Global optimization of data quality checks on 2-D and 3-D networks of GPR cross-well tomographic data for automatic correction of unknown well deviations Page: 2 of 4
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the additional quality constraint of insuring that there is
continuity in velocity between immediately adjacent
tomograms. A sudden shift in the mean velocity indicates
that either position deviations are present or there is a shift
in the pick times.
Small errors in well geometry may be effectively treated
during inversion by including weighting, or relaxation,
parameters into the inversion (e.g. Bantu et al., 2006). In
the technique of algebraic reconstruction tomography
(ART), which is used herein for the travel time inversion
(Peterson et al., 1985), a small relaxation parameter will
smooth imaging artifacts caused by data errors at the
expense of resolution and contrast (Figure 2). However,
large data errors such as unaccounted well deviations
cannot be adequately suppressed through inversion
weighting schemes. Previously, problems with tomograms
were treated manually. However, in large data sets and/or
A) Parallel Wells R=Q.O5 B) Parallel Wells F
networks of data sets, trial and error changes to well
geometries become increasingly difficult and ineffective.
Our method consist of three parts: 1) a forward model to
describe a deviated well in Cartesian coordinates, 2) the
calculation of a merit function related to QC of well
deviation, and 3) a global optimization method to minimize
the merit function.
In selecting a model for well deviation we considered that
many of our GPR data sets are from within shallow
aquifers, where the overall length of wells are relatively
small. We also assumed that deviations would be relatively
small over the length of the well with no sudden changes in
direction. Complicated models of well deviation that
includes several changes in azimuth and dip were purposely
C .0 )c -- - elaive
I U m
i .0 25 W, .
0.0 2.5 5.0 0.0 2.5
- r o 5.
A . 5
Tomograms for 5 deg well deviation
Assumed II R=0.05
E) Assumed 11 R=0.50
r I .
5.0 0.0 2.5
Figure 2. Inversion results generated from travel time picks from FDTD simulation of a geostatisical model of dielectric properties (C).
Panels A and B show the results for a pair of parallel tomograms with a relaxation weight R of 0.05 and 0.5, respectively. Panels D and E
show the effects of a deviated well when the wells are assumed to be parallel for a relaxation weight R of 0.05 and 0.5, respectively. Panel
F show the inversion results when the correct well geometry is used for the deviated well.
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Sassen, D. S. & Peterson, J. E. Global optimization of data quality checks on 2-D and 3-D networks of GPR cross-well tomographic data for automatic correction of unknown well deviations, article, March 15, 2010; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc1015623/m1/2/: accessed March 24, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.