One key to understanding the history of resurfacing on Venus is better constraints on the emplacement timescales for the range of volcanic features visible on the surface. A figure shows a Magellan radar image and topography for a putative lava dome on Venus. 175 such domes have been identified with diameters ranging from 19 - 94 km, and estimated thicknesses as great as 4 km. These domes are thought to be volcanic in origin and to have formed by the flow of viscous fluid (i.e., lava) on the surface

Baloga, Steve M.

Glaze, Lori S.

Stofan, Ellen R.

NASA Technical Reports Server

EMPLACEMENT SCENARIOS FOR VOLCANIC DOMES ON VENUS.  L. S. Glaze1, S. M. Baloga2, E. R. Stofan2,  
1NASA Goddard Space Flight Center (Code 698, Greenbelt, MD 20771), Lori.S.Glaze@nasa.com) 2Proxemy Re-
search (20528 Farcroft Lane, Laytonsville, MD 20882 steve@proxemy.com, ellen@proxemy.com) 
 
Introduction: One key to understanding the histo-
ry of resurfacing on Venus is better constraints on the 
emplacement timescales for the range of volcanic fea-
tures visible on the surface. Figure 1 shows a Magellan 
radar image and topography for a putative lava dome 
on Venus.  175 such domes have been identified with 
diameters ranging from 19 – 94 km, and estimated 
thicknesses as great as 4 km [1-2]. These domes are 
thought to be volcanic in origin [3] and to have formed 
by the flow of viscous fluid (i.e., lava) on the surface.  
 
 
Figure 1.  (a) Magellan image of a typical steep-sided dome 
in the Rusalka Planitia at 3°S, 151°E. (b) Topographic data 
for the dome shown in (a) with ~20x vertical exaggeration. 
The four transects depict topography from a digital elevation 
model generated from stereo Magellan images [4]. 
 
 Fundamental issues surrounding the Venus steep-
sided domes are the nature of their emplacement (e.g., 
duration), their composition, and the rheology of the 
lavas. A significant conundrum still persists: higher 
viscosity lavas are implied by the need to sustain the 
extremely thick flows (1 – 4 km) (e.g., [3]). However 
lower viscosity lavas are needed to provide the rela-
tively “smooth” upper surface (e.g., [2]). There are 
also numerous quantitative issues that have implica-
tions for sub-surface magma ascent and local surface 
stress conditions. These include the nature and dura-
tion of lava supply, how long the conduit remained 
open and capable of supplying lava, the volumetric 
flow rate, and the role of rigid crust in influencing 
flow and final morphology.  
Here we investigate a variety of scenarios for the 
emplacement of volcanic domes.  Each scenario ex-
plores the effect of different boundary conditions on 
the solution of the Boussinesq equation for pressure-
driven fluid flow in a cylindrical geometry: 
31 0
3
h g hrh
t r r r
           (1) 
One scenario assumes a constant volume of materi-
al, as has been proposed by previous investigators [5-
8]. In this case, the dome thickness boundary condition 
at the source decays with time. We have found an ex-
act analytical solution of (1) for this boundary condi-
tion based on an extended similarity analysis. Our so-
lution removes the nonphysical singularities present in 
previous studies of volcanic domes on Earth and Ve-
nus [6-8].  A second scenario, just submitted for publi-
cation [9], allows a constant volume flow rate at the 
source of the dome. The approach used by [9] to solve 
(1) employs a combination of similarity analysis and 
singular perturbation theory. A final scenario revisits 
the concept of a viscosity that changes only with time, 
rather than with distance from the source, as suggested 
by [8]. 
Fixed Volume Scenario: One approach to model-
ing the viscous expansion of a dome is the assumption 
that most of the volume is emplaced rapidly, supply 
terminates, and the dome is formed by  subsequent 
radial relaxation [5-8].  Results in [5-8] have used a 
similarity solution with a singularity at the origin, 
which also results in an infinite flow depth at the 
origin. Because (1) is based on lubrication theory 
(small Reynolds’s number and h/r), the validity of 
such a solution is dubious. 
We have found an alternative to the approach by 
[5] (upon which [6-8] are based) to solving (1) that 
removes the singularity in the similarity solution by 
taking advantage of the translational invariance of (1) 
with respect to time (e.g., [13-14]).  We have thus ob-
tained the solution for flow thickness, 
   
1/3
2
1/ 4 1/ 4 2
1( , ) 1
1 / 1 /
o
o
h rh r t
rt t 
      
 (2) 
where the time constant, , is given by 
4 323
4 4
or
g V
           
         (3)  
The thickness profile in (2) is finite for all values of r 
and t. However, because this boundary condition as-
sumes all the material is already present on the surface, 
finding physically plausible values for both ro and ho 
(radius and thickness of dome when relaxation “be-
gins”) is a challenge (Figure 2). Even with an ro of 5 
km, half the final radius, the height at the dome center 
would have to be 4 km which strains plausibility. With 
relaxation starting when ro is 2 km,  the height of the  
https://ntrs.nasa.gov/search.jsp?R=20120003875 2019-08-30T19:46:48+00:00Z
Figure 2.  Initial ho as a function of ro  for a dome that relax-
es to a final radius of 10 km and thickness of 1 km. 
 
