3D Characterization of a Coastal Freshwater Aquifer in SE Malta (Mediterranean Sea) by Time-Domain Electromagnetics

water

Article 3D Characterization of a Coastal Freshwater Aquifer in SE Malta (Mediterranean Sea) by Time-Domain Electromagnetics

Potpreecha Pondthai 1,*, Mark E. Everett 1 , Aaron Micallef 2,3 , Bradley A. Weymer 3 , Zahra Faghih 3 , Amir Haroon 3 and Marion Jegen 3 1 Department of Geology and Geophysics, Texas A&M University, College Station, TX 77843, USA; [email protected] 2 Marine Geology and Seaﬂoor Surveying, Department of Geosciences, University of Malta, MSD 2080 Msida, Malta; [email protected] 3 GEOMAR—Helmholtz Centre for Ocean Research Kiel, Wischhofstraße 1-3, D-24148 Kiel, Germany; [email protected] (B.A.W.); [email protected] (Z.F.); [email protected] (A.H.); [email protected] (M.J.) * Correspondence: [email protected]

Received: 27 March 2020; Accepted: 27 May 2020; Published: 30 May 2020

Abstract: Electromagnetic (EM) geophysical methods are well equipped to distinguish electrical resistivity contrasts between freshwater-saturated and seawater-saturated formations. Beneath the semi-arid, rapidly urbanizing island of Malta, offshore groundwater is an important potential resource but it is not known whether the regional mean sea-level aquifer (MSLA) extends offshore. To address this uncertainty, land-based alongshore and across-shore time-domain electromagnetic (TDEM) responses were acquired with the G-TEM instrument (Geonics Ltd., Mississauga, ON, Canada) and used to map the onshore structure of the aquifer. 1-D inversion results suggest that the onshore freshwater aquifer resides at 4–24 m depth, underlain by seawater-saturated formations. The freshwater aquifer thickens with distance from the coastline. We present 2D and 3D electromagnetic forward modeling based on finite-element (FE) analysis to further constrain the subsurface geometry of the onshore freshwater body. We interpret the high resistivity zones that as brackish water-saturated bodies are associated with the mean sea-level aquifer. Generally, time-domain electromagnetic (TDEM) results provide valuable onshore hydrogeological information, which can be augmented with marine and coastal transition-zone measurements to assess potential hydraulic continuity of terrestrial aquifers extending offshore.

Keywords: coastal hydro-geophysics; groundwater; mean sea-level aquifer; transient electromagnetics

1. Introduction Groundwater resources in many coastal regions worldwide are currently under stress because of increasing population, agricultural demands, tourism and economic growth. Fresh groundwater in coastal regions may be a resource that can help to mitigate the water scarcity experienced by coastal communities [1]. However, several ﬁrst-order questions need to be addressed before the fresh groundwater can be used sustainably. There is a lack of understanding regarding the location, nature, and geometry of coastal aquifer systems and their oﬀshore connectivity. Large-scale desalination of seawater is a technologically viable solution, but there are important energy and environmental impacts that must be considered [2]. Terrestrial time-domain electromagnetic (TDEM) methods of geophysical exploration employing a loop or grounded dipole source can be used to explore the

Water 2020, 12, 1566; doi:10.3390/w12061566 www.mdpi.com/journal/water Water 2020, 12, 1566 2 of 22 onshore component of coastal aquifers that may extend offshore. TDEM methods are useful because they have good depth penetration in saline environments compared to other geophysical techniques, such as ground-penetrating radar (GPR) and electrical resistivity tomography (ERT). TDEM methods are sensitive to electrical resistivity which, in turn, is diagnostic of important aquifer parameters such as porosity, water saturation and salinity [3]. Transient electromagnetic (EM) methods respond to the interaction between an applied time-varying magnetic flux and the geoelectrical structure beneath the transmitter. In order to interpret transient electromagnetic responses, the key physical mechanism is the induction process governed by Faraday’s law, which is equivalent to diffusion into a conducting medium of an image of the transmitter (TX) loop current. A fundamental overview of the physical principles underlying the EM geophysical method is given elsewhere [4,5], and there are many reviews related to near-surface applications of EM techniques, e.g., [6,7]. The TDEM method has been widely used for groundwater studies [8–14], including coastal aquifer characterization. The EM methods distinguish electrical conductivity contrasts between freshwater-saturated or brackish-water saturated formations (resistivity ~10–100 Ωm, or more) and seawater-saturated formations (resistivity ~1–10 Ωm). A hydraulic connection implies a continuous hydraulic pathway beneath the coastal zone, such that an offshore aquifer could be recharged by its onshore counterpart, or depleted by pumping of its onshore counterpart. Terrestrial EM geophysical surveys can provide valuable information about the existence of such connections. This knowledge is important if we are to ensure the long-term sustainability of groundwater resources and it can serve as a valuable constraint for hydrogeological modeling studies. Onshore-offshore connectivity also has implications for possible onshore land subsidence due to offshore drilling and extraction [15,16]. It should also be noted that the electromagnetic method remains largely undeveloped for data acquisition in the important coastal shallow-water transition zone. This study is part of a multi-disciplinary project that aims to investigate potential onshore-offshore groundwater aquifer connections based on terrestrial and offshore TDEM geophysical data from SE Malta (Mediterranean Sea). Here we utilize 2D and 3D electromagnetic forward modeling based on finite-element (FE) analysis to constrain the 3D geometry of the onshore freshwater body, in this case, the mean sea-level aquifer in SE Malta. To accomplish this objective, TDEM responses were acquired with the Geonics G-TEM instrument. The analysis of the TDEM data generated geoelectrical models that are used to better understand the variable coastal hydrogeology along a short segment of the Maltese coastline. This helps to characterize the potential groundwater resources of the semi-arid, rapidly urbanizing island of Malta. Future work, currently in the planning stages, will involve conducting additional EM measurements both offshore and within the coastal transition zone.

2. Characterization of Mean Sea-Level Aquifer and Study Area The Maltese Islands, comprising of Malta, Gozo and Comino, are composed of marine sedimentary rocks deposited between the Late Oligocene and Late Miocene epochs [17]. The ﬁve sedimentary formations outcropping across the Maltese Islands include, from top to bottom: Upper Coralline Limestone (162 m), Greensand (11 m), Blue Clay (75 m), Globigerina Limestone (207 m), and Lower Coralline Limestone (up to 1 km, of which the top ~140 m is exposed) (numbers in brackets denote maximum thickness) (see Figure1a) [ 18,19]. This succession contains a range of lithologies and facies, but overall it is dominated by marine carbonates of shallow water origin. The rock formations exhibit a gentle regional ﬂexure and normal faulting is widespread [20]. The older (Early Miocene) and most widespread system of faults is oriented SW–NE and includes the Great Fault or Victoria Fault, which is ~11 km long and traverses the entire width of the island. A younger system of faults (Late Miocene-Early Pliocene) is present along the southern coastline and often cross-cuts pre-existing faults. The longest of the younger faults is the NW–SE striking Maghlaq Fault. The climate of Malta is semi-arid Mediterranean characterized by a hot, dry summer and a mild, humid winter. The mean annual precipitation is 550 mm, which mainly falls between September and April [21,22]. Water 2020, 12, 1566 3 of 22 Water 2020, 12, x FOR PEER REVIEW 3 of 23

FigureFigure 1. (1.a) ( Geologicala) Geological map map of theof the island island of Maltaof Malta and and an an inset inset map map showing showing location location of of Malta Malta in in the Mediterraneanthe Mediterranean Sea as Sea a red as square. a red square. Modified Modified from Geologicalfrom Geological Map ofMap Maltese of Maltese Islands, Islands, 1993 1993 [19]. [19]. Black linesBlack denote lines faults. denote The faults. lithological The lithological profile isprofile provided is provided in the right in the panel. right Studypanel. siteStudy is shownsite is shown as blue square.as blue (b )square. Detail of(b) the Detail study of the site study in SE site Malta; in SE transect Malta; Atransect is aligned A is NW–SEaligned NW–SE and B is and aligned B is aligned NE–SW. Time-domainNE–SW. Time electromagnetic‐domain electromagnetic (TDEM) soundings (TDEM) aresoundings marked asare squares marked with as squares black squares with black inside; thesquares difference inside; in colors the difference denotes diinff colorserent acquisitiondenotes different dates. acquisition White symbols dates. show White TDEM symbols sounding show locationsTDEM from sounding July 2018.locations Additional from July soundings 2018. Additional investigated soundings during investigated June and July during 2019 June are and indicated July by cyan2019 are and indicated purple symbols, by cyan and respectively. purple symbols, respectively. Water 2020, 12, 1566 4 of 22

