Heterogeneity of the East Thessaly Aquifer System in Greece’

‘Geostatistical Simulation of hydrofacies heterogeneity of the East Thessaly Aquifer System in Greece’

A dissertation presented by

Maria I. Bolgkoranou

for the degree of Master of Science (M.Sc.)

in the subject of

Geostatistics

Thessaloniki, Greece

June, 2017

Inter-University Master of Science Program

‘Exploration & Exploitation of Hydrocarbons’

GEOSTATISTICAL SIMULATION OF HYDROFACIES HETEROGENEITY OF THE EAST THESSALY AQUIFER SYSTEM IN GREECE

Maria Bolgkoranou: Mining Engineer, M.Sc./M.Eng.

Scientific committee:

Konstantinos Modis: Associate Professor, National Technical University of Athens (Supervisor)

Andreas Georgakopoulos: Professor, Aristotle University of Thessaloniki

Konstantinos Voudouris: Associate Professor, Aristotle University of Thessaloniki

Thessaloniki, Greece

June, 2017

The copyright of this thesis rests with author. No quotation from it should be published without author’s permission and information derived from it should be acknowledged.

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Acknowledgements

I would first like to thank my supervisor Dr. Konstantinos Modis, Associate Professor of School of Mining and Metallurgical Engineering at National Technical University of Athens for the continuous support of my M.Sc. thesis. His guidance was valuable throughout the research and writing of this thesis. He allowed this dissertation to be my own work but steered me in the right direction whenever I needed it.

My sincere thanks also goes to Dr. Andreas Georgakopoulos, Professor of School of Geology at Aristotle University of Thessaloniki, for his continuous support and help during the last two years.

Furthermore, I would like to thank Dr. Konstantinos Voudouris, Associate Professor of School of Geology at the Aristotle University of Thessaloniki, for his important remarks and participation to the scientific committee.

Beside my professors, I would like to express my gratitude to Dr. Daphne Sideri, for her help during the research procedure.

Last but not least, I would like to thank my family for their encouragement and support all of these years.

Abstract

In this study the spatial differentiation of hydrofacies was investigated in the alluvial aquifer system of East Thessaly basin in Greece. The alluvial deposits of this basin constitute a system of unconfined shallow aquifers which extend in the upper layers, while successive confined-artesian aquifers are developed in the deep permeable layers. This system, besides the percolated surface water, is supplied by water through lateral infiltration from karstic aquifers in alpine carbonate formations that outcrop along the margins of the basin. The overexploitation of the aquifers in the area during the last decades led to the manifestation of land subsidence phenomena, with extended damages in certain sites. The Civil Protection Agency of Greece and various research institutions are continuously involved in managing environmental hazards and planning future development of damaged areas. This action requires the knowledge of the characteristics of subsoil down to a certain depth. Within this framework, Plurigaussian Simulation techniques were applied to a set of borehole data from that basin, in order to simulate the alluvial hydrofacies. The results show a spatial differentiation regarding the facies proportions. According to the output model, the biggest part is covered by Clay (CL), which is definite a factor of subsidence phenomena. Especially, in certain North and NE parts (Giannouli, Melissochori and Omorfochori villages), several central areas (Nikaia and Halki villages) and a South-eastern district (Kileler village) of the basin, where the presence of clay dominates, there is high possibility of subsidence phenomena to be developed. Furthermore, according to the output of the model, uplift of the Basement is occurred in many parts of the basin, especially in the central and SE section. Larissa city appears stable as its geological background is mostly Basement. The possibility of these parts to develop subsidence phenomena is confirmed by observations that have been made in the area with Persistent Scatterer Interferometry (PSI) the revolutionary remote sensing technique of Persistent Scatterer Interferometry (PSI). Moreover, Sand and Gravel (SG) facies create a continuous internal architecture and, as permeable facies, can generate channels in which the water can flow. This characteristic is beneficial to the cultivation and irrigation of the land.

Περίληψη

Σκοπός της παρούσας εργασίας είναι η μελέτη της χωρικής κατανομής των υδροφάσεων στο αλλουβιακό σύστημα του υδροφόρου ορίζοντα στην λεκάνη της Ανατολικής Θεσσαλίας. Τα αλλουβιακά ιζήματα της λεκάνης συνιστούν ένα σύστημα ελεύθερων, ρηχών υδροφορέων που επεκτείνονται έως τα πάνω επίπεδα, ενώ αντίστοιχοι αρτεσιανοί υδροφορείς αναπτύσσονται στα βαθύτερα στρώματα. Αυτό το σύστημα, εκτός από επιφανειακή κατείσδυση των νερών, τροφοδοτείται επίσης πλευρικά από καρστικούς υδροφόρους σε αλπικούς ανθρακικούς σχηματισμούς που βρίσκονται κατα μήκος των περιθωρίων της λεκάνης.

