Tectonics of planetary loading: A general model and results

Abstract

The tectonic response of a planet's lithosphere to an imposed load contains information on the mechanical properties of the lithosphere, particularly its thickness, from which more general planetary properties, such as heat flow and rheology, may be inferred. Traditionally, mathematical models of the lithosphere's response to loads were constructed using either a flat plate or thin shell approximation and tectonic patterns were predicted as a function of the lithospheric thickness. Such predictions were then compared with the observed tectonics to determine the thickness of the lithosphere at the time of loading. Many of these models, however, are restricted in the size of features that can be treated by assumptions on load width and/or lithospheric thickness. Additionally, since membrane stresses dominate over bending stresses for broad laods, many of these models consider only the membrane stresses. We here develop a general model for planetary tectonics due to an axisymmetric load that is valid for arbitrary shell thicknesses and load widths. The model predicts two distinct tectonic styles. The first, which results from narrow loads on thick lithospheres, is the style familiar to terrestrial geologists: successive regions of radial thrust, strike‐slip and concentric normal faulting with increasing radial distance from the load. We call this pattern the “plate” response. The second style is the result of wide loads on thin lithospheres: successive regions of disorganized thrust, concentric thrust, and strike‐slip faulting. We call this pattern the “membrane” response. While this second style of faulting may not be as familiar, it agrees with the predictions of membrane theory. The transition between these two styles is not abrupt but occurs over a range of lithospheric thicknesses. It is marked by the development of bands of radial thrust and radial normal faults. On Mars, if the Tharsis Rise is treated strictly as a load, only this transitional regime can produce the observed radial normal faulting for reasonable lithospheric thicknesses. Since it occurs in the transitional regime, it is not predicted by either the traditional flat plate or membrane approximations. We use the model to determine the limits of shell thickness and load width where the use of the end‐member approximations is appropriate. The overall style of tectonic response turns out to be a function of the interplay between shell thickness, load width, and the ratio of buoyancy to flexural support, and cannot be predicted on the basis of any one of these. For example, some authors extend membrane theory to an arbitrarily chosen lithospheric thickness of 10% of the planetary radius. Our results show that such an extension is valid only for very broad loads on small, icy moons. For terrestrial planets, the tectonic response predicted by membrane theory is realized only when the lithospheric thickness is less than 5% of planetary radius, depending on the load width. Tectonic analysis on a planetary scale must take account of these different response styles and the limited range of load widths and lithospheric thicknesses for which they occur.