Present-Day Geodynamics

By present-day geodynamics we mean that we use the wide variety of geophysical constraints that we have of the present day earth (like plate motions, geodesy, gravity, seismicity and seismic structure) to better understand the forces and processes acting. The advantage of this present-day approach is that we can exploit the high fidelity of geophysical observations within high resolution models. However, the methods are highly complementary to the historical geodynamic models that we also formulate (with different geological data sets) (see the pages that we have for this work). Increasingly, we are able to use constitutive relations (rheology laws) are are the same or imilar to those found in the laboratory. The classic problem we address is that of the forces which drive and resist plate motions. Here we describe several current or recently completed projects that give will give you a feeling for the breadth of the topics and the approaches we take. The first is aimed at better understanding the forces on the plates (i.e. plate driving forces). The second is aimed at at trying to better understand the mechanical properties within the mantle wedge in a subduction zone. A final example uses gravity and other data to understand the long-elusive intra-cratonic basins (in the case, the Congo Basin of Africa).

Plate Motions

The goal of this work is to better understnad the forces that drive and resist plate motion. Another fundamental aspect of this work is that it involved the development and testing of new algorithms for Adaptive Mesh Refinement (AMR) carried our with Omar Ghattas and his group at The University of Texas at Austin. This work is notable as it as it not only allowed us to to acheive the critical resolution of 1 km in global geodynamic models, but demsonstrated the scalablity of AMR on Peta-Scale computers. The work appeared on the front cover of Science Magazine and was twice a Finalist for the Gordon Bell Prize at Supercomputing 2008 and 2010. In addition Laura Alisic, Carsten Burstedde, and Georg Stadler, shared the Computational Science and Engineering (CSE) Prize 2011 from Springer for "their exceptional research on plate tectonics simulation".
Figure 1. Untrahigh-resolution global model showing the mesh in a cross section across the South West Pacific from Australia (AUS) in the East, across New Hebrides (NH), through Tonga (TO) and into the Pacific Plate (PAC). The color coding is viscosity and shows strong slabs, faulted plate margins (in Red), the Plastic failure in the hinge Zone of the bending plate. This figure is from Stadler et al. [2011] by breaking important ground with the highest resolution dynamic model evel (down to nearly 500 meters where needed).
This project involved the construction of the temperature field that allowed us to simulate dynamics down to 1 km where needed. A number of global data sets were merged from the distribution of oceans and continents, the age of the ocean floor, the seismicity of slabs, and deep mantle tomography. We have been able to create what we believe is the most refined global input model to date. In addition, we used data from inter-plate earthquakes to construct the detailed interface between subducting and over-riding plates (see Figure 1). Using this method, we have explored the force balance on plates at an unprecedented resolution, down to 500 meters km at specific plate boundaries. We overcame a major stabling block in that the driving forces deep in the mantle and within slabs can be transmitted up through the slabs and into the downgoing plates. A significant amount of resistance to plate motion comes through the plastic failure of the subducting oceanic plates at trenches.
Unexpectedly, during thr work, we have found ourselves facing a sort of dynamic dilemma. We easily matched the direction, essentially the Euler pole, of some oceanic plates, such as the Indo-Australian, Nazca, and the Cocos plates. We need a sufficiently small yield stress, several tens of MPa, so that the oceanic plate can bend and yield at an oceanic trench. If we make the yield stress smaller that eventually we don’t get plates and the “plateness” is very poor. However, for the same acceptable yield stresses, we have been able to get an acceptable plate direction or plateness for the Pacific plate. Essentially, the Pacific is so large, with subduction zones on two sides, essentially it can fall apart depending of it's strength. This is the first time plate models experienced this problem since such non-linear rheologies have never been used before in models. Indeed it was always easy to get the Pacific motion correct. We are currently searching for a single set of parameters that gives the best fit to all plates, which would be an important result.
Figure 2. Global view of the surface viscosity (raster image) and velocity (vectors) frm a Rhea Run
We had a major breakthrough in this work when we discovered that the regional scale dynamics of backarc basin extension within the Western Pacific (in particular for the Tonga-Kermadec and the New Hebrides) subduction zones were emergent in the global models. This is the first time in any model tailored to the real world was this behavior found which was all the more important because the models were global.