H διαρκής υπεράντληση του υδροφόρου ορίζοντα την τελευταια δεκαετία, οδήγησε στην ανάπτυξη φαινομένων καθίζησης σε πολλές περιοχές κατα μήκος της λεκάνης. Η περιοχή της Ανατολικής Θεσσαλίας αποτελεί την μεγαλύτερη αγροτική περιοχή στην Ελλάδα. Η συνεχής άντληση νερού μέσω των υδρογεωτρήσεων και η κατανάλωση μεγάλης ποσότητας νερού λόγω άρδρευσης σε συνδυασμό με την παρουσία αργίλου οδήγησαν σε φαινόμενα καθιζήσεων. Η Υπηρεσία Πολιτικής Προστασίας καθώς και άλλοι οργανισμοί, μελετούν συστηματικά την περιοχή και εκτιμούν την πιθανότητα περαιτέρω ανάπτυξης καθιζήσεων.

Για το σκοπό αυτό, κρίνεται απαραίτητη η δημιουργία του παρόντος γεωλογικού μοντέλου, καθώς και η διερεύνηση της επικοινωνίας μεταξύ των υδροπερατών σχηματισμών. Εντός αυτού του πλαισίου, εφαρμόστηκε η μέθοδος της «Πολυ- γκαουσσιανής Προσομοιώσης» σε 149 δείγματα από 14 γεωτρήσεις, έτσι ώστε να δημιουργηθεί το γεωλογικό μοντέλο. Η Προσομοίωση πραγματοποιήθηκε με το γεωστατιστικό λογισμικό ISATIS, της εταιρίας Geovariances.

Το γεωλογικό μοντέλο που δημιουργήθηκε έδειξε πως η παρουσία αργίλου είναι αισθητή και κυριαρχεί σε όλη την λεκάνη. Tα αργιλικά εδάφη, λόγω της ικανότητας που έχουν να συγκρατούν το νερό και να διαστέλλονται και στην συνέχεια λόγω της υπεράντλησης του

νερού να συρρικνώνονται και να σπάνε αποτελούν την βασικότερη αιτία των καθιζήσεων.

Ειδικότερα, σύμφωνα με το μοντέλο, η παρουσία της αργίλου είναι κυρίαρχη στο Βόρειο και Βορειοανατολικό και κεντρικό τμήμα της λεκάνης. Συγκεκριμένα τα χωριά: Γιάννουλης, Μελισσοχώρι και Ομορφοχώρι στο Βόρειο τμήμα, καθώς και τα χωριά: Χάλκη και Νίκαια στο κεντρικό τμήμα κινδυνεύουν από καθιζήσεις, καθώς η παρουσία της αργίλου είναι ιδιαίτερα έντονη. Από την άλλη πλευρά, σε πολλά τμήματα της λεκάνης-όπως στο κεντρικό και νότιο-φαίνεται η ανύψωση του υποβάθρου έως την επιφάνεια. Η πόλη της Λάρισας φαίνεται να να είναι ευσταθής καθώς είναι ανεπτυγμένη πάνω σε σκληρούς σχηματισμούς υποβάθρου.

Τα αποτελέσματα του μοντέλου καθώς και οι εκτιμήσεις των καθιζήσεων επιβεβαιώνονται από τις παρατηρήσεις μετακίνησης του εδάφους που έχουν πραγματοποιηθεί μέσω Persistent Scatterer Interferometry (PSI) από την υπηρεσία Terrafirma της Ευρωπαικής Διαστημικής Υπηρεσίας (ESA). Σύμφωνα με τα αποτελέσματα των παρατηρήσεων των εδαφικών μετακινήσεων, τα χωριά Χάλκη, Νίκαια και Γιάννουλη έχουν υποστεί καθιζήσεις. Η Λάρισα δεν παρουσίασε φαινόμενα καθιζήσεων.

Τέλος, οι φάσεις του αμμοχάλικου και άλλων υδροπερατών σχηματισμών φαίνεται να επικοινωνούν μεταξύ τους και όχι να είναι διασκορπισμένες σ’ όλη την έκταση του μοντέλου και να δημιουργούν με τον τρόπο αυτό ένα είδος εσωτερικών καναλιών. Το αμμοχάλικο ορίζεται ως διαπερατό, επομένως το νερό μπορεί να κινείται ευκολότερα μέσω των διαύλων επικοινωνίας που δημιουργούνται, γεγονός που ευνοεί την άρδευση και καλλιέργεια της Γης.

