Arkoprovo Biswas Shashi Prakash Sharma Advances in Modeling … · 2020. 1. 2. · the last few years, on “Advances in Modeling and Interpretation in Near Surface Geophysics.”

Springer Geophysics

Arkoprovo BiswasShashi Prakash Sharma Editors

Advances in Modeling and Interpretation in Near Surface Geophysics

Springer Geophysics

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Arkoprovo Biswas • Shashi Prakash SharmaEditors

Advances in Modelingand Interpretation in NearSurface Geophysics

123

EditorsArkoprovo BiswasDepartment of GeologyBanaras Hindu UniversityVaranasi, Uttar Pradesh, India

Shashi Prakash SharmaDepartment of Geology and GeophysicsIndian Institute of Technology KharagpurKharagpur, West Bengal, India

ISSN 2364-9119 ISSN 2364-9127 (electronic)Springer GeophysicsISBN 978-3-030-28908-9 ISBN 978-3-030-28909-6 (eBook)https://doi.org/10.1007/978-3-030-28909-6

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Preface

Historically, geophysics has been used to illustrate deep exploration targets, such aseconomic mineralization, groundwater resources, and oil and gas deposits, as wellas environments that are relatively free of human impact. Together, geologist,hydrogeologist, civil engineers, archaeologists, soil scientists, and others haveapplied the customary geophysical methods with long-trusted but simple interpre-tation schemes to detect, classify, and describe buried geological or anthropogenictargets in the shallow subsurface which is just a few meters below the Earth’ssurface and is of great importance. In recent times, there is an urgent need forsubsurface resources has increased. There is a coercing need for exploration targetshave been completed by noteworthy advances in near-surface applied geophysicstechniques and interpretation theory that have caused existing textbooks andmonographs on the subject to become outdated.

Recent advances in geophysical methods and interpretation approaches havemade the integrated geophysical exploration as an important approach for exploringnatural resources as well as for tackling different geotechnical and environmentissues. Among the different possible fields of application, most common arehydrological and hydro-geological characterization and monitoring, mineralexploration, archaeological surveys, locating voids, soil classification, contaminantassessment, etc. Moreover, modeling and interpretation of such subsurface featuresare very important in identifying the actual zones of interest. For this motivation,there is coercing in the scientific community toward the modeling and integratedinterpretation of several geophysical data sets, in order to identify and distinguishthe subsurface from the analysis of different physical properties.

This edited book provides a stimulating, theoretical advancement in near-surfacegeophysics and its applications in various fields of investigations. Techniquescovered include gravity, magnetics, resistivity imaging, VLF-EM, TEM, MT,ground-penetrating radar, and more. Some chapters on the data analysis and inversetheory are provided and chapters are amply illustrated by case studies. This is animportant edited book for advanced undergraduate and graduate students in geo-physics, and a treasured reference for enthusiastic geophysicists, geologists,hydrologists, archaeologists, civil and geotechnical engineers, and others who use

v

geophysics and its application in their professional research and teaching. The bookwill also serve as a valuable reference for geoscientists, engineers, and othersengaged in academic, government, or industrial pursuits that call for a near-surfacegeophysical investigation. The accessible techniques are characterized by differentpenetration and resolution capabilities. Sections on Theoretical advancements,modeling, inversion, joint inversion, and new methods are amply illustrated.Various case studies on the application of near-surface geophysics are alsoillustrated.

Varanasi, India Arkoprovo BiswasKharagpur, India Shashi Prakash Sharma

vi Preface

Acknowledgements

The present work has developed from a protracted series of lively communicationwith my colleagues, seniors, and juniors both in India and abroad, especially, duringthe last few years, on “Advances in Modeling and Interpretation in Near SurfaceGeophysics.” The present book will showcase some advancement in near-surfacegeophysical methods, mathematical modeling, and its application in real-field data.The present work also stresses the significance of exploration, contamination, andenvironmental problems. The book has a broad literature survey, and all pains havebeen taken to take care of proper citation at the requisite places. We would per-sonally like to thank them on behalf of me and the authors of other chapters,respectively. Any inadvertent error/omission in this regard is sincerely regretted. Inaddition, we also thank all the “Authors” of the respective chapters, who havecontributed to the same with their valuable time, effort and expertise in the respectivearea of research/study, as provided in each chapter. Many persons have providedwarm friendship, steady guidance, firm support and valuable guidance throughoutthe years; the following are those who have particularly stood out as being instru-mental to the successful completion of this book. Apart from all the contributors whoalso helped us in reviewing the chapters of the present book, we would personallylike to thank Prof. N. Sundararajan, SQU, Oman; Prof. E. L. Ekinci, BEU, Turkey;Prof. K. Essa, CU, Turkey; Prof. N. Bhatt, MSU, India; and Dr. T. Acharya, PU,India. Special thanks to Dr. Anand Singh, IIT Bombay, India, and Mr. ReetamBiswas, UT, Austin, USA, for providing useful suggestions and helping me inreviewing many chapters. We would also like to thank our Institutions/University forsupporting us for the successful development of this book.

