GNGTS 2021 - Atti del 39° Convegno Nazionale

GNGTS 2021 S essione 3.2 434 current switch-off ( exponent. Starting ρ 0 and m 0 models are chosen to be the  and  models achi iteration using the fast ERT/IP inversion The dataset is expressed in terms of the electric potential measured before and a switch-off d =[ u DC , u IPi ] ) at different time gates i = 1 , 2 ,…, N G and the TD step-off derived at any time t > 0 after the current switch-off through an inverse Fourier t frequency-domain response Z q ( ω ) for each quadrupole q (Fiandaca et al., 2012): V q ( t ) = Z q ( ω = 0 ) − 2 π ∫ 0 ∞ ℑ ( − Z q ( ω ) iω ) sin ( ωt ) d ω , t fferent time gates expone t. Starting ρ 0 and m 0 models are chosen to be the  and  models achiev iteration using the fast ERT/IP inversion The dataset is expressed in terms of the el ctric potential measured before and aft switch-off ( d =[ u DC , u IPi ] ) at differ nt time ga i = 1 , 2 ,…, N G and the TD step-off re derived at any time t > 0 after the current switch-off through an inverse Fourier tra frequency-domain response Z q ( ω ) for each quadrupole q (Fiandaca et al., 2012): V q ( t ) = Z q ( ω = 0 ) − 2 π ∫ 0 ∞ ℑ ( − Z q ( ω ) iω ) sin ( ωt ) d ω , an e D step- off response c the so-called frequency odels achieved at the last efore and after the current D step-off respon V ( t ) is se Fourier transform of the , 2012): (1) derived at any time t > 0 after the current switch-off through an inverse Fourier transform of the frequency-domain response exponent. Starting ρ 0 and m 0 models are chosen to be the  and  iteration using the fast ERT/IP inversion The dataset is expressed in terms of the electric potential measured switch-off ( d =[ u DC , u IPi ] ) at different time gates i = 1 , 2 ,…, N G and the deriv d at any time t > 0 after the current switch-off through an inver fr quency-domain respon Z q ( ω ) for each quadrupole q (Fiandaca et al. V q ( t ) = Z q ( ω = 0 ) − 2 π ∫ 0 ∞ ℑ ( − Z q ( ω ) iω ) sin ( ωt ) d ω , for each quadrupole q (Fiandaca et al., 2012): 0 0 exponent. Starting ρ 0 and m 0 models are chosen to be the  and  models achieved iteration using the fast ERT/IP inversion The dataset is expressed in terms of the electric potential measured before and after t switch-off ( d =[ u DC , u IPi ] ) at different time gates i = 1 , 2 ,…, N G and the TD step-off respo derived at any time t > 0 after the current switch-off through an inverse Fourier transf frequency-domain response Z q ( ω ) for each quadrupole q (Fiandaca et al., 2012): V q ( t ) = Z q ( ω = 0 ) − 2 π ∫ 0 ∞ ℑ ( − Z q ( ω ) iω ) sin ( ωt ) d , (1) where m ρ 0 ,m 0 , τ , c ) to retrieve the spectral behavior of the selected dataset (Pelton et al., 1978), ρ 0 is the DC resistivity, m 0 the chargeabili y, τ the relaxation time and c the o-called freq exponent. Starting ρ 0 and m 0 models a chosen to be the  and  mod ls chieved at t iteration using the fast ERT/IP inversion The data et is expressed in terms of th electric potential measured before and after the c switch-off ( d =[ u DC , u IPi ] ) at different time gates i = 1 , 2 ,…, N G and the TD step-off response derived at any time t > 0 after the current switch-off through an inverse Fourier transform frequency-domain response Z q ( ω ) for each quadrupole q (Fiandaca et al., 2012): V q ( t ) = Z q ( ω = 0 ) − 2 π ∫ 0 ∞ ℑ ( − Z q ( ω ) iω ) sin ( ωt ) d ω , is the angular frequency and the integral in (1) is evaluated in terms of a Fast Hankel transform, for fixed log-spaced values of the variable t , by implementing and improving the Matlab code after Ingeman-Nielsen and Baumgartner (2006). The frequency-domain response is calculated using the 2.5D forward modeling code for complex resistivity by De Donno and Cardarelli (2017), where the solution is achieved for 5 points per decade, thus interpolating to 10 point per decade through cubic splines for ensuring accuracy of the Hankel transform. Then the real stacked potential is calculated by superimposing alternating pulses with proper signs, using the procedure after Fiandaca et al. (2012) for