A strain-rate-dependent force model of lithospheric strength

Abstract

Summary This study investigates the rate of intraplate deformation, the vertically integrated stress magnitude and vertical distributions of tectonic stress in continental lithosphere that is subjected to horizontal tectonic force. The fundamental assumption of this study is that the magnitude of the imposed tectonic force depends on the rate of deformation. This modification of the often applied strength envelope concept accounts for resistance forces generated externally to the lithospheric section that the calculated vertical stress distribution is considered to represent. The model presented overcomes the difficulties that arose in previous constant strain rate and constant force approaches and thus proves to be physically more realistic. Results are discussed with emphasis on the effects related to the strain‐rate‐dependent force assumption and on differences from the results of both previous approaches. The strain‐rate‐dependent force model predicts that in and adjacent to a weak and fast‐deforming lithospheric plate, the integrated stress magnitude is significantly reduced due to externally derived resistance forces. Modelling results suggest that the rate of intraplate deformation in many cases is controlled by the balance of externally derived deformation‐driving and externally derived deformation‐resisting forces, but is relatively insensitive to the low internal strength of the deforming lithosphere. The integrated stress level in regions of active intraplate deformation, in contrast, is predicted to be largely controlled by the time‐independent brittle strength. The strain‐rate‐dependent force model provides a geodynamic concept that allows one to investigate intraplate stress distribution depending on tectonic force magnitude, lithospheric strength and rate of intraplate deformation.

State of lithosphere beneath Tien Shan from petrology and electrical conductivity of xenoliths

“…In a more realistic model the lithospheric strength of Tien Shan for a given strain rate 10 −14 to 3 × 10 −15 s −1 was estimated as an integral of the limiting yield stress over the thickness of the whole lithosphere (∼140 km). The limiting yield stress was chosen as the minimum of the brittle strength rocks according to the Byerlee law, with a gradient of brittle strength of rocks of 110 MPa km −1 at depths above 4 km and with a depth gradient of 57.7 MPa km −1 plus a constant 210 MPa at depths below 4 km [ Stüwe , 2007]; the ductile stress was calculated from the dislocation creep [ Ranalli , 1987; Porth , 2000]. Brittle failure as a function of depth was taken for the case of a normal fault deformation where the maximum principal stress ( σ 1 ) is equal to the lithostatic stress ρgz , and the vertical stress is equal to the minor principal stress ( σ 3 ) [ Stüwe , 2007].…”

“…The lithospheric strength or the magnitude of integrated differential stress F t beneath the south Tien Shan may vary from 7.9 to 4.0 × 10 12 N m −1 for the observed strain rates from 10 −14 to 3 × 10 −15 s −1 , which is close to the F t estimations of the compressional force near the Tibetan Plateau, 7 × 10 12 N m −1 [ Molnar and Lyon‐Caen , 1988]. In Tarim Basin this force is not enough to produce any lithospheric deformation because the lithospheric strength beneath Tarim Basin that corresponds to a heat flux of 45–50 mW m −2 is higher than 30 × 10 12 N m −1 [ Porth , 2000]. At the moment of the India collision with the Eurasian plate, the heat flux beneath Tien Shan was even larger, ∼80–85 mW m −2 (Figure 12), and the integrated lithosphere strength was less than 10 12 N m −1 .…”

“…At the moment of the India collision with the Eurasian plate, the heat flux beneath Tien Shan was even larger, ∼80–85 mW m −2 (Figure 12), and the integrated lithosphere strength was less than 10 12 N m −1 . Thus, the initial strain rate of Tien Shan shortening could have been higher than that today, >10 −14 s −1 [ Porth , 2000]. The low heat flux and high lithospheric strength beneath Tarim Basin explain why the indentation of the Indian continent into the Eurasian plate resulted in the shortening of the weak Tien Shan lithosphere rather than the cold adjacent lithosphere beneath Tarim Basin in the first place.…”

Seismic anisotropy and mantle creep in young orogens

“…Rutter & Brodie (1991), Meissner & Mooney (1998) and Porth (2000) discuss the validity and applicability of this equation. Rutter & Brodie (1991), Meissner & Mooney (1998) and Porth (2000) discuss the validity and applicability of this equation.…”

“…Please note that we calculated the escape velocity twice: for the simple 2-D case (eq. Weertman 1970;Ranalli 2000;Porth 2000). (A4a) (last column) using average viscosity values of 10 21 and 10 22 Pa s according to Fig.…”