Piecewise 1D laterally constrained inversion of resistivity data

In a sedimentary environment, layered models are often capable of representing the actual geology more accurately than smooth minimum structure models. Furthermore, interval thicknesses and resistivities are often the parameters to which nongeophysicist experts can relate and base decisions on when using them in waste site remediation, groundwater modelling and physical planning. We present a laterally constrained inversion scheme for continuous resistivity data based on a layered earth model (1D). All 1D data sets and models are inverted as one system, producing layered sections with lateral smooth transitions. The models are regularized through laterally equal constraints that tie interface depths and resistivities of adjacent layers. Prior information, e.g. originating from electric logs, migrates through the lateral constraints to the adjacent models, making resolution of equivalences possible to some extent. Information from areas with well-resolved parameters will migrate through the constraints in a similar way to help resolve the poorly constrained parameters. The estimated model is complemented by a full sensitivity analysis of the model parameters, supporting quantitative evaluation of the inversion result. Examples from synthetic 2D models show that the model recognition of a sublayered 2D wedge model is improved using the laterally constrained inversion approach when compared with a section of combined 1D models and when compared with a 2D minimum structure inversion. Case histories with data from two different continuous DC systems support the conclusions drawn from the synthetic example. I N T R O D U C T I O N Electrical methods have been used successfully for a long time in environmental and hydrogeophysical studies (Fitterman 1987; Dodds and Ivic 1990; Sandberg and Hall 1990; Taylor, Widmer and Chesley 1992; Robineau et al. 1997; Albouy et al. 2001). Nowadays, standard methods allow a more detailed mapping by continuously gathering profile orientated data using either multiple electrode systems, such as the continuous vertical electrical sounding (CVES) system (Dahlin 1996; Bernstone and Dahlin 1999) or systems like the pulled ar∗E-mail: [email protected] ray continuous electrical sounding (PACES) system (Sørensen 1996) and others (Panissod, Lajarthe and Tabbagh 1997). Programs for inverting single sounding data with 1D models have been available for a number of years (e.g. Inman, Riju and Ward 1975; Johansen 1977). Both the CVES and the PACES methods result in dense profile-orientated data coverage with large sensitivity overlaps between individual soundings. This, of course, is very suitable for 2D interpretations but unfortunately 2D inversion is still a relatively slow process, considering the amount of data collected. Furthermore, the most widely used routines produce smooth earth models (Oldenburg and Li 1994; Loke and Barker 1996) in which formation boundaries are hard to recognize. This is not as severe when using a robust inversion scheme (the L1-norm) as when C © 2005 European Association of Geoscientists & Engineers 497