The Maltese Islands obtain ~55% of their potable water supply from groundwater, while the rest comes from seawater desalination [22]. Aquifers are the primary source of portable water as there is no appreciable surface water streamflow. The mean sea-level groundwater body lies within the pores and fissures of Lower Coralline Limestone (LCL) in the interval where the formation sub-crops at sea-level south of the Victoria fault [23]. The LCL formation is predominantly composed of an algal fossiliferous limestone with sparse corals. The rocks exhibit moderate, irregular or channel-like permeability [24]. The primary porosity of LCL ranges between 7 and 20%, whereas its intrinsic permeability is low 7 9 (10− –10− m/s). Effective porosity and secondary permeability, both of which are dependent on 6 fissures and weathering, have values of 10–15% and 10− m/s [23,25]. The mean sea-level groundwater body is in lateral and vertical contact with seawater. A body of fresh water in the form of a ‘lens’ floats on saline water due to its lower density [26,27]. The thicker part of the lens is situated in the central part of Malta, with its height decreasing towards the coastline. The mean-sea level groundwater is not at rest, but flows horizontally outward from the thickest part. The aquifer is recharged by the infiltration of rainwater in every winter, and groundwater is either discharged offshore at the coastline or else removed by abstraction (pumpage) for agricultural purposes. The mean sea-level aquifer (MSLA) has a mean thickness of 67.5 m and covers an area of >200 km2 [28]. This water is mainly abstracted for potable supply and agricultural use. A number of discontinuous perched aquifers with a limited saturated thickness occur north of the Great Fault in the Upper Coralline Limestone above the impermeable Blue Clay, and they are exclusively used for agricultural purposes. The study site is situated on the SE coast of the island of Malta ~6 km SE of Valletta, the capital city. The elevation of the study site is ~10 m above the sea surface (see Figure1a). The rocks exposed at the study site consist of the lower member of the Globigerina Limestone formation, which overlies the upper members of the LCL formation. There is a geological well at 3.5 km west of the study site that shows 35 m of Lower Globigerina above 34 m of Lower Coralline and the elevation of the well is 35 m [29]. There is another well drilled for hydrological purposes, located 2.5 km west of the study site, where the top of the water table is 1 m above sea level [26].

3. Methods This study utilizes the near-surface TDEM geophysical method to determine the geometry and characteristics of the onshore MSLA along the coast at the survey site in SE Malta. The TDEM measurements were carried out using the Geonics G-TEM system consisting of a portable battery-operated transmitter-receiver (TX-RX) console, a TX antenna deployed as 4 turns of a 10 10 m × square loop of wire laid on the ground, a 0.6 m diameter RX rigid coil with pre-amplifier, and the supporting cables. In field operations, the equipment was deployed as shown in Figure2. In this study, all soundings were acquired in the 20 time-gate mode, corresponding to investigation depths of 60–100 m. The 30-gate mode with longer acquisition time allowing for deeper exploration was not used. The depth of investigation also depends on the TX power, which is a product of the loop size, current, and its number of turns, in addition to the subsurface conductivity and the RX sensitivity [30]. The operating principle of TDEM is based on the EM induction process. An abrupt shut-off of a steady value of TX current in the wire loop, according to Faraday’s law, generates an impulsive electromotive force (emf) that drives eddy current flow in the conductive earth. After the shut-off, the emf vanishes and the eddy currents start to decay. A weak secondary magnetic field is produced in proportion to the deceasing amplitude of the eddy currents. The multi-turn receiver coil located at the ground surface measures the time rate of change of the decaying secondary vertical magnetic field, the decay rate being diagnostic of the subsurface electrical resistivity. Water 2020, 12, 1566 5 of 22 Water 2020, 12, x FOR PEER REVIEW 5 of 23

Figure 2. Field deployment of Geonics G G-TEM‐TEM geophysical equipment in SE Malta.

3.1. Data Acquisition The geophysical survey procedure was asas follows.follows. At each sounding location, the wire loop was laid out on thethe ground.ground. Then the RX coil with its pre-amplifierpre‐amplifier was set up in the center of the wire loop,loop, toto achieveachieve aa central-loopcentral‐loop sounding.sounding. The portable TX-RXTX‐RX console was set up immediately outside thethe TXTX loop loop for for convenience. convenience. A A ramp-o ramp‐ffoffcurrent current was was passed passed through through the the wire wire loop loop using using the signalthe signal generator generator in the in TXthe console.TX console. The The resultant resultant signal signal received received by theby RXthe coilRX coil was was recorded recorded by the by RXthe console,RX console, averaged averaged over severalover several thousand thousand repetitions repetitions to improve to improve signal-to-noise signal‐to ratio.‐noise The ratio. overall The timeoverall to acquiretime to eachacquire sounding each sounding response response was ~5 min. was Then ~5 min. the TXThen loop the and TX RXloop coil and were RX picked coil were up, alongpicked with up, thealong TX-RX with console, the TX‐RX and console, moved forwardand moved to the forward next sounding to the next location. sounding The location. center of The the RXcenter coil of represents the RX coil the represents location of the each location sounding, of each the sounding, latter recorded the latter by handheld recorded GPS. by handheld The operating GPS. frequency,The operating i.e., frequency, the repetition i.e., ratethe repetition of the TX rate on/ oofff thecycle, TX ison/off in the cycle, kHz is range in the (i.e., kHz well range outside (i.e., well the mainoutside power the main supply power at 50 Hzsupply and cellat 50 phones Hz and at ~1cell GHz.) phones The at TDEM ~1 GHz.) method The isTDEM non-invasive, method is and non no‐ significantinvasive, and environmental no significant disturbance environmental is made todisturbance natural flora, is wildlife,made to or natural agriculture. flora, wildlife, or agriculture.The two orthogonal transects acquired in SE Malta comprising a total of 23 TDEM central-loop soundingsThe two in Julyorthogonal 2018 are transects marked asacquired black-and-white in SE Malta symbols comprising in Figure a total1b. Profile of 23 TDEM A is oriented central from‐loop SEsoundings to NW along in July the 2018 shoreline are marked with a as total black length‐and of‐white 150 m,symbols while profilein Figure B is 1b. aligned Profile from A is NE oriented to SW withfrom aSE length to NW of 60along m (Figure the shoreline3). The with two profilesa total length cross each of 150 other m, while at stations profile A7 B and is aligned B4, respectively. from NE Anto SW additional with a datasetlength of of 60 31 soundingsm (Figure (cyan3). The and two purple profiles symbols cross ineach Figure other1b; at see stations also Figure A7 and3) was B4, addedrespectively. to this An area additional from a second dataset field of 31 survey soundings conducted (cyan during and purple June and symbols July 2019.in Figure One 1b; of the see 2019 also soundingsFigure 3) was (station added 431) to wasthis area performed from a at second the crossing field survey point ofconducted the two previousduring June transects and July (A, 2019. B) to checkOne of signal the 2019 repeatability. soundings The (station 2019 431) survey was was performed performed at the in order crossing to expand point of the the coverage two previous of the surveytransects from (A, theB) to previous check signal year. repeatability. The rationale The for 2019 adding survey more was soundings performed is thatin order the denser to expand spatial the distributioncoverage of the of data survey enables from us the to previous better construct year. The a fully rationale 3D geoelectrical for adding model.more soundings is that the denser spatial distribution of data enables us to better construct a fully 3D geoelectrical model. Water 2020, 12, 1566 6 of 22 Water 2020, 12, x FOR PEER REVIEW 6 of 23

Figure 3. Location of TDEM soundings and four 2D transects are shown. A symbol denotes position of each sounding and differences differences in colors refer to didifferentfferent measurementmeasurement dates.dates. TDEM soundings deployed during JulyJuly 2018, 2018, June June 2019, 2019, and and July July 2019 2019 are are indicated indicated by black-and-white,by black‐and‐white, black-and-cyan black‐and‐ cyanand black-and-purple and black‐and‐purple symbols, symbols, respectively. respectively. 3.2. Data Analysis 3.2. Data Analysis 3.2.1. D Inversion 3.2.1. D Inversion The 1D inversion of G-TEM transient EM sounding curves is performed using the IXG-TEM softwareThe from1D inversion Interpex Limitedof G‐TEM (Golden, transient CO, EM USA). sounding After importing curves is aperformed data file containing using the a IXG measured‐TEM softwaresounding from curve, Interpex the software Limited generates (Golden, aColorado, consistent USA). 1D smooth After importing model of a electrical data file resistivitycontaining vs. a measureddepth, based sounding on the iterativecurve, the Occam software regularization generates method a consistent [31]. The 1D usersmooth is required model toof defineelectrical the resistivityminimum vs. and depth, maximum based depths, on the and iterative also the Occam starting regularization resistivity for method initiating [31]. the The model user iterates.is required We toseek define the 1D the inverted minimum model and that maximum gives a satisfactorydepths, and fit also to the the TDEM starting data resistivity with minimal for initiating variation the in modelelectrical iterates. resistivity We seek between the 1D adjacent inverted layers. model Such that a “smooth” gives a satisfactory model generally fit to the provides TDEM a preferabledata with minimalrepresentation variation of subsurface in electrical geoelectrical resistivity structuresbetween adjacent compared layers. to a “rough” Such a “smooth” model that model may fit generally the data providesbetter but a contains preferable unrealistically representation large of variations subsurface in geoelectrical resistivity between structures adjacent compared layers. to An a “rough” example modelof an inversion that may tofit 100 the mdata depth better of G-TEMbut contains sounding unrealistically from station large A7 variations is shown in in resistivity Figure4. The between data adjacent layers. An example of an inversion to 100 m depth of G‐TEM sounding from station A7 is points on the left indicate the Earth-response signal recorded by the RX coil as a function of time (in shown in Figure 4. The data points on the left indicate the Earth‐response signal recorded by the RX ms) after current is shut off in the TX loop. The red line on the right indicates an initial guess of Earth coil as a function of time (in ms) after current is shut off in the TX loop. The red line on the right resistivity, which in this case is a uniform 10 Ωm half-space. The dark green line on the right indicates indicates an initial guess of Earth resistivity, which in this case is a uniform 10 Ωm half‐space. The the calculated smooth depth profile of Earth resistivity, the predicted response of which (continuous dark green line on the right indicates the calculated smooth depth profile of Earth resistivity, the dark green curve passing through the data points on the left) best fits the observed response, subject to predicted response of which (continuous dark green curve passing through the data points on the the smoothness constraint. At this location, a high-resistivity zone of ~80–100 Ωm appears at ~4–22 m left) best fits the observed response, subject to the smoothness constraint. At this location, a high‐ depth, underlain by a uniform low-resistivity zone of ~2–3 Ωm. resistivity zone of ~80–100 Ωm appears at ~4–22 m depth, underlain by a uniform low‐resistivity zone of ~2–3 Ωm. Water 2020, 12, 1566 7 of 22 Water 2020, 12, x FOR PEER REVIEW 7 of 23

