Can plate tectonics happen quickly? Clues from mineral physics and Venus
I will admit that I am not an expert in this field- however, I have read two recent books on Geology and one on Paleogeology1. It doesn’t make me an expert, but it can at least help me explain some of the difficult terminologies and concepts that will follow in this article. I am happy to discuss anything in further detail with anyone – as long as I can use my reference books.
As far back as the early 1960s, it was known that for materials whose effective viscosity is described by an Arrhenius-like relationship2 the phenomenon of thermal runaway can potentially occur. The Arrhenius equation is a formula for the temperature dependence of reaction rates. It can be used to model the temperature variation of diffusion coefficients, creep rates, and many other thermally-induced processes/reactions. It also expresses the relationship between rate and energy.
The viscosity of such materials varies as e(E*/RT), where T is absolute temperature, E* is the activation energy, and R is the gas constant. A large variety of materials including silicate minerals behave in this manner. A graphic representation of the equation would be like this:
In particular, Gruntfest in 1963 showed that, with this type of temperature dependence of viscosity, both the deformation rate and the temperature of a viscous fluid layer subject to constant shear stress increase without limit, that is, it becomes out of control.3 What does this mean? It shows that what is required is that the time constant associated with viscous heating of rock material is much smaller than the characteristic thermal diffusion4 of the layer. Confusing? Read on.
Several investigators explored the possibility of thermal runaway of lithospheric slabs in the mantle in the late 1960s and early 1970s. Anderson and Perkins, for example, suggested that the widespread Cenozoic volcanism in the southwestern US might be a consequence of thermal runaway of chunks of lithosphere in the low viscosity upper mantle with resulting surges of melt expressed in episodes of volcanism at the surface. 5 Such lithospheric slabs, because of an average temperature some 1,000 K (1,340 F) or more lower than that of the upper mantle but with a similar chemical composition, are several percent denser than the surrounding rock and therefore have a natural ability to sink.
The gravitational body forces acting on a slab lead to high stresses, especially within the mechanical boundary layer surrounding the slab. As a slab sinks, most of its gravitational potential energy is released in the form of heat in these regions of high stress. If conditions are right, the weakening arising from heating can lead to an increased sinking rate, an increased heating rate, and greater weakening. This positive feedback can result in runaway.6
Experimental studies of the deformational behavior of silicate minerals over the last several decades (by a variety of secular and Biblical scientists) have revealed the strength of such materials also depends strongly on the state of stress. At shear stresses of the order of 10-3 times the low-temperature elastic shear modulus and temperatures of the order of 80% of the melting temperature, silicate minerals deform by a mechanism known as dislocation creep in which slip occurs along preferred planes in the crystalline lattice.7
(The above diagram kind of shows how the crystal shape can deform without losing its actual structure. Now how scientists can actually calculate this and determine it for a fact is a mystery to me, and I read all the articles and am trying to provide a summary for you folks. If you can’t make ‘hide nor hair’ of it then please read the articles referenced by 6 and 7 above and tell me how you can explain it better. All of the reference articles can be loaned to your local library or community college library. Thank you. LEM).
In this type of solid deformation, the deformation rate depends on the shear stress in a strongly nonlinear manner, proportional to the shear stress to approximately the third power. At somewhat higher levels of shear stress, these materials display a plastic yield behavior, where their strength decreases in an even more nonlinear way, in this case inversely with the deformation rate. When these stress-weakening mechanisms are combined with the temperature weakening discussed above, the potential for slab runaway from gravitational body forces is enhanced dramatically. A point many people fail to grasp is that these weakening mechanisms can reduce the silicate strength by ten or more orders of magnitude without the material ever reaching its melting temperature.7
(Basically what he is saying that with a large crystal silicate structure that is under a great deal of stress it can become a runaway structure without reaching it’s melting point).
The NASA Magellan mission to Venus in the early 1990s revealed that Earth’s sister planet had been globally resurfaced in the not so distant past via a catastrophic mechanism internal to the Venus mantle.8 Magellan’s high-resolution radar images showed evidence of extreme tectonic deformation that generated the northern highlands known as Ishtar Terra with mountains having slopes as high as 45°.9
(The outline of the United States is superimposed on the radiographic image of Ishtar Terra to give an indication of its size. It’s slopes are at a 45 degree angle. By comparison on the U.S. Interstate highway system the steepest grade allowed is 7 %
Some roads that I know of, the Wickenburg to Prescott highway, Salt River Canyon road, and the Guadalupe pass in Southwest New Mexico are up to 15% and have ‘runaway truck exits at most corners going down hill.)
More than half of the Venus surface had been flooded with basaltic lava to produce largely featureless plains except for linear fractures caused by cooling and contraction. Runaway sinking of the cold upper thermal boundary layer of the planet seems the most plausible mechanism to explain such catastrophism at the surface.10 Given such clear and tangible evidence for runaway in a planet so similar in size and composition as Venus, it is not unreasonable to consider lithospheric runaway as the mechanism behind the global scale catastrophism so apparent in the Earth’s Phanerozoic (of, relating to, or denoting the eon covering the whole of time since the beginning of the Cambrian period, and comprising the Paleozoic, Mesozoic, and Cenozoic eras) sedimentary record.
