GNGTS 2021 - Atti del 39° Convegno Nazionale

433 GNGTS 2021 S essione 3.2 2-D TIME-DOMAIN IP DATA INVERSION FOR MAPPING SALINE INTRUSION IN COASTAL AQUIFERS G. De Donno 1 , M. Cercato 1 , F. Rondinelli 1 1 “ Sapienza” University of Rome – DICEA, Area Geofisica Introduction The increasing global food production expected in the next twenty years requires more efforts to improve productivity, as about 15% of the world’s total land has been affected by physical and chemical degradation, including soil and groundwater salinization (Wild, 2003). However, currently in Europe and particularly in Italy, only a limited number of maps are available for areas subjected to salinization (Van Beek and Tóth, 2012), even though it is well-known that large parts of the coastal territory have been damaged due to salinization. In coastal areas, demanding water tourism activities let the aquifers be recharged by seawater and become saline. Additionally, greatly increased rates of extraction of groundwater in coastal regions of rapid agricultural development have a huge impact on surface water systems and consequently the management of groundwater resources has become pivotal. Electrical resistivity mapping of coastal aquifers has been often conducted employing low- resolution methods, such as electromagnetics (e.g. Viezzoli et al., 2011) or, where resolution is increased i.e. using the electrical resistivity tomography (ERT) (e.g. De Franco et al., 2009). However, using ERT standalone may not be the best choice in complex geological scenarios where resistivity ranges related to different lithotypes may overlap. Nowadays, the additional contribution given by the induced polarization (IP) technique is recognized to be pivotal for resolving the ambiguity arising in such contexts, given the high polarization response of clay minerals and anthropogenic contaminants (Slater and Lesmes, 2002). Therefore, the tomographic inversion of direct-current (DC) resistivity and time-domain (TD) IP data has been surely the most applied method for many environmental applications (e.g. Kemna et al., 2012) during recent years, although still rarely applied for mapping saline intrusion (e.g. Slater and Lesmes, 2002). The TD DC/IP data processing is often conducted by a rapid inversion using the DC resistivity and the integral chargeability as model parameters, discarding the spectral information contained within the IP decay curves without considering the actual transmitter waveform and the receiver transfer function (Fiandaca et al., 2012). The spectral analysis can provide piecewise parameters, which can be used for predicting key parameters for coastal aquifers, such as permeability and porosity (Kemna et al., 2012). This work aims to explore the potential of the TDIP method for mapping saline intrusion on coastal aquifers. Forward modeling and inversion algorithm Our code encompasses a two-step procedure: firstly, we determine resistivity 1 “Sapienza” University of Introduction The increasing global foo improve productivity, as chemical degradation, incl in Europe and particularly to salinization (Van Beek coastal territory have been activities let the aquifers increased rates of extracti have a huge impact on su resources has b come pivo Electrical resistivity map resolution methods, such increased i.e. using the e However, using ERT stan resistivity ranges related to Nowadays, the additiona recognized to be pivotal polarization response of cl Therefore, the tomographi data has been surely the al., 2012) during recent ye and Lesmes, 2002). The T DC resistivity and the information co tained wi waveform and the receiv provide piecewise paramet such as permeability and p This work aims to explore aquifers. Forward modeling and i Our code encompasses a chargeability  models t Oldenburg and Li (1994), (2017). Then, the spectra m =[ ρ 0 ,m 0 , τ , c ] ) to retriev ρ 0 is the DC resistivity, m exponent. Starting ρ 0 and iteration using the fast ER The dataset is expressed i switch-off ( d =[ u DC , u IPi ] ) derived at any time t > 0 frequency-domain respons V q ( t ) = Z q ( ω = 0 ) − 2 ∫ ∞ ℑ and integral chargeability n the next twenty years requires more efforts to ’s total land has been affected by physical and ter salinization (Wild, 2003). However, currently number of maps are available for areas subjected though it is well-known that large parts of the ation. In coastal areas, demanding water tourism ater and become saline. Additionally, greatly oastal regions of rapid agricultural development d consequently the management of groundwater rs has been often conducted employing low- g. Viezzoli et al., 2011) or, where resolution is ography (ERT) (e.g. De Franco et al., 2009). est choice in complex geological scenarios