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

A 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.