vii

Contents

1 Resolving Suppression Ambiguity in Schlumberger SoundingData Through Joint Interpretation with Audio-Magnetotelluric(AMT) Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Shashi Prakash Sharma, K. Pratima Panda and M. K. Jha

2 GPR and ERT Investigations of Karst Structuresat the Buhui-Cuptoare Cave System, Anina Karst Region(Banat Mountains, Romania) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Laurențiu Artugyan, Adrian C. Ardelean and Petru Urdea

3 Integrated Geoelectrical and Hydrochemical Investigationof Shallow Aquifers in Konkan Coastal Area, Maharashtra,India: Advanced Artificial Neural Networks Based SimulationApproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Saumen Maiti and Gautam Gupta

4 Modeling Streaming Potential in Porous and Fractured Media,Description and Benefits of the Effective Excess ChargeDensity Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61D. Jougnot, D. Roubinet, L. Guarracino and A. Maineult

5 Forward Modeling and Inversion of Very Low FrequencyElectromagnetic Data Over Rugged Topography Using 2DTriangular Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Anand Singh, S. K. Maurya and Shashi Prakash Sharma

6 Forward and Inverse Modeling of Large Loop TEM DataOver Multi-layer Earth Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Satya Prakash Maurya, Nagendra Pratap Singhand Ashish Kumar Tiwari

7 Global Optimization of Near-Surface Potential Field AnomaliesThrough Metaheuristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155Yunus Levent Ekinci, Çağlayan Balkaya and Gökhan Göktürkler

ix

8 Global Optimization of Model Parameters from the 2-D AnalyticSignal of Gravity and Magnetic Anomalies Over Geo-Bodieswith Idealized Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189Sonam Trivedi, Prashant Kumar, Mahesh Prasad Parijaand Arkoprovo Biswas

9 Role of Euler Deconvolution in Near Surface Gravityand Magnetic Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223Roman Pašteka and David Kušnirák

10 Magnetic Data Interpretation Using Advanced Techniques:A Comparative Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263Khalid S. Essa, Mahmoud Elhussein and Mohamed A. Youssef

11 Coal Fire Study Over East Basuria Colliery . . . . . . . . . . . . . . . . . . 295Sanjit Kumar Pal and Jitendra Vaish

12 Geothermal Potential and Circulation Depth of Hüdai ThermalSprings (Sandıklı-Afyonkarahisar, Türkiye) Using Magnetic,Geothermometry and Heat Flow Data . . . . . . . . . . . . . . . . . . . . . . 335Nafiz MADEN, Mustafa Afşin, Fatma Aksever and Ayşen Davraz

13 Geophysical Characterization of Chumathang (Ladakh)Hot Spring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363Gautam Rawat, S. K. Bartarya, Bhoop Singhand Rajinder Kumar Bhasin

14 Airborne Geophysical Surveys and Their IntegratedInterpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377V. C. Baranwal and J. S. Rønning

15 How to Deal with Uncertainty in Inverse and ClassificationProblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401J. L. Fernández-Martínez, Zulima Fernández-Muñiz, Ana Cernea,J. L. G. Pallero, Enrique J. DeAndrés-Galiana,Luis M. Pedruelo-González, Oscar Álvarezand Francisco J. Fernández-Ovies

x Contents

Editors and Contributors

About the Editors

Dr. Arkoprovo Biswas is Assistant Professor atDepartment of Geology, Institute of Science, BanarasHindu University (BHU), Varanasi. He received hisB.Sc. (2002) in Geology from Presidency College,University of Calcutta, M.Sc. (2004) in GeologicalScience, M.Tech. (2006) in Earth and EnvironmentalScience from IIT Kharagpur, P.G. Diploma (2009) inPetroleum Exploration from Annamalai University. Hejoined Geostar Surveys India Pvt. Ltd. as a Geophysicistin 2006 and later joinedWesternGeco Electromagnetics,Schlumberger as an On Board Data Processing FieldEngineer/Geophysicist in 2007 and served there till2008. In 2013, he received his Ph.D. in ExplorationGeophysics from IIT Kharagpur. Later, he joined theDepartment of Earth and Environmental Sciences,Indian Institute of Science Education and ResearchBhopal as a Visiting Faculty in 2014 and completed histenure in 2015. He again joined Wadia Institute ofHimalayan Geology (WIHG) Dehradun in 2016 asResearch Associate and later he joined BHU on October2017. His main research interest includes Near-SurfaceGeophysics, Integrated Electrical and ElectromagneticMethods, Geophysical Inversion, Mineral andGroundwater Exploration, and Subsurface contamina-tion. He has published several papers on theoreticalmodeling, inversion, and application in practical geo-science problems in peer-reviewed international,national journals and book chapters. He is also a Life

xi

Member of Indian Geophysical Union and an Activemember of SEG (USA). He is also an Associate Editorof Journal of Earth System Sciences, Springer andreviewer of many international journals.