wh re y overlap. y the induced polarization (IP) technique is iguity arising in such contexts, given the high ogenic contaminants (Slater and Lesmes, 2002). rrent (DC) resistivity and time-domain (TD) IP many environmental applications (e.g. Kemna et applied for mapping saline intrusion (e.g. Slater is often conducted by a rapid inversion using the as model parameters, iscarding the spectral ves without considering the actual transmitter andaca et al., 2012). The spectral analysis can or predicting key parameters for coastal aquifers, 12). P method for mapping aline intrusion on coastal firstly, we determine resistivity  and integral inversion using the linear approximation of VEMI lgorithm by De Donno and Cardarelli ed using a Cole-Cole model parametrization ( of the selected dataset (Pelto t al., 1978), where e relaxation time and c the so-called frequency to be t e  and  models achieved at the last potential measured before and after the current 1 , 2 ,…, N G and the TD step-off response V ( t ) is -off through an inverse Fourier transform of the pole q (Fiandaca et al., 2012): (1) models through a fast ERT/IP inversionusing the linear approximationof Oldenburg and Li (1994), as implemented in the VEMI algorithm by De Donno and Cardarelli (2017). Then, the spectral inversion is performed using a Cole-Cole model parametrization ( 2-D time-domain IP data G. De Donno 1 , M. Cercato 1 “Sapienza” University of Introduction The increasing global foo improve productivity, as chemical degradation, incl in Europe and particularly to salinization (Van Beek coastal territory have been activities let the aquifers increased rates of extracti have a huge impact on su resources has b come pivo Electrical resistivity map resolution methods, such increased i.e. using the e However, using ERT stan resistivity ranges related to Nowadays, the additiona rec nized to be pivotal polarization response of cl Therefore, the tomographi data has been surely the al., 2012) during recent ye and Lesmes, 2002). The T DC resistivity and the information contained wi waveform and the receiv provide piecewise paramet such as permeability and p This work aims to explore aquifers. Forward modeling and i Our code encompasses a chargeability  models t Oldenburg and Li (1994), (2017). Then, the spectra m =[ ρ 0 ,m 0 , τ , c ] ) to retriev ρ 0 is the DC resistivity, m exponent. Starting ρ 0 and iteration using the fast ER The dataset is expressed i switch-off ( d =[ u DC , u IPi ] ) derived at any time t > 0 ) to retrieve the spectral behavior of the selected dataset (Pelton et al., 1978), where 2-D time-domain IP da G. D Donno 1 , M. Cerca 1 “Sapienza” University Introduction The increasing global fo improve productivity, a chemical degradation, in in Europe and p rticularl to salinization (Van Be coastal territory have be activities l t the aquife increased rates of extrac have a huge impact on resources has become pi Electrical resistivity m resolution methods, suc increased i.e. using the However, using ERT sta resistivity ranges related Nowadays, th additio recognized to be pivot polarization response of Therefore, the tomograp data has been surely the al., 2012) during recent and Lesmes, 2002). The DC resistivity and the informatio contained waveform and the rec i provide piecewise param such as permeability and This work aims to explo aquifers. Forward modeling and Our code enco passes chargeability  models Oldenburg and Li (199 (2017). Then, the spect m =[ ρ 0 ,m 0 , τ , c ] ) to retri ρ 0 is the DC resistivity, exp ent. Starting ρ 0 a iteration using the fast E The dataset is expresse switch-off ( d =[ u DC , u IPi ] is the DC resistivity, 2-D time-domain IP data inversion for mapping saline intrusion in coastal aquifers G. De Donno 1 , M. Cercato 1 , F. Rondinelli 1 1 “Sapienza” University of Rome – DICEA, Area Geofisica Introduction The increasing global food production expected in the next twenty years requires more improve productivity, as about 15% of the world’s total land has been affecte by phy chemical degradation, including soil and groundwater salinization (Wild, 2003). However, in Europ and particularly in I aly, only a limited number of maps are available for areas to salinization (Van Beek and Tóth, 2012), even though it is w ll-known that large par coastal territory have been damaged due to salinization. In coastal areas, demanding wate activities let the aquifers be recharged by seawater and become saline. Additionally increased rates of extraction of groundwater in coastal regions of rapid agricultural dev have a huge impact on surface water systems and consequently the management of gro sources has become pivotal. Electrical resistivity apping o coastal aquifers has been often conducted employ resolution methods, such as electromagnetics (e.g. Viezzoli et al., 2011) or, where res increased i.e. using the electrical resistivity tomography (ERT) (e.g. De Franco et al However, using ERT standalone may not be the best choice in complex geological scenari resistivity ranges related to different lithotypes may overlap. N wadays, the additional contribution given by the induced p larization (IP) tech rec gnized o be pivotal for resolving the ambiguity arising in such contexts, given polarization response of clay minerals and anthropogenic contaminants (Slater and Lesme Therefore, the tomographic i version of direct-current (DC) resistivity and time-domain data has been surely the most applied method for many environmental applications (e.g. al., 2012) during recent years, although still rarely applied for mapping saline intrusion (e and Lesmes, 2002). The TD DC/IP data processing is often conducted by a rapid inversion DC resistivity and the integral chargeability as model parameters, discarding the informatio con ai ed within t e IP decay curve without considering the actual tr waveform and the receiver transfer function (Fiandaca et al., 2012). The spectral ana provide piecewise parameters, which can be used for predicting key parameters for coastal such as permeability and porosity (Kemna et al., 2012). This work aims to explore the potential of the TDIP method for mapping saline intrusion o aquifers. Forward modeling and inversion algorithm Our c de encompasses a two-step procedure: firstly, we determine resistivity  and chargeability  models through a fast ERT/IP inversion using the linear approxim Oldenburg and Li (1994), as implemented in the VEMI algorithm by De Donno and (2017). Then, the spectral inversion is performed using a Cole-C le odel p rametr m =[ ρ 0 ,m 0 , τ , c ] ) to retrieve the spectral behavior of the selected datase (Pelton et al., 197 ρ 0 is the DC resistivity, m 0 the chargeability, τ the relaxation time and c the so-called f exponent. Starting ρ 0 and m 0 models are chosen to be the  and  models ac ieved a iteration using the fast ERT/IP inversion The dataset is expressed in terms of the electric potential measured before and after th 1 2 the chargeabil ty, 2-D time-domain IP data inversion for mapping saline intrusion in coas G. De Donno 1 , M. Cercato , F. Rondinelli 1 1 “Sap enza” University of Rom – DICEA, Area Geofisica Introduction The increasing global food production expected i the next twenty yea s improve productivity, as about 15% of the world’ total land has been a chemical degradati n, i cluding soil and groundwater salinization (Wild, 20 in Europe and p rticularly in Italy, only a limited number of maps are avail to salinization (Van Beek and Tóth, 2012), even though it is well-known coastal territory have been damaged due to salinization. In coastal areas, d activities let the aquifers e r charged by seawater nd become salin incr ased rates of extraction of groundwater i c ast l regions of r pid a have a huge impact on surface water sy tems and consequently the mana resources h s become pivot l. Electrical resistivity m pping o coastal aquifers has been oft n c n resolution methods, such as electromagnetics (e.g. Viezzoli et al., 2011) increased i.e. using the electrical resistivity tomography (ERT) (e.g. D However, using ERT standalone may not be the best choice in complex ge resistivity ranges related to different lithoty es may overlap. Nowadays, the additional contri ution given by the induced polariza recognized t b pi otal for resolving the amb guity arisi g in such c larization respo se of clay minerals and anthropogenic contaminants (Sl Therefore, the tomographic inversion of direct-current (DC) resistivity a data has been surely the most applied method for many environmental app al., 2012) du ing recent years, although still rarely applied for mapping sal and Lesmes, 2002). The TD DC/IP data processing is often conducted by a r D resistivity and the inte r l ch rgeability as mo el parameters, i f rmation con ai ed within the IP decay curve withou considering waveform and the receiver transfer function (Fiandaca et al., 2012). Th provide piecewise parameters, which can be used for redicting key parame such as permeability and porosity (Kemna et al., 2012). This work aims t xplore the potential of the TDIP method for mapping sa aquifers. Forw r model ng nd inversion algorithm Our code encompasses a two-step procedure: firstly, we determine re chargeabili y  models through a fast ERT/IP inversion using the li Oldenburg and Li (1994), as implemented in the VEMI algorithm by D (2017). Then, the spectral inversio i perform d using a Cole-Col m =[ ρ 0 ,m 0 , τ , c ] ) to retriev the spectral behavior of the sel c ed dat set (Pe