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Contents

Acknowledgements ...... iv

Abstract ...... v

Περίληψη ...... vi

Contents ...... viii

Introduction ...... 10

Chapter 1 ...... 12

Site Description ...... 12

1.1 Location and climate ...... 12

1.2 Tectonics and Geology ...... 14

1.3 Data Analysis ...... 17

Chapter 2 ...... 21

2.1 The fundamental idea of Truncated and Plurigaussian Simulations ...... 21

2.2 Truncated Gaussian Simulation ...... 24

2.3 Plurigaussian Simulation ...... 28

2.4 Main Properties of the Plurigaussian Simulation ...... 28

2.4.1 The rock type rule ...... 28

2.4.2 The Gibbs Sampler ...... 29

2.4.3. Back Transformation ...... 29

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Chapter 3 ...... 30

Data Processing ...... 30

3.1 Definition of the boundary surfaces ...... 30

3.2 Discretization and Flattening ...... 32

3.3 The ‘Rock Type Rule’ ...... 32

3.4 Conditional Simulation ...... 35

Chapter 4 ...... 36

Results and Conclusions ...... 36

Future Research ...... 41

References ...... 42

Introduction

Geostatistics is a widely used subject with a number of applications in both Petroleum and Mining industries and generally in Geosciences. Statistical modeling in these fields started in early sixties with the developments of Matheron in applied stochastic models. He took into consideration the variability in space of different quantities, i.e. metal concentrations, hydraulic conductivity, solute transfer, etc, in order to estimate several parameters of interest (Kitanidis, 1997).

Several stochastic approaches have been developed since then in order to model the complex geology of subsurface deposits, being either geostatistical estimations or simulations (Stafleu et al., 2011; Mariethoz et al., 2009; Deutsch, 2006; Bierkens and Burrough, 1993). The latter category is widely applicable to the characterization of hydrofacies distribution within alluvial deposits (Modis and Sideri, 2013).

More specifically, geostatistical simulations for the characterization of complicated geological structures has been advancing mainly in the last two decades. The two initial approaches (the “Usual Continuous” and ‘the “Multigaussian”) that Matheron proposed in 1965, had difficulties to simulate a wide range of connectivity patterns for the structures with high permeability (Mariethoz et al., 2009; Journel and Alabert, 1990; Gómez Hernández and Wen, 1998; Zinn and Harvey 2003; Kerrou et al., 2007; Renard, 2007). Another, more flexible proposal, is to model, first, the geological facies, and then add the heterogeneous hydraulic and transport parameters (Mariethoz et al., 2009).

Geostatistical Simulation of categorical variables is widely used for modelling the spatial distribution of geological domains, e.g. lithofacies in an oil/gas reservoir or a geological formation, hydrofacies in an aquifer, mineralogical domains in an orebody. Geostatistical Simulation describes, probabilistically, the geological domains and enhances the geological control for the petrophysical variables of interest (porosity, permeability, concentration, etc.), when the variables are homogeneous within each geological domain,

but the layout of the domain boundaries is uncertain (Emery, 2007; Dowd, 1994; Dubrule, 1993; Emery and Gonzalez, 2007). The main purpose of Simulation is to create equiprobable images of the real situation that show the attributes of the phenomena, e.g. variability of the dataset and probability distribution function (Modis and Sideri, 2013; Deutsch and Journel, 1997; Chiles and Delfiner, 1999).

In this study, Plurigaussian Simulation (PS) techniques (Armstrong et al, 2011) were applied for modeling the East Thessaly basin. The latter, consists an area with large subsidence phenomena, in certain sites, due to the overexploitation of the aquifers. PS allows setting up one or more simulations of standard normal random functions in the area of interest. The purpose of the simulation(s) is the estimation of the lithotype which depends on the simulated values at each point (Modis and Sideri, 2012; Armstrong et al., 2011). Simulation of the drill-hole data was conducted using the geostatistical software Isatis, which was produced by French company Geovariances. Further analysis could be performed in order to study the effect of hydraulic parameters to subsidence phenomena (flow-model) in the framework of future research.

Chapter 1

Site Description 1.1 Location and climate

The Thessaly basin is located in Central Greece. Its total area is about 4520 km2 and is drained by Pinios River. The whole area is divided into two regions by a group of hills, East Thessaly (Larissa) and West Thessaly (Trikala and Karditsa) (Modis and Sideri, 2013).

Figure 1: The map of Greece. The area of East Thessaly is located within the red box (Esri)

Figure 2: The East Thessaly basin that is examined in this study (Esri)

The mean annual precipitation of the area is about 700 mm and is not distributed regularly (Vassilopoulou et al., 2013). The climate is Mediterranean, which is characterized by dry, hot summers and rainy winters.