Shashi Prakash Sharma is Professor at theDepartment of Geology and Geophysics, IndianInstitute of Technology, Kharagpur, India. He gradu-ated (1988) from Banaras Hindu University, Varanasi,and received a Ph.D. (1994) from the NationalGeophysical Research Institute, Hyderabad, India. Heworked in the Rajasthan Groundwater Department from1994 to 1996 and Oulu University, Finland, from 1996to 1999 before joining IIT Kharagpur at 1999. Hisresearch interests include electrical and electromagneticgeophysics, joint inversion, global optimization, VLFElectromagnetics, integrated interpretation, and ground-water and mineral exploration. He received the MarieCurie fellowship for advanced research 2008–2009 atEotvos Lorand Geophysical Research Institute,Budapest, Hungary. He was visiting Professor atUniversity of Hokkaido, Japan, in 2015. He is alsoactive as editorial board member of national journalsand reviewer of some international journals. He haspublished numerous papers on theoretical modeling,inversion, and application in practical Geoscienceproblems in peer-reviewed international, national jour-nals, and book chapters. Till date, seven students havebeen awarded Ph.D. degrees under his supervision.

Contributors

Mustafa Afşin Department of Geology, Aksaray University, Aksaray, Türkiye

Fatma Aksever Department of Geology, Süleyman Demirel University, Isparta,Türkiye

Oscar Álvarez Group of Inverse Problems, Optimization and Machine Learning,Department of Mathematics, University of Oviedo, Oviedo, Spain

Adrian C. Ardelean Department of Geography, West University of Timișoara,Timișoara, Timiș, Romania;Department of Archeology, National Museum of Banat, Timișoara, Romania

xii Editors and Contributors

Laurențiu Artugyan Department of Geography, West University of Timișoara,Timișoara, Timiș, Romania

Çağlayan Balkaya Department of Geophysical Engineering, Süleyman DemirelUniversity, Isparta, Turkey

V. C. Baranwal Geological Survey of Norway (NGU), Trondheim, Norway

S. K. Bartarya Wadia Institute of Himalayan Geology, Dehradun, Uttarakhand,India

Rajinder Kumar Bhasin Norwegian Geotechnical Institute, Oslo, Norway

Arkoprovo Biswas Department of Geology, Centre of Advanced Study, Instituteof Science, Banaras Hindu University, Varanasi, Uttar Pradesh, India

Ana Cernea Group of Inverse Problems, Optimization and Machine Learning,Department of Mathematics, University of Oviedo, Oviedo, Spain

Ayşen Davraz Department of Geology, Süleyman Demirel University, Isparta,Türkiye

Enrique J. DeAndrés-Galiana Group of Inverse Problems, Optimization andMachine Learning, Department of Mathematics, University of Oviedo, Oviedo,Spain;Department of Informatics and Computer Science, University of Oviedo, Oviedo,Spain

Yunus Levent Ekinci Department of Archaeology, Bitlis Eren University, Bitlis,Turkey;Career Application and Research Center, Bitlis Eren University, Bitlis, Turkey

Mahmoud Elhussein Geophysics Department, Faculty of Science, CairoUniversity, Giza, Egypt

Khalid S. Essa Geophysics Department, Faculty of Science, Cairo University,Giza, Egypt

J. L. Fernández-Martínez Group of Inverse Problems, Optimization andMachine Learning, Department of Mathematics, University of Oviedo, Oviedo,Spain

Zulima Fernández-Muñiz Group of Inverse Problems, Optimization andMachine Learning, Department of Mathematics, University of Oviedo, Oviedo,Spain

Francisco J. Fernández-Ovies Group of Inverse Problems, Optimization andMachine Learning, Department of Mathematics, University of Oviedo, Oviedo,Spain

Gökhan Göktürkler Department of Geophysical Engineering, Dokuz EylülUniversity, İzmir, Turkey

Editors and Contributors xiii

L. Guarracino CONICET, Facultad de Ciencias Astronómicas y Geofísicas,UNLP, La Plata, Argentina

Gautam Gupta Indian Institute of Geomagnetism, Mumbai, India

M. K. Jha Department of Agricultural and Food Engineering, IIT, Kharagpur,West Bengal, India

D. Jougnot Sorbonne Université, CNRS, EPHE, UMR 7619 METIS, Paris,France

Prashant Kumar Department of Geology, Centre of Advanced Study, Institute ofScience, Banaras Hindu University, Varanasi, Uttar Pradesh, India

