Neoproterozoic sand wedges: crack formation in frozen soils under diurnal forcing during a snowball Earth Adam C. Maloof a;  , James B. Kellogg a , Alison M. Anders b a Department of Earth and Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, MA 02138, USA b Department of Geological Sciences, University of Washington, Seattle, WA 98195, USA Received 2 May 2002; received in revised form 16 September 2002; accepted 16 September 2002 Abstract Thermal contraction cracking of permafrost produced sand-wedge polygons at sea level on the paleo-equator during late Neoproterozoic glacial episodes. These sand wedges have been used as evidence for high ( v 54‡) paleo- obliquityoftheEarth’secliptic,becausecracksthatformwedgesarehypothesizedtorequiredeepseasonalcoolingso the depth of the stressed layer in the ground reaches v 1 m, similar to the measured depths of cracks that form wedges. To test the counter hypothesis that equatorial cracks opened under a climate characterized by a strong diurnal cycle and low mean annual temperature (snowball Earth conditions), we examine crack formation in frozen ground subject to periodic temperature variations. We derive analytical expressions relating the Newtonian viscosity to the potential crack depth, concluding that cracks will form only in frozen soils with viscosities greater than V10 14 Pa s. We also show numerical calculations of crack growth in frozen soils with stress- and temperature-dependent rheologies and find that fractures may propagate to depths 3^25 times the depth of the thermally stressed layer in equatorial permafrost during a snowball Earth because the mean annual temperature is low enough to keep the ground cold and brittle to relatively great depths. ß 2002 Elsevier Science B.V. All rights reserved. Keywords: ice wedges; snowball Earth; obliquity of the ecliptic; Neoproterozoic; periglacial features; permafrost; paleoclimatol- ogy; Mars 1. Introduction The presence of sand-wedge polygons at the paleo-equator led Williams [1^3] to suggest that a higher obliquity of the Earth’s ecliptic relative to the plane of the solar system ( v 54‡ as com- pared to 23.25þ1.25‡ today) was required in the Neoproterozoic both to drop mean annual tem- perature below 0‡C and to increase seasonality at the paleo-equator. The snowball Earth hypothesis [4^6] wasproposedasanalternativetohighEarth obliquity in an attempt to explain the association ofdistinctivecapcarbonaterocks [7^10] withlow- latitude glacial deposits. We use analytical and numerical models of tensile stress and potential 0012-821X/02/$ ^ see front matter ß 2002 Elsevier Science B.V. All rights reserved. PII:S0012-821X(02)00960-3 * Corresponding author. Tel.: +1-617-495-0367; Fax: +1-617-496-0434. E-mailaddress: maloof@fas.harvard.edu (A.C. Maloof). Earth and Planetary Science Letters 204 (2002) 1^15 www.elsevier.com/locate/epsl