Rheology of the Earth and a thermoconvective mechanism for sedimentary basin formation

Abstract

A power-law non-Newtonian fluid is usually assumed to model slow flows in the mantle and, in particular, convective flows. However, the power-law fluid has no memory, in contrast to a real material. A new non-linear integral ( having a memory) model is proposed to describe the rheology of rocks. The model is consistent with the theory of simple fluids with fading memory and with laboratory studies of rock creep. The proposed model reduces to the power-law fluid model for stationary flows and to the Andrade model for flows associated with small strains. Stationary convection beneath continents has been studied by Fleitout & Yuen (1984), who used the power-law fluid model and obtained the cold immobile boundary layer (continental lithosphere). In a stability analysis of this layer, the Andrade model must be used. The analysis shows that the lithosphere is overstable (the period of oscillation is about 200 Ma). In the present study, it is suggested that these thermoconvective oscillations of the lithosphere are a mechanism for sedimentary basin formation. The vertical crustal movement in sedimentary basins can be considered as a slow subsidence on which small-amplitude oscillations are superimposed. The longest period of oscillatory crustal movement is of the same order of magnitude as the period of convective oscillation of the lithosphere found in the stability analysis. Taking into account the difference between depositional and erosional transport rates we can explain the permanent subsidence as well as the oscillations.

Rheology of the lithosphere and the folding caused by horizontal compression

“…In the case of stationary flows causing large defor mations, the nonlinear hereditary rheological model of the creep (Birger, 1998) is reduced to the power law fluid model with rheological parameter B whose values are determined by the rheological parameter A of the Andrade transient creep model and by the value of the second invariant of the creep strain tensor ε tr , at which the creep process passes to the steady state ctage:…”

“…Second, this model does not describe the transient creep that takes place at small (within a few percent) strains. A nonlinear hereditary (i.e., having a memory) rheological model of the lithosphere was suggested in (Birger, 1998). At time constant stresses, this model is reduced to the power law model, and at small strains, to the linear hereditary Andrade model describing the transient creep.…”

Transient creep of the lithosphere and its role in geodynamics

“…Decaying memory means that the current stress depends on the recent strains much stronger than on the strains that existed in the distant past. Birger (1998) proposed a new nonlinear integral (having a memory) model for high temperature dislo cation creep of rocks. This model is consistent with the theory of simple fluids with fading memory and is determined by the equation (10) where (11) ε = (ε kl ε kl /2) 1/2 is the second invariant of the strain ten sor, and R(s) is defined by (9).…”

“…Nonlinear integral model (10) reduces to the linear Andrade model (8) for flows associated with small strains. At stationary flows, causing large strains, the model is reduced, as shown in (Birger, 1998), to the model of power law fluid with rheological parameters B and n, whose values are determined by the rheological parameters A, m, and ε tr in (10), (11). If m = 1/3 in the Andrade law, the relations are The transition value of strain is estimated as ε tr ≈ 10 -3 -10 -2 .…”

“…Low amplitude thermoconvective oscillations of the cra tonic lithosphere cause oscillatory movements of the Earth's surface. Taking into account the significant difference between the rate of sedimentation and ero sion, the lithosphere thermoconvective oscillations can be considered as a mechanism for the formation and evolution of sedimentary basins on continental cratons (Birger, 1998;2004).…”