(1890 - 1965)
Imagine the Earth's interior in constant deformation and computerized algorithms to track the currents. Well, you may say, I have heard about simulating the circulation of the atmosphere and oceans, but simulating circulation in the Earth's? Actually, attempts to understand the deformation of the deep Earth (mostly the solid mantle and the liquid outer core) have a long tradition. As far back as 1944 the great british geologist Arthur Holmes saw convection of the solid mantle as the machinery to accomplish continental drift, thus rendering Alfred Wegner's now famous proposition of moving continents a viable hypothesis. Holmes proposed that the lighter continents would blanket vast regions of the underlying mantle. Suitably insulated, these blanketed areas would warm up over the age of the Earth. The warm and lighter rocks in turn rise to the surface, pushing the overlying continents apart. Thus continental drift could be 'engineered' by the quantitative and well understood mechanism of thermal convection.
Since then more than 50 years have passed and geophysical fluid dynamics, the field concerned with understanding fluid motion on the planet, has moved ahead. One of the greatest wind-falls in recent years has come from rapid progress in computing. Geophysicists have long turned to numerical approximations for their equations. The move is necessary, because the Navier-Stokes equations, which govern fluid motion, are difficult to solve by analytic methods for all but the simplest cases. Detailed 3D spherical simulation models today can resolve the entire mantle at a scale of 20 km, sufficient to approach the dynamic regime of mantle convection.
Of course, mantle dynamics has turned out to be by far more interesting than envisioned early on by Holmes. An important question, discovered along the way, is why there are so few subduction zones. In fact, the only two major subduction systems active today are situated along the edges of the pacific ocean, and they have been there for at least the past 150 million years as far as we can tell. Technically speaking the question translates into why the mantle prefers lengthscales of order 10,000 km, although it is in a state of vigorous convection. We now understand that it is the relatively high mechanical strength of the lower mantle below a depth of about 660 km (relative to the softer upper mantle), which makes mantle convection forget about the shorter lengthscales. The same effect is responsible to shape subduction zones into their peculiar form along large, linear belts. The answers have arisen largely through careful examination of numerical convection simulations.
tomographic image under North
America (S. Grand, R. v. Hilst)
What makes the field of computational geodynamics so exciting today is the dramatic wealth of new observational data for the deep Earth, delivered largely by seismic tomographers. The new data allows us to test competing geodynamic hypotheses through carefully posed numerical simulations. The field of seismic tomography (named in analogy to medical imaging) is changing our views on the relationship between global plate tectonic motions and the upwellings and downwellings of mantle convection that drive them. Tomographers are using many types of seismic vibrations to probe the Earth. When a seismic "ray" passes through a fast or slow velocity region it correspondingly speeds up or slows down, perturbing the arrival time of the ray. If the earthquakes are well-located, thousands of such measured arrival times may be mathematically "inverted" to obtain images of heterogeneous velocity structure of the mantle. These images show that mantle flow is organized into concentrated structures, with high-velocity anomalies corresponding to regions of the Earth where cold lithospheric plates have sunk into the mantle at convergent plate margins, or subduction zones.
Taken at face value, the seismic images imply a straightforward relation between the history of subduction and large scale mantle heterogeneity. The relation can be tested in mantle convection simulations. From the view point of geophysics this is essential, because such tests allow us to evaluate quantitatively a number of competing mantle dynamics hypotheses. For example, the transition zone between the upper and the lower mantle (located at a depth between 400 km and 700 km) is subject to suite a of complicated mineral phase reactions. The reactions accommodate the higher pressure at depth by packing atoms more closely together. It has been speculated for many years that the density effects of such phase reactions would help to seal the upper from the lower mantle. That this is not case can now be demonstrated in detailed mantle convection simulations.
Geodynamic Earth Model
with Farallon Slab
A fascinating new subject made possible by computer simulations is the field of paleogeography. Individual chunks of subducted ocean floor are now located sufficiently precise to prompt geodynamic speculations on the position of extinct paleo plate boundaries. The goal is to exploit the "memory" of the mantle to learn more about ancient plate tectonic regimes. Such ancient regimes would remain largely unknown, if we had to rely only on measurements made at the surface. The Munich Geodynamics group is actively involved in this exciting research. For example, in a recent publication in the journal Nature we show the old Farallon plate is found about 1500 km to the east of where simple subduction history models might place it (see Figure 2). This is important information, because the misfit is probably directly related to the late mesozoic/cenozoic (past 80 million years) uplift history of the Rocky Mountains from Mexico the Canadian border. These examples show how seismic and geodynamic mantle models allow geologists and geophysicists to begin refining models for both past plate motions and mantle convection to arrive at a more complete picture of Cenozoic and Mesozoic Earth history.
Beowulf PC-Cluster (Geowulf)
The Munich Geodynamics group is building a unique computer lab to run their simulations directly in the Geophysics Section of the Department of Earth and Environmental Sciences. The design is incorporating ideas we developed at the Los Alamos National Laboratory and Princeton University. Traditionally computational scientists rely on large mainframes to run their simulations. These mainframes are expensive and must be shared among many groups. More importantly the appetite for computing time is high, and hence access to the computers is tightly regulated. However, leaning on computational experience we gained early on at Los Alamos, and which we perfected at Princeton University later on, the Munich geodynamics group is following a different path. As a pivote departmental supercompute platform, we designe and custom-built a massively parallel computer based on high-end PCs. We pioneered a similar, albeit less powerful, machine - named the Geowulf - at Princeton University some years ago. Geowulf's design has been highly successful and widely shared among geophysics community. Our new machine will used both for teaching and research at Munich Geophysics. The cluster components are much cheaper than a mainframe, and so the geodynamics group will be able to build their new machine sufficiently large to outperform some of the biggest compute centers. This is necessary to press ahead with new and ambitious simulations.
These examples are intended to show how computational geodynamics can give important insight into the dynamic evolution of the Earth. Computational geodynamicists work highly interdisciplinary, drawing on the fields of seismology, mineral physics, fluid dynamics, tectonics and computer science. An important current problem for global geodynamic models is to better account for the complicated mechanical behavior of the rigid outer surface of the Earth, the lithosphere. The behavior of lithospheric plates is dominated by brittle failure along plate margins, which is difficult to produce in the current generation of mantle models. Yet, modeling plate like behavior will be essential, if we are to understand the plate tectonic convection style of Earth.