Theory of Gravity Instability With Variable Overburden and Compaction

Abstract

The gravitational instability of a simple two-layered medium resting on a rigid base has been treated in terms of the analog model of Biot. In order to avoid complications of purely mathematical nature which are unrelated to the physics of the process of instability and do not affect the results significantly, the analysis is presented for the two-dimensional case? It is shown that such a system is unstable if the density contrast Ap between the top layer (overburden) and the bottom layer (salt) is positive. The physically important parameters of the instability are the viscosity ratio and the thickness ratio between overburden and salt and the relative density contrast Ap/pl. These parameters determine the amplification rate of a given initial sinusoidal perturbation of wavelength L of the overburden-salt interface. For the purpose of isolating the role of each parameter and to rovide an understanding of the underlying mechanics, several tables are presented which show the influence of eat 1 of these parameters as well as the wavelength of maximum amplification rate (dominant wavelength) and the time in which a thousandfold amplification is obtained (characteristic time). This form of presentation of results is well suited to geological problems including the variable time dependence of the overburden due to gradual sedimentation. The influence of either an additional surface layer of water or a nonrigid base of high viscosity is small. The special condition of keeping the surface of the upper layer flat while the volume is held constant, termed "redistribution," leads to an increased rate of growth and slightly longer dominant wavelength.The geologically more significant case of an instability with time-dependent thickness and compaction of overburden is solved by introduction of an effective density ps of the overburden. The characteristic times and'dominant wavelengths of salt structures in a salt layer of initial thickness of 1,000 m and viscosity of lOIT poises overlain by sediment of viscosity of 1WOpoises are in excellent agreement with observed facts.

The effective viscosity of rocksalt: implementation of steady-state creep laws in numerical models of salt diapirism

“…Harmonic perturbations have been shown to grow exponentially with a specific growth rate (e.g. Biot and Ode, 1965). Therefore, in the initial stages of the calculations the time step was reduced using a criterion based on growth rate (Schmeling, 1987) to be able to follow the exponential growth of the interface amplitude.…”

“…The density and viscosity of the basement are (arbitrarily) chosen to be pbasement = 2400 kg m-3 and qbasement = 1O23 Pa s, which effectively guarantees that the basement does not deform during the dynamical evolution of the salt, mimicing rigid, crystalline rock. The overburden has uniform viscosity v,,diment = lo*' Pa s. For the sediment density, we have now included the effect of compaction on the sediments and used the approximation of Biot and Ode (1965) to Nettleton's (1934) estimates of the densitydepth relation for sediments in the Gulf Coast region. This is written: psediment( z) = 2490 -590 eenr -az ePPZ kg rnp3 (20) in which z is the depth in m, cx = 0.59 X lo-" m-', /3 = 1.6 X 10e3 m-', and a = 5 X 10m5 kg mp3.…”

Salt tectonics as a self‐organizing process: A reaction, transport, and mechanics model

“…If the tip of the salt diapir is too far below the surface of the sediment, then this coupling is diminished so that there is a limited depth range for the operation of this mech- The sedimentation to salt deformation dynamic is just one of a family of feedback processes operating in a salt tectonic province. Buoyancy of salt relative to compacted sediment also can drive an instability analogous to the Benard instability wherein overturning convection can emerge when a denser fluid overlies a lighter one [Nicolis, 1995;Biot and Ode, 1965;Biot, 1966]. The complex rheology of the rocks surrounding salt, however, may mask the patternforming process.…”

Rheological stability with couple stresses and its application to geological folding

“…The four unknowns are the two displacements at the top and bottom of region A and the characteristic equation is a 4 x 4 determinant. Particular cases of this model have been analysed previously for an infinitely thick region B (Biot 1961) and for the,case of pure gravity instability (Biot & Ode 1965 ;Biot 1966 b). The latter treatment, included the effect of variable thickness and compaction of the overburden with special reference to the formation of salt structures.…”