Shape reconstruction with level sets for 3D Electromagnetic Induction Tomography

Joint work with
the IMAGE group, University of British Columbia, Vancouver, Canada

Here is an example for a 3D reconstruction of buried objects from electromagnetic data with level sets. The data are given from 12 sources (large wire loops) above the surface of the earth, and about 40 - 80 receivers (small wire loops) are distributed in four boreholes at the corners of the domain. (In practice, only few receiver loops are moved up and down in the four boreholes for collecting the same data set). The size of the imaging domain is 200m in each direction (x-y-z), and the frequency of the probing fields is 1 kHz. Therefore, the fields behave diffusive rather than wave-like. The full system of Maxwell's equations in 3D needs to be employed in order to be able to correctly model this situation. The expected resolution is quite low due to the diffusive behavior of the fields and due to the very limited view. The following example shows that nevertheless useful reconstructions can be achieved in this situation with our shape evolution technique.

The geometrical setup of the above experiment is shown in the next figure. Displayed in the above figure is only the area of interest (i,j=10...30 and k=30..50). The forward modelling has been done on the complete numerical domain (i,j=1...40, k=1..60) in order to avoid artificial reflections from the numerical boundaries.

Some more info regarding the theory and the setup of this numerical experiment can be found here.

See also the IMAGE homepage

This page has been last modified on: March 5, 2004.