ρ 0 is the DC resistivity, m 0 the chargeability, τ the relaxation time nd c exponent. Starting ρ 0 and m 0 models are chosen to be the  and  mod it ration using the fast ERT/IP inversion The dataset is expressed in terms of he e ectric potential me sured befo 1 2 relaxa on time and 2-D time-domain IP da a version for m pp g ali G. De Donn 1 , M. Cercato 1 , F. Rondinelli 1 1 “Sapienza” University of Rome – DICEA, Area Geofis Introduction The increasing global food production exp c ed in th i prov pr ductivity, as about 15% of the world’s t chemical degrad tion, including soi and ground ater s in Europe n particularly in Italy, only a limited num to salinizatio (Van Beek a d Tóth, 2012), even tho coastal territory have been damaged du to salinizatio activities let the aquifers be rech rged by seaw ter increased rates of extraction f groundwater in coasta have a huge impact on surface water sys ems and c resources has become p votal. Elec rical resistivity m pping of coastal aquifers h resolution m thods, such as electromagn ics (e.g. Vi increas d i.e. using the electrical resistivity t mogra However, using ERT standal n may n t be the best c resistivity ranges r lated to different lithotypes may ove Nowadays, the additional contribut on given by t recognized to be pivotal for resolving the ambiguit p l rization sponse of cl y minerals a d anthropoge Therefore, he tomographic inv rsion of direct-curren data has been surel e m st pplied method for man al., 2012) during recent years, lthough still rarely app and Lesmes, 2002). The TD DC/IP data processi g is o DC r sist vity and th integral chargeability a information contained within the IP decay curves waveform and the rec iver transfer function (Fi nda provide piecewise parameters, which an be used for pr such s permeability and porosity (Kemna et al., 2012). This work aims to explore the pot tial of the TDIP m aquifers. Forward m deling and inversion algorithm Our code encompasses a two-step procedure: firstl chargeability  models throu h a fast ERT/IP inv Oldenburg and Li (1994), as imple en ed in the VE (2017). Then, the pectral inv sion is performed u m =[ ρ 0 ,m 0 , τ , c ] ) to r trieve the sp ctral behavior of th ρ 0 is the DC resistivity, m 0 he chargeabili y, τ th re xpon nt. Starting ρ 0 and m 0 models are chos n to i eration using the fast ERT/IP inversion The datase s expr ssed in terms of the electric pote 1 2 the so-called frequency exponent. Starting 2-D time-domain IP data inversio for mapping saline intrusion in coastal aquifers G. D Donno 1 , M. Cerc to 1 , F. Rondinelli 1 1 “Sapienza” University of Rome – DICEA, Area Geofisica Introduction The increasing global fo producti n expected in the next twenty years requires more improve productivity, as about 15% of the w rld’s total land ha been ffecte by ph ch mical de radation, including soil and groun water salinization (Wild, 2003). However n Europe and particularly in Italy, only a limi ed number of maps are available for are s to salinization (Va B ek and Tóth, 2012), even though it is well-known that large p oastal territory hav be n damaged due to salinization. In coastal areas, demanding wat activities let the aquifers be r charged by seawat r and become saline. Additi nall increased rates of extraction of groundwater in co tal regions of rapid agricultural de have a huge impact on surface water systems and consequently the management of gr r sources has become pivotal. Electrical r istivity mapping of coastal aquifers has been often c nducted emplo resolution methods, such as electromagnetics (e.g. Viezzoli et al., 2011) or, where re increased i.e. using the electrical resistivity tomography (ERT) (e.g. De Franco et However, using ERT standalon may not be the best choice in complex geological scena resistivity ranges related to different lithotyp s may v rlap. adays, th additional contribution giv n by the induced pol rization (IP) tec recognized to be pivotal for resolving the ambiguity rising in such contexts, give pol rization re ponse of clay minerals and anthropogenic contaminants (Slat r and Les Therefor , the tomographic inversion of direct-c rrent (DC) esistivity and time-domai data has been surely the most applied method for many environmental applications (e.g. al., 2012) duri g recent years, although still rarely ap lied for mapping saline intrusion ( and Lesmes, 2002). The TD DC/IP data processing is often conducted by a rapid inversio DC resistivity a d the integral chargeability as model parameters, discarding th informatio cont ined with n the IP decay curves without considering th actual t waveform and the rec iv r transfer function (Fiandaca et al., 2012). The spectral n provide piecewise parameters, which can be used for predicting key para