Dynamics of the mantle wedge

As long appreciated by petrologists, there must be a a signficant input of volatiles into the mantle above slabs as the oceanic plates are returned to the mantle. Geodynamic models long failed to incorporate the kind of complex processes that may be occuring in the so called mantle wedge region. Earlier, in our group, former Ph.D. student Magali Billen, now a Professor at the University of California, found that the mantle wedge is likely to be extremelow low in viscosity in order to match the present day topography and gravity anomalies in back-arc basins.
With Paul Asimow (a Professor of Geochemistry here at Caltech), gradiate student Laura Hebert set out to determine what the disctribution of low viscosity is from multi-physics models. She used a petrological model (pHMELTS), coupled with a 2D thermal and variable viscosity flow model, to describe and compare fundamental processes occurring within subduction zones. By studying the thermal state and phase equilibria of the subducting oceanic slab and adjacent mantle wedge, she was able to constrain fluid flux into the mantle wedge. An innovative, but computationally intensive method, that used a Lagrangian particle distribution was emploed to perform thousands of thermodynamically equilibrated calculations;n this way, the chemical state of the domain was continuously updated. Compositionally and thermally dependent buoyancy and viscosity terms provide a consistent linkage between the effect of water addition to and flow within the mantle wedge.
Figure 3. Image from Laura Hebert's thesis showing the development of a how viscosity channel above the slab in multi-physics models of a subduction zone.
She found that the coupling between chemistry and dynamics resulted in behavior previously unresolved, including the development of a continuous, slab-adjacent low viscosity channel (LVC) defined by hydrous mineral stability and higher concentrations of water in nominally anhydrous minerals (NAM). As the LVC evolves to fluid saturation, slab-derived components are able to migrate vertically upwards to the water-saturated solidus, forming a melting region that bounds the top of the LVC. The LVC develops due to fluid ingress into the mantle wedge from the dehydrating slab, and can be responsible for slab decoupling, large-scale changes in the wedge flow field, and a mechanism by which hydrated slab adjacent mantle material can be transported to the deep mantle. Varying model parameters indicates that slab age and slab dip angle exert primary control over LVC shape and thickness, due to changing fluid release patterns within the slab. Younger slabs tend to have thinner, more uniform LVCs, while older slabs tend to have a thinner LVC at shallow depths with a large increase in LVC thickness at ∼100 km depth. Slab convergence velocity appears to have a secondary role in controlling LVC shape.
Laura's discovery of a low viscosity channel in dynamic models was timely because with the 100-seismometer experiment in Mexico, the so-called MesoAmerican Seismic Experiment the Caltech group discovered that the Mexican slab was sliding beneath the over-riding plate for about 300 km with no coupling between the slab and the surface. Post-doc Vlad Manea picked up on Laura's idea and incoporated it into dynamic models of slabs where the dip could re-adjust to the rheology of the the mantle wedge. Vlad discovered that the that slab could slid below the over-riding plate for 100's of kilometers!
Vlad Manea is now a Professor of Geophysics at the National University of Mexico.

Present Day Dynamics of the Congo Basin

Figure 4. Present day topography of Africa.
One of the classical problems in geology is the formation of so-called intracratonic basins, especially the circular ones like the Michigan Basins. Of of the problems is that these basins are not at all easoly related to Plate Tectonics and indeed many of these basins formed hundreds of millions of years ago. A number of theories have been advanced, but these mechanisms are poorly understood because there are few currently active cratonic basins.
One cratonic basin thought to be active is the Congo basin located in equatorial Africa (Figure 4). The Congo basin is coincident with a large negative free-air gravity anomaly(Figure 5), an anomalous topographic depression, and a large positive upper mantle shear wave velocity anomaly. Localized admittance models show that the gravity anomaly cannot be explained by a flexural support of the topographic depression at the Congo. Geophysics graduate student Nathan Downey analyzed these data and showed that they can be explained by the depression of the Congo basin by the action of a downward dynamic force on the lithosphere resulting from a high-density object within the lithosphere. He formulated instantaneous dynamic models describing the action of this force on the lithosphere.
Figure 5. Prediction of the free-air gravity of the Conga Basin and the residual of this prediction wit the observed field (right). From Nathan Downey's thesis which is also described in a detailed JGR paper.
These models show that the gravity and topography of the Congo basin are explained by viscous support of an anomalously dense region located at 100 km depth within the lithosphere. The density anomaly has a magnitude within the range of 27–60 kg m^3 and is most likely compositional in origin. Our models do not provide a constraint on the lithospheric viscosity of the Congo craton because the shallow location of the anomaly ensures strong coupling of the anomaly to the surface regardless of viscosity structure.

Where are we headed?

One of the new directions we are headed into is to recaste some of these problems as inverse approaches, now that we have started to better appreciate now we can reproduce the data in formward models. As you can read in the description we have posted on our time-dependent models, we have already started to move into creating inverse models of the energy equation. But similar approaches can also be applied using our powerful models of the the present day earth.

Recommended Readings

Stadler, G., M. Gurnis, C. Burstedde, L. C. Wilcox, L. Alisic, and O. Ghattas, The dynamics of plate tectonics and mantle flow: From local to global scales, Science, 329, 1033-1038, 2010.
Downey, N. J. and M. Gurnis, Instantaneous dynamics of the cratonic Congo basin, Journal of Geophysical Research, 114, B06401, doi:10.1029/2008JB006066, 29 pp., 2009.
L. B. Hebert, P. Antoshechkina, P. Asimow, and M. Gurnis, Emergence of a low-viscosity channel in subduction zones through the coupling of mantle flow and thermodynamics, Earth and Planetary Science Letters, 278, 243–256, 2009.
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Last Updated November 30, 2015
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