Figure 4.4. ExampleExample of of G-TEM G‐TEM data data shown shown as squareas square symbols symbols and theand computed the computed resistivity resistivity depth profiledepth displayedprofile displayed as a curve as passinga curve throughpassing allthrough data points all data with points root meanwith root square mean (RMS) square misfit (RMS) 6.8% misfit (left); the6.8% fitted (left model); the fitted is marked model as is the marked dark greenas the line dark while green the line red while line is the the red starting line is model the starting (right ).model (right). 3.2.2. D Forward Model Context 3.2.2.In D thisForward study, Model we used Context a well-tested, in-house FORTRAN program to compute 1D transient responsesIn this based study, on we a finite-radius, used a well‐ inductively-coupledtested, in‐house FORTRAN loop source program deployed to compute over a layered 1D transient earth. Forresponses such a based 1D model, on a thefinite resistivity‐radius, inductively changes only‐coupled in a vertical loop source direction. deployed A series over of 1Da layered responses earth. at diForff erentsuch frequenciesa 1D model, is the computed resistivity using changes the well-known only in a vertical frequency-domain direction. A series analytic of 1D solution responses [32,33 at]. Thedifferent transient frequencies response is is computed then obtained using by the taking well an‐known inverse frequency Fourier transform‐domain analytic of the frequency-domain solution [32,33]. responsesThe transient using response a Padé summationis then obtained method by [ 34taking]. an inverse Fourier transform of the frequency‐ domain responses using a Padé summation method [34]. 3.2.3. D and 3D Forward Model Context

3.2.3.This D and study 3D alsoForward utilizes Model 2D and Context 3D forward modeling of transient EM responses to further constrain the geometry of the onshore geoelectrical structure of the SE Malta aquifer system. The computation This study also utilizes 2D and 3D forward modeling of transient EM responses to further of time-harmonic EM responses of aquifer geoelectrical models is performed using a finite-element constrain the geometry of the onshore geoelectrical structure of the SE Malta aquifer system. The (FE) analysis of the governing Maxwell equations in the magnetoquasistatic regime. The FE computation of time‐harmonic EM responses of aquifer geoelectrical models is performed using a algorithm [35,36] generates a rectangular mesh that is used to discretize buried 1D, 2D and 3D finite‐element (FE) analysis of the governing Maxwell equations in the magnetoquasistatic regime. structures by defining rectangular prisms, or slabs, and assigning them certain dimensions, locations, The FE algorithm [35,36] generates a rectangular mesh that is used to discretize buried 1D, 2D and and electrical conductivities (the inverse of resistivity). 3D structures by defining rectangular prisms, or slabs, and assigning them certain dimensions, In our simulations, the G-TEM transmitter (TX) in ‘vertical dipole’ mode is approximated by 4 locations, and electrical conductivities (the inverse of resistivity). turns of a circular current loop with 5.64 m effective radius (equivalent to the in-field-survey of a In our simulations, the G‐TEM transmitter (TX) in ‘vertical dipole’ mode is approximated by 4 10 10 m square loop) lying on the air-earth interface at the origin of the computational grid. A single turns× of a circular current loop with 5.64 m effective radius (equivalent to the in‐field‐survey of a 10 receiver position is assigned to the center of the TX loop to simulate the central-loop configuration. × 10 m square loop) lying on the air‐earth interface at the origin of the computational grid. A single The resistivity model is discretized using 100 100 100 nodes of a uniform rectilinear mesh with receiver position is assigned to the center of the× TX ×loop to simulate the central‐loop configuration. cell-size 0.8 0.8 0.8 m. The modeling-domain limits are { 40 m, 40 m}, { 40 m, 40 m} and { 20 m, The resistivity× model× is discretized using 100 × 100 × 100 nodes− of a uniform− rectilinear mesh− with 60 m} in the x, y and z directions, respectively. A typical mesh contributes roughly 4 million degrees of cell‐size 0.8 × 0.8 × 0.8 m. The modeling‐domain limits are {−40 m, 40 m}, {−40 m, 40 m} and {−20 m, freedom to the finite-element system of equations since there are four complex degrees of freedom 60 m} in the x, y and z directions, respectively. A typical mesh contributes roughly 4 million degrees associated with each interior mesh node in the A, Ψ formulation, described below. The CPU time of freedom to the finite‐element system of equations since there are four complex degrees of freedom associated with each interior mesh node in the 𝐴, 𝛹 formulation, described below. The CPU time required to compute a single controlled‐source electromagnetic (CSEM) response for a model of this size at one frequency on the Aspen Systems Texas A&M cluster is ~20 min. Water 2020, 12, 1566 8 of 22 required to compute a single controlled-source electromagnetic (CSEM) response for a model of this size at one frequency on the Aspen Systems Texas A&M cluster is ~20 min. The FE formulation is cast in terms of two Coulomb-gauged electromagnetic potentials, namely a magnetic vector potential A and a scalar electric potential Ψ. The Coulomb gauge condition is applied, A = 0. A set of known primary potentials (Ap, Ψp) is specified, which consists of the analytic ∇· expression for electromagnetic induction in a homogeneous formation with σp constant (see [35,36]. Secondary potentials As and Ψs are then defined according to A = Ap + As and Ψ = ΨP + Ψs, in which case the governing equations become

2 As iωµ σ(As + Ψs) = iωµ σs Ap + Ψp , (1) ∇ − 0 ∇ 0 ∇ h i [ iωµ σ(As + Ψs)] = iωµ σs Ap + Ψp , (2) ∇· − 0 ∇ ∇· 0 ∇ where σs = σ σp is the difference between the conductivity distribution σ(r) whose response is − required and the background value σp whose response is known. The value of electric field E and the induction field B are derived, after calculation of the Coulomb-gauged electromagnetic potentials, according to E = iω(A + Ψ), (3) − ∇ B = A (4) ∇ · The spatial derivatives in the above equations are performed numerically in the post-processing stage of the algorithm. To summarize, Maxwell’s equations are formulated in terms of frequency-domain magnetic vector and electric scalar secondary potentials. The primary potentials are set by the aforementioned analytic solution and added to the calculated secondary potentials in order to obtain the total response at the prescribed frequency. At a given receiver location, such as the center of the TX loop, the total vertical magnetic field component is computed by numerical differentiation of the computed potentials. This procedure is repeated for a number of frequencies spanning several decades, building up the frequency-domain response. For this study, responses are evaluated at 43 logarithmically-spaced frequencies, at 6 frequencies per decade over the range 101–108 Hz. After its inverse Fourier transform into the time-domain, the resulting computed transient responses may be directly compared to the G-TEM sounding curves measured in the field.

4. Results

4.1. D Scenario First we analyze the transient EM soundings from the two orthogonal G-TEM transects of July 2018 comprising 23 locations along and across-shore SE Malta. The field dataset is divided into two transects, labeled A and B. All soundings are plotted in terms of Earth-response voltage as a function of time on a single log-log display for each transect (Figure5a,b). This format illustrates the variability, or scatter, in the temporal decay of the signals following shut-off in the TX current. A definition of time gate is provided in AppendixA. At station A3, a distinctive and unusual decay curve is observed, which is thought to be caused by effects of localized 3D subsurface structures of unknown origin. This curve, plotted as blue dots in Figure5a, is clearly distinguished from the other curves and it cannot be fit by the response of a 1-D model. At A3, the unusual response—perhaps from inductive or IP coupling to steel infrastructure—exhibits a sign reversal (from solid to open circles) after gate 13 of the transient and it is not considered for further analysis. The central-loop response of a 1-D layered model cannot generate such a sign change. Water 2020, 12, 1566 9 of 22 Water 2020, 12, x FOR PEER REVIEW 9 of 23

FigureFigure 5.5.G-TEM G‐TEM data data from from 23 soundings23 soundings in SE in Malta. SE Malta. (a) All ( 16a) soundingsAll 16 soundings in proﬁle in A; (profileb) soundings A; (b) fromsoundings the 7 stations from the belonging 7 stations to belonging Proﬁle B. to Profile B.