eters for coasta such as per eability and porosity (Kemna t al., 2012). This work aims to xplore the potential of the TDIP method for mapping saline intrusion aquifers. Forward m deling and inversion algorithm Our code encompasses a two-step procedure: firstly, we determine resistivity  an chargeability  models through a fast ERT/IP inversion using the linear approxi Oldenburg and Li (1994), as implemented in the VEMI lgorithm by De Donno and (2017). Then, the spectral inversion is performed using a Col -Cole mod l param m =[ ρ 0 ,m 0 , τ , c ] ) to retrieve the spectral behavior of the selected dataset (Pelton et al., 19 ρ 0 is the DC resistivity, m 0 the chargeability, τ the relaxation time and c the so-called xponent. Starting ρ 0 and m 0 models are chosen to be the  and  models achieved it ration using the fa t ERT/IP inversion The dataset is expressed in terms of the electric potential measured before and after t and 2-D time-domain IP data inversion for mapping saline intrusion in coastal aquife G. e D nno 1 , M. Cercato 1 , F. Rondinelli 1 1 “Sapienza” University of Rome – DICE , Area Geofisica Introduction Th increasing global f od production expected in th ext twenty years requires m improve produc ivity, as about 15% f the world’s total land has been affecte by chemical degradatio , in luding soil a d grou dwater salinization (Wild, 2003). Howe in Eur pe and particul rly in Italy, only a limite number of maps are available for to salin zation (Van Beek and Tóth, 2012), eve th ugh it is well-know that larg coa al ter itory have be n d ma du to salin zatio . In coastal areas, de anding c vities let the aquifers b rech rged by seawater and become saline. Additio incr ased rates f ext acti n of groundwater in oastal regions of rapid agricultural have a huge impact on surface water ystems and cons quently the management of resources has become pivotal. Ele trical resis ivity mapping of coastal aquifers has been often conduct d m resolution methods, such as ele tromagnetics (e.g. Viezzoli et al., 2011) or, where incr ased i.e. using the ele trical resis ivi y tomogr phy (ERT) (e.g. De Franco However, using ERT st ndalone may not b th best cho ce in complex geological sc resis ivity rang s r la ed to differe t lith types may overlap. Nowadays, the additi nal contribution given by the induced pol rization (IP) recognized t be pivotal for resolving the ambiguity arisin in such contexts, gi polarization response of clay minerals and anthropogenic con aminants (Slater and L Therefore, the t mographic inversion f direct-current (DC) resistivity n time-do dat has been surel the most pplied method for man environmental application ( al., 2012) during recent years, lthough still rarely applied for mapping saline intrusi and Lesmes, 002). The TD DC/IP data processing is often conducted by a rapid inver DC resis ivity and t e integral chargeability as model parameters, disca ding nform ti n co tained within the IP decay curv s without considering the actu waveform and the receiv r transf r function (Fiandaca et al., 2012). The spectr l provide piecewise parameters, whi h can be us d for predicting key par meters for co such as p rmeability nd porosity (Kemna et al., 2012). This work aims to explor the potential of the TDIP method fo m pping sali e intrus aquifers. F rward modeling and inversion algorithm Our code encompasses a two-step procedure: firstly, we determin resis i ity charge bility  models through fast ERT/IP inversion using the linear appr Oldenburg and Li (1994), as implem ted in the VEMI algor thm by De Donno (2017). Then, the spectral inversion is performed using a Cole-Cole model para m =[ ρ 0 ,m 0 , τ , c ] ) to r triev the spectral behavior of the selected dataset (Pelton et al., ρ 0 is the DC resis ivity, m 0 the chargeability, τ the relaxation time and c th so-cal expone t. Starting ρ 0 and 0 models are chose to be the  and  models achiev iter tion using the fast ERT/IP inversion The dataset is expr ssed in terms of the ele tric po ential measured before and af models are chosen to be he 2-D ti e-domain IP da a inversion for mapp ng al G. De Donno 1 , M. Cercato 1 , F. Rondinelli 1 1 “Sapienza” University of Rome – DICEA, Area Geofi I troduction The increasing global fo d production expected in t improve pr ductivity, as about 15% of the world’s chemical degr dation, including oil and ground ater in Europ an particularly in It ly, only a limit d nu to s linization (Van Beek nd Tóth, 2012), even th oastal territory have been damag d du to salinizati a tiviti s let the aquifers be echarged by seawat i creased r tes of ex action f groundwater in coas ha e huge impact on surface wat r systems a d c resource ha become pivo al. Electrical r sistivity mapping of astal aquifers