Case studies of incorporation of prior information in electrical resistivity tomography: comparison of different approaches

Abstract

Many geophysical inverse problems are ill-posed and their solution non-unique. It is thus important to reduce the amount of mathematical solutions to more geologically plausible models by regularizing the inverse problem and incorporating all available prior information in the inversion process. We compare three different ways to incorporate prior information for electrical resistivity tomography (ERT): using a simple reference model or adding structural constraints to Occam's inversion and using geostatistical constraints. We made the comparison on four real cases representing different field applications in terms of scales of investigation and level of heterogeneities. In those cases, when electromagnetic logging data are available in boreholes to control the solution, it appears that incorporating prior information clearly improves the correspondence with logging data compared to the standard smoothness constraint. However, the way to incorporate it may have a major impact on the solution. A reference model can often be used to constrain the inversion; however, it can lead to misinterpretation if its weight is too strong or the resistivity values inappropriate. When the computation of the vertical and/or horizontal correlation length is possible, the geostatistical inversion gives reliable results everywhere in the section. However, adding geostatistical constraints can be difficult when there is not enough data to compute correlation lengths.When a known limit between two layers exists, the use of structural constraint seems to be more indicated particularly when the limit is located in zones of low sensitivity for ERT. This work should help interpreters to include their prior information directly into the inversion process through an appropriate way.

Covariance-constrained difference inversion of time-lapse electrical resistivity tomography data

“…The generalized range can be subsequently used to compute the value of the covariance (equation 1) for any combination of model parameters in the grid and build the parameter covariance matrix used during the inversion process. Applications for static conditions (Linde et al, 2006;Hermans et al, 2012;Caterina et al, 2014) have shown that the use of a CCI has generally led to a strong improvement of the resulting image compared with SCI. This operator also smooths the distribution of model parameters through the covariance matrix, but to a level that can be controlled by the correlation length.…”

“…However, such a constraint is often not coherent with the geology. Thus, many alternatives have been developed in static imaging, such as blocky inversion (Farquharson and Oldenburg, 1998), structural inversion (Kaipio et al, 1999;Doetsch et al, 2012a), minimum support (MS) and gradient support functionals (Portnaguine and Zhdanov, 1999;Blaschek et al, 2008), or other prior information incorporation methods (Caterina et al, 2014).…”

Gravimetric water distribution assessment from geoelectrical methods (ERT and EMI) in municipal solid waste landfill

“…Borehole EM data could also be used as prior information to further improve the 571 ERT inversion (e.g. Caterina et al, 2014). 572…”

Geophysical Methods for Monitoring Temperature Changes in Shallow Low Enthalpy Geothermal Systems

“…New constraints have been developed including blocky inversion [77], minimum gradient support [78], structural inversion [79], geostatistical inversion [44] or guiding images [80]. These constraints have proved to be efficient in many field cases (e.g., [81]). …”