Our unit is very active in geoelectrical imaging. In the last years, we focused on the development of improved imaging tools for time-lapse electrical resistivity tomography. Although the smoothness-constrained inversion is not always coherent with the (hydro)geological process under study, it is still the most applied technique to invert time-lapse data.
In collaboration with our colleague of Bonn University (Andreas Kemna), we developed two regularization functionals in the difference inversion code CRTomo.
The first functional is based on the minimum-gradient support (MGS) approach. The novelty in our approach is to use a data-driven approach to choose the optimum value of the MGS parameter. The methodology is demonstrated with a synthetic example and on a field salt tracer experiment in fractured limestone.
Nguyen, F., Kemna, A., Robert, T., & Hermans, T. (2016). Data-driven selection of the minimum-gradient support parameter in time-lapse focused electrical imaging. Geophysics, 81(1), A1-A5.
The second functional is based on parameter-difference covariance matrix (geostatistical constraint or CCI). Instead of imposing smooth parameter changes, the covariance matrix approach tends to recover a model with a defined correlation length. The latter can be estimated through independent measurements, borehole logs for example. The methodology is demonstrated with synthetic examples and on a field heat tracer experiment in an alluvial aquifer.
Hermans, T. , Kemna, A., Nguyen, F. (in press). Covariance-constrained difference inversion of time-lapse electrical resistivity tomography data. Geophysics.
As can be seen from the figure above, the different functionals are relatively similar qualitatively (two zones of reduced resistivity are observed) but yield relatively different quantitative results due to the assumption made on the resistivity change distribution (expressed in the regularization functionals). The MGS tends to produce homogeneous zone with sharp boundaries, whereas the two others produce smoother variations. In the geostatistical constraint, the smoothing is controlled by the imposed correlation length which tends to reduce the area affected by a decrease in resistivity. In this specific case, this is the solution the closest to the true distribution, as demonstrated by the comparison with direct measurements (figure below).