resolutio m thods, such as electromagnetics (e.g. increa ed i.e. using the electrical r sistivity tomog However, using ERT standal ne may n t be the best sist vity ranges related to different lithotyp s m y o N wadays, the additio al contribut o given by reco ized to be pivotal for r solving the mbigu pol riz tion resp nse of clay miner ls and anthropog Therefore, he tomographic inver ion of d rect-curre data has been su ly the most applied m thod for ma l., 2012) du ing recent years, although ti l rarely p and Lesmes, 2002). Th TD DC/IP data rocessing s DC r sistivity a d the i teg al charge bility a information co tained wi hin the IP decay urves w veform and the r c iv r transfer function (Fiand provide piecewise parameter , which can b used for such as permeability and porosity (Kemna et al., 2012 This work aims to xplore the potential of the TDIP aquifers. Forward modeling and inversio algorithm Our code encompasses a two-step proc dure: firs chargeability  mo els t rou h a fast ERT/IP in Oldenburg and Li (1994), as i pl me ted in the V (2017). Then, the p ctral inversion is p rform d m =[ ρ 0 ,m 0 , τ , c ] ) to retriev the spectral behavior of t ρ 0 is the DC r sistivity, m 0 the chargeability, τ th r xpon nt. Starting ρ 0 and m 0 mo els are chos n to it rati using the fast ERT/IP inversion The datase s expressed in terms of th el ctric pot and ain IP data inversion for mapping saline intrusion in coastal aquifers 1 , M. Cercato 1 , F. Rondinelli 1 University of Rome – DICEA, Area Geofisica g global food producti n expected in th next twenty years requires more efforts to uctivity, as about 15% of the world’s total land has been affected by physical and radation, including soil and groundwater salinization (Wild, 2003). However, currently d particularly in Italy, only a limited number of maps are available for areas subjected n (Van Beek and Tóth, 2012), even though it is well-known that large parts of the ry have been damaged due to salinization. In coastal areas, demanding water tourism the aquifers be recharged by seawater and become saline. Additionally, greatly es of extraction of groundw ter in coas l regions of rapid agricultur l development impact on surface water systems and consequently the management of groundwater become pivotal. sistivity mapping of coastal aquifers has been often conducted employing low- ethods, such as electromagnetics (e.g. Viezzoli et al., 2011) or, where resolution is . using the electrical resistivity tomography (ERT) (e.g. De Franco et al., 2009). ng ERT standalone may not be the best choice in complex geological scenarios where ges related to diff rent lithotypes may overlap. he additional contribution given by the induced olarization (IP) te hnique is o be pivotal for resolving the ambiguity arising in such contexts, given the high esponse of clay minerals and anthropogenic contaminants (Slater and Lesmes, 2002). e tomographic inversion of direct-current (DC) resistivity and time-domain (TD) IP surely the most applied method for many environmental applications (e.g. Kemna et ring recent years, although still rely applied for mapping saline intrusion (e.g. Slater 2002). The TD DC/IP data processing is often conducted by a rapid inversion using the ty and the integral chargeability as model parameters, discarding the spectral contained within the IP decay curves without considering the actual transmitter d the receiver transfer function (Fiandaca et al., 2012). The spectral analysis can wise parameters, which can be used for predicting key parameters for coastal aquifers, eability and porosity (Kemna et al., 2012). s to explore the potential of the TDIP method for mapping saline intrusion on coastal deling and inversion algorithm compasses a two-step procedure: firstly, we determine resistivity  and integral  models through a f t ERT/IP inversion using the linear approximation of d Li (1994), as implem nted in the VEMI algorithm by D Donno and Cardarelli , the spectral inversion is performed using a Cole-Cole model parametrization ( , c ] ) to retrieve the spectral behavior of the selected dataset (Pelton et al., 1978), where resistivity, m 0 the chargeability, τ the relaxation time and c the so-called frequency arting ρ 0 and m 0 models ar chosen to be the  nd  m dels achi ved at the last g the fast ERT/IP inv rsion s expressed in terms of the electric potential measured before and after the current =[ u DC , u IPi ] ) at different time gates i = 1 , 2 ,…, N G and the TD step-off response V ( t ) is y time t > 0 after the current switch-off through an inverse Fourier transform of the odels ac ieved a the last itera o using the fas ERT/IP inversion The dataset is expressed in terms of the electric potential measured befor nd after th