Sinker tectonics: An approach to the surface of Miranda
Authors: Janes D. M. , Melosh H. J. 
Published: February 2008

Images of the Uranian moon Miranda show three areas of complex terrain, trapezoidal to ovoid in shape, with no previously known counterpart. These features, called coronae, are characterized by an inner core of intersecting ridges and troughs surrounded by a series of subparallel and concentric bands. Two of the proposed explanations for these tectonic features involve mantle convection driven by density anomalies. The present study determines the surface stresses induced by such density anomalies and their expected surface expression. Miranda is modeled as having a rigid core surrounded by a mantle capable of viscous flow which is overlain by a thin, elastic lithosphere. The density anomaly is modeled as a point mass representing the sinker or riser. The model is developed in a spherical coordinate system having axial symmetry about a θ=0 axis passing through the sinker. The flow field set up by the sinking (or rising) mass is expressed in terms of a stream function using Legendre sums. Streamlines are functions of the position of the mass anomaly and the radii of the core/mantle and mantle/lithosphere boundaries only. Magnitudes of the stream function depend upon the size of the mass anomaly, its local gravitational field, and the mantle/lithosphere radius. The stresses on the base of the lithosphere are then determined from the equations of motion. The viscosity of the mantle material has no effect on the stresses produced at any given time but does control the velocity of the anomaly. Expressions for displacements and stresses in the elastic shell are developed as Legendre sums and coupled to the viscous mantle solution with appropriate boundary conditions. The stresses derived yield a pattern of expected tectonic expression. This tectonic style varies with the radius of the body. For a small body, surface stresses are dominant in the area above the mass anomaly, while farther away stresses at the base of the lithosphere control the tectonics. Directly over a sinker and extending outward ∼15° is a zone of both latitudinal (θ) and longitudinal (Φ) surface compression which produces folding and thrust faults with no preferred orientation. Beyond 15°, longitudinal stresses at the base of the lithosphere are extensional, while latitudinal stresses are compressional, producing a zone of folding and thrusts concentric about the sinker. Stresses induced by a riser are opposite in sign and predict extensional features with the same orientation as the compressional features predicted for a sinker. Stress magnitudes generally decrease with distance from the sinker and also decrease with both increasing sinker depth and lithosphere thickness. The predictions of the sinker model are in good agreement with the tectonic styles of the banded and ridged terrains of Miranda as determined from the topography as imaged by Voyager 2. This agreement supports the idea that the coronae on Miranda were produced by dense masses, originally located near the surface, that sank into Miranda's interior. For larger bodies, the stresses at the surface and base are nearly equal. Longitudinal stresses are greater than latitudinal stresses resulting in compressional features with a preferred orientation radial to the sinker location. The changeover in tectonic styles occurs at a planetary radius of approximately 1500 km.