AfterAfter examining examining the the remaining remaining 21 sounding 21 sounding curves curves comprising comprising the alongshore the alongshore profile, the profile, responses the fromresponses the southernmost from the southernmost stations A2, stations and A4–A9 A2, and may A4–A9 be classified may be classified as one group as one since group they since exhibit they veryexhibit similar very decaysimilar patterns. decay patterns. A separate A 1Dseparate inversion 1D inversion was performed was performed for each of for these each soundings. of these Thesoundings. resulting The 1D resistivityresulting 1D models resistivity from each models station from were each used station as initial were resistivity used as distributions initial resistivity in an attemptdistributions to find in a an single attempt 1D model to find that a single could 1D fit these model southernmost that could fit soundings. these southernmost After many soundings. iterations ofAfter computation many iterations and model of computation adjustment usingand model the 1-D adjustment analytic forward using the code, 1‐D a simpleanalytic 3-layer forward 1D code, model a wassimple found 3‐layer to be 1D the model most consistent was found with to the be fieldthe most responses consistent (Figure with6, right). the field This resistivityresponses model(Figure for 6, theright). southern This resistivity section of model profile for A consists the southern of a three section layered-earth of profile ofA 5.5consistsΩm and of a 25 threeΩm layeredresistivity‐earth with of 45.5 and Ωm 15 and m thicknesses, 25 Ωm resistivity respectively, with and4 and including 15 m thicknesses, a basal resistivity respectively, of 1.8 Ω mand. The including fit of this a model basal toresistivity the sounding of 1.8 curves Ωm. The A2, fit A4–A9 of this is model shown to in the Figure sounding6, left. curves A2, A4–A9 is shown in Figure 6, left. We used the same procedure to analyze the sounding curves from all 21 stations comprising the reduced SE Malta 2018 dataset and the additional 31 soundings from the field survey conducted during June and July 2019. Another unusual decay curve is found at station 432 (black squares, Water 2020, 12, x FOR PEER REVIEW 10 of 23

Figure 7). At the late‐time of this sounding, the observed signal decays significantly slower compared to neighboring stations, i.e., station 433, which is located only 15 m to the north. The Wateranomalous2020, 12, 1566response may be due to the effects of a localized highly‐conductive body; this will10 of 22be discussed later.

Water 2020, 12, x FOR PEER REVIEW 10 of 23

Figure 7). At the late‐time of this sounding, the observed signal decays significantly slower compared to neighboring stations, i.e., station 433, which is located only 15 m to the north. The anomalous response may be due to the effects of a localized highly‐conductive body; this will be discussed later.

FigureFigure 6.6. ((leftleft)) 1D1D analyticanalytic forwardforward resultresult forfor stationstation A2,A2, A4A4 toto A9A9 shownshown asas thethe blackblack solidsolid line;line; ((rightright)) The The resistivity resistivity model model corresponds corresponds to to the the response response (sold (sold line) line) displayed displayed in in the the left left panel. panel.

We used the same procedure to analyze the sounding curves from all 21 stations comprising the reduced SE Malta 2018 dataset and the additional 31 soundings from the field survey conducted during June and July 2019. Another unusual decay curve is found at station 432 (black squares, Figure7). At the late-time of this sounding, the observed signal decays significantly slower compared to neighboringFigure 6. stations, (left) 1D i.e.,analytic station forward 433, result which for station is located A2, A4 only to A9 15 shown m to as the the north. black solid The line; anomalous response may(right) be The due resistivity to the model effects corresponds of a localized to the highly-conductiveresponse (sold line) displayed body; in this the will left panel. be discussed later.

Figure 7. Decay curves of some measured G‐TEM soundings at the western section of study area. An unusual decay at station 432 denoted as black squares may be due to a localized highly‐ conductive body.

After investigating all of the decay curves, we observe certain systematics in the spatial variabilityFigureFigure 7.in the Decay7. Decay measured curves curves ofofresponses. some measured measured Over G ‐distancesTEM G-TEM soundings soundings of a at few the at westerntens the of western section meters, of section study for example,area. of study it is area.An An unusual unusual decay decay at atstation station 432 432 denoted denoted as asblack black squares squares may may be due be dueto a tolocalized a localized highly highly-‐ conductiveconductive body. body.

After investigating all of the decay curves, we observe certain systematics in the spatial variability in the measured responses. Over distances of a few tens of meters, for example, it is Water 2020, 12, 1566 11 of 22

Water 2020, 12, x FOR PEER REVIEW 11 of 23 After investigating all of the decay curves, we observe certain systematics in the spatial variability inshown the measured below that responses. the lateral Over changes distances in ofsubsurface a few tens resistivities of meters, for in example, the across it‐ isshore shown direction below that are themuch lateral stronger changes than in subsurfacethose in the resistivities alongshore in thedirection. across-shore As regards direction the are locations much stronger of soundings than those and insimilarity the alongshore of decay direction. patterns, As many regards of the the more locations recently of soundings acquired soundings and similarity are similar of decay to patterns, those of manythe earlier of the acquired more recently transects acquired A and soundings B. For example, are similar consider to those soundings of the earlier 430 acquiredand 429, transects which are A andsituated B. For 15 example, and 25 m consider south of soundings station B3, 430 respectively and 429, which (see Figure are situated 3). The 15 responses and 25 m from south these of station three B3,stations, respectively along (seewith Figure that of3). station The responses 428, can from be thesesorted three as one stations, group along due with to their that ofsimilar station decay 428, canpattern. be sorted The best as one‐fitting group 1D due model to their of these similar four decay stations, pattern. whose The best-ﬁttingresponse is 1D illustrated model of as these the fourthin stations,black line whose in Figure response 8, consists is illustrated of a three as the layered thin black‐earth line of in 5.5 Figure Ωm and8, consists 18.2 Ωm of resistivity a three layered-earth with 4 and of12 5.5 m Ωthicknesses,m and 18.2 respectively;Ωm resistivity with with the 4 andbasal 12 resistivity m thicknesses, of 1.8 respectively; Ωm. This model with theis displayed basal resistivity as the ofcolumn 1.8 Ωm. beneath This model station is B3 displayed in Figure as 9b. the column beneath station B3 in Figure9b.

FigureFigure 8.8.1D 1D forward forward modeling modeling result result for for station station 428, 428, 429, 429, 430 and 430 B3 and shown B3 shown as a black as a line black (see line column (see beneathcolumn B3beneath in Figure B3 in9b Figure for the 9b model.). for the model.).

From the 1-D forward modeling results, two pseudo-2D resistivity models have been constructed and they are depicted in Figure9. These models are obtained by merging, or “stitching”, the 1D forward model results from groups of adjacent stations. With regards to the alongshore profile shown at the top, the upper-layer resistivity value is constant and it exhibits no variation in thickness observed along the 150 m transect. In the very near surface, from the surface to 3–4 m depth, the uppermost layer represents a spatial average over a heterogeneous region and we do not attempt to interpret this layer. The second layer spans the depth range 4–19 m in the SE part of the profile, but the layer becomes thinner and slightly more conductive in the NW part. A huge contrast in vertical resistivity variations of maximum 0.1 Ωm beneath the sounding A1 compared with a neighboring sounding A2 is suggestive of structure with very low resistivity at depth, such as steel infrastructure. The lateral variations in resistivity of geological origin are much stronger in the across-shore transect, shown at the bottom. The top layer of this profile becomes slightly less resistive and thicker towards the coast. In contrast, the underlying resistive zone becomes thinner as the sounding location is located closer to the sea. Water 2020, 12, 1566 12 of 22 Water 2020, 12, x FOR PEER REVIEW 12 of 23

Figure 9. Stitched version of resistivity profiles obtained from 1D forward modeling results of the 2018 Figure 9. Stitched version of resistivity profiles obtained from 1D forward modeling results of the (a) alongshore Profile A and (b) across-shore Profile B surveys. The white line provides a rough guide 2018 (a) alongshore Profile A and (b) across‐shore Profile B surveys. The white line provides a rough to the geometry of the thinning of the freshwater lens towards the coast, where it becomes brackish to guide to the geometry of the thinning of the freshwater lens towards the coast, where it becomes mildly saltwater. brackish to mildly saltwater. In Figure 10, another set of pseudo-2D resistivity models, corresponding to TDEM profiles C and From the 1‐D forward modeling results, two pseudo‐2D resistivity models have been D (see Figure3), are obtained by combining 1D forward model results from the 2018 and 2019 datasets. constructed and they are depicted in Figure 9. These models are obtained by merging, or These models enable visualization of the resistivity structure in the western and northern parts of the “stitching”, the 1D forward model results from groups of adjacent stations. With regards to the study area. The model from profile C shown at the top (Figure 10a) is located ~30 m west of Profile A. alongshore profile shown at the top, the upper‐layer resistivity value is constant and it exhibits no Profile C runs NW–SE alongshore and intersects profile B at station B7 (Figure3). The resistivity model variation in thickness observed along the 150 m transect. In the very near surface, from the surface of this transect appears to be similar to that of Profile A. However, the resistivity values of the second to 3–4 m depth, the uppermost layer represents a spatial average over a heterogeneous region and and basal layers are higher in Profile C due to its greater distance inland, i.e., away from the seawater. we do not attempt to interpret this layer. The second layer spans the depth range 4–19 m in the SE The second layer of Profile C is also thicker compared to that of Profile A. Lateral heterogeneity of part of the profile, but the layer becomes thinner and slightly more conductive in the NW part. A resistivity at depth of ~17.5 m to 60 m can be observed in the SE part of this transect similar to that of huge contrast in vertical resistivity variations of maximum 0.1 Ωm beneath the sounding A1 Profile A beneath soundings 432 and 433. The across-shore resistivity distribution in the northern part compared with a neighboring sounding A2 is suggestive of structure with very low resistivity at of the study area, labeled Profile D, is shown in Figure 10b. Profile D is located 90 m northward from depth, such as steel infrastructure. The lateral variations in resistivity of geological origin are much the intersection of transects A and B. There is no significant change in either the thickness or resistivity stronger in the across‐shore transect, shown at the bottom. The top layer of this profile becomes of the uppermost structure of this profile as compared to Profile B. With respect to the middle, resistive slightly less resistive and thicker towards the coast. In contrast, the underlying resistive zone layer along Profile D, the shape is comparable to the resistive zones found in Profile B, except they are becomes thinner as the sounding location is located closer to the sea. less resistive and somewhat thinner. In Figure 10, another set of pseudo‐2D resistivity models, corresponding to TDEM profiles C and D (see Figure 3), are obtained by combining 1D forward model results from the 2018 and 2019 datasets. These models enable visualization of the resistivity structure in the western and northern parts of the study area. The model from profile C shown at the top (Figure 10a) is located ~30 m Water 2020, 12, x FOR PEER REVIEW 13 of 23