dome for this mode of emplacement would have to be 
25 km which is clearly implausible. So, at best, this 
emplacement scenario might only apply to the very last 
stage of emplacement.  Once this mode is reached, the 
flow front, rf, advances at a rate that is unexpected for 
a diffusion-like process described by equation (1): 
 1/8( ) 1 /f or t r t       (4) 
     From the definition of  in (3), dynamic bulk vis-
cosities on the order of 1016 - 1017 Pa-s cannot be rig-
orously precluded, and suggest that this approach will 
over predict the viscosity and under predict the em-
placement time.  Note that the duration of lava supply 
cannot be estimated by this method because the pre-
relaxation phase is ignored. Application of this ap-
proach (with the corrected math) to the dimension of 
Venus domes (e.g., Figure 1) suggests viscosities 
comparable to rhyolites. Even with the removal of the 
singularity, it is difficult to favor any inferences based 
on the decaying thickness boundary condition. It re-
mains to be determined whether some combination of 
space and time viscosity changes can result in a viable 
emplacement scenario for this boundary condition. 
Constant Flow Rate Scenario. The alternative is 
to assume the dome is fed continuously for the majori-
ty of the emplacement time. Unfortunately no analytic 
similarity solution has yet been found for this bounda-
ry condition and the numerical integration of the re-
sulting ordinary differential equation is questionable. 
The similarity variable η=r2/t is an obvious choice, 
producing the radial expansion of a dome proportional 
to t½, as expected from the structure of (1).  
 However, as reported in [9], a combination of sin-
gular perturbation theory and similarity analysis pro-
vides a uniformly valid and accurate solution of (1) for 
a cylindrically symmetric flow that is fed continuously 
at a constant rate. The approach is based on a suite of 
analytic and numerical studies [10-12] not commonly 
referenced in the volcanologic literature. The volumet-
ric flowrate used in [9] depends on an arbitrary power 
of the flow depth, making it possible to distinguish 
between Newtonian and other rheologies describing 
terrestrial and planetary mass flows. The flow depth 
profiles (Figure 3) are shown to thicken as the front 
advances. Emplacement times are intimately correlated 
with the bulk rheology.  Detailed fitting of the theoret-
ical profiles to the shape of a typical dome on Venus 
indicates a bulk dynamic viscosity of 1012 - 1013 Pa-s 
and emplacement times of approximately 2 - 16 years, 
both consistent with basaltic andesite composition and 
both significantly less than prior estimates.  
Figure 3.  Axially symmetric Newtonian fluid flow profiles 
at four times and altimetry from Figure 1b. 
 
Conclusions:  The only emplacement scenario that 
appears credible at the present state of understanding 
of the steep-sided domes on Venus is one that involves 
the constant supply of lava for a period of years to a 
decade or so. The dimensions of these domes also sug-
gests a composition that is more consistent with basal-
tic andesite, rather than more silicic compositions as 
has been previously suggested. No modeling to date 
has shown that significant periods of waxing or wan-
ing in the flow rate are reflected by the topography, 
dimensions, and morphology of the Venus domes. 
These results have significant implications for subsur-
face conditions and processes that can sustain such 
conditions.  
References: [1] Pavri, B., et al. (1992) JGR, 97, 
13,445 - 13,478. [2] Stofan, E.R., et al. (2000), JGR, 
105 (E11), 26,757-26,771. [3] Head, J.W., et al. 
(1991) Science, 252 (5003), 276-288. [4] Gleason, 
A.L. (2008), Masters Thesis, UAF. [5] Huppert, H.E. 
(1982) JFM, 121, 43 - 58. [6] Huppert, H.E., et al. 
(1982) JVGR, 14, 199 - 222. [7] McKenzie, D., et al. 
(1992) JGR, 97 (E10), 15,967 - 15,976. [8] Sakimoto, 
S.E.H., and M.T. Zuber (1995) JFM, 301, 65 - 77. [9] 
Glaze, L.S. et al. (2012) JGR, submitted. [10] Babu, 
D.K., and M.T. van Genuchten (1979) Q App Math, 
April. [11] Babu, D.K., and M.T. Van Genuchten 
(1979), Water Resource Res, 15 (4), 867 - 872.  [12] 
Babu, D.K., and M.T. van Genuchten (1980) J Hyd, 
48, 269 - 280. [13] Ames, W.F. (1965) Nonlinear Par-
tial Differential Equations in Engineering, 511 pp., 
Academic Press. [14] Bluman, G.W., and J.D. Cole 
(1969) J Math Mech, 18 (11), 1025 - 1042. 


Emplacement Scenarios for Volcanic Domes on Venus

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