Numerical methods now exist for modeling and investigating this runaway mechanism. Considerable challenge is involved, however, because of the extreme gradients in material strength that arise. 11,12 W.-S. Yang focused much of his Ph.D. thesis research effort at the University of Illinois on finding a robust approach for dealing with such strong gradients in the framework of the finite element method and an iterative multi-grid solver. He showed that what is known as a matrix dependent transfer multi-grid approach allows one to treat such problems with a high degree of success. Although his thesis dealt with applying this method to 3-D spherical shell geometry, he subsequently developed a simplified 2-D Cartesian version capable of much higher spatial resolution within current computer hardware constraints. 13
Figure 1. (Three snapshots from a 2-D mantle runaway calculation in a box 11,500 km wide by 2,890 km high at problem times of 5, 12.5, and 20 days. Arrows denote flow velocity and are scaled to the peak velocity ‘umax’. Contours denote temperatures in the upper panel and base 10 logarithm of viscosity in the lower panel of each frame. Numbers on the contours correspond to a scale from 0 to 10 for the range of values indicated beneath each plot. A viscosity of 1013 Pa-s, corresponding to the minimum value in the viscosity plots, represents a reduction in the viscosity by a factor of one billion relative to the strength of the rock material when the velocities are negligible. Much of the domain exhibits viscosity values near this minimum during the runaway episode. Deformation rate-dependent weakening, observed experimentally in silicate minerals, is the crucial physics underlying the runaway process.)
Note that runaway diapirs ( a domed rock formation in which a core of rock has moved upward to pierce the overlying strata) emerge from both top and bottom boundaries. The upwelling from the lower boundary releases gravitational potential energy stored in the hot buoyant material at the base of the mantle. Such upwelling’s from the bottom boundary have dramatic implications for transient changes in sea level during the Flood since they cause a temporary rise in the height of the ocean bottom by several kilometers.
Baumgardner showed that a 3-D spherical shell model of the Earth’s mantle initialized with surface lithospheric plates corresponding to an approximate Pangean configuration of the continents and bands of cold rock along the Pangean boundary yields a pattern of plate motions that resemble in a remarkable way the inferred Mesozoic-to-present plate motions for the Earth.14 This solution was obtained simply by solving the conservation equations for mass, momentum, and energy in this spherical shell domain starting from relatively simple but plausible initial conditions. Such a calculation confirms that a subduction driven mantle flow, with very few other assumptions, generates the style of plate motions recorded in the rocks of today’s ocean floor.
Although this calculation simply adopted the reduced viscosity observed in high resolution 2-D calculations during runaway, with continued improvements in computer technology it should soon be feasible to achieve the required resolution in the 3-D spherical model to capture the runaway behavior in a fully self-consistent fashion. The advantage of a 3-D spherical model, of course, is that its output can be compared directly with geological observation. Realization of this crucial objective is an extremely high priority for those who desire a credible defense of the Flood to a skeptical world. (Unfortunately, the computer industry is concentrating on tablets and play laptops instead of advancing high-end heavy duty computers.)
1 The Story of Earth: The First 4.5 Billion Years, from Stardust to Living Planet by Robert M. Hazen;
Geology by James Geikie and ; The Holocene: An Environmental History 2nd Edition by Neil Roberts.
2 Levine, I.N., Physical Chemistry, 4th Edition, McGraw-Hill, New York, pp. 517–521, 1995.
3 Gruntfest, I.J., Thermal feedback in liquid flow; plane shear at constant stress, Trans. Soc. Rheology 8:195–207, 1963. Currently working at Microsoft.com as an Research Scientist in Analytic Chemistry.
4 A phenomenon in which a temperature gradient in a mixture of fluids gives rise to a flow of one constituent relative to the mixture as a whole. (In other words, the solid rocks move at different speeds than the molten ones and molten granite flows at a rate different than molten basalt.
5 Anderson, O.L. and Perkins, P.C., Runaway temperatures in the asthenosphere resulting from viscous heating, J. Geophys. Res. 79:2136–2138, 1974.
6 Baumgardner, J.R., Numerical simulation of the large-scale tectonic changes accompanying the Flood; in: Walsh, R.E., Brooks, C.E. and Crowell, R.S. (Eds), Proceedings of the International Conference on Creationism, Vol. II, Creation Science Fellowship, Pittsburgh, pp. 17–28, 1987.
7 Kirby, S.H., Rheology of the lithosphere, Rev. Geophys. Space Phys. 25:1219–1244, 1983.
8 Strom, R.G., Schaber, G.G. and Dawson, D.D., The global resurfacing of Venus, J. Geophys. Res. 99:10899–10926, 1994.
9 Ford, P.G. and Pettengill, G.H., Venus topography and kilometer scale slopes, J. Geophys. Res. 97:13103–13114, 1992.
10 IBID Strom, R.G.
11 Baumgardner, J.R., 3-D finite element simulation of the global tectonic changes accompanying Noah’s Flood; in: Walsh, R.E. and Brooks, C.E. (Eds), Proceedings of the Second International Conference on Creationism, Vol. II, Creation Science Fellowship, Pittsburgh, pp. 35–45, 1991.
12 Baumgardner, J.R., Runaway subduction as the driving mechanism for the Genesis Flood; in: Walsh, R.E. (Ed.), Proceedings of the Third International Conference on Creationism, Technical Symposium Sessions, Creation Science Fellowship, Pittsburgh, pp. 63–75, 1994.
13 Yang, W.-S. and Baumgardner, J.R., Matrix-dependent transfer multigrid method for strongly variable viscosity infinite Prandtl number thermal convection, Geophys. and Astrophys. Fluid Dyn. 92:151–195, 2000.
14 Baumgardner, J.R., Computer modeling of the large-scale tectonics associated with the Genesis Flood; in: Walsh, R.E. (Ed.), Proceedings of the Third International Conference on Creationism, Technical Symposium Sessions, Creation Science Fellowship, Pittsburgh, pp. 49–62, 1994.