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GLOBAL VARIATIONS IN THE LITHOSPHERIC THICKNESS ON VENUS: IMPLICATIONS FOR THE EVOLUTION OF VOLCANISM C. P. Orth and V. S. Solomatov. (Dept. of Earth and Planetary Sciences, Washington University in Saint Louis, St. Louis, MO, USA) Summary We focus on the long-wavelength Venusian topography and geoid and place constraints on the global average lithospheric thickness by assuming that the stagnant lid overlying the convective mantle is in isostatic equilibrium – the isostatic stagnant lid (ISL) approximation. Application of the ISL approximation to Venus suggests that the global lithospheric thickness is around 300 km and that crustal thickening is required only in a few regions to satisfy gravity and topography data. To model the evolution of volcanic activity we first assume that at some point in Venusian history the planet was substantially molten and large amounts of magmatism were present. The convective heat flux at the base of the lid is assumed to be negligible and the decline in volcanism is caused by the growth of a conductively cooling lid. If no mechanism is present to maintain sufficient thinning of the lithosphere, then at some point the lid will grow either to a depth where the temperature profile no longer intersects the solidus or to a depth below the solid/melt density inversion (around 300 km) and melting will cease. The Isostatic Stagnant Lid Approximation The ISL approximation requires the stagnant lid (including both the lithosphere and the crust embedded in the upper part of the lithosphere) to be in isostatic equilibrium and ignores any contribution of dynamic, elastic, and transient effects on the topography. Therefore, in the ISL approximation, the primary support mechanism for the longwavelength topography is thermal isostasy due to the convective thinning of the lithosphere (Figure 1). However, on Venus, variations in lithospheric thickness alone are insufficient to explain the observed topography and geoid because it would require thinning of the lithosphere beyond that expected for stagnant lid convection. Therefore, limited regions of thickened crust are required to restrict the lithospheric thinning to values consistent with those expected for stagnant lid convection which is consistent with previous works (Kucinskas and Turcotte, 1994; Phillips and Hansen, 1998; Anderson and Smrekar, 2006). The errors associated with the ISL approximation are on the order of 20% depending on various factors such as the assumed mantle rheology. These errors are comparable to and even smaller than other uncertainties in the dynamic models of Venus. To reduce the errors due to the ignored contribution from mantle convection beneath the stagnant lid we improve the ISL approximation by taking into account the contribution from the mantle by using the constraints from 2D convection calculations on the correlation between the stagnant lid thickness and the amplitude of mantle thermal anomalies. In particular the lateral temperature variations associated with convective motions where regions of rising material have slightly higher temperature than the ambient mantle temperature and regions of sinking material have a slightly lower temperature. This second-order effect is described by the following simple formula: δT ( x) = C h( x) δ rh δTrh hrms d Where h(x) is the topography, hrms is the r.m.s. topography, δ rh is the thickness of the rheological sub layer (the most unstable part of the lid), d is the mantle thickness, δTrh = d ln η dT −1 T =Tmantle is the rheological temperature scale which describes the temperature variations below the stagnant lid, η is the mantle viscosity C is a constant of the order of unity (which has to be determined numerically). The constant C can only be determined within a factor of 2 or so because both the uncertainties in the convective parameters (such as Rayleigh number and the viscosity law) as well as temporal fluctuations within the convective layer (the current state of the Venusian mantle is just a snapshot in time). The temperature variations required to fit the geoid are about 1K, when scaled to the Venusian mantle. For a given rheology, this correction substantially reduces the errors and at least theoretically can eliminated the errors completely (in a statistically averaged sense) resulting in an approximation that can be as good as the actual 3D models. The main advantage of the ISL approximation is that it allows inversion of gravity and topography data assuming a convective planet but avoids costly 3D convection calculations. culated from the Bouguer gravity anomaly and added to the geoid anomaly from the lithosphere resulting in the total geoid anomaly. Figure 1: The relative magnitudes of the total topography (top, red curve) and isostatic topography (top, blue curve) indicates that the dynamic topography is negligible in the well developed stagnant lid convection regime of temperature dependent viscosity convection (e.g., Solomatov and Moresi, 1996; Vezolainen et al., 2004; Solomatov, 2008; Orth and Solomatov, 2009; 2010). The topography (top) corresponds to a 2D simulation of stagnant lid convection (bottom) with bottom heating, exponential viscosity law, and viscosity contrast 106. The Model We consider a spherical harmonic representation of the Venusian geoid and topography (Konopliv et al., 1999; Rappaport et al., 1999) truncated to degree and order 20 to correspond to the scale of the expected convective cells (~2,000 to 3,000 km). This truncation limits the ISL approximation to the long-wavelength topography and geoid and does not consider the wavelengths where the elastic effects are important. The crustal thickness, lithospheric thickness, and mantle temperature variations are used to calculate the lateral variations in the radial temperature profile for a number of cooling models. The deviation in the temperature from a reference temperature profile (corresponding to zero topography) leads directly to the calculation of the density anomaly. We calculate the model geoid directly from the density variations using 3D integration over the sphere rather than the HOT (Haxby-OckendonTurcotte) approximation (Kucinskas and Turcotte, 1994; Moore and Schubert, 1995; Turcotte and Schubert, 2002) (the latter predicts a substantially thinner lithosphere). The component of the geoid anomaly associated with the crustal, lithospheric, and mantle density structure is calculated from a spherical harmonic representation of the density anomaly (Hager and Clayton, 1989) while the component associated with the topography is cal- Results A reference model was