Improved hydrogeophysical characterization using joint inversion of cross‐hole electrical resistance and ground‐penetrating radar traveltime data

Abstract

[1] 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.

Underground structure defect detection and reconstruction using crosshole GPR and Bayesian waveform inversion

“…(14) demonstrates that the size of matrix R is exactly similar to that of Q, and thus the standard DCT operation does not reduce parameter dimensionality. Indeed, each coordinate of the matrix Q with values of e r has its own DCT-coefficient.…”

“…We store the values of each grid cell in the matrix Q and derive the S × W matrix R consisting of P DCT-coefficients using Eq. (14). This matrix R is plotted in Fig.…”

“…Such methods can be formulated using either a measure theoretic or random variable approach, the first being the most formal and axiomatic definition of probability and preferred by theoreticians, and the latter more easy and practical to use and therefore favored by practitioners. Among these methods, Bayesian inference coupled with Markov chain Monte Carlo (MCMC) simulation has found widespread application and use in GPR inversion [6,[13][14][15][16][17][18][19][20]. This approach results in a posterior parameter distribution and quantifies the uncertainty in the modeling results emerging from the model, observed data, likelihood function and prior distribution.…”

Semiautomatic and Automatic Cooperative Inversion of Seismic and Magnetotelluric Data

“…As noted earlier, any change of pore water conductivity could prove problematic for application of strict cross-gradient methods (Linde et al 2006). The cross-gradient approach may also prove inappropriate where clay type (e.g., high cation-exchange clays) is key driver for distribution and direction of change of electrical conductivity.…”

“…In hydrogeophysics joint inversions of electrical resistivity and radar slowness have been applied (Doetsch et al 2010;Linde et al 2006). Doetsch et al (2010) investigated the merits of structural cross-gradient methods by incorporating time-lapse cross-hole electrical resistivity tomography (ERT) data and first-arrival ground-penetrating radar (GPR) traveltimes to recover soil moisture content changes within the vadose zone.…”