west of Profile A. Profile C runs NW–SE alongshore and intersects profile B at station B7 (Figure 3). The resistivity model of this transect appears to be similar to that of Profile A. However, the resistivity values of the second and basal layers are higher in Profile C due to its greater distance inland, i.e., away from the seawater. The second layer of Profile C is also thicker compared to that of Profile A. Lateral heterogeneity of resistivity at depth of ~17.5 m to 60 m can be observed in the SE part of this transect similar to that of Profile A beneath soundings 432 and 433. The across‐shore resistivity distribution in the northern part of the study area, labeled Profile D, is shown in Figure 10b. Profile D is located 90 m northward from the intersection of transects A and B. There is no significant change in either the thickness or resistivity of the uppermost structure of this profile as compared to Profile B. With respect to the middle, resistive layer along Profile D, the shape is Watercomparable2020, 12, 1566 to the resistive zones found in Profile B, except they are less resistive and somewhat13 of 22 thinner.

FigureFigure 10. 10.Stitched Stitched version version of of resistivity resistivity modelsmodels from ( a)) Profile Profile C C along along the the western western boundary boundary and and (b)( Profileb) Profile D in D the in northernthe northern part part of the of study the study site. Thesite. white The white line provides line provides a rough a guiderough toguide the geometry to the of thegeometry thinning of ofthe the thinning freshwater of the lens freshwater towards thelens coast, towards where the it coast, becomes where brackish it becomes to mildly brackish saltwater. to mildly saltwater. 4.2. D and 3D Scenarios 4.2. D and 3D Scenarios In the previous section, we used the analytic solution of the TDEM forward problem to determine stitchedIn 1D the resistivity previous depth-profilessection, we used across the the analytic SE Malta solution study of area. the TDEM In this section,forward weproblem use the to FE analysisdetermine to compute stitched frequency-domain1D resistivity depth responses‐profiles across of 2D the and SE 3D Malta models. study The area. time-domain In this section, response we is obtaineduse the FE by analysis splining to the compute frequency-domain frequency‐domain response responses evaluated of at2D each and of 3D the models. designated The discretetime‐ frequencies.domain response Subsequently, is obtained the by set splining of time-domain the frequency responses‐domain are response used as evaluated the input at from each which of the we developdesignated a series discrete of 2D frequencies. and 3D forward Subsequently, model iterative the set adjustments. of time‐domain The responses best 2D and are 3D used models as the that resultinput from from this which analysis we develop are then a further series of evaluated 2D and 3D and forward interpreted. model The iterative adjustments adjustments. are made The by best trial and2D error and since3D models insuffi cientthat result computational from this resourcesanalysis are are then available further to evaluated achieve an and automated interpreted. inversion The process. Since a single forward run takes ~14 h of CPU time on our computational platform, and an automated inversion would require many thousands of forward runs, even with a highly efficient algorithm it is envisioned that both coarse-grained and fine-grained massive parallelization are a prerequisite for a fully 3D inversion. Such algorithmic development is beyond the scope of this study, but is definitely recommended for future work. Figure 11 shows FE-calculated responses at two stations based on the fully 2-D model constructed from the stitched 1-D resistivity models shown in Figure9. The calculated response at station A7 obtains from the alongshore 2D resistivity model in Figure9a. This model allows spatial variations in resistivity only in the SE-NW direction. That criterion is kept for all soundings along Profile A. Similarly, the 2D lateral resistivity distribution used to compare with the observed soundings at each station along Profile B is based on the across-shore transect shown in Figure9b. The yellow dots in Figure 11, left, represent the field response actually measured at station A7. The modeling result of the Water 2020, 12, x FOR PEER REVIEW 14 of 23 adjustments are made by trial and error since insufficient computational resources are available to achieve an automated inversion process. Since a single forward run takes ~14 h of CPU time on our computational platform, and an automated inversion would require many thousands of forward runs, even with a highly efficient algorithm it is envisioned that both coarse‐grained and fine‐ grained massive parallelization are a prerequisite for a fully 3D inversion. Such algorithmic development is beyond the scope of this study, but is definitely recommended for future work. Figure 11 shows FE‐calculated responses at two stations based on the fully 2‐D model constructed from the stitched 1‐D resistivity models shown in Figure 9. The calculated response at station A7 obtains from the alongshore 2D resistivity model in Figure 9a. This model allows spatial variations in resistivity only in the SE‐NW direction. That criterion is kept for all soundings along Profile A. Similarly, the 2D lateral resistivity distribution used to compare with the observed Watersoundings2020, 12 at, 1566 each station along Profile B is based on the across‐shore transect shown in Figure14 of 9b. 22 The yellow dots in Figure 11, left, represent the field response actually measured at station A7. The modeling result of the alongshore 2D structure, computed using the 3D FE code, is marked as the alongshore 2D structure, computed using the 3D FE code, is marked as the solid line. Another sounding solid line. Another sounding at the intersection of the two transects, namely station B4, is displayed at the intersection of the two transects, namely station B4, is displayed in green diamonds in Figure 11, in green diamonds in Figure 11, right, with the corresponding across‐shore 2‐D model response right, with the corresponding across-shore 2-D model response shown by the solid line. shown by the solid line.

Figure 11. 2D modeling results of station A7 and B4 from left toto right.right. A computed step-ostep‐offﬀ voltage from 3D forward modeling code at cross-sectioncross‐section pointpoint ofof twotwo transectstransects isis shownshown asas aa blackblack line.line.

At the bottombottom ofof Figure Figure 12 12,, the the step-o step‐ffoffvoltage voltage response response as aas result a result of 3D of forward3D forward modeling modeling was wascomputed computed at station at station locations locations A7 and A7 B4. Theand 3DB4. model The 3D shown model at the shown top of at Figure the top 12 isof constructed Figure 12 byis constructedcombining the by 2D combining models from the 2D the models three transects, from the namely three transects, Profiles A, namely B (in Figure Profiles9) and A, CB (in (Figure Figure 10a). 9) andFor theC (Figure sake of better10a). For visualization, the sake of only better a local visualization, portion of the only complete a local 3D portion model of that the is complete indicative 3D of modelthe structure that is beneath indicative station of the A7 structure is illustrated beneath within station the modeling-domain A7 is illustrated limits within of the { 40 modeling m, 40 m},‐ − {domain40 m, 40limits m} and of {0{−40 m, 60m, m}40 inm}, the {− x,40 y andm, 40 z directions, m} and {0 respectively. m, 60 m} Partin the of thex, y model and z that directions, is above − respectively.ground surface Part up of to the 20 mmodel high isthat also is excludedabove ground for better surface visualization; up to 20 m the high size is of also 10 excluded10 m square for × TXbetter loop visualization; is shown for the scaling. size of The 10 complete × 10 m square 3D model TX representingloop is shown the for subsurface scaling. The structure complete beneath 3D modelSE Malta, representing covering a the surface subsurface area of structure 16,500 m 2beneath, is depicted SE Malta, in Figure covering 13. Some a surface of the area sounding of 16,500 points m2, isare depicted included in to Figure better indicate13. Some the of location the sounding and orientation points are of included the 3D model to better with respectindicate to the the location G-TEM andsurvey orientation layout. A of brief the sensitivity 3D model analysis with respect is provided to the in AppendixG‐TEM surveyB. layout. A brief sensitivity analysisThe is computed provided misfit in Appendix at each sounding B. location is plotted in terms of relative error, visualized using various circle sizes, for the 1D, 2D and 3D models. These misfit circles are shown in black, blue, and red, respectively (Figure 14). The misfits of the responses at gate 1 and 2 for all soundings are excluded from the display since the amplitude of the early-time responses is very large. The relative errors of the 2D model are shown only at the 21 stations of the reduced SE Malta 2018 dataset located along transects A and B. The reader should note that the misfit of the preferred 3D model at a given station may exceed the misfit of the 1D model at that station. The important point is that a single 3D model has been found that fits all the observations reasonably well, sometimes at the cost of locally increasing the misfit compared to a 1D model that strictly applies only to an individual station. The actual geoelectrical structure of the Earth is 3D rather than locally 1D beneath the G-TEM measurement stations. WaterWater2020 2020,,12 12,, 1566 x FOR PEER REVIEW 15 of 2223