David Kušnirák Department of Applied and Environmental Geophysics, Facultyof Natural Sciences, Comenius University, Bratislava, Slovak Republic

Nafiz MADEN Department of Geophysics, Gümüşhane University, Gümüşhane,Türkiye

A. Maineult Sorbonne Université, CNRS, EPHE, UMR 7619 METIS, Paris,France

Saumen Maiti Department of Applied Geophysics, IIT (ISM), Dhanbad, India

S. K. Maurya Department of Geology and Geophysics, Indian Institute ofTechnology-Kharagpur, Kharagpur, West Bengal, India

Satya Prakash Maurya Department of Geophysics, Institute of Science, BanarasHindu University, Varanasi, Uttar Pradesh, India

Sanjit Kumar Pal Department of Applied Geophysics, IIT (ISM) Dhanbad,Dhanbad, India

J. L. G. Pallero ETSI Topografía, Geodesia y Cartografía, UniversidadPolitécnica de Madrid, Madrid, Spain

K. Pratima Panda Department of Geology and Geophysics, IIT, Kharagpur, WestBengal, India

Mahesh Prasad Parija Wadia Institute of Himalayan Geology, Dehradun,Uttarakhand, India;CSIR National Geophysical Research Institute (NGRI), Hyderabad, Telangana,India

Roman Pašteka Department of Applied and Environmental Geophysics, Facultyof Natural Sciences, Comenius University, Bratislava, Slovak Republic

Luis M. Pedruelo-González Group of Inverse Problems, Optimization andMachine Learning, Department of Mathematics, University of Oviedo, Oviedo,Spain

xiv Editors and Contributors

Gautam Rawat Wadia Institute of Himalayan Geology, Dehradun, Uttarakhand,India

J. S. Rønning Geological Survey of Norway (NGU), Trondheim, Norway;Norwegian University of Science and Technology (NTNU), Trondheim, Norway

D. Roubinet Geosciences Montpellier, UMR 5243, CNRS, University ofMontpellier, Montpellier, France

Shashi Prakash Sharma Department of Geology and Geophysics, Indian Instituteof Technology-Kharagpur, Kharagpur, West Bengal, India

Anand Singh Department of Earth Sciences, Indian Institute of Technology-Bombay, Powai, Mumbai, India

Bhoop Singh NRDMS and NSDI Division, Department of Science andTechnology, New Delhi, India

Nagendra Pratap Singh Department of Geophysics, Institute of Science, BanarasHindu University, Varanasi, Uttar Pradesh, India

Ashish Kumar Tiwari Department of Geophysics, Institute of Science, BanarasHindu University, Varanasi, Uttar Pradesh, India

Sonam Trivedi Department of Geology, Centre of Advanced Study, Institute ofScience, Banaras Hindu University, Varanasi, Uttar Pradesh, India

Petru Urdea Department of Geography, West University of Timișoara, Timișoara,Timiș, Romania

Jitendra Vaish Department of Applied Geophysics, IIT (ISM) Dhanbad,Dhanbad, India

Mohamed A. Youssef Nuclear Material Authority, Maadi, Cairo, Egypt

Editors and Contributors xv

Chapter 1Resolving Suppression Ambiguityin Schlumberger Sounding DataThrough Joint Interpretationwith Audio-Magnetotelluric (AMT) Data

Shashi Prakash Sharma, K. Pratima Panda and M. K. Jha

Abstract In the present study, joint inversion of Direct Current (DC) resistivityand Audio-Magnetotelluric (AMT) sounding data has been attempted to overcomethe limitation of Schlumberger resistivity sounding data in depicting the concealedaquifer layers at large depth. It is observed that Schlumberger resistivity soundingdata is unable to reflect the presence of multiple aquifer layers located at depth. Thestudy reveals that 4-layer, 6-layer or 8-layer subsurface structures in the study areayield Schlumberger sounding data that reflects only 4-layer KH-type soundingcurves. Therefore, it is not possible to predict 6- and 8-layers from theSchlumberger sounding data measured in the area. However, unlike Schlumbergersounding data, theoretically it has been observed that AMT data over the same4-layer, 6-layer or 8-layers subsurface structures yields different responses.Therefore, it is possible to resolve the suppression ambiguity arising inSchlumberger sounding data using joint interpretation of Schlumberger soundingand AMT sounding data. It is interesting to highlight that even AMT sounding dataalso does not reflect the exact number of layers from either apparent resistivity orphase data, but systematic inversion/joint inversion is able to resolve the abovementioned ambiguity and delineate the presence of aquifers at depth. The Very FastSimulated Annealing (VFSA) global optimization approach has been used to thestudy the efficacy of joint interpretation of DC resistivity and AMT sounding insolving the practical problem in the area. The approach is general and similarapproach can be used to solve practical problems associated with other geophysicalapplications such as mineral investigation.

