Joint inversion of crosshole ground-penetrating radar
and seismic data can improve model resolution and fidelity
of the resultant individual models. Model coupling obtained
by minimizing or penalizing some measure of structural
dissimilarity between models appears to be the most versatile
approach because only weak assumptions about
petrophysical relationships are required. Nevertheless,
experimental results and petrophysical arguments suggest
that when porosity variations are weak in saturated unconsolidated
environments, then radar wave speed is approximately
linearly related to seismic wave speed. Under such
circumstances, model coupling also can be achieved by
incorporating cross-covariances in the model regularization.
In two case studies, structural similarity is imposed
by penalizing models for which the model cross-gradients
are nonzero. A first case study demonstrates improvements
in model resolution by comparing the resulting models
with borehole information, whereas a second case study
uses point-spread functions. Although radar seismic wavespeed
crossplots are very similar for the two case studies,
the models plot in different portions of the graph, suggesting
variances in porosity. Both examples display a close, quasilinear
relationship between radar seismic wave speed in
unconsolidated environments that is described rather well
by the corresponding lower Hashin-Shtrikman (HS) bounds.
Combining crossplots of the joint inversion models with HS
bounds can constrain porosity and pore structure better than
individual inversion results can.