We introduce a new inverse approach
for efficiently identifying parameter structures (zonation) for the permeability
field using the level set method, given spatially distributed observations of
the permeability field (both lithology and/or permeability values) and hydraulic
head measurements at various locations. In this preliminary study, the permeability
field includes two different lithologies. In this method, the boundaries of
zones are represented by a level set function. Starting from an initial choice,
the boundary is then implicitly manipulated through the evolution of the level
set function, which is sequentially optimized to match the observed data. No
assumption has been made on the shape, size, locations, and the number of these
zones, or the correlation structure and the proportion of different lithology.
A synthetic example shows that this method can locate those embedded zones efficiently.