S. P. Sharma (&) � K. P. PandaDepartment of Geology and Geophysics, IIT, Kharagpur, West Bengal 721302, Indiae-mail: [email protected]

K. P. Pandae-mail: [email protected]

M. K. JhaDepartment of Agricultural and Food Engineering, IIT, Kharagpur,West Bengal 721302, Indiae-mail: [email protected]

© Springer Nature Switzerland AG 2020A. Biswas and S. P. Sharma (eds.), Advances in Modelingand Interpretation in Near Surface Geophysics, Springer Geophysics,https://doi.org/10.1007/978-3-030-28909-6_1

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Keywords Resistivity sounding � AMT sounding � Suppression � Joint inversion �Groundwater

1.1 Introduction

Electrical method of geophysical prospecting is the most reliable method for thedelineation of shallow subsurface structures (Telford et al. 1990). The method hasbeen widely used for different applications related with mineral, groundwater, civilengineering applications as well as archaeological investigations (Auken et al. 2006;Goldman and Neubauer 1994; Guerin and Benderitter 1995; Loke et al. 2013). Theelectrical method possesses simple mathematical development, easy and welldeveloped interpretation approaches, cheap instrumentation, and simple dataacquisition. With the rapid development in instrumentation and data acquisitionapproaches, these days it is possible to record multidimensional measurementsefficiently (Loke et al. 2013). Apart from its simplicity, electrical method also suffersfrom different ambiguity in the data interpretation like all other geophysical methods(Sharma and Kaikkonen 1999). The Equivalence and Suppression are the two majorambiguities (Sharma and Verma 2011) associated with the interpretation of resis-tivity sounding data. Equivalence is a condition where either product or ratio of thethickness & resistivity of the sandwiched layer is interpreted from the resistivitysounding data (Bhattacharya and Patra 1968). Further, Suppression deals with aproblem where the presence of a layer is not reflected in the resistivity sounding data.

Various joint inversion schemes have been proposed in the past to resolve thesetwo ambiguities by using different geophysical data sets (Vozoff and Jupp 1975;Raiche et al. 1985; Dobroca et al. 1991; Verma and Sharma 1993; Gallardo andMeju2003; Monteiro Santos et al. 2006). However, most of the studies deal with theresolution of equivalence problem only. Suppression problem is trickier thanequivalence and it has remained unsolved. Further, there are different types ofsuppression problems in the field measurement. In a continuously increasing sub-surface resistivity distribution, it is not possible to identify the number of layers fromapparent resistivity data. For example, a continuously increasing apparent resistivityfield data could be fitted equally well with the model data from a two-layer ormultiple layers. Further, when a thin conducting layer is located at depth in a ratherresistive subsurface, then the presence of conducting layer is also not reflected in theSchlumberger sounding data or in multidimensional resistivity imaging data. Thelater scenario is more practical and it is related with groundwater and mineralinvestigations. Sharma and Verma (2011) have presented an extensive study toresolve both equivalence and suppression. However, their study concluded that onlyequivalence could be solved but solution of suppression is ambiguous. Only aprioriinformation from other geophysical measurements or geological information couldhelp in reducing the suppression ambiguity to some extent.

In the present study, an attempt is made to solve suppression type ambiguity thatwas observed in Schlumberger sounding data measured in a lateritic terrain of West

2 S. P. Sharma et al.

Bengal, India. Schlumberger soundings carried out in the area exhibits only a4-layer KH type sounding curve. A typical data measured using Schlumberger arrayin the area is presented in Fig. 1.1. According to the interpretation of sounding datashown in Fig. 1.1 there is no conducting layer below 30 m depth in the area as theresistivity sounding curve shows continuously increasing apparent resistivity trend.Information available from a few deep boreholes in the area reveals that there couldbe two thin aquifer layers at depth and they are located around 100 and 200 mdepth ranges. However, these two layers may or may not be present at any par-ticular location in the area. This uncertainty in the area results in failure of a largenumber of deep tube-wells. Since, Schlumberger soundings performed in the areaare unable to reveal any information about these aquifers at depth, alternate geo-physical approach is required that could solve this problem. This problem wastheoretically examined by Sharma et al. (2018) by employing different electricaland EM methods. They pointed out that AMT method could be the best approachthat yields significantly different responses in the presence and absence of deeperaquifers. Therefore, in the present study, a subsurface model is proposed from theavailable borehole information in the area. Forward modeling is performed tocompute DC resistivity as well as AMT sounding data for the proposed models.Since neither DC resistivity data nor AMT data reveals the exact number of layers,systematic inversion/joint inversion will be carried out in this study which couldresolve the suppression problem and delineate deeper aquifers in the area.