The Thessaly Plain has been used for agriculture over the past years. The crops that are cultivated are, mostly, cotton, wheat and maize. The cultivation has led to overexploitation of ground-water because of the high water demands. The large amount of water which have been removed, led to land subsidence phenomena (Vassilopoulou et al., 2013).

1.2 Tectonics and Geology

The current morphology of the area of Thessaly was created by the post-orogenic collapse of the External Hellenides. The NE-SW extension caused a series of horsts and grabens bordered by NW-SE faults. The East Thessaly basin was generated by these NE- SW faults (Vassilopoulou et al., 2013). During the Middle to Late Pleistocene a deformational phase was started with the trending from EW to ESE-WNW. This phase created several faults (Vassilopoulou et al., 2013).

Figure 3: The geological map of the East Thessaly basin (Vassilopoulou et al., 2013)

Regarding the geological structure, Quaternary deposits (mainly alluvial) are occurred. The plain was previously the Karla Lake (Quaternary Lake), which was artificially drained in the 1960s, in order to provide land for cultivation (Vassilopoulou et al., 2013).

Specifically, the geological formations developed in the area are the following (Modis and Sideri, 2013):

 Neogene formations

Neogene formations consist of clayey silts and sands which have fluvial and lacustrine origin. Furthermore, gravels and conglomerates of various origin are occurred in the area.

Marls, conglomerates and sandstones of lacustrine origin are consisted the basement (Modis and Sideri, 2013; Mariolakos et al., 2011).

 Pleistocene Sediments

Another major part of the basin, is covered by clayey silts, sandy silts, sandy clays and sands with gravels of terrestrial origin. This lithology is ideal for the development of potential aquifers that undergo extensive exploitation (Modis & Sideri, 2013; Rozos & Tzitziras, 2002).

 Alluvial deposits

Alluvial deposits such as clays to sandy clays lie around the area of Thessaly. Their origin is, mainly, fluvial (Modis & Sideri, 2013).

Figure 4: Typical Stratigraphic column of the East Thessaly basin (Modis & Sideri, 2013; Bornovas et al., 1969)

1.3 Data Analysis

The Thessaly basin has been continuously examined, and hundreds of boreholes have been drilled in order to provide data for geotechnical and hydrogeological studies. East Thessaly, though, has been less extensively examined. The data for this case study were taken from SOGREAH (1974). Specifically, 149 samples were used from 14 boreholes. These samples determined the lithological horizons, and going further, the general stratigraphy of the geological model.

Figure 5: Typical section of one of the boreholes (SR36) that have been used for this study (SOGREAH, 1974)

Figure 6: Map of the examined area with the boreholes (Esri).

After examination of the 14 boreholes, eight lithological types were identified and coded as:

1. Peat (PT) 2. Sand and Clay (SC) 3. Sand (S) 4. Sand, Gravel and Clay (SGC) 5. Clay (C) 6. Gravel and Clay (GC) 7. Sand and Gravel (SG) 8. Basement (BASE)

These geological types were simplified into five hydrofacies, in order to create easier the geological model. The re-arrangement of the types is the following (Figure 7):

1. Peat (PT) Sand and Clay (SC) Clay (C) 2. } (C) Gravel and Clay (GC) Sand, Gravel and Clay (SGC) 3. Sand (S) 4. Sand and Gravel (SG) 5. Basement (BASE)

Figure 7: Correlation between initial geological types (8) and simplified lithotypes (5)

Figure 7 shows the correspondence between the initial geological types and the final lithotypes in which the initial ones were summarized. Each type represents a specific indicator variable. This reduction based on the permeability of the lithofacies. Sand (S) and Sand & Gravels (SG) are considered water-permeable, whereas Peat (PT), Clay (C) and Base (BASE), are accepted as water-impermeable.

Once these five lithotypes are simulated and geological model is completed, a flow model could be created in order to study the water management of the basin. However, this is beyond the purpose of this study.

Chapter 2 Mathematical Background 2.1 The fundamental idea of Truncated and Plurigaussian Simulations

The first step in Truncated Simulation is to simulate one or more variables (N(0,1) distribution) at every point of the field area and then use the rock type rule in order to convert these values back to lithotypes (Figure 8). The left image shows the Gaussian value at each point in space. The right image shows values that represent one facies. These values are below -0.6 and their colour is dark grey. The values that are greater of 0.5 are coloured white and intermediate values are coloured light grey. Τhis interval classification consists the rock type rule (Armstrong et al., 2011).