both the on- and the off-time of the signal. We employed a Gauss-Newton iterative formulation for inverting time-domain IP data for Cole-Cole parameters, where the model update vector where  is the angular frequency and the integral in (1) is evaluated in terms of a Fas transform, for fixed log-spaced values of the variable t , by implementing and improving th code after Ingeman-Nielsen and Baumgartner (2006). The fr quency-domain respo se i alculated using the 2.5D forward modeling code for resistivity by De Donno and Cardarel i (2017), wher the solution is achieved for 5 p deca , thus interpolating to 10 int per decade through cubic splines for ensuring accura Hankel transform. Then the real stacked potential is calculated by superimposing alternating pulses with pro using the procedure after Fiandaca et al. (2012) for both the on- and the off-time of the sign We employed a Gauss-Newt n iterative formulation for inverting time-domain IP data f Cole parameters, where the model update vec o δ m is calculated by: δ m n =[ J T W T WJ + β n R T R + λ n I ] − 1 { J T W T W δ d − R ¿ , being J = ∂ d ∂m the Jacobian matrix), W = diag ( 1 s 2 ) the data weight matrix ( s are the standard deviations), R the smoothness matrix, I the identity matrix, δ d the data misfit vec and  regularization parameters at the n -iteration. The Jacobian matrix is calculated by using the same time-transform (1) used for the computation, where the frequency-domain Jacobian is derived by a matrix multiplicatio frequency domain sensitivity with the partial derivative of the complex resistivity with r the Cole-Cole parameters (Madsen et al., 2020). The parameters β 0 and λ 0 are set to be equal to the initial misfit level and to J T W T WJ + β n R T R )), respectively and then decreased by a cooling factor of 0.9. Results The study site is located near the Fogliano Lake, the largest coastal lak Pontina Plain (Central Italy), included within the Circeo National park area of about 5 km 2 . During the recent years, the rapid agricultural develop increased tourism activities have led to groundwater salinization and mapping vulnerability is now required. The near surface geological setting (0-35 m b.s.l.) is dominated by deposits, which host different silt/clay content for thin layers at d depths and distance from the sea throughout the Plain. The wate (freshwater) is found at shallow depths (2-3 m) according to well obser in the study area. Five DC/IP TD lines were executed normally to the seashore, usi SyscalPro resistivimeter, with 48 electrodes spaced 5 m apart and a gradient array (Fig. 1). The spatial distribution of the ERT lines is constrained by the National Park limitations to the geophysical survey. is calculated by: Correzioni testo GNGTS 2021 – Sessione 3.2. Primo autore: De Donno G., titolo: 2-D time domain IP data inversion for mapping saline intrusion in coastal aquifers  pag. 22 equazione 2 e righe adiacenti: testo vecchio: testo nuovo: Cole-Cole parameters, where the model update vector is calculated by: = [ T T + T + ] −1 { T T − ( − 0 } , ( being = the Jacobian matrix), = diag( 1 2 ) the data weight matrix ( s are the observ  pag. 22, ultima riga del paragrafo “ Forward modeling and inversion algorithm ” prima di “Results” : testo vecchio: testo nuovo: max(diag( T T + T )), respectively and then decreased by a cooling factor of 0.  pag. 25 riga 2: testo vecchio: “decay times of ~0.5 - 07 s” - testo nuovo: “decay times of ~0.5- 0.7 s” (2) being Correzioni testo GNGTS 2021 – Sessione 3.2. Primo autore: De Donno G., titolo: 2-D time- domain IP data inversion for mapping saline intrusion in coastal aquifers  pag. 22 equazione 2 e righe adiacenti: testo vecchio: testo nuovo: Cole-Co e parameters, where the model update vector is calculated by: = [ T T + T + ] −1 { T T − ( − 0 } , (2 bein = the Jacobian matrix), = diag( 1 2 ) the data weight matrix ( s are the observe  pag. 22, ultima riga del paragrafo “ Forward modeling and inversion algorithm ” prima di “Results” : testo vecchio: testo nuovo: max(diag( T T + T )), respectively and then decreased by a cooling factor of 0.9  pag. 25 riga 2: testo vecchio: “decay times of ~0.5 - 07 s” - testo nuovo: “decay times of ~0.5- 0.7 s” he Jacobian matrix), Correzioni tes o GNGTS 20 1 – Sessione 3.2. Primo autore: De Donno G., titolo: 2-D time- domai IP dat inversion for mapping saline intrusion i coast l quifers  pag. 22 equazione 2 e righ adi centi: tes o vecchio: tes o nuovo: Cole-Cole parameters, where the model update v ctor is calcu ated by: = [ T T + T + ] −1 { T T − ( − 0 } , (2) being = the Jacobian m trix , = diag( 1 2 ) the da a weight matrix ( s are the observ d  pag. 22, ultima riga del paragr fo “ Forward modeling and inversion algorithm ” prima di “Results” : tes vecchio: tes o nuov : max(diag( T T + T )), resp ctively and then decr as d by a cooling factor f 0.9.  pag. 25 riga 2: tes o vecchio: “decay times of ~0.5 - 07 s” - tes o nuovo: “decay times of ~0.5- 0.7 s” the data weight matrix ( s are the obs rved standard deviations), R the smoothness matrix, I the identity matrix, where  is the angular frequency and the integral in (1) is evaluated in transform, for fixe log-spaced valu s of t e variable t , by im l menting a code after Ingeman-Nielsen and Baumgartner (2006). The frequency-domain response is calculated using the 2.5D forward mo resistivity by De Donno and Cardarelli (2017), where the solution is a decade, thus interpol ting to 10 point per decade through cubic splines for Hankel transform. Then t real stacked potential is calculated by superimposing alternating using the procedure after Fiandaca et al. (2012) for both the on- and the off We employed a Gauss-Newton iterative formulation for inverting time-d Cole parameters, where the model update vector δ m is calculated by: δ m n =[ J T W T WJ + β n R T R + λ n I ] − 1 { J T W T W δ d − R ¿ , being J = ∂ d ∂m the Jacobian matrix), W = diag ( 1 s 2 ) the data weight mat standard deviations), R the smoothness matrix, I the identity matrix, δ d th a d  regularization par meters at the n -iteration. The Jacobian matrix is calculated by using the same time-transform ( computation, wher the fr quency-d main Jacobian is derived by a mat frequency domain sensitivity with the p rtial derivative of the complex r the Cole-Cole parameters (Madsen et al., 2020). The parameters β 0 and λ 0 are set to be equal to the initial misfit J T W T WJ + β n R T R )), respectively and then decreased by a cooling factor of Results The study site is located ear the Fogli n Lake, the larges Po tina Plain (Central Italy), included within the Circeo N area of about 5 km 2 . During the recent years, the rapid agri increased tourism activities have led to groundwater salinization a vulnerability is now required. The near surf ce geological setting (0-35 m b.s. .) is d deposits, which host different silt/clay content for thin depths and distance from the sea throughout th Plai (freshwa er) is found at shallow depths (2-3 m) according in the study area. Five DC/IP TD lines were execut d normally to the s SyscalPro resistivimeter, with 48 electrodes spaced 5 m a the data misfit vector and and e  is the angular frequency and the integral in (1) is evaluated in terms of a Fast Hankel form, for fixed log-spaced values of th v riabl t , by implementing and improving the Matlab after Ingeman-Nielsen nd Baumgartner (2006). requency-domain response is calculated using th 2.5D forward modeling code for complex ivity by De Donno an Cardarelli (2017), where the solution is achieved for 5 points per e, thus int rpolating to 10 point per decad through cubic splines for ensuring accuracy of the el transform. the real stacked potential s calculated by superimposing alternating pulses with pr per signs, the procedure after Fiandaca et al. (2012) for both the on- and the off-time of the signal. mployed a Gauss-New on iterative fo mulation for inv rting time-domain IP d a for Cole- parameters, where the model update vector δ m is calculated by: [ J T W T WJ + β n R T R + λ n I ] − 1 { J T W T W δ d − R ¿ , (2) J = ∂ d ∂m the Jacobian matrix), W = diag ( 1 s 2 ) the data weight matrix ( are the observed ard deviations), R the smoothness matrix, I the identity matrix, δ d the data misfit vector and β regularization parameters at the n -iteration. Jacobian matrix is calculated by using the same time-transform (1) used for the forward utation, where the frequency-domain Jacobian is derived by a matrix multiplication of the ency domain sensitivity with the partial derivative of the complex resistivity with respect to ole-Cole parameters (Mads n et l., 2020). parameters β 0 and λ 0 are set to be equal to the initial misfit level and to max(diag( T WJ + β n R T R )), respectiv ly and then decre sed by a cooling factor of 0.9. lts study site is located near the Fogliano Lake, the largest coastal lake of the ina Plain (Central Italy), included within the Circeo National park with an of about 5 km 2 . During the recent years, the rapid agricultural development and ased tourism activities have led to groundwater salinization and mapping aquifer erability is now required. near surface geological etting (0-35 m b.s.l.) is dominated by sandy sits, which host different silt/clay ontent for thin layers at different hs and distance from the sea t roughout the Plain. The w ter t ble hwater) is found at shallow ept s (2-3 m) according to well observations e study area. DC/IP TD lines were executed normally to the s ashor , using the alPro resistivimeter, with 48 electrodes spaced 5 m apart and a multiple regularization parameters at the n -iteration. The Jacobian matrix is calculated by using the same time-transform (1) used for the forward computation, where the frequency-domain Jacobian is derived by a matrix multiplication of the frequency domain sensitivity with the partial derivative of the complex resistivity with respect to the Cole-Cole par meter (Madsen et al., 2020). The parameters where  is the angular frequency and the integral in (1) is evaluated in terms of a F transform, for fixed log-spaced values of the variable t , by imp ementi g and improving code after Ingeman-Nielsen and Baumgartner (2006). The frequency-domain response is c lculated using the 2.5D forward modeling code f r sistivity by De Donno a d Card e li (2017), wh re the solution is achieved for 5 decade, thus interpolating to 10 point per decade thr ug cubic splin s or ensuring acc Hankel transfo m. Then the real stacked pote tial is calculated by uperimposing alternating pulses with p using th procedure aft r Fiandaca et al. ( 012) for both the on- and th off-time f the si We em l y a Gauss-New on i erative formulati for inverting time-d main IP dat ole parameters, where th model update vector δ m is calculated by: δ m n =[ J T W T WJ + β n R T R + λ n I ] − 1 { J T W T W δ d − R ¿ , being J = ∂ d ∂m the Jacobian matrix), W = diag ( 1 s 2 ) the data weig t matrix ( s are th standard deviations), R the smoothness matrix, I the identity matrix, δ d the data misfit v and  regularization parameters at the n -iteration. The Jacobian matrix is calculated by using the same time-tra sform (1) used for t computation, where the frequency-domain Jacobian is derived by a matrix multiplica frequency domain sensitivity with the partial derivative of the complex resist vity wit the Cole-Cole parameters (Madsen et al , 2020). The parameters β 0 and λ 0 are set to be equal to the initial misf t level and to J T W T WJ + β n R T R )), respectively and then decreased by a cooling factor of 0.9. Results The study site is located near the Fogliano Lake, the larg st coastal la Pon ina Plain (Central Italy), included within the Circeo National par area of bout 5 km 2 . During the recent years, the rapid agricultural devel increased tourism activities have l d to groundwater salinization and mappin vulnerability is now required. The near surface geological setting (0-35 m b.s.l.) is dominated deposits, whi h host ifferen silt/clay cont nt for thin layers at depth and distance from the sea thr ughout the Plain. The wa (freshwater) is found at hallow dep s (2-3 m) according to well obs in the study