Appropriate regularizations of geophysical inverse problems and joint
inversion of different data types improve geophysical models and
increase their usefulness in hydrogeological studies. We have developed
an efficient method to calculate stochastic regularization operators for
given geostatistical models. The method, which combines circulant
embedding and the diagonalization theorem of circulant matrices, is
applicable for stationary geostatistical models when the grid
discretization, in each spatial direction, is uniform in the volume of
interest. We also used a structural approach to jointly invert
cross-hole electrical resistance and ground-penetrating radar traveltime
data in three dimensions. The two models are coupled by assuming, at all
points, that the cross product of the gradients of the two models is
zero. No petrophysical relationship between electrical conductivity and
relative permittivity is assumed but is instead obtained as a by-product
of the inversion. The approach has been applied to data collected in a
U. K. sandstone aquifer in order to improve characterization of the
vadose zone hydrostratigraphy. By analyzing scatterplots of electrical
conductivity versus relative permittivity together with petrophysical
models a zonation could be obtained with corresponding estimates of the
electrical formation factor, the water content, and the effective grain
radius of the sediments. The approach provides greater insight into the
hydrogeological characteristics of the subsurface than by using
conventional geophysical inversion methods.