A new sensitivity-controlled focusing regularization scheme for the inversion of induced polarization data based on the minimum gradient support

Abstract

We present a new application of a focusing regularization scheme for the inversion of resistivity and induced polarization ͑IP͒ data that supports large resistivity magnitude and phase contrasts. Similar approaches so far have only been used for the interpretation of gravity, magnetic, or seismic data sets. Unlike methods based on smoothness constraints, the approach is able to resolve sharp boundaries of bodies and layers, and it allows slight parameter variations within them. Therefore, it can be used in hydrogeologic applications where we need focused images to resolve high-contrast aquifer boundaries. Our approach is based on the minimum gradient support, which seeks to minimize the occurrence of parameter contrasts, independent of their magnitude. We study the effects of a variable control parameter on the reweighting optimization, allowing a continuous transition from smooth to sharp images. We also take the spatially varying sensitivity into account to allow focusing even where sensitivities are small. The implemented weighting leads to increased smoothing in well-resolved areas and a decrease in regions of lower sensitivity. The opposite approach is examined as well. This gradient-dependent sensitivity weighting is basically an extension of depth-dependent sensitivity weighting. We demonstrate the effectiveness and limitations of the approach and the influence of the control parameter using different synthetic models and field data from a hydrogeophysical test site. The technique has proven particularly suitable for revealing sharp parameter contrasts.

Voxel inversion of airborne electromagnetic data for improved groundwater model construction and prediction accuracy

“…The second regularization method is the minimum gradient support (Portniaguine and Zhdanov, 1999;Blaschek et al, 2008;Vignoli et al, 2015), which allows for large sharp vertical and horizontal model transitions. The minimum gradient support regularization seeks to minimize the spatial variations vertically and laterally by penalizing the vertical and horizontal model gradients through the stabilizer expressed as (Vignoli et al, 2015) …”

“…If, for example, smooth regularization is used to estimate resistivity models in a sharply layered system, it will produce a blurred resistivity distribution from which one should be careful with inferring the spatial distribution of hydraulic conductivity to be used in a groundwater model. In this case, it would be better to use minimum gradient support regularization (Portniaguine and Zhdanov, 1999;Blaschek et al, 2008;Vignoli et al, 2015) for the geophysical inversion because the estimated resistivity distribution will tend to consist of fewer, more sharply defined layer boundaries (vertically and horizontally). However, it is often ignored that geophysical data can be inverted using alternative regularization schemes, and to test whether the alternative geophysical models affect the predictive capability of a groundwater model.…”

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

“…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).…”

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

“…Besides, many efforts have been made in the last decade to improve static ERT inversion by incorporating prior information in the inversion process. 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]).…”