Using GPR Data as Constraints in RMT Data Inversion for Water Content Estimation: A Case Study in Heby, Sweden MEHDI MOHAMMADI VIZHEH, 1,2 BEHROOZ OSKOOI, 1,3 MEHRDAD BASTANI, 2,4 and THOMAS KALSCHEUER 2 Abstract—This study uses ground penetrating radar (GPR) data as constraints in the inversion of radio-magnetotelluric (RMT) data, to provide an improved model at shallow depth. We show that modification of the model regularization matrix using all GPR common-offset (CO) reflections can mislead the constrained inversion of RMT data. To avoid such problems, common mid- point (CMP) GPR data are translated to a resistivity model by introducing a new petrophysical relationship based on a combina- tion of Topp’s and Archie’s equations. This model is updated through a semi-iterative method and is employed as an initial and prior model in the subsequent inversion of RMT data. Finally, a water content model that fits the GPR CMP and RMT data is derived from the resistivity model computed by the constrained inversion of RMT data. To assess the proposed scheme, it is applied to a synthetic data set. Then, real RMT data collected along an 870 m-long profile across a known aquifer situated in the north of Heby, central Sweden, are inverted. By removing the smooth- ness constraints across GPR CO interfaces or using CMP-based inversion, thick ( [ 10 m) vadose and saturated zones are resolved and shown to correlate with logs from nearby boreholes. Never- theless, the application of our CMP-based inversion was the only efficient scheme to retrieve thin (* 3 m) saturated zones and the water table at a depth of 7–15 m in the RMT models. The estimated models of water content are in good agreement with the available hydrogeological information in the study area. Keywords: Constrained inversion, RMT, GPR, water content, CMP, groundwater. 1. Introduction Near-surface geophysical methods such as radio- magnetotellurics (RMT), direct current (DC) resistivity, and ground penetrating radar (GPR) are widely used for groundwater investigations (van Overmeeren 1998; Tezkan et al. 2000; Doolittle et al. 2006; Bastani et al. 2012; Yogeshwar et al. 2012; Yochim et al. 2013). These methods might individ- ually be insufficient for an accurate subsurface investigation. For instance, RMT data have limited resolution for resistive structures beneath the lower edges of thick conductive units, whereas the upper edges of conductive units are very well resolved (Candansayar and Tezkan 2008; Kalscheuer et al. 2010, 2018). Owing to the high signal frequencies ( [ 10 MHz), the skin effect leads to a relatively low penetration depth of GPR signals. Even in clean sand and gravel, GPR pulses significantly attenuate below the water table due to the associated increase of electrical conductivity. Therefore, reflections from the underlying bedrock cannot be distinguished in GPR sections and, in most cases, the aquifer thick- ness is not determined (Neal 2004; Perttu et al. 2012). The primary objectives of hydrogeological studies are to determine parameters such as reservoir volume, water content, and porosity (Greaves et al. 1996; Turesson 2006; Brunet et al. 2010; Giroux and Chouteau 2010; Mukherjee et al. 2010; Yochim et al. 2013). Water content and porosity are usually esti- mated from resistivity models, inverted from geoelectric (DC resistivity) or electromagnetic (EM) data, and empirical relationships such as Archie’s formula (Archie 1942). Typical examples include the studies by Garambois et al. (2002), Mota and Santos (2006), Turesson (2006), and Bastani et al. (2012). The estimation of parameters in Archie’s equation is not straightforward, and additional information is needed to limit the parameters to meaningful ranges (Brunet et al. 2010). Furthermore, resistivity models 1 Institute of Geophysics, University of Tehran, Tehran, Iran. E-mail: mohammadivizheh@ut.ac.ir; boskooi@ut.ac.ir 2 Department of Earth Sciences, Uppsala University, Upp- sala, Sweden. E-mail: mehrdad.bastani@sgu.se; thomas.kalscheuer@geo.uu.se 3 Department of Civil, Environment and Natural Resources Engineering, Lulea ˚ University of Technology, Lulea ˚, Sweden. 4 Geological Survey of Sweden, Uppsala, Sweden. Pure Appl. Geophys. Ó 2019 Springer Nature Switzerland AG https://doi.org/10.1007/s00024-019-02391-1 Pure and Applied Geophysics