1.2 Forward Formulation

(a) DC resistivity sounding

Schlumberger sounding is the commonly used electrical method for the investi-gation of vertical variation in resistivity. The expression for apparent resistivity forthis array, qa(s), over multi-layered structure is given by Koefoed (1979) inEq. (1.1) (s is half of current electrode separation).

Fig. 1.1 Resistivity soundingdata measured in theproblematic area

1 Resolving Suppression Ambiguity in Schlumberger … 3

qaðsÞ ¼ s2Z10

TðkÞJ1ðksÞkdk: ð1:1Þ

The resistivity transform, T(k), in the above expression is expressed by thefollowing recurrence relation:

Ti ¼ Tiþ 1 þ qi tanhðkhiÞ1þ Tiþ 1 tanhðkhiÞ

qi

ð1:2Þ

In Eq. (1.2), the resistivity and thickness of the ith layer are qi and hi, respec-tively, TN = qN, and i = N − 1, …1. Ghosh (1971a) used the following change ofvariables, x = ln(s) and y = ln(1/k), to transform Eq. (1.1) from Henkel integral toconvolution integral.

qaðxÞ ¼Z1�1

TðyÞfe2ðx�yÞJ1ðex�yÞgdy ð1:3Þ

The convolution integral shown in Eq. (1.3) can be written in finite terms ofmultiplication and summation and used to calculate theoretical Schlumbergerresistivity sounding data. In Eq. (1.3) the first term (resistivity transform) is theinput function and the second term is the filter function. Digital linear filteringtechnique proposed by Ghosh (1971a, b) has made computation of a forwardresponse very simple. Ghosh (1971b) and Koefoed (1979) have developed the setsof coefficients for this filter function to compute the Schlumberger apparent resis-tivity. An optimized short length 19 point filter (Guptasarma 1982) is used tocompute the resistivity sounding data in the present study.

(b) AMT sounding

The apparent resistivity (qa) and phase (u) over a multi-layered model is obtainedfrom the surface impedance Z1 given by Vozoff (1991):

qaðxÞ ¼ 1xl

Z1j j2; ð1:4Þ

In Eq. (1.4) x is the angular frequency and µ = µ0 = 4p � 10−7H/m. Thesurface impedance Z1 is computed by following recurrence relation:

ZiðxÞ ¼ Ziþ 1 þ Ti1þ SiZiþ 1

Zn ¼ kffiffiffiffiffiqn

p;


where Ti and Si are given by:

Ti ¼ kffiffiffiffiqi

p� �tanh khiffiffiffiffi

qip� �

; Si ¼ 1kffiffiffiffiqi

p tanh khiffiffiffiffiqi

p� �

:

k ¼ ðixlÞ1=2, x ¼ 2pf , f is frequency varying from 104 to 1 Hz.The term Z1 is Eq. (1.4) will be a complex quantity and it is used to determine

phase change as

u ¼ tan�1 ImðZ1ÞReðZ1Þ� �

: ð1:5Þ

Apparent resistivity and phase are computed over a large frequency range todepict the variation in responses from different models shown in Table 1.1.

1.3 Global Inversion

A large number of global optimization methods are being used these days forminimization of objective function (different norms between the observed andmodel data). Simulated Annealing (SA), Genetic algorithm (GA), Particle SwarmOptimization (PSO), Artificial Neural Network (ANN), Artificial Bee Colony(ABC) optimization etc. are in used for multi-parametric optimization (Goldbergand Deb 1991; Sen and Stoffa 1995; Storn and Price 1997; Sharma and Kaikkonen1999; Singh et al. 2005; Juan et al. 2010). It has been observed that a variant of SAwhich very fast simulated annealing (VFSA) is the most efficient for interpretingresistivity sounding data (Sharma and Verma 2011). For complete description of theVFSA method readers are referred to Sharma and Verma (2011) and Sharma and

Table 1.1 Resistivity model in the area depicting a 4-, 6- and 8-layer subsurface structures

Layernumber

4-Layer 6-layer 8-layer

Resistivity(Ωm)

Thickness(m)

Resistivity(Ωm)

Thickness(m)

Resistivity(Ωm)

Thickness(m)

1 5.0 0.5 5.0 0.5 5.0 0.5

2 25 3.5 25 3.5 25 3.5

3 10 25 10 25 10 254 7500 7500 70 7500 70

5 10 10 10 106 7500 7500 70

7 10 108 7500


Kaikonnen (1998). However, a short description is presented below for a quickunderstanding of the process.

