Inelastic models of lithospheric stress-I. Theory and application to outer-rise plate deformation

Abstract

S U M M A R YOuter-rise stress distributions determined in the manner that mechanical engineers evaluate inelastic stress distributions within conventional materials are contrasted with those predicted using simple elastic-plate models that are frequently encountered in studies of outer-rise seismicity. This comparison indicates that the latter are inherently inappropriate for studies of intraplate earthquakes, which are a direct manifestation of lithospheric inelasticity. We demonstrate that the common practice of truncating elastically superimposed stress profiles so that they are not permitted to exceed laboratory-based estimates of lithospheric yield strength will result in a n accurate characterization of lithospheric stress only under relatively restrictive circumstances. In contrast t o elastic-plate models, which predict that lithospheric stress distributions depend exclusively upon the current load, inelastic plate models predict that stress distributions are also significantly influenced by the plate-loading history, and, in many cases, this influence is the dominant factor in determining the style of potential seismicity (e.g. thrust versus normal faulting). Numerous 'intuitive' interpretations of outer-rise earthquakes have been founded upon the implicit assumption that a unique relationship exists between a specified combination of plate curvature and in-plane force, and the resulting lithospheric stress distribution. We demonstrate that the profound influence of deformation history often invalidates such interpretations. Finally, we examine the reliability of 'yield envelope' representations of lithospheric strength that are constructed o n the basis of empirically determined frictional sliding relationships and silicate plastic-flow laws. Although representations of this nature underestimate the strength of some major interplate faults, such as the San Andreas, they appear to represent a reliable characterization of the strength of intraplate oceanic lithosphere.

Inelastic models of lithospheric stress-11. Implications for outer-rise seismicity and dynamics

“…As demonstrated by Mueller et al (1996, Figs 3a and 6b), however, outer-rise-type plate bending invariably reduces the likelihood and/or extent of brittle compressional failure. Although we concur that high levels of in-plane compression are essential to the occurrence of thrust-faulting outer-rise seismicity, we reject the notion that a combination of bendinginduced compression and in-plane compression may act to mutually reinforce the likelihood of thrust-faulting activity.…”

“…The plate-bending model, which represents a highly plausible explanation for normalfaulting outer-rise events, implies that these events are mechanically restricted to relatively shallow depths (e.g. Mueller et al 1996, Fig. 3a).…”

“…For example, assuming a modest slab dip of 45" and convergence rate of 6 cm yr-', the slab-pull force associated with 100 Ma oceanic lithosphere is approximately 5 x 1013 N m-' (Davies 1983), whereas the relevant net tensional lithospheric strength is unlikely to exceed 1.3 x 1013 N m -l (e.g. Mueller, Choy & Spence 1996).…”

Bearing of plate geometry and rheology on shallow-focus mega-thrust seismicity with special reference to 26 December 2004 Sumatra event

“…A maximum increase in internal stress by more than 30% is estimated also from rock mechanical studies (Ward, 1984) without any significant deformation in the plate profile. The enhanced stress is accommodated either within the flexural rigidity of the upper brittle part or through time-dependant progressive deformation within semi-brittle/ductile part of the lithosphere till stress build-up reaches the yield envelope at corresponding rheological conditions (Mueller et al, 1996). In Fig.…”

“…4 we superimposed the stress versus depth profile for the highest plate curvature considered in this study on to the reconstructed yield envelope. Fiber Stresses were estimated following the relationship r b ¼ KEd where k is the curvature, E is young's modulus (65 Gpa; Mueller et al, 1996) and 'd' is the distance from the neutral surface. Assuming arc geometry for a bent plate the maximum curvature (K) in a subduction margin around the flexing zone can be estimated as…”