Finite deformation in and around a fluid sphere moving through a viscous medium: implications for diapiric ascent

Abstract

Different types of geodynamically active regions like mountain belts, hot spots, or areas of salt tectonics are characterized by diapirism. One key for the reconstruction of the dynamic history of such structures is the progressive strain, which can sometimes be determined from field observations. Successful interpretation of such observations requires a quantitative model of the finite strain in and around a rising diapir. A constant viscosity fluid sphere of radius R rising through another isoviscous fluid is assumed to approximate the buoyant motion of a diapir. Known analytical solutions for the velocity fields are used to numerically evaluate the finite deformation in and around the sphere. Regions of very high strains are found in a tube with a radius 1 2 R behind the sphere and in a shell of thickness of 0.1 R around the sphere. The following three-dimensional strain regimes can be identified: In the half space above the sphere down to its equator finite strains are oblate. Behind the sphere they progressively change to plane strain. In the diapiric source region they are prolate. Viscous drag at the sphere's surface leads to an internal circulation with one overturn after 10 R of rise, if the sphere has a relatively low viscosity. Finite strains within the fluid sphere show a continuous increase with superimposed cyclic straining and unstraining. After several body radii of rise, the strains become highly inhomogeneous inside the sphere except along the vertical axis and just inside the sphere's surface, where strong prolate and oblate strains are observed, respectively. Finite strain determinations in a falling ball experiment (Cruden, 1988) are compared with the theoretical results. At horizontal distances of a few body radii from the fall axis, the effect of confining container walls is clearly seen in the experimental strain data. The results are compared briefly with available strain data from the field which seem to be significantly lower than predicted. Proposed explanations include a short memory of the rock fabric, and a lack of recognition of the strain concentration which would be expected for a temperature-dependent rheology. It might also be possible that few natural diapirs rise more than a few radii in the solid state.