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 Δρ 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 [Formula: see text]. 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 provide an understanding of the underlying mechanics, several tables are presented which show the influence of each 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 [Formula: see text] 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 [Formula: see text] poises overlain by sediment of viscosity of [Formula: see text] poises are in excellent agreement with observed facts.