Most of the global optimization techniques (including VFSA used in presentstudy) require the minimum and maximum limits (search range) for each modelparameters. Therefore, first, both DC resistivity and AMT sounding data are used todetermine the number of layers present in the subsurface and the possible searchrange for each model parameter. Accordingly the search range for each modelparameter (resistivity and thickness) is set by observing the measured responses.The resistivity of the subsurface structures is allowed to vary in logarithmic steps asit varies over a large range (1–105 Ωm), however, thickness is restricted to vary in alinear domain (<500 m). Various other variable required for VFSA optimizationsuch as the initial and final temperatures (T0 and Tf) which resembles the misfit errorat initial and final iterations, the number of random moves at a particular temper-ature level (NM), the rate at which temperature is lowered in subsequent iteration(cooling schedule CS) and number of solutions required to arrive at the globalsolutions are set in the beginning of the VFSA procedure.

First, in the predefined model space Pimin � Pi � Pi

max, a model (Pi) with ithlayer resistivity (qi) and thickness (hi) is selected randomly. The forward responses(apparent resistivity for D.C. resistivity sounding and apparent resistivity and phasefor AMT soundings) are computed for model (Pi) selected above. Equation (1.6)given below is used to calculated the misfit error (e) between the observed andmodel data.

e ¼ 1NS

XNSi¼1

lnðqOi;1Þ � ln qCi;1

� �lnðqOi;1Þ

0@

1A

2

þ 1NF

XNFi¼1

lnðqOi;2Þ � lnðqCi;2ÞlnðqOi;2Þ

!2

þ 1NF

XNFi¼1

lnðuOi Þ � lnðuC

i ÞlnðuO

i Þ� �2

ð1:6Þ

In above equation qOi;1 and qCi;1 are the ith observed and computed (model)apparent resistivity for Schlumberger array, qOi;2 and qCi;2 are the ith observed and

computed (model) apparent resistivity for AMT data, u0i and u

ci are the ith observed

and computed (model) phases AMT data, respectively. In Eq. (1.6) NS is thenumber of observation points (current electrode spacings) for Schlumbergersounding data and NF are the numbers of frequencies for AMT sounding mea-surements. All the responses (observed and computed) are transformed in loga-rithmic domain and normalized with respect to the observed response in order toavoid bias in the objective function towards a particular data set. The modelparameters (resistivities and thicknesses) and associated misfit error of the aboverandomly selected model are kept in memory. Subsequently, each model parameteris modified (updated) with respect to its previous value according to the Cauchyprobability distribution given in Eq. (1.7). The factor yi used to update ith parameteris given by the expression:


yi ¼ sgnðui � 0:5ÞTi 1þ 1Ti

� �j2ui�1j�1

" #: ð1:7Þ

In Eq. 1.7, ui is a random variable drawn between 0 and 1 such that yi variesbetween −1 and +1. The variable Ti denotes the temperature which could be thesame or different for various model parameters. Ti may be kept different for eachmodel parameters for faster convergence of the solution, however, in the presentstudy we kept is same for all model parameters as the computation time is verysmall. A new model Pi

m+1 is obtained with respect to its previous value Pim using

Eq. (1.8).

Pmþ 1i ¼ Pm

i þ yi Pmaxi � Pmin

i

� � ð1:8Þ

Next, the misfit error is calculated for the new model obtained using Eq. (1.8)and it is compared with the previous model. Now suppose the misfit error of thenew models is e2 and the previous model is e1 and De = e2 − e1, then there could betwo possible situations for the selection and rejection of the new model. (i) Whenthe misfit error of the new model (e2) is smaller than previous model (e1), the newmodel is accepted with probability exp(−De/T), (ii) When the misfit error of the newmodel (e2) is larger than that of the previous model (e1), a random number is drawnbetween 0 and 1 and compared it with the estimated probability (exp(−De/T)). If theprobability is greater than the random number drawn, then also the new model isaccepted with the same probability, otherwise new model is rejected keeping theprevious model and its misfit error in the memory. Further, at a particular tem-perature level, a predefined number of moves are made by accepting and rejectingthe models according to the selection criterion mentioned above. This makes aniteration of the process at a particular temperature level (say, kth). Next, the tem-perature level is lowered according to the following cooling schedule:

Ti kð Þ ¼ T0iexp �cik1=M

� �: ð1:9Þ

T0i is the initial temperature, ci is a constant and its value is used as unity in thepresent study, k is the iteration number varying from 1 to 500, 1/M is known ascooling schedule where M is number of parameters. In the present study T0i is usedas 0.01 and 1/M as 0.4 to reduce the computation time.

After reducing the temperature at subsequent lower levels and selecting bettermodels by performing required number of moves at each level, we finally reach tothe lowest temperature level and get the best fitted model with least misfit error.This yields one solution. The same procedure is repeated several times by startingfrom different randomly selected initial model and reaching to the final solution. Inthe present study we obtain 10 different best fitted models and statistical meanmodel and associated uncertainties are estimated. If NR is the number of runs and ek


is the misfit error obtained at the kth run then the statistical mean model �Pi iscomputed from Eq. (1.10) given below (Tarantola 1987).