Figure 8: Left image, simulated greytone image/Right image, the same image after truncated at the cutoffs -0.6 and o.5. Values lower than -0.6 are coloured shaded dark grey, those between -0.6 and 0.5 are coloured light grey and values greater than 0.5 are white (Armstrong et al., 2011)

In the right image, is obvious that black and white facies are not connected, whereas the grey facies touches both the black and white facies.

Figure 9: Normal distribution (Armstrong et al., 2011)

Figure 9 shows the standard normal distribution, N(0,1). From this histogram, we can- easily-calculate the three areas and then extract the proportion that each facies occupies. There is a relationship between the thresholds and the proportions. First, we calculate the proportions, experimentally, and then we use them in order to deduce the thresholds (Armstrong et al., 2011).

One of the main problems of Truncated Gaussian Simulation is that it has many restrictions, e.g. if a specific facies is connected with more than two faces or if there is no logical (natural) sequence between the facies. When we have one certain facies that is in contact with two or more facies, then, we can use Plurigaussian Simulation (two or more Gaussian variables).

Figure 10: Top images are realizations of plurigaussian. The bottom right image shows the rock type rule. The bottoms left image illustrates the lithotypes (Armstrong et al., 2011)

Figure 10 illustrates the Plurigaussian Simulation for the case of two Gaussians. The two images at the top are Gaussians and simulations were obtained using Gaussian Random Functions. The difference of these two images is the direction of the range. The one on the left has its long range in the NS direction, whereas the right image has its long range in the EW direction. The square that is colored with black, grey and white, on the bottom right, shows the rock type rule. The values of the first Gaussian (Y1) are plotted on the

23 horizontal axis, while, these of the second Gaussian (Y2) are plotted on the vertical axis. The range of the values is between (-∞, +∞). Regarding this rock type rule, we can summarize the following (Armstrong et al., 2011):

 If Y2<0 the rock is coded as dark grey.

 If Y2>0 and Y1<0 the rock is considered white.

 If Y2<0 and Y1>0 the rock is classified as light grey. The result of these three combinations is illustrated in the left image, on the bottom. The basic idea of Truncated and Plurigaussian Simulation is to simulate the Standard Normal Random Functions, within the area of interest, and to characterize the lithotype or facies depending on the simulated values of each point.

2.2 Truncated Gaussian Simulation

The main purpose of Truncated Gaussian Simulation is to create realizations of one continuous Gaussian variable and next truncating it into thresholds in order to generate categorical facies (Deutsch and Pyrcz, 2014; Armstrong et al., 2003; Beucher et al., 1993; Emery, 2007; Matheron et al., 1987; Xu & Journel, 1993).

Figure 11: Illustration that describes the general concept of Truncated Gaussian Simulation (Pyrcz & Deutsch, 2014)

Figure 11 illustrates the general concept of Truncated Gaussian Simulation. The horizontal axis (x) shows the categorical variable. The thick black curve is the continuous Gaussian function. The latter is cut into thresholds (vertical axis, y). It is the simplest version (1D), although shows the main concept of Truncated Gaussian (Deutsch and Pyrcz, 2014).

Generally, in Truncated Gaussian Simulation a stationary Gaussian random function is simulated first, and then it is transformed (via truncation) into the lithofacies variable (Modis and Sideri, 2013; Armstrong et al., 2011).

In the simple existence of two lithotypes, F1 and F2, the transformation of the Gaussian variable into facies values is performed with the straight forward rule. According to the latter, if the value of the Gaussian variable is lower than a number t1, then the dominant is the first facies, F1, otherwise the dominant facies is the second, F2. The number t1, is the threshold.

Let’s assume that x is a point which lies in the simulated area of interest. F1 and F2 are the lithotypes and IF1(x) and ΙF2(x) are their indicators respectively. Z(x) is the simulated Gaussian function. The transformation can be expressed mathematically as follow (Armstrong et al., 2011):

퐼퐹1(푥) = 1 ↔ −∞ ≤ 푍(푥) < 푡1 (1)

In the case that we have more than two lithotypes, the above equation becomes:

푥 ∈ 퐹푖 ↔ 퐼퐹푖(푥) = 1 ↔ 푡푖−1 ≤ 푍(푥) < 푡푖 (2)

Generally, the probability (P) of having Fi facies at the point x, is proportional to the percentage of the facies Fi at that point:

푃퐹푖 = E{퐼퐹푖(푥)} (3)

Where E{} is the mean value operator

So the Equation (3) can be written:

푃퐹푖(푥) = 푃(푡푖−1 ≤ 푍(푥) < 푡푖) = 푃(−∞ < 푍(푥) < 푡푖) − 푃(−∞ < 푍(푥) < 푡푖−1) (4)

Proportions and Thresholds in Truncated Gaussian Simulation

The first assumption that is made in Truncated Gaussian simulation is about the proportions of the facies: they are considered known at any location x, in a layer A, which is pk(x), k = 1,..., K-1, u ∈ A, where K is the number of thresholds. The cumulative proportions are generated as following (Deutsch and Pyrcz, 2014):

푘 푐푝푘(푥) = ∑푗=1 푝푗(푥) 푤𝑖푡ℎ 푘 = 1, … , 퐾 푓표푟 ∀ 푥 ∈ 퐴 (5)

It is apparent that, cpo=0 and cpk=1.

