Download GLOBAL VARIATIONS IN THE LITHOSPHERIC THICKNESS ON

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. Global Mapping
of Crustal and Lithospheric Thickness on Venus. J.
Geophys. Res. Planets 111 (E8).
Hager, B. H., Clayton, R. W., 1989. Constraints on the
Structure of Mantle Convection using Seismic Observations, Flow Models, and the Geoid. In: Peltier, W. R.
(Ed.), Mantle Convection: Plate Tectonics and Global
Dynamics. Vol. 4. Gordon and Breach Science Publishers, pp. 675–763.
Ivanov, M. A. and Head, J. W., 1996. Tessera Terrain on
Venus: A Survey of the Global Distribution, Characteristics, and Relation to Surrounding Units from Magellan
Data. J. Geophys. Res. Planets 101 (E6), 14861–
14908.
Konopliv, A. S., Banerdt, W. B., Sjogren, W. L., 1999.
Venus Gravity: 180th Degree and Order Model. Icarus
139 (1), 3–18.
Kucinskas, A. B., Turcotte, D. L., 1994. Isostatic Compensation of Equatorial Highlands on Venus. Icarus 112
(1), 104–116.
Moore, W. B., Schubert, G., 1995. Lithospheric Thickness and Mantle Lithosphere Density Contrast Beneath
Beta Regio, Venus. Geophys. Res. Lett. 22 (4), 429–
432.
Orth, C. P., Solomatov, V. S., 2009. The Effects of Dynamic Support and Thermal Isostasy on the Topography and Geoid of Venus. In: Lunar and Planetary
Science XL. Lunar and Planetary Institute, Houston, p.
Abstract #1811.
Orth, C. P., Solomatov, V. S., 2010. The Effects of Dynamic Support and Thermal Isostasy on the Topography and Geoid of Venus. In: Lunar and Planetary
Science XLI. Lunar and Planetary Institute, Houston, p.
Abstract #2056.
Phillips, R. J., Hansen, V. L., 1998. Geological evolution
of Venus: Rises, plains, plumes, and plateaus. Science
279 (5356), 1492–1497.
Rappaport, N. J., Konopliv, A. S., Kucinskas, A. B., Ford,
P. G., 1999. An Improved 360 Degree and Order Model
of Venus Topography. Icarus 139 (1), 19–31.
Reese, C. C., Solomatov, V. S., Orth, C. P., 2007. Mechanisms for Cessation of Magmatic Resurfacing on
Venus. J. Geophys. Res. Planets 112 (E4).
Smrekar, S. E., Phillips, R. J., 1991. Venusian Highlands: Geoid To Topography Ratios and Their Implications. Earth Planet Sci. Lett. 107 (3-4), 582–597.
Solomatov, V. S., 2008. How Large is the Dynamic Topography on Venus? In: European Planetary Science
Congress Abstracts. Vol. 3. European Planetary
Science Congress, pp. Abstract #EPSC2008–A–2003.
Solomatov, V. S., Moresi, L. N., 1996. Stagnant Lid
Convection on Venus. J. Geophys. Res. Planets 101
(E2), 4737–4753.
Turcotte, D. L., Schubert, G., 2002. Geodynamics, 2nd
Edition. Cambridge University Press.
Vezolainen, A. V., Solomatov, V. S., Basilevsky, A. T.,
Head, J. W., 2004. Uplift of Beta Regio: ThreeDimensional Models. J. Geophys. Res. Planets 109
(E8).