�Pi ¼PNR

k¼1 Pi;k expð�ekÞPNRk¼1 expð�ekÞ

ð1:10Þ

Since square root of the diagonal element of the covariance matrix is used toestimate the uncertainty in the final solution, the covariance matrix is computedfrom

CovPði; jÞ ¼PNR

k¼1 ðPi;k � �PiÞðPj;k � �PjÞ expð�ekÞPNRk¼1 expð�ekÞ

ð1:11Þ

In above equation i and j vary from 1 to M. The uncertainties (dPi) in the meanmodel is given as

dPi ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiCovP i; ið Þ

p: ð1:12Þ

1.4 Results

First, DC resistivity measurement (Schlumberger sounding) from a problematicarea is presented in Fig. 1.1 which reveals 4 layer (KH-type) subsurface structure.According to the interpreted result shown in Fig. 1.1, the third layer which hasresistivity 9.89 Ωm and thickness 24.45 m forms an unconfined aquifer in the area.Below this layer there is massive resistive layer with resistivity around 7500 Ωm.Geologically, this layer is compact laterite. The study area reveals this kind ofgeological sequences. It is important to highlight that the 4th layer is not infinite &uniform but it may have at least two more aquifer layers at depth. This has beenrevealed from 800 ft deep borehole in the study area. The area is problematic from agroundwater point of view and the aquifers may or may not be present in the entirearea. Now the problem is that resistivity sounding reveals only 4 layer structuresand aquifers located at larger depth are not reflected in the DC resistivity soundingcurves. Sharma and Biswas (2013) proposed the measurement of normalized cur-rent flow which indicates the presence of aquifer at depth qualitatively. The elec-trode separations where current flow consistently increases reveal conducting layersat depth. However, the normalized current flow approach is qualitative in nature andincreased current flow may be due to some other factors as well. Therefore, there isa need for suitable approach that could detect the presence of aquifers at depth inthis area.

Based on the litholog of the successful boreholes in the area, Table 1.1 is pre-pared which depicts the 4, 6 and 8-layer sequences. Theoretical apparent resistivityhas been calculated for these 3 models and presented in Fig. 1.2. Figure 1.2 reveals


that it is not possible to assess the number of layers more than 4 from the measureddata.

Sharma et al. (2018) had proposed that AMT sounding would be the bestapproach to solve such suppression problems in DC resistivity measurement. Next,theoretical AMT soundings data has been computed for the models shown inTable 1.1 and shown in Fig. 1.3. AMT soundings clearly reveal different responsesfor 4-, 6-, and 8-layer models. However, the dilemma is that one cannot assess thenumber of layers from AMT soundings as well. Therefore, joint interpretation ofDC resistivity and AMT soundings is proposed for the solution of this problem.Since, individual inversions cannot solve this problem, only joint inversion resultsof DC resistivity and AMT data have been presented systematically assumingvarious situations arising in the field.

Fig. 1.2 Apparent resistivityfor 4-, 6- and 8-layer modelsdepicting only 4-layersounding curve

Fig. 1.3 Apparent resistivity and phase data for 4-, 6- and 8-layer models (Table 1.1) depictingdifferent AMT sounding curves (unlike similar DC resistivity sounding curves)


(i) Joint inversion of 4-layer data using 4-layer model

In the study area there can be such locations too where only 4-layer structure can bepresent in the subsurface. In such case even individual inversion of DC resistivitydata will yield the correct result. However, we cannot be assured from DC resis-tivity data that 2nd and 3rd aquifers are not present at this location. Therefore, jointinversion of DC resistivity and AMT data is a must. Figure 1.4 depicts the jointinversion results of DC resistivity and AMT data when the observed data actuallycorresponds to a 4-layer subsurface structure only. The fitting between the observedand model data for all 3 data sets is very good. Since the fitting for both DCresistivity and AMT data is perfect while using a 4-layer model, it can be concludedthat subsurface structure has four layers only. Table 1.2 presents the actual modelparameters, their search ranges and interpreted model parameters. We can see thatall the parameters are resolved very well and the actual model parameter lies withinthe estimated uncertainties for each model parameter.

(ii) Joint inversion of data measured over 6-layer structure considering4-layer and 6-layer models

Next, DC Resistivity and AMT data generated for a 6-layer subsurface structure(Table 1.1) is jointly inverted using a 4-layer model only. This is because neither

Fig. 1.4 Fitting between the observed and model data for DC resistivity and AMT data over4-layer structure

Table 1.2 Model parameter after joint inversion of DC resistivity and AMT data over 4-layerstructure

Model parameters Actual value Search range Interpreted models

q1(Ωm) 5.0 1–10 5.29 ± 1.25

q2(Ωm) 25 