The thresholds, which transform the continuous Gaussian variable into Truncated are given below (Deutsch and Pyrcz, 2014):

푡 −1 푍푘(푥) = 퐺 (푐푝푘(푥)) 푤𝑖푡ℎ 푘 = 1, … , 퐾 − 1 푓표푟 ∀ 푥 ∈ 퐴 (6)

Where,

푡  푍푘, 푘 = 1, … , 퐾 − 1 푎푟푒 푡ℎ푒 푡ℎ푟푒푠ℎ표푙푑푠 푡 푍0 = −∞ 푡 푍퐾 = +∞  퐺−1(∙) 𝑖푠 푡ℎ푒 𝑖푛푣푒푟푠푒 푐푢푚푚푢푙푎푡𝑖푣푒 푑𝑖푠푡푟𝑖푏푢푡𝑖표푛 푓푢푛푐푡𝑖표푛 푓표푟 푡ℎ푒 푆푡푎푛푑푎푟푑 푁표푟푚푎푙 퐷𝑖푠푡푟𝑖푏푢푡𝑖표푛

 푐푝푘(푥), 푎푟푒 푡ℎ푒 푐푢푚푢푙푎푡𝑖푣푒 푝푟표푏푎푏𝑖푙𝑖푡𝑖푒푠 푎푡 푙표푐푎푡𝑖표푛 푢

The facies coding is as following (Deutsch and Pyrcz, 2014):

푡 푡 푓푎푐𝑖푒푠 푎푡 푥 = 푘 𝑖푓 푍푘−1(푥) < 푍(푥) ≤ 푍푘(푥) (7)

It is worth mentioning that, the Gaussian values, Z(x), are stationary. Then, transformation of categorical data into continuous Gaussian conditioning data takes place. All facies are transformed for conditional Gaussian Simulation (Deutsch and Pyrcz, 2014).

2.3 Plurigaussian Simulation

In Plurigaussian Simulation, there are more than two facies and, going further, more than two Gaussian functions. According to the most usual approach, Plurigaussian Simulation uses the dominant facies indicator variogram and transforms it (numerically) to the corresponding normal scores variogram. The variogram has almost the same range and anisotropy (Deutsch and Pyrcz, 2014).

Plurigaussian Simulation offers the advantage to provide a valid indicator cross- covariance model, because the latter is deducted from the covariance model of the Gaussian variables. In PS, a standard covariance model is fitted to the Gaussian variables. This ensures that indicator covariances are valid covariance functions. The covariances of the two Gaussian variables are considered stationary (Modis and Sideri, 2013).

The Plurigaussian model is used for the simulation of geological facies, with the aim of capturing the uncertainty in the domain boundaries and optimizing the geological controls in the characterization of quantitative attributes (Emery, 2007).

2.4 Main Properties of the Plurigaussian Simulation 2.4.1 The rock type rule

Plurigaussian Simulation uses the rock type rule. The rock type rule, uses a rectangle and splits this rectangle into other sub-rectangles. Every rectangle corresponds to a lithotype. The position of each sub-rectangle signifies the contact of each lithotype with another.

The lithotype rule is considered general and assumes that the proportions are constant and the field that will be simulated is large enough in order to be representative (Modis and Sideri, 2013).

2.4.2 The Gibbs Sampler

Sampling of complicated distributions is usually made with random algorithms belonging to the class of Markov chain Monte Carlo (McMC) methods. Metropolis - Hastings and Gibbs Sampler are the most popular ones. The latter can be seen as a specific case of the Metropolis - Hastings algorithm (Armstrong et al., 2011).

In Plurigaussian simulation, each lithotype belongs to a known interval (Gaussian thresholds). The Gibbs algorithm is used when the lithotype is known and a specific value must be given to the Gaussian variable: Each lithotype data point takes a random starting value which is within the Gaussian thresholds. The Gibbs sampler process allows these random values to be assigned to the random values of the lithotypes until a steady state value is reached with respect to the covariance model of the Gaussian function (Dunn, 2011). The algorithm, allows the simultaneous consideration of the experimental data (conditioning data) and the connection between the samples in order to reproduce the model and the constraints (Modis and Sideri, 2013)

2.4.3. Back Transformation

When the appropriate values are given to the categorical data within the Gaussian intervals (Gibbs Sampler), after the simulation, the values have to be transformed again into categorical data with respect to their locations within the thresholds of the Gaussian functions (Dunn, 2011). This procedure is simple, in the case of two facies, but things become more complex when the lithotypes are more than two.

