| |
    
|
by Gregory Lauer
In a dimly-lit room cluttered with stacks of scribbled notes and scientific papers, candy wrappers and coffee mugs, researchers at the Minnesota Supercomputer Institute are quietly uncovering the secrets of the inner earth. Working with some of the most powerful computing equipment on the planet, the geological community is gaining a glimpse into worlds we cannot see with traditional tools and scientific methods.
The geologists of today are just as likely to be staring at the dull glare of a monitor as squinting at a sample of quartz or limestone. At the Minnesota Supercomputer Institute Dr. David Yuen, a professor of geophysics and scientific computation, and others are studying mantle convection.
As recently as the seventeenth and eighteenth centuries, it was believed that all of the Earth's features--mountains, valleys, and oceans--were formed as a result of several great catastrophes. Many thought these events had occurred relatively recently and matched the chronology of catastrophic events recorded in the Bible.
In 1795, James Hutton published The Theory of the Earth and proposed the Principle of Uniformitarianism. His revolutionary thinking laid the groundwork for a more scientific and rational approach to geology.
Then in the early 1900s, a virtually unknown German meteorologist introduced a new paradigm to the geological community. Alfred Wegener explained the appearance of similar fossils and rock formations on land forms separated by oceans, the jigsaw-like appearance of the continents, and several other puzzling phenomena with a theory now commonly known as plate tectonics. Wegener's ideas weren't completely accepted until the 1960s when mounting evidence from around the world supported his once-controversial thinking.
Using the theory of plate tectonics, scientists can explain the driving mechanism associated with the movement of the continents. It is believed that dense lithospheric plates containing the continents and ocean basins "float" on the aesthenosphere. In a perpetual game of cat-and-mouse, the continents chase one another across the globe, powered by forces deep beneath the surface of the earth. Although the geological community has made giant strides in exploring and explaining parts of the Earth we can see and touch directly, our understanding of the Earth more than several miles beneath the surface is relatively shallow.
Investigating the composition, structure, and behavior of the mantle is one of the hot topics in geological research today. Because scientists can't study the mantle and the core directly, they must rely on other methodologies and techniques. Computer simulations and numerical models offer unique insights into processes we can't see or measure directly. Most promising, current modeling efforts may one day expand our understanding of continental drift and the cause of volcanoes, or even predict future earthquakes.
The computational models employed by Dr. Yuen and his researchers at the Minnesota Supercomputer Institute are based on the fundamental equations of physics-the conservation of mass, momentum, and energy. These mathematical expressions are repeatedly applied to a grid of data points representing a two- or three-dimensional model. After an initial condition is given, the solution is calculated with the aid of a finite element scheme.
The sheer size and complexity of fluid dynamical phenomena, such as thermal convection or the airflow past a Boeing 757, require substantial computational resources. With the supercomputers at the Minnesota Supercomputer Center, memory and speed are measured in hundreds of megabytes and billions of floating point operations per second respectively. Enormous amounts of data are generated from numerical simulations of mantle convection.
The computational models of Dr. Yuen et al. attempt to capture the salient details of the earth's mantle and core. Assumptions must be made, though, as the study of mantle convection is still in its infancy. Scientists simply don't know the rheological composition of the mantle, for example, or the details of the interface between the core and the mantle. Numerical laboratories like the Minnesota Supercomputer Institute offer researchers a unique opportunity to test hypotheses that cannot be investigat ed with more conventional experiments.
Many models of mantle convection rely on the assumptions of a constant core-mantle boundary temperature and a constant rate of internal heating. These simplified models, however, are not valid over a time scale of a few billion years because of the cooling of the core by mantle circulation. Additionally, the major radioactive elements in the mantle have a mean half-life of between one-fourth to two times the age of the present Earth. The heat emitted from the decay of these elements is an exponentially decreasing function; modeling internal heating as a constant may be a dangerous simplification.
At the U of M, researchers are modeling the core-mantle boundary temperature and internal heating as time-dependent forcings of a mantle convective system. This non-equilibrium approach is considered more representative of the actual Earth, and results differ significantly from the behavior of models using standard equilibrium conditions. This method, however, is much more computationally intensive and difficult to implement.
The numerical grid representing the mantle is usually a non-dimensionalized Cartesian model, although recent efforts include the use of spherical shells. The depth of the mantle is typically estimated to be 2000 km.
From seismic analysis and other methods, geologists theorize the existence of two major phase transitions. Material composition and properties and physical conditions such as heat and pressure change abruptly at these locations. The two principal phase transitions, olivine to spinel and spinel to perovskite, are located at approximately 400 and 670 km respectively. The buoyancy effect and the latent heat release at the phase transitions are modeled with an effective depth-dependent thermal expansivity.
Using this approximation, the numerical model accounts for the background variation as well as the sharp variation in the zone in the immediate vicinity of the phase transition. The fineness of the model, i.e. the number of grid points, is increased in the vicinity of phase transitions to increase vertical resolution.
Once a numerical model is created, the response of a system to a particular set of parameters and initial conditions must be calculated using the resources of the Minnesota Supercomputer Center. Researchers do not rely on explicit equations to determine the behavior of mantle convective systems. Instead they "inch" their way towards a solution by calculating many intermediate points along the way.
At each timestep, the heat flux from the core is calculated and used in computing the new core temperature and the temperature drop across the mantle through an ordinary differential equation. A dimensionless timestep of 0.001 corresponds to approximately 127 million years in the evolution of the earth. These equations are applied repeatedly; in some of the cases, the number of timesteps required may run into the tens of thousands.
Using advanced workstations like Silicon Graphics machines, researchers visualize the massive amounts of data produced in order to gain a better understanding of the physical phenomena of mantle convection and its related processes. A wide variety of software applications are used in preparing these materials. Specialized packages such as BOB (the program Brick of Bytes was developed at the nearby Army High Performance Computing Research Center) and more common spreadsheet applications like Excel are often used. The graphics contained in this article were all generated by researchers working under the direction of Dr. Yuen.
The efforts of Dr. David Yuen and his researchers at the Minnesota Supercomputer Institute offer a wide array of benefits. Work at the Institute is driving the development of ever more sophisticated and powerful computers. Most importantly, their work is expanding our understanding of geophysical processes deep inside the earth.