FigureFigure 12. 12. ((aa)) 3D 3D resistivity resistivity model model showing showing the the subsurface subsurface geoelectrical geoelectrical distribution distribution beneath beneath A7 andA7 and B4; (B4;b) The (b) The computed computed step-o stepﬀ voltage‐off voltage according according to the to resistivity the resistivity model model in (a) in is (a) displayed is displayed as a black as a black line. line. Water 2020, 12, 1566 16 of 22 Water 2020, 12, x FOR PEER REVIEW 16 of 23

FigureFigure 13. The 13. preferred The preferred 3D model3D model representing representing the the subsurface subsurface geoelectrical geoelectrical structure structure beneath beneath study study siteWater in 2020site SE , Malta. in12 ,SE x FOR Malta. PEER REVIEW 17 of 23

The computed misfit at each sounding location is plotted in terms of relative error, visualized using various circle sizes, for the 1D, 2D and 3D models. These misfit circles are shown in black, blue, and red, respectively (Figure 14). The misfits of the responses at gate 1 and 2 for all soundings are excluded from the display since the amplitude of the early‐time responses is very large. The relative errors of the 2D model are shown only at the 21 stations of the reduced SE Malta 2018 dataset located along transects A and B. The reader should note that the misfit of the preferred 3D model at a given station may exceed the misfit of the 1D model at that station. The important point is that a single 3D model has been found that fits all the observations reasonably well, sometimes at the cost of locally increasing the misfit compared to a 1D model that strictly applies only to an individual station. The actual geoelectrical structure of the Earth is 3D rather than locally 1D beneath the G‐TEM measurement stations.

FigureFigure 14. Misﬁt 14. Misfit of 1D, of 1D, 2D 2D and and 3D 3D models, models, from from left left to right. Size Size of of circle circle represents represents a relative a relative error error for eachfor sounding.each sounding. Only Only 21 points21 points of of misﬁts misfits are are shown shown for 2D 2D model model along along 2018 2018 dataset. dataset.

5. Discussion The results presented in this study suggest that the structure of the mean sea‐level groundwater aquifer near the shore in SE Malta exhibits a lenticular shape, with decreasing thickness towards the coast. The combination of TDEM models derived from the summer 2018 and 2019 datasets shows distinct high‐resistivity zones. These are interpreted as the signature of a brackish water‐saturated geological medium, in this case corresponding to the LCL formation hosting the mean sea‐level groundwater body. Based on the preferred 3D TDEM model in Figure 13, the top layer up to 5 m deep is interpreted as the overlaying Globigerina Limestone and there is no geophysical indication of freshwater in this low‐resistivity formation. We also find that the depth to the top of LCL and water table in the study area is 4–5 m. Our study is in good agreement with a regional groundwater modeling study (MARSOL, 2015) of the South Malta region which points out that the elevation of the top of the formation holding fresh groundwater is in the range +20 to −20 m with reference to mean sea level [37]. The zones of high resistivity below the depth of 4–5 m in the 2D and 3D models are indicative of a (moderately brackish) freshwater‐bearing formation with resistivity in the range 𝜌 ~10–100 Ωm (i.e., the purple‐blue‐cyan colors in Figure 13). The steeper base compared to the gentler top of the groundwater body is consistent with the geometry of a Ghyben‐Herzberg‐type lens. Below the freshwater region, from depths ~13–22 m down to the TDEM depth of investigation at 60 m, the underlying rocks situated beneath sea level are much less resistive, attaining values 𝜌 ~1.25–2.5 Ωm (i.e., the green‐yellowish green colors in Figure 13). These low resistivity (conductive) zones are indicative of a seawater‐saturated formation. The shallow resistive freshwater lens sits on top of a more conductive formation, the latter being indicative of lateral landward movement of saltwater, i.e., intrusion. The boundary between the zones of high and low resistivity indicates the presence of the interface or transition zone along the two across‐shore transects. Within the areas closest to the shoreline a mixing zone of freshwater and seawater appears to be present. Zones of moderate resistivity ρ ~5 Ωm are observed along the northeastern parts of the across‐shore transects by the coast and this could be indicative of brackish groundwater. Water 2020, 12, 1566 17 of 22

5. Discussion The results presented in this study suggest that the structure of the mean sea-level groundwater aquifer near the shore in SE Malta exhibits a lenticular shape, with decreasing thickness towards the coast. The combination of TDEM models derived from the summer 2018 and 2019 datasets shows distinct high-resistivity zones. These are interpreted as the signature of a brackish water-saturated geological medium, in this case corresponding to the LCL formation hosting the mean sea-level groundwater body. Based on the preferred 3D TDEM model in Figure 13, the top layer up to 5 m deep is interpreted as the overlaying Globigerina Limestone and there is no geophysical indication of freshwater in this low-resistivity formation. We also find that the depth to the top of LCL and water table in the study area is 4–5 m. Our study is in good agreement with a regional groundwater modeling study (MARSOL, 2015) of the South Malta region which points out that the elevation of the top of the formation holding fresh groundwater is in the range +20 to 20 m with reference to mean sea level [37]. The zones of high − resistivity below the depth of 4–5 m in the 2D and 3D models are indicative of a (moderately brackish) freshwater-bearing formation with resistivity in the range ρ ~10–100 Ωm (i.e., the purple-blue-cyan colors in Figure 13). The steeper base compared to the gentler top of the groundwater body is consistent with the geometry of a Ghyben-Herzberg-type lens. Below the freshwater region, from depths ~13–22 m down to the TDEM depth of investigation at 60 m, the underlying rocks situated beneath sea level are much less resistive, attaining values ρ ~1.25–2.5 Ωm (i.e., the green-yellowish green colors in Figure 13). These low resistivity (conductive) zones are indicative of a seawater-saturated formation. The shallow resistive freshwater lens sits on top of a more conductive formation, the latter being indicative of lateral landward movement of saltwater, i.e., intrusion. The boundary between the zones of high and low resistivity indicates the presence of the interface or transition zone along the two across-shore transects. Within the areas closest to the shoreline a mixing zone of freshwater and seawater appears to be present. Zones of moderate resistivity ρ ~5 Ωm are observed along the northeastern parts of the across-shore transects by the coast and this could be indicative of brackish groundwater. In order to assess the groundwater quality implications of our model, we calculate the bulk resistivity of the fluid-saturated rock using Archie’s law [38] for various porosities of limestone assuming that all pore spaces are filled with freshwater with resistivity of 2 Ωm. This latter value is equal to the water resistivity found in a well located 2.5 km inland. For porosities of 10% and 15% we find 126.2 and 60.8 Ωm, respectively, as the formation bulk resistivity. These values of estimated resistivity are slightly higher than the range of those in the 3-D TDEM model (ρ ~10–100 Ωm). In addition, we have estimated bulk resistivity for saturated limestone filled with seawater of 0.2 Ωm with 10%, and 15% porosities. These are 12.6 and 6.1 Ωm, respectively, which is also slightly higher than our model’s prediction of low resistivity seawater-saturated formations of 1.25–2.5 Ωm. As we move inland, our values are consistent with the borehole’s fluid resistivity saturating a formation of 10 to 15% porosity. Closer to the shoreline, the TDEM bulk resistivity is lower, reflecting more brackish water. Thus, the groundwater freshens as we move inland. Of course, Archie’s law is not a perfect petrophysical model for the fractured limestone lithology, since the law was founded on lab measurements made on clean sandstone cores, but an Archie-type calculation should be approximately correct. To assess confidence in the spatial structure of our model, we also consider which of the model slabs indicative of the freshwater-bearing formation are best resolved based on the sensitivity analysis (see AppendixB for details). At the lower frequency of 100 Hz, the best-resolved slab is slab 3; whereas the responses from slabs 5, 6 and 7 are more sensitive to perturbations in their resistivity than the responses of slabs 1 and 2. At the high frequency 1 MHz, the misfit-change distribution indicates that changing a slab’s resistivity affects only the sounding that is situated directly over that slab. Slab 6 seems to be the most well-resolved slab at the intermediate frequency 31.6 kHz. Slabs located further inland appear to be not as well resolved as those closer to the sea. The latter are thin and more conductive relative to the thicker, more resistive inland slabs and it is well known that terrestrial TDEM better resolves thin conductive layers. Water 2020, 12, 1566 18 of 22

We do not have sufficient data coverage to infer a possible offshore extension of the freshwater aquifer at the SE Malta study site. The landward encroachment of seawater decreases the resistivities of the near-coastline region and possibly interacts with the fresh groundwater of the MSLA. There are unpublished ground-penetrating radar (GPR) data that appear to show infiltrated meteoric water trapped in fractures above water table in some areas of the study site [39]. More across-shore measurements throughout Malta are recommended in order to investigate the lateral subsurface geoelectrical variation in the direction perpendicular to the coast.