Chapter 3

Data Processing

The main steps of Plurigaussian Simulation are the following (Modis and Sideri, 2013; Armstrong et al., 2011):

 First, we choose the type of the model. In the case that we have complex geology (as in our case with alluvial deposits) we use two Gaussians, otherwise we can use one Gaussian (when there is a sequential ordering of the lithotypes).  Afterwards, we generate the main parameter values. Specifically, the proportion of each facies, the lithotype rule and the underlying Gaussian random function(s). All of these parameters determine the thresholds in which the several Gaussians are truncated.  Next, we assign to each core sample a Gaussian value, with respect to the variogram model.  Once the Gaussian values are assigned to each sample, the Gibbs algorithm is used for the conditional simulation of the values at grid nodes.  The final step is to convert the Gaussian Values back to facies with the lithotype rule.

Discretization of the working domains and further application of Plurigaussian simulations were performed using ISATIS® software from Geovariances.

3.1 Definition of the boundary surfaces

Two surfaces (lower and upper) should be defined in order to specify the three- dimensional grid area which includes all the available data. According to the available data (SOGREAH, 1974), there is an alluvial aquifer system in the East Thessaly sub- basin. The surface of the aquifer system was created in ArcMap, and consists the lower

30 boundary surface. The upper boundary surface is the Earth’s surface. A Digital Elevation Model (DEM) was created for the purpose of simulation. The aquifer lies between elevations 183 and -440 m. The total area is discretized into a structural grid of 112 × 88 × 52 (512,512) blocks of 500 × 500 × 10 m. The coordinates of the centre of the lower left block are x = 351,060 m, y = 4,357,835 m and z = -455 m.

Figure 12: Boundary surfaces. The orange surface consists the surface of the Earth and the blue to yellow surface is the bottom of the aquifer.

3.2 Discretization and Flattening

The data from the drill-holes are not segmented regularly along each line. For the purposes of simulation, each line has preferably to be discretized into equal segments. In our case, the total area was partitioned into 512,512 blocks as previously mentioned. This discretization allows us to create composite samples, each sample corresponding to a single model block.

The structural grid thus created, consist the main area in which the analysis of the lithotype proportions and the simulation takes place. But, before starting the stochastic modelling, we should take into account the discontinuities/continuities of the lithology of each horizon. Generally, the base of each horizon presents a kind of spatial continuity. For keeping this continuity, each horizon is deformed to a new shape with a new plane base. The deformation (flattening) is conducted with the transformation of the coordinates and the base of the horizon is used as a new reference surface (Modis & Sideri; Armstrong et al., 2011). After simulation, the results are transformed to the original coordinates.

3.3 The ‘Rock Type Rule’

The rock type rule “wizard” in ISATIS™ (Figure 13) consists of three sections: the left section where the contacts between the lithotypes are shown, the central section which summarizes the five lithotypes and the right section which includes the histograms of contacts between the associated lithotypes of the central section. The rock type rule is shown in the left pane. The histograms on the right show the proportion of each facies that are in contact with the facies of the middle column. For example, the biggest part of Clay (C) is in touch with Basement (Base). As mentioned above, Plurigaussian

Simulation (PS) uses two Gaussian functions, G1 and G2.

Figure 13: Lithotype rule: the left section shows the contacts between the lithotypes, the central section shows the five lithotypes and the right section presents the histograms of the associated lithotypes of the central section.

G1 represents the transition between Sand (S) to Basement (Base) and Basement (Base) to Sand and Gravel (SG). G2 represents the transition between Peat (Pt) to Clay (C) and then Clay (C) to all the other lithotypes. Several lithotype rules have been examined, in accordance with variograms, and the above lithotype rule (Figure) leads to improved variogram fitting.

In Plurigaussian Simulation, direct adjustment of the Gaussian functions to the experimental variograms is not possible, since the only variograms that are available are the variograms of the Indicator functions, whereas the variograms that are needed for the model are the variograms of the underlying and continuous multi-Gaussian functions. So, the next step in the process is the interference of the variogram models for the Gaussian functions.

