Three dimensional modelling of convection in the Earths MantleBy Jochen Schröder and Adam Antonio
Heat released from the earths core and transported through the mantle via convection plays a large role in the activity of the planets surface. We set out to construct a 3 dimensional model of this phenomenon.
Contents
IntroductionCreated over 5 billion years ago, the earth consists of 4 distinct layers:
The following diagram is a slice through the center of the earth, and illustrates the various layers (layer thicknesses not to scale):
Seismic TomographySeismic Tomography aims to measure the 3 dimensional velocity structure of the earths mantle using seismic waves. The mantles viscous nature means that currents of heated, less-dense material rise to the surface, cool off, and sink in an endless cycle - some have described it as the original lava-lamp. These mantle currents, combined with heat released from the core drive plate tectonic motions of the sea floor and continents. Because the mantle is relatively homogenous, variations in seismic measurement are due to density variations, which are caused by temperature variations. The challenges involved with this form of measurements are due to the sheer size of the data needed to construct a reasonably detailed model, and the fact that these measurements are heterogeneously spread over the earth. Most surface geology, however, is due to activity stemming back millions and even billions of years ago. Reliable measurements exist back 70 million years, about the time of the extinction of dinosoars. We need a way to relate the structure of the mantle at these times with past geological records.
Current WorkSeismic Tomography research was first carried out by Professor Adam M. Dziewonski, who "created a 3-D model from travel time anomalies observed for many ray paths, criss-crossing the Earth between various points near the Earth's surface and reaching different depths in its interior". Harvard University maintains a this Seismology website at http://www.seismology.harvard.edu/projects/3D/.
Harmen's site can be found at http://www.geo.uu.nl/~bijwaard/
Other work has been carried out at The University of Calgary in Canada - these results can be found at http://www.geo.ucalgary.ca/~wu/SeismTomog.html .
Some impressive visualisation have been done by Paul Tackley, Assistant Professor, Department of Earth and Space Sciences, UCLA. He performs very complex and realistic simulations (not using real tomography), even comparing earth with one of Jupiters Moons. Tackley's work can be found at http://www.npaci.edu/enVision/v14.2/tackley.html.
Aim of the ProjectWith this project we wanted to visualise the density structure of the earths mantle in a 3 dimensional structure earth-like structure, unlike the 2-dimensional circles above and the 3-dimensional "boxes" shown above. We show three different visualisation techniques that could be used for this data. The aim was not to give a complete visualization for a very specific problem, but rather to give a brief overview of the possibilities of using these techniques to visualizing the data. They could be combined in any way to give a better insight into certain aspects of the data.
MethodologyThe data was provided to us as ASCII files. The data was organized as a field with a implicit grid in spherical polar coordinates. The first problem was read the data into OpenDX or AVS, because both have their data model based on cartesian coordinates. The first try was to convert the positions into cartesian coordinates using a fortran program, and the read the data into OpenDX or AVS as scattered data. The results from this were very unsatisfactory, because neither AVS nor OpenDX are able to manipulate scattered data in a sufficient manner. We then used a number of tools found on the Cornell Theory Center web site, to deal with the data. First the data was read into OpenDX as partly regular data, with regular connections, with the longitudinal values on the x, the latitudes on the y and the radial values on the z-axis. This data had to be transposed, so the latitudinal values were on the x-axis and the longitudinal on the y-axis, because the module to convert the cartesian into polar coordinates needed them in that way. The positions were then converted into polar coordinates using the sphere-macro from the Cornell web site and could then be manipulated with other modules, such as isosurface and others.
Our VisualisationsDifferent IsosurfacesThe first visualisation shows a sequence of different isosurfaces corresponding to different densities in the earth mantle. This was achieved by using a sequencer. The values. These were connected to the isosurface value button via a compute module, to control the exact values. This enables us to move through different values for the isosurfaces, and adjusting the stepsize through the compute module. To give a better inside over the position inside the earth, a world map, was layed over the globe, with a macro from the CTC, which we reprogrammed to allow opacity and coloured contours around the continents. The rotation of the earth was achieved by connecting the sequencer to a rotation module. View the video of this visualisation in Quicktime format [ Small (1.7MB) ] [ Large (5.8MB) ]
Different RadiiThis visualisation shows the density distribution for a certain radius. This can be done by using the slab module and cutting out one certain radius. This was animated again using the sequencer module. This technique can easily be generalized to cutting out a certain volume out of the earth, or taking just a slice at e.g a latitude between 60 degrees and 80 degress of 1000 km depth. View the video of this visualisation in Quicktime format [ Small (2.6MB) ] [ Large (4.9MB) ]
Development over TimeThe last visualisation technique shows the the development of the density distribution inside the earth mantle over a period of 78 million years. It was done using animated filenames, and importing the data for every timestep from a different file. Here just two fixed isosurface values have been used to illustrate the development over time, they could be easily changed to any other values. View the video of this visualisation in Quicktime format [ Small (2.8MB) ] [ Large (7.7MB) ]
ProblemsOne problem we ran into can be observed very clearly in the second visualisation. Unfortunatly the module we used to convert the cartesian into polar coordinates does not connect the last longitudinal with the first longitudinal values, thus leaving a gap between them. One way to solve this would be to change the data in that way, that we repeat the first value again after the last, so that we have the same longitudinal value at -180 degrees and 180 degrees and they overlap. This is not a very good solution though, because normaly the data is not put in that way, and it would increase the size of data files without providing more information. We are currently trying to develop a macro module for OpenDX that does the connections.
UpdateWe managed to close the gap between the maximum and minimum longitudinal value in the sphere. To solve the problem a new macro had to be programmed (picture of module). The macro takes a slab at both the minimum and maximum longitude (see network). Then we add 360 degrees to the minimum longitude and stack both together. This is the missing part of the sphere. If we now combine this part with the field with the gap, we have the full sphere without a gap. For the module we combine the grids in rectangular form and warp them into a sphere afterwards, this is faster than warping both first, and then combining them. View the updated movie in Quicktime format [ Small (2.5MB) ] [ Large (7.3MB) ]
References and AcknowledgementsGu, Yu (1997), Harvard Seismology: 3-D Earth Structure, Bijwaard, Harmen (2001), All slices must be perfect, Su, W., R.L. Woodward & A.M. Dziewonski (1994), Tackley, Paul, As the World Churns: Modeling Convection in the Earth's Mantle, Müller, R. Dietmar (2001), Deep Earth Structure and Global Tectonics, We would also like to thank PhD student Craig O'Neill and Dr Dietmar Müller of the Department of Geology and Geophysics at the University of Sydney for their help with this project.
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Dr. Harmen Bijwaard at Utrecht University in The Netherlands completed a PhD in 1999. A sample of the work that he completed is shown at right.