6. Conclusions This study demonstrates the utility of the TDEM geophysical method along with 1D, 2D and 3D forward modeling as a means to study coastal freshwater aquifers in water-scarce regions. Here we image the geometry of the onshore aquifer within the permeable Lower Coralline Limestone formation along the SE Malta coast. Our results show 2D and 3D resistivity models found by iterative adjustments of FE forward modeling. The final preferred 3D model provides information to depth of 60 m, covering an area of ~16,500 m2 and shows diagnostic spatial variations in subsurface electrical resistivity. The geophysical modeling provides a basis for determining important characteristics of the MSLA that fit our observations, namely the decreasing thickness of fresh groundwater bodies towards the coastline. Zones of fresh groundwater have been identified, but these are located preferentially inland from the coast. Thus, there is no indication from the electromagnetic data of a robust offshore extension of the MSLA at this location. However, it is argued that method that we used can be applied across the entire Maltese archipelago to better constrain the geometry, dimensions and distribution of terrestrial and coastal aquifers providing valuable information for future water management of the stressed groundwater reserves of Malta.

Author Contributions: Conceptualization, A.M., B.A.W., P.P. and M.E.E.; P.P. prepared the manuscript with contributions from all co-authors; M.E.E., A.M., Z.F. and B.A.W. collected the G-TEM data during summer 2018 fieldwork; P.P., M.E.E., A.M. and B.A.W. collected the 2019 dataset; P.P. analyzed the data with supervision from M.E.E.; M.E.E., A.M., A.H. and M.J. contributed to the discussion on the modeling results. All authors have read and agree to the published version of the manuscript. Funding: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 677898 MARCAN). Acknowledgments: The authors are grateful to Rob Evans for helping out in the field work in June, 2019. We would like to thank the two anonymous reviewers for valuable comments that have greatly improved the paper. We also thank GEOMAR for travel and equipment transportation support during the SMART summer school 2019 at the University of Malta. SMART is funded by GEOMAR and the Helmholtz Association of German Research Centres – European Partnering Initiative. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A. Receiver Gates and Time The G-TEM receiver records the characteristics of transient response by sampling it at 20 or 30 sequential time intervals or gates. The gates are logarithmically-spaced times that ﬁll the measurement period and their widths (separation) exponentially increase with time [40]. Table A1 lists the center time of each gate that occurs after TX shut-oﬀ for repetition rate of 237.5 Hz at 20-gates acquisition mode. Water 2020, 12, 1566 19 of 22

Table A1. Gate center times.

Time Time Gate Gate (µs) (µs) 1 6.813 11 77.94 2 8.688 12 99.38 3 11.13 13 126.7 4 14.19 14 166.4 5 18.07 15 206 6 23.06 16 262.8 7 29.44 17 355.2 8 37.56 18 427.7 9 47.94 19 545.6 10 61.13 20 695.9

Appendix B. Sensitivity Analysis It is of interest to examine which of the slabs indicative of the freshwater-bearing formation responds most sensitively to the time-domain electromagnetic excitation. Conducting a sensitivity analysis provides information about how small perturbations to an independent variable, in this case a slab resistivity, affect the 3D model’s overall misfit. Herein, the resistivity of each slab is subjected to a 5% decrease and the 3D response re-computed, with only one slab changed at a time. We compute the vertical magnetic fields at three different frequencies to determine the changes in subsequent responses after each slab’s resistivity is changed compared with the responses of the unperturbed preferred model shown in Figure 13. The choices of 100 Hz, 31.6 kHz, and 10 MHz generate low, medium, and high frequency responses, respectively. Seven slabs with various resistivities ranging from 8.3 to 100 Ωm are chosen and the corresponding seven sounding locations on the surface nearest the center of each slab are selected for monitoring the change of computed responses (see Figure A1). For example, station B7 is underlain by slab 1, station B4 overlies slab 2, station B3 is above slab 3, and so on. The computed misfit resulting from a model that includes a perturbation in a slab’s resistivity is displayed in terms of relative change, illustrating using a color plot for the three different frequencies in Figure A2. Water 2020, 12, x FOR PEER REVIEW 20 of 23

Figure A1. FigureIllustration A1. Illustration of the of location the location of of selected selected slabs slabs (numbered (numbered 1–7) that 1–7) are thatsuggestive are suggestiveof a of a water‐bearing formation, and the TDEM sounding locations where the sensitivity analysis is water-bearingperformed. formation, Value and of unperturbed the TDEM resistivity sounding is shown locations for each where slab. the sensitivity analysis is performed. Value of unperturbed resistivity is shown for each slab. At low frequency (100 Hz), Figure A2 top left, the changes in frequency‐domain responses at each station are mainly due to the directly underneath slab and to the neighboring slabs. This is indicated by the larger values of percentage misfit mainly along the diagonal of the plot. An exception is the change caused by decreasing in resistivity of slab 1 that did not appreciably affect the misfit at any of the 7 stations. Surprisingly, the sounding 494, beneath slab 5, is most sensitive to the decrease of resistivity of slab 3 at frequency of 100 Hz. At moderate frequency (31.6 kHz), Figure A2 top right, slab 1 has a minor impact on the data if its resistivity decreases. The misfit plot shows how the change in one slab’s resistivity affects almost all the surrounding stations by different amounts. Moreover, the change in resistivity of slab 6 has a large effect on observed responses at the soundings A16 and 484, located above slabs 6 and 7, respectively. At high frequency 10 MHz, bottom left of Figure A2, the misfit‐change distribution indicates that decreasing a slab’s resistivity is likely to affect only the sounding that situated over that slab. This result is not surprising since the footprint of a TDEM sounding is smallest at high frequencies. Water 2020, 12, 1566 20 of 22

At low frequency (100 Hz), Figure A2 top left, the changes in frequency-domain responses at each station are mainly due to the directly underneath slab and to the neighboring slabs. This is indicated by the larger values of percentage misfit mainly along the diagonal of the plot. An exception is the change caused by decreasing in resistivity of slab 1 that did not appreciably affect the misfit at any of the 7 stations. Surprisingly, the sounding 494, beneath slab 5, is most sensitive to the decrease of resistivity of slab 3 at frequency of 100 Hz. At moderate frequency (31.6 kHz), Figure A2 top right, slab 1 has a minor impact on the data if its resistivity decreases. The misfit plot shows how the change in one slab’s resistivity affects almost all the surrounding stations by different amounts. Moreover, the change in resistivity of slab 6 has a large effect on observed responses at the soundings A16 and 484, located above slabs 6 and 7, respectively. At high frequency 10 MHz, bottom left of Figure A2, the misfit-change distribution indicates that decreasing a slab’s resistivity is likely to affect only the sounding that situated over that slab. This result is not surprising since the footprint of a TDEM sounding is smallest at high frequencies. Water 2020, 12, x FOR PEER REVIEW 21 of 23

Figure A2.A2. ResponseResponse misfitsmisfits for 100100 Hz,Hz, 31.631.6 kHzkHz andand 1010 MHz.MHz. ColorColor plotplot denotesdenotes aa relativerelative changechange inin percentage misfitmisfit forfor examplesexamples of seven soundings after each slab’s resistivity decreases by 5%. TheThe whitewhite regionregion inin eacheach plotplot signifiessignifies thatthat therethere isis nono eeffectffect fromfrom perturbationperturbation toto aa particularparticular slabslab detected byby that that sounding sounding location. location. The The misfits misfits over 0.25%over at0.25% each frequencyat each frequency are considered are considered significant bysignificant rough estimation, by rough andestimation, this will and affect this the will 1D, affect 2D and the 3D 1D, modelling 2D and 3D misfits modelling of transient misfits EM of responses transient inEM Figure responses 14. in Figure 14.

References

1. Post, V.E.; Groen,Groen, J.; J.; Kooi, Kooi, H.; H.; Person, Person, M.; M.; Ge, Ge, S.; S.; Edmunds, Edmunds, W.M. W.M. O Offshoreﬀshore fresh fresh groundwater groundwater reserves reserves as as a globala global phenomenon. phenomenon.Nature Nature2013 2013,, 504 504, 71–78., 71–78. [CrossRef ][PubMed] 2. Jones, E.;E.; Qadir, Qadir, M.; M.; van van Vliet, Vliet, M.T.H.; M.T.H.; Smakhtin, Smakhtin, V.; Kang, V.; S.M.Kang, The S.M. state The of desalination state of desalination and brine production: and brine Aproduction: global outlook. A globalSci. outlook. Total Environ. Sci. Total2019 Environ., 657, 1343–1356. 2019, 657, [ CrossRef1343–1356.][ PubMed] 3. Archie, G.E.G.E. Electrical Electrical Resistivity Resistivity Log Log as anas Aidan Aid in Determining in Determining Some Some Reservoir Reservoir Characteristics. Characteristics.Trans. AIMETrans. 1942AIME, 146 1942,, 54–67. 146, 54–67. [CrossRef ] 4. Nabighian, M.N.; Macnae, J.C. Time Domain Electromagnetic Prospecting Methods. In Investigations in Geophysics No 3. Electromagnetic Methods in Applied Geophysics; Nabighian, M.N., Ed.; Society of Exploration Geophysicists: Tulsa, OK, USA, 1991; pp. 427–514. 5. Everett, M.E.; Chave, A.D. On the physical principles underlying electromagnetic induction. Geophysics 2019, 84, w21–w32. 6. Everett, M.E. Theoretical Developments in Electromagnetic Induction Geophysics with Selected Applications in the Near Surface. Surv. Geophys. 2012, 33, 29–63. 7. Fitterman, D.V. Tools and techniques: Active‐source electromagnetic methods. In Resources in the Near‐ Surface Earth, Treatise on Geophysics; Slater, L., Ed.; Elsevier B. V.: Amsterdam, Netherlands, 2015; Volume 11, pp. 295–333. 8. Yogeshwar, P.; Tezkan, B. Two‐dimensional basement modeling of central loop transient electromagnetic data from the central Azraq basin area, Jordan. J. Appl. Geophys. 2017, 136, 198–210. 9. Fitterman, D.V.; Stewart, M.T. Transient electromagnetic sounding for groundwater. Geophysics 1986, 51, 995–1005. 10. Kafri, U.; Goldman, M.; Lang, B. Detection of subsurface brines, freshwater bodies and the interface configuration in‐between by the time domain electromagnetic method in the Dead sea rift, Israel. Environ. Geol. 1997, 31, 42–49. Water 2020, 12, 1566 21 of 22