area. Fiv DC/IP TD lines were executed norma ly to the seashore, u SyscalPro resistivimeter, with 48 lectrod s spaced 5 m apart and a gradient array (Fig. 1). T e sp tial distribution of the ERT lines i constrained by the National Park limitations the geophysical survey. SPAZIO PER LA FIGURA 1 a d r i t lar f n t i t l i i l t i t tran for , f ix d l -spa lues of th ia l t , y i l tin a d i i c e a t em n-Nielsen n B m artn (2006). The fr quenc -do i is calcul ted sing t . li si ti ity b D o n a arda el i 2017), w re th sol ti is a hi ved f r dec de, t us nterpolati to 0 point per d ca thro g cubic s lines nsuring ac u Hankel t ansfo m. h re l st ck d t tial i calc l te u ri sin lt rnati g ul e ith r u ing th p o e re af r Fian a t l. (2012) f r bot t n- d h o f-time f the i We em l ye a Gauss-Newton it rativ ormulatio for i v r ing time d mai IP t C l parameters, here th mo l update ve t δ m i alcul t by: δ n =[ T WJ + β n R R λ n I ] 1 { J δ d R ¿ , b in = m the acobi n at ix), W = di ( 1 2 the data weig t mat ix s a t t i ti , t t e mat i , I the id ntit m t ix, δ d th ta i fit v  r l rization rameters at th n iteration. cobian matrix is c l ulated by sing the me tim -tran fo m 1 use for t computation, whe e the fr qu y-domain Jacobian is i ed by matrix multi li frequ ncy domain s iti ity wit the a ti l derivativ o t e c mplex re isti ty ith the Col -Cole ra e ers (Ma s et al., 2020 . paramete 0 a λ 0 are set to b e u l t th initial isfit l v l to J T W W + n R )), resp ti ely and th decrease by a cooling a tor of 0. . sul s The tu it is l c n e Fo li a e t l s a l l o ti l in Central I al i l d ithi he Circ o ational p k ar a a u 5 m 2 . Du i g e ent ea s, t pid agric ltural e lo incre se t ris ctivities hav le to r und at s liniz io nd m p i uln r il ty is ow requi ed. he ear su e eol gical se i g -35 b.s l.) is domi a e d posit , hic ho t diff ren silt clay con e for thi lay rs t de n ista m the ea ro hout Plain. he t fre ater) found a h l w e t (2 3 ) acco i to w l in t st dy are Fi D I TD l s e ex c te l t eas e, Sys l ro si i imet r, with 8 l r d s c a art n g a i a ra Fig 1). T e p ial distributi of the E lines i const aine by he N ti l P k li itati n o the g phy ic l s y P ER L GU r set to be equal to the initial misfit level and to max(diag( Correzioni testo GNGTS 2021 – Sessione 3.2. Primo autore: De Don o G., titolo: 2-D time- domain IP data inversion f r mapping saline intrusion i coastal aquifers  pag. 22 equazione 2 e righe ad acenti: testo vecchio: testo nuovo: Cole-Cole paramet rs, wher the mode update vector is calcula ed by: = [ T T + T + ] −1 { T T − ( − 0 } , (2) b ing = the Jacobian m trix , = diag( 1 2 ) the da a weight matrix ( are the observe  pag. 22, ultima riga del paragrafo “ Forward mo eling and inversion lgorithm ” prima di “Results” : t st vecchio: testo nuovo: max(diag T T + T )), respectively and then decreased by a cooling factor of 0.9.  pag. 25 riga 2: testo vecchio: “decay times of ~0.5 - 07 s” - testo nuovo: “decay times of ~0.5- 0.7 s” ), respectively an then d creased by a cooling factor o 0.9. Results The study site is located near the Fogliano Lake, the largest coastal lake f the Pontina Plain (Central Italy), includ d within the Cir eo National park with an area of ​about 5 km 2 . During the recent years, the rapid agricultural development and increased tourism activities have led to groundwater salin zation and mapp g aquif r vulne ability is now requ red. The ne r surface geol gical setting (0-35 m b.s.l.) is dominated by sandy deposits, which host different silt/clay co t nt for thin layers at different dep hs and distance from the sea roughout the Plain. The water table (freshwater) is found at shallow depths (2-3 m) according to well observations in the study area. Five DC/IP TD lines were executed normally to the seashore, using the SyscalPro resistivimeter, with 48 electrodes spaced 5 m apart and a multiple gradient array (Fig. 1). The spatial distribution of the ERT lines is mainly constrained by the National Park limitations to the geophysical survey.