chosen where the maximum allowed lithospheric thinning is set to 50% of the global average lithospheric thickness (i.e. zct= 0.5zsl, Figure 2), the global average crustal thickness (h, Figure 2) is set to 50 km, and the temperature distribution is chosen to be that of the Plate Cooling Model with constant mantle temperature. With these parameters, we vary the global average lithospheric thickness from 100 km to 500 km and calculate the misfit between the observed and calculated geoid. The minimization of this misfit gives the best fit global average lithospheric thickness. Figure 2: Schematic representation of a region of thinned lithosphere (red) and thickened crust (blue). The dashed lines indicate the global average crustal (h) and lithospheric (zsl) thicknesses while zct indicates the maximum allowed convective thinning of the lithosphere. We consider variations from the reference model to calculate the global average lithospheric thickness for a number of different parameters including variations in the mantle temperature, maximum allowed lithospheric thinning, and global average crustal thickness. As discussed earlier, the inclusion of lateral temperature variations within the mantle reduces the errors associated with the ISL approximation. We correlate the temperature variations with the r.m.s of the topography and vary the amplitude from 0 K in the reference model to 0.5 K, 1 K, 1.5 K, and 2 K. In the absence of fully threedimensional calculations of mantle convection the maximum allowed lithospheric thinning (zct) is varied from the 50% in the reference model to 5%, 10%, 25%, and 75% to quantify the effects of the amount of convective thinning on the global average lithospheric thickness. The maximum crustal thickness is limited by the depth to the basalt- eclogite transition where the crustal material delaminates and sinks into the mantle. Here we consider average crustal thicknesses of 25 km and 75 km and compare them to the reference model (50 km). In general, both higher temperature variations within the mantle and decreased allowed lithospheric thinning result in much thicker global average lithospheric thicknesses while thicker global average crustal thicknesses result in thinner best fit global average lithospheric thicknesses (Table 1). The reference model predicts a global average lithospheric thickness of ~170 km (Figure 3); however, including mantle temperature variations of 1K results in a global average lithospheric thickness nearly 30% thicker. Also, decreasing the total maximum allowed lithospheric thinning by a factor of two increases the best fit global average lithospheric thickness by nearly another 30%. Taking these two adjustments into account the global average lithospheric thickness increases to ~300 km. Table 1: Summary of the results compared to the reference model showing the best fit global average lithospheric thickness and the deviation from the reference model. Negative values are denoted with parentheses and the variation of the degree and order indicates a minimal change in global average lithospheric thickness when higher harmonics are included The results of this study indicate that most of the Venusian topography can be explained by the thermal isostasy associated with variations in the lithospheric thickness and only spatially limited crustal thickness variations are required to explain the observed geoid. Both the surface area of the regions of thickened crust and the maximum crustal thickness decreases with increasing global average lithospheric thickness. For example, with an average lithospheric thickness of 200 km only 12% of the crust is thickened with a maximum thickness of 80 km (slightly less than the expected depth of the basalt-eclogite phase transition) compared to only 3% of thickened crust with a maximum thickness of 65 km for a 400 km average lithospheric thickness. Also, for a given value of lithospheric thinning the minimum global average lithospheric thicknesses before generating melt are 115 km, 120 km, 145 km, 220 km, and 440 km for the cases of 5%, 10%, 25%, 50%, and 75%, respectively. These thicknesses indicate that a number of the best fit cases exhibit both regions of thickened crust and regions of melt generation. Implications for the Evolution of Volcanism The improved estimates for the variations in the lithospheric thickness provide stronger constraints on the evolution of volcanism on Venus. It has been argued that at some point in Venusian history the planet was substantially molten with large amounts of magmatism and that the decline in volcanism is caused by the growth of a conductively cooling lid (Reese et al., 2007). The global average lithospheric thickness determined in this work is consistent with that expected from a cooling time of 0.5 to 1 billion years. However, if the planet is simply allowed to conductively cool, the lithosphere would continue to thicken and at some point it would either grow to a depth where the temperature profile no longer intersects the solidus or to a depth below the melt density inversion and all melting would cease. Furthermore, since the variations in lithospheric thickness are correlated with topography the thinnest lithosphere corresponds to the highest topography so the oldest to youngest regions would occupy correspondingly from the lowest to highest topography. This could explain at least to first order the topography age correlations between the volcanic rises and the surrounding lowland plains, but it cannot explain the observation that the oldest terrains tend to concentrate at higher elevations (Ivanov and Head, 1996). Furthermore, without continued plume activity not only would the variations in the lithospheric thickness become smaller with time and not be able to generate the observed geoid and topography anomalies but the volcanic rises would also tend to subside with time rather than grow as suggested by geological observations and geodynamic models. However, with continued plume activity the lithosphere could conductively thicken while still maintaining the necessary lithospheric thinning to produce regions of melt generation. These regions of magmatism could then continue for an extended period of time following the initial rapid decline in volcanism. Figure 3: Observed topography (A) and geoid (B) calculated up to degree and order 20; lithospheric thickness (C), thickness of crust (D), and calculated geoid anomaly for the reference model (E). The left hemisphere is centered at 90o East and the right hemisphere at 90o West. References: Anderson, F. S., Smrekar, S. E., 2006. 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