4. Nabighian, M.N.; Macnae, J.C. Time Domain Electromagnetic Prospecting Methods. In Investigations in Geophysics No 3. Electromagnetic Methods in Applied Geophysics; Nabighian, M.N., Ed.; Society of Exploration Geophysicists: Tulsa, OK, USA, 1991; pp. 427–514. 5. Everett, M.E.; Chave, A.D. On the physical principles underlying electromagnetic induction. Geophysics 2019, 84, w21–w32. [CrossRef] 6. Everett, M.E. Theoretical Developments in Electromagnetic Induction Geophysics with Selected Applications in the Near Surface. Surv. Geophys. 2012, 33, 29–63. [CrossRef] 7. Fitterman, D.V. Tools and techniques: Active-source electromagnetic methods. In Resources in the Near-Surface Earth, Treatise on Geophysics; Slater, L., Ed.; Elsevier B. V.: Amsterdam, The Netherlands, 2015; Volume 11, pp. 295–333. 8. Yogeshwar, P.; Tezkan, B. Two-dimensional basement modeling of central loop transient electromagnetic data from the central Azraq basin area, Jordan. J. Appl. Geophys. 2017, 136, 198–210. [CrossRef] 9. Fitterman, D.V.; Stewart, M.T. Transient electromagnetic sounding for groundwater. Geophysics 1986, 51, 995–1005. [CrossRef] 10. Kafri, U.; Goldman, M.; Lang, B. Detection of subsurface brines, freshwater bodies and the interface configuration in-between by the time domain electromagnetic method in the Dead sea rift, Israel. Environ. Geol. 1997, 31, 42–49. [CrossRef] 11. Danielsen, J.E.; Auken, E.; Jørgensen, F.; Søndergaard, V.; Sørensen, K.I. The application of the transient electromagnetic method in hydrogeophysical surveys. J. Appl. Geophys. 2003, 53, 181–198. [CrossRef] 12. Siemon, B.; Christiansen, A.V.; Auken, E. A review of heliopter-borne electromagnetic methods for groundwater exploration. Near Surf. Geophys. 2009, 7, 629–646. [CrossRef] 13. Costabel, S.; Siemon, B.; Houben, G.; Günther, T. Geophysical investigation of a freshwater lens on the island of Langeoog, Germany—Insights from combined HEM, TEM and MRS data. J. Appl. Geophys. 2017, 136, 231–245. [CrossRef] 14. Kalisperi, D.; Kouli, M.; Vallianatos, F.; Soupios, P.; Kershaw, S.; Lydakis-Simantiris, N. A Transient ElectroMagnetic (TEM) Method Survey in North-Central Coast of Crete, Greece: Evidence of Seawater Intrusion. Geosciences 2018, 8, 107. [CrossRef] 15. Morgan, L.K.; Werner, A.D.; Patterson, A.E. A conceptual study of offshore fresh groundwater behaviour in the Perth Basin (Australia): Modern salinity trends in a prehistoric context. J. Hydrol. Reg. Stud. 2018, 19, 318–334. [CrossRef] 16. Yu, X.; Michael, H.A. Offshore Pumping Impacts Onshore Groundwater Resources and Land Subsidence. Geophys. Res. Lett. 2019, 46, 2553–2562. [CrossRef] 17. Pedley, H.M.; House, M.R.; Waugh, B. The geology of Malta and Gozo. Proc. Geol. Ass. 1976, 87, 325–341. [CrossRef] 18. Micallef, A.; Foglini, F.; Le Bas, T.; Angeletti, L.; Maselli, V.; Pasuto, A.; Taviani, M. The submerged paleolandscape of the Maltese Islands: Morphology, evolution and relation to Quaternary environmental change. Mar. Geol. 2013, 335, 129–147. [CrossRef] 19. Directorate, O.E. Geological Map of the Maltese Islands;Office of the Prime Minister: Valletta, Malta, 1993. 20. Illies, J.H. Graben formation—The Maltese Islands, a case study. Tectonophysics 1981, 73, 151–168. [CrossRef] 21. Galdies, C. The Climate of Malta: Statistics, Trends and Analyses 1951–2010; National Statistics Office: Valletta, Malta, 2013. 22. FAO. Malta Water Resources Review; FAO: Rome, Italy, 2006. Available online: http://www.fao.org/3/a-a0994e.pdf (accessed on 18 February 2020). 23. Stuart, M.E.; Maurice, L.; Heaton, T.H.E.; Sapiano, M.; Micallef Sultana, M.; Gooddy, D.C.; Chilton, P.J. Groundwater residence time and movement in the Maltese islands—A geochemical approach. Appl. Geochem. 2010, 25, 609–620. [CrossRef] 24. MARSOL. Demonstrating Managed Aquifer Recharge as a Solution to Water Scarcity and Drought Characterisation of the Sea-Level Aquifer System in the Malta South Region; Institution of Applied Geosciences: Darmstadt, Germany, 2016. Available online: http://www.marsol.eu/files/marsol_d10-4_malta-groundwater-model.pdf (accessed on 14 January 2020). 25. Bakalowicz, M.; Mangion, J. The limestone aquifers of Malta: Their recharge conditions from isotope and chemical surveys. Hydrology of the Mediterranean and Semiarid Regions (Proceedings of an international symposium held at Montpellier. Int. Assoc. Hydrol. Sci. Publ. 2003, 278, 49–54. Water 2020, 12, 1566 22 of 22

26. Malta Environment and Planning Authority and the Malta Resources Authority. The Water Catchment Management Plan for the Maltese Islands; Malta Environment and Planning Authority and the Malta Resources Authority: Marsa, Malta, 2011. Available online: https://era.org.mt/en/Documents/1st%20WCMP_final.pdf (accessed on 16 January 2020). 27. Mangion, J.; Sapiano, M. The Mean Sea Level Aquifer, Malta and Gozo. In Natural Groundwater Quality; Blackwell Publishing: Ames, IA, USA, 2008; pp. 404–420. 28. BRGM. Study of the Fresh Water Resources of Malta; Appendix 7: Water Quality and Environmental Aspects, R 33691 EAU 4S 91; BRGM: Orleans, France, 1991. 29. Malta Environment and Planning Authority. Minerals Subject Plan for the Maltese Islands 2002; Entec UK Ltd.: London, UK, 2003. 30. Spies, B.R. Depth of investigation in electromagnetic sounding methods. Geophysics 1989, 54, 872–888. [CrossRef] 31. Constable, S.C.; Parker, R.L.; Constable, C.G. Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics 1987, 52, 289–300. [CrossRef] 32. Ward, S.H.; Hohmann, G.W. Electromagnetic Theory for Geophysical Applications, in Electromagnetic Methods in Applied Geophysics Theory. Soc. Explor. Geophys. 1988, 1, 131–311. 33. Everett, M.E. Near-Surface Applied Geophysics; Cambridge University Press: Cambridge, UK, 2013. 34. Chave, A.D. Numerical integration of related Hankel transforms by quadrature and continued fraction expansion. Geophysics 1983, 48, 1671–1686. [CrossRef] 35. Badea, E.A.; Everett, M.E.; Newman, G.A.; Biro, O. Finite-element analysis of controlled-source electromagnetic induction using Coulomb-gauged potentials. Geophysics 2001, 66, 786–799. [CrossRef] 36. Stalnaker, J.L.; Everett, M.E.; Benavides, A.; Pierce, C.J. Mutual induction and the effect of host conductivity on the EM induction response of buried plate targets using 3-D finite-element analysis. IEEE Trans. Geosci. Remote Sens. 2006, 44, 251–259. [CrossRef] 37. MARSOL. Demonstrating Managed Aquifer Recharge as a Solution to Water Scarcity and Drought Characterisation of the Sea-Level Aquifer System in the Malta South Region; Institution of Applied Geosciences: Darmstadt, Germany, 2015. Available online: http://www.marsol.eu/files/marsol_d10-1_msla-characterisation.pdf (accessed on 11 January 2020). 38. Fofonoff, N.P.; Millard, J.R.C. Algorithms for the computation of fundamental properties of seawater. In UNESCO Technical Papers in Marine Sciences; UNESCO: Paris, France, 1983; Volume 44. 39. Enzo Rizzo. Personal communication. Available online: https://hyfrew.wordpress.com/ (accessed on 1 May 2020). 40. Geonics. G-TEM Operating Manual; Geonics Limited: Mississauga, ON, Canada, 2016.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).