A model for sedimentary compaction of a viscous medium and its application to inner-core growth

Abstract

S U M M A R YA detailed study of the physics of a 1-D sedimentary compaction of a viscous medium was carried out both numerically and analytically for columnar and self-gravitating spherical cases, in view of applying it to the inner-core growth process of the Earth. The effects of sedimentation rate and surface porosity upon the porosity profile were investigated. It was found that the porosity profile differs depending on whether or not the sedimentation rate is larger than the Darcy velocity (velocity of the solid matrix when the fluid flows by buoyancy alone). When the sedimentation rate is larger than the Darcy velocity, a thick, constant-porosity layer develops at the surface, and below it, the porosity decreases gradually towards the bottom. When the sedimentation rate is smaller than the Darcy velocity, the porosity profile is characterized by a mushy layer at the top, where the fluid is expelled by the deformation of the solid, underlain by a thick layer of constant porosity, termed the residual porosity. Such a porosity profile can be understood as the propagation of a half-sided solitary wave. The study was extended further for the self-gravitating spherical case. Formation of an unstable porosity structure and the appearance of solitary waves were discovered for the case of monotonically decreasing sedimentation rate. Given the size of the sphere formed by sedimentary compaction, according to the magnitude of the ratio of sedimentation rate to Darcy velocity, three types of porosity structure, which differ in force balance and the typical length scale required for porosity decrease, were discovered. One such structure is where a low-porosity layer forms at the top, accompanied by solitary waves beneath it, indicating that a crust-like region can develop at the surface of the inner core.

Decompaction weakening and channeling instability in ductile porous media: Implications for asthenospheric melt segregation

“…In contrast to most earlier studies that neglected the porosity dependence of the bulk viscosity, i.e., by explicitly or implicitly taking m = 0 in equation (12), we consider the case m = 1. This choice is theoretically justified in the small porosity limit [Nye, 1953;Sumita et al, 1996], is consistent with both experimental [Ashby, 1988;Renner et al, 2003] and natural [Connolly and Podladchikov, 2000] compaction profiles, and precludes unrealistic behavior such as negative porosity Podladchikov, 1998, 2000].…”

“…Theory [Nye, 1953;Sumita et al, 1996] and both field [Connolly and Podladchikov, 2000] and experimental [Ashby, 1988;Renner et al, 2003] observations support the contention that z / 1/f, yielding a logarithmic relationship between amplitude and speed (equation (26)). Given the asthenospheric compaction timescale (t*(y) $ 6 ffiffiffi m p /f 0 , Table 1), melt extraction at porosities <10…”

“…The simplest model for pure mode I deformation that satisfies the physical requirement that the viscosity must be infinite in the limit f ! 0 is z $ m s /f, where h s is the solid shear viscosity [Nye, 1953;Sumita et al, 1996]. In contrast, mode III decompaction is limited by the rate at which fluid is able to fill newly created porosity (i.e., viscous).…”

Short wavelength topography on the inner-core boundary

“…An alternative explanation, which we cannot completely rule out, involves time-varying topography, which could be due to dynamic processes related to inner-core growth (24). In this scenario, the viscosity at the top of the inner core would need to be Ͻ10 16 Pa (4) to allow time variability on the time scale of a decade.…”

Blob instability in rotating compositional convection

“…Experiments with metal alloys (Jack- The form of compositional convection that takes place in the ICB transition region depends partially on processes that are not modeled in these and other laboratory experiments. The process of compaction has been applied to inner core growth by Sumita et al (1996). Deformation of the solid mush occurs due to stresses that arise from the density difference between solid and liquid in the mush.…”