Interaction of Membrane Stresses and Magma Ascent at Large Impact Basins on Mars and Mercury

Introduction: Impact basins are among the most striking structures on planetary surfaces. Impacts excavate substantial amounts of crustal material, resulting in lateral and upward displacement of both crustal and mantle material. This movement, along with magma emplacement, can result in loading of the surrounding lithosphere, with implications for the stress state. Stresses, in turn, influence subsequent magmatic em-placement modes. Here, we use a simple mathematical model of the broad-scale loading effects induced by basins to investigate how such loading may control magmatism within and around the basins. Method: By the term " basin " , we mean an impact structure of substantial diameter relative to the circumference of the planet (see Table 1). Such loads are supported dominantly by a " membrane " , or stretching, response of the lithosphere [e.g., 1], with stresses that are constant with depth. This stress state can be interpreted via the criterion of Anderson [2]: magma tends to move in intrusions that form perpendicular to the least compressive principal stress. Thus, models with at least one horizontal normal stress in extension favor magma ascent in dikes, whereas models with both horizontal normal stresses compressive will inhibit ascent. Note that flexural (plate bending) stresses are important for narrower loads; they vary with depth, requiring an additional magma ascent criterion [3-4]. We use an elastic spherical shell solution in the membrane stress limit with a Gaussian load [1] to illustrate the effects of broad-scale basin loading states on lithospheric stresses. We assume that the baseline post-impact-adjustment compensation state is Airy isostasy, neglecting stresses from crustal thickness gradients [5-7]. We then explore departures from isostasy, expressed as upward or downward loads. Loads that could cause a net downward deflection of the litho-sphere include an initial super-isostatic state [e.g., 8], dense intrusions, or surface loads [e.g., 9], whereas uplift-inducing loads include an sub-isostatic initial adjustment, upward mantle flow in response to melt or thermal perturbations [10], or lateral crustal flow [6-7]. Results: Downward load: The radial stress is com-pressional everywhere (Fig. 1a). The circumferential stress passes from central compression to distal extension at r trans ≈ 0.55 r 0 , with a peak at r peak ≈ 0.9 r 0. The intrusion ascent criterion predicts a shutoff at the center of the basin (effect is strongest at center, decreasing with increasing r). Beyond r trans , ascent is possible in conduits perpendicular to extensional hoop stress: radial dikes, …