GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.1 GNGTS 2024 , (1) where is the number of frequencies for each observaton, represents the uncertainty associated with each of the measured data and is the forward response of the model . Clearly, retrieving the inverse model by simply minimizing Eq. 1 would be challenging because of non-uniqueness and instability of the soluton with respect to the data. In the deterministc inversion framework, the originally ill-posed problem is turned into a conditonally well-posed one by minimizing a stabilizing term (formalizing the available prior informaton; e.g. the presence of smooth transitons between lithologies) with the constraint that . A common choice for the stabilizing term is ; in this specifc case, the soluton is selected as it produces a response compatble with the observed data ( ) while being as close as possible to the reference model . Within this research, the reference models are the 1D models consttutng the 2D resistvity secton crossing the survey area (Fig. 1b), obtained through the inversion of ERT data. However, in the proposed scheme, this spatal constraint enforced by the stabilizing term acts uniquely in the lateral directon, whereas, along the vertcal directon, the prior informaton is incorporated by selectng the possible solutons among the realizaton of the ensemble . In this way, the informaton provided by the reference model is laterally propagated across the entre survey and the possibly very complex (and realistc) prior informaton is infused into the soluton by selectng it among the element of the ensample (supposedly generated in accordance with our expectatons about the subsurface). Fig. 1 – Field data. a ) the locaton of the collected EMI, ERT and GPR data; b ) the result of the ERT inversion (the vertcal lines delineate the porton crossing the EMI survey area); c ) the GPR secton. To validate the proposed approach, we conducted various geophysical measurements on a test site located in the south of Sweden. Specifcally, we acquired 1550 frequency soundings using the Profler EMP-400 from GSSI at three frequencies: 5, 10, and 15 KHz. Additonally, an ERT line was collected across the EMI area using the Terrameter LS2 instrument from GuidelineGeo (Fig. 1). Lastly, we performed a grid of Ground Penetratng Radar (GPR) measurements that overlapped with the EMI area. It's important to note that the GPR data was utlized uniquely for validatng the χ 2 = N −1 δ −1 ( F ( m ) − d ) 2 2 N δ d F ( m ) m m χ 2 = 1 s ( m ) = m − m apr 2 2 m χ 2 = 1 m apr P P