The variogram interference was based on a trial and error iterative process in which first the type and the parameters of the variogram models are defined, and afterwards the variograms were used to create an unconditional Plurigaussian Simulation. The variograms of the Indicators of the facies were calculated from the simulated field. The

33 initial ranges of the variograms of the multi-Gaussian functions were adjusted (manually) until the experimental variograms approached the calculated.

Figure 14: Experimental (dotted line) and simulated (continuous line) vertical indicator simple and cross-variograms.

Figure 15: Experimental (dotted line) and simulated (continuous line) horizontal indicator simple and cross- variograms.

3.4 Conditional Simulation

Once the lithotype rule and the variogram models have been applied, conditional simulation can be performed to the drill-hole data. The Gibbs Sampler is used to assign normal scores values to the data points (lithotypes). First, an algorithm is used to perform an unconditional simulation from the underlying covariance function and afterwards a conditional simulation is performed via kriging between the conditioning data at known locations and the unconditioned values. Finally, the Gaussian values are back- transformed into lithotypes.

Chapter 4 Results and Conclusions

Plurigaussian Simulation techniques were applied to a set of borehole data (14 boreholes). PS method is based on the simulation of the multi-Gaussian functions. The aquifer is simulated in a 3D working grid.

One of the biggest advantages of PS is that combines the general geological concept with the stochastic simulation. The most important characteristic of PS is that uses the geological rule. The latter is not only derived from geostatistical analysis, but requires geological and empirical knowledge, too.

PS technique is very effective and representative in reproducing the spatial characteristics of hydrofacies as derived by their proportions in the borehole samples. One of the main advantages of PS is that can model complex facies structures (transitions) which is difficult to be simulated with other Gaussian techniques.

Figure 16: 3D Plurigaussian Simulation model of the East Thessaly aquifer system.

The resulting model (Figure 16) shows a spatial differentiation regarding the facies proportions. According to this model, the biggest part is covered by Clay (CL). Clay soils have the ability to change their volume when they are wetted or dried. So, when they are wetted they will swell (expand) and when they are dried they will shrink. Clays are prone to swell/shrink due to their crystalline structure (iterative arrangement of atoms). The bonds between the clay crystals are weak and water can intrude into spaces and push them apart. As a result, there is high risk of subsidence in most parts of the basin, where the presence of clay dominates.

Especially, North and NE parts of the basin (Giannouli, Melissochori and Omorfochori villages) and central parts (Nikaia and Halki villages) have highly possibility to develop subsidence phenomena because of the clay presence which is dominant (Figure 17). In the South-eastern part of the basin, the area around Kileler village appears to be likely for subsidence, because of its geological background which is mostly clay, too.

Figure 17: Horizontal projection of the East Thessaly basin with the stable and unstable areas.

Furthermore, according to the output of the model, uplifts of the Basement occur in many parts of the basin, especially in the central and SE sections, which is confirmed by the general tectonic of the area. During the Oligocene, extensive tectonism took place in Pelagonian zone that led to the orogenic collapse which had as result the rising of the basement. Platykampos, Armenio and Karla areas are examples of this type. Larissa city

38 also appears unsusceptible to subsidence, as its geological background is mostly Basement (Figure 18).

Figure 18: Section that shows the differentiation of the facies in accordance with the depth.

The previous results are confirmed by observations that have been made in the area (Vassilopoulou et al., 2013) supported by Terrafirma, one of the ten services maintained by European Space Agency’s (ESA) Global Monitoring for Environment and Security (GMES) Service Element Programme. Terrafirma provides ground motion hazard information service by the revolutionary remote sensing technique of Persistent Scatterer Interferometry (PSI). The ground deformation of the Larissa city was extended examined by PSI. The obtained results showed that the area North and East of Larissa, systematically subsides. Furthermore, significant subsidence is appeared in Giannouli, Nikaia and Halki villages. Larissa, is appeared, generally, stable with no significant subsidence phenomena.

Additionally, it is obvious from the fence diagram model (Figures 18 and 19) that the Sand and Gravel (SG) and the Sand (S) facies create a continuous internal architecture and, as permeable facies, can generate channels in which the water can flow. The latter is advantageous in the cultivation and irrigation of the land since, as mentioned earlier, the Thessaly Basin is a major agriculture region of Greece and its economy depends mostly on agriculture. Unfortunately, the availability of the irrigation water led to overexploitation and depletion of groundwater table and thus, soil degradation is coupled with the pressure of intensive agriculture.

Figure 19: Plurigaussian Simulation fence diagram model of the East Thessaly aquifer system.

Future Research

After the geological models are generated by PS, a proposed step of the research will be to enrich these models with heterogeneous hydraulic parameters. The updated numerical models can then be used as input to appropriate software for the investigation of future variation of groundwater level and the possibility of encountering subsidence phenomena in the area.

References

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