A flexural-cantilever simple-shear/pure-shear model of continental lithosphere extension: applications to the Jeanne d’Arc Basin, Grand Banks and Viking Graben, North Sea

Abstract

Mathematical models have been constructed of the geometric, thermal and flexural-isostatic response of the lithosphere to extension by faulting (simple-shear) in the upper crust and plastic, distributed deformation (pure-shear) in the lower crust and mantle. Models involving upper-crustal extension by both listric and planar faults have been developed. These coupled simple-shear/pure-shear models have been used to calculate extensional sedimentary basin geometry, subsidence history and crustal structure. Basin geometry and subsidence history are controlled by fault geometry (planar or listric), the amount of fault extension, fault dip, the depth of the transition from simple-shear to pure-shear, and the flexural rigidity of the lithosphere during both syn-rift and post-rift stages of basin formation. For the planar fault model, footwall and hangingwall blocks are considered to behave as two interacting flexural cantilevers; the response of these cantilevers to the isostatic forces produced by extension generating footwall uplift and hangingwall collapse. For a set of adjacent planar faults the lateral superposition of flexural footwall uplift and hangingwall collapse generates the familiar ‘domino’-style block-rotation of such multiple fault systems. The listric fault model assumes that the hangingwall collapses onto a rigid footwall by vertical shear, and that the tectonic denudation of the upper crust by faulting generates isostatic uplift producing limited footwall uplift. Deep seismic reflection data and earth-quake seismology suggest that the fundamental basement faults controlling lithosphere extension are planar. It is argued that the vertical shear construction of hangingwall collapse onto a rigid footwall is inappropriate for basement response. The coupled simple-shear/pure-shear models of extensional basin formation, using both listric and planar fault geometries, have been applied to the formation of the Jeanne d’Arc basin, Grand Banks, and the Viking Graben of the northern North Sea. The numerical modelling shows that the crustal thinning, thermal and sediment-fill loads generated during and after lithosphere extension need to be distributed flexurally in order to generate the observed basin depth and geometry. The flexural-cantilever, planar-fault model provides closer agreement to observed basin depth and subsidence than the listric-fault model. The planar fault model also produces more footwall uplift than a listric fault model. Erosion of this footwall uplift generates substantial isostatic uplift through unloading, leading to a large underestimate of the horizontal displacement on basin-bounding faults. The low values of effective elastic thickness obtained by extensional basin modelling are substantially less than the thickness of the cool, brittle upper crust. It is suggested that flexural bending stresses associated with lithosphere extension on planar faults are sufficiently large to generate brittle failure within the upper crust, so producing the low values of effective elastic thickness. This is consistent with the predictions of the flexural-cantilever model.

Normal faulting on Europa: implications for ice shell properties

“…Weissel and Karner, 1989;Kusznir et al, 1991;Brown and Phillips, 1999). Since the elastic thickness of the icy satellites is considerably smaller than that of most terrestrial settings, flexurally-modified fault profiles are likely to occur.…”

“…We use the flexural cantilever model of Kusznir et al (1991) to model the fault-related topography. This model assumes a thin elastic layer, as opposed to an elastic half-space; such a layer is appropriate to a situation in which the fault displacement may be comparable with the likely elastic layer thickness (e.g.…”

“…On Earth and Venus, normal fault observations have been used to infer various mechanical properties of the material in which they form (e.g. Jackson and White, 1989;Kusznir et al, 1991;Foster and Nimmo, 1996). Here, we apply some simple techniques from the terrestrial literature to probe the mechanical properties of the ice shell on Europa.…”

Geomorphological consequences of weak lower continental crust, and its significance for studies of uplift, landscape evolution, and the interpretation of river terrace sequences

“…One suggestion, by Kusznir et al (1991), was that warping of the brittle layer causes much of its thickness to fracture, making it unable to support elastic stress and thus concentrating this stress in a thin 'fibre' at depth. In this scheme, values of H e determined from equation (4) represent estimates of the actual thickness of this fibre.…”

Modeling the formation of a half graben using realistic upper crustal rheology

“…Flexural deformation of a faulted upper crust has normally been modeled by treating it as an elastic layer underlain by a fluid substratum [Turcotte and Schubert, 1982, p. 127]. Elastic flexural modeling of half grabens typically yields anomalously low estimates of 3 to 6 km for the effective thickness Te of the elastic layer [Warner, 1987;Kusznir et al, 1991]. This is probably because classical flexural analysis ignores the finite strength envelope of the brittle upper crust [Buck, 1988;Kusznir et al, 1991].…”