear strength τ evolves toward a steady state value τss(V). Stability analysis show that for dτss(V)/dV < 0 (i.e., velocity weakening), steady state sliding is unstable to any perturbation in systems of sufficiently low stiffness and is unstable to sufficiently large perturbations in systems of higher stiffness. Hence a surface with dτss(V)/dV < 0 is potentially unstable. Conversely, dτss(V)/dV > 0 (velocity strengthening) implies stable steady state sliding, at least for a broad class of constitutive laws more fully described in the paper. Experiments by Dieterich and by Tullis and Weeks on Westerly granite with mature sliding surfaces indicate that dτss(V)/dV is negative at room temperature, whereas higher‐temperature experiments by Stesky show that dτss(V)/dV becomes positive above approximately 300°C. Therefore, in the case of the earth, where temperature increases with depth, the above observations seem to suggest that the depth cutoff of crustal earthquake activity can be understood in terms of the variation of the frictional response with depth, from a regime with dτss(V)/dV < 0 to one with dτss(V)/dV > 0. This is not inconsistent with, but rather refines, the suggestion by Sibson and others that the depth cutoff is due to a transition from brittle friction to ductile flow. Further, our results show definitively that the shallow depth confinement of seismicity is compatible with a model in which deformation is localized to a fault zone extending well below the seismogenic depth. The depth confinement does not require a model showing transition to a zone of broadly distributed creep flow beneath the seismogenic zone. Following Mavko, a two‐dimensional quasi‐static strike‐slip fault model is analyzed but using different numerical procedures and a depth variation of frictional properties based on the laboratory data mentioned above and the Lachenbruch‐Sass depth variation of temperature for the San Andreas fault. The resulting predictions of such features as the confinement of crustal earthquakes to shallow depths, the development of locked patches, the recurrence time for the seismic cycle, the seismic stress drop and displacement, etc., are generally in agreement with the observed characteristics of large‐scale strike‐slip earthquakes along the San Andreas fault. Calculations based on the laboratory data predict, for example, that stick‐slip nucleates around 5–7 km, that large seismic motion occurs around the nucleation depth and above but diminishes gradually to zero at 13–15 km depths, that rapid postseismic creep occurs over another 3–4 km depth, and that at greater depths, steady slip consistent with the average plate velocity is only modestly perturbed by the earthquakes occurring above. The most uncertain parameter is the slip weakening distance L for evolution of fault surface state; we illustrate how features of the predicted earthquake cycles vary with L over the range for which calculations are feasible.

Control of rupture by fault geometry during the 1980 El Asnam (Algeria) earthquake

Summary. The El Asnam earthquake of 1980 October 10 (Ms= 7.3) occurred on a segmented reverse fault in the Atlas Mountains of Algeria. This report re-examines the teleseismic data for the main shock and major aftershocks in the light of detailed studies of the surface breaks, geodetic changes and aftershock distribution. The observed thrust fault is split into southern, central and northern segments by distinct offsets and changes in trend. The southern and central segments are each about 12 km long, but the northern segment showed only 3–4 km of surface thrust breaks. However, widespread tensional faulting on ridges in the north-east area, together with focal mechanisms of locally-recorded aftershocks, indicates that a series of imbricate listric thrusts exists to the north of the northern fault segment. Using ISC arrival-time lists, a relative relocation scheme is applied to the main shock and major aftershocks to improve their locations with respect to the mapped faults. The main shock epicentre was at the south-west end of the fault system, in a zone where the thrust has a zig-zag surface trace. By contrast most of the major aftershocks were located further north-east, and were associated with the northern thrust segment and the imbricate thrusts to the north. The largest aftershock (mb= 6.1), which occurred about 3 hr after the main shock, was located to the east of the main thrust fault, beneath the Chelif alluvial basin. First-motion fault plane solutions are presented for the main shock and largest aftershock. The main shock solution indicates a fault plane dipping 54° NW, with strike 040°. The aftershock solution, however, has a more E–W trend (080°), in agreement with the trends of the basin edges near its location. The rupture history of the main shock is investigated by forward modelling of the long-period P-waves. Four subevents are clearly distinguishable. The first three subevents occurred in rapid succession and contributed to the first cycle of the P-wave radiation. These three subevents represent the successive rupturing of the southern, central and northern fault segments. In order to match the observed waveforms, these three ruptures must have different mechanisms and moments: the fault segments have successively shallower dipts from south to north (54°, 45° and 40° respectively), and the central segment had the largest moment release (in agreement with the geodetic data of Ruegg et al.). The delay times between the three sources suggest a rupture velocity of about 3.5 km s−1 and their–nucleation depths were 7 km. The junctions between the fault segments acted as geometric barriers to the rupture propagation, but were broken by its passage. The fourth subevent of the main shock produced the second cycle of the P-wave radiation. It began about 18 s after the first, i.e. several seconds after the end of the third rupture. Nabelek demonstrates that the fourth subevent occurred on a shallow-angle (20°) thrust plane; examination of the locally recorded aftershocks suggests that this plane is a decollement surface underlying the imbricate thrusts of the north-east area. The total seismic moment found from the body-wave modelling is 7.7 × 1026 dyne cm, in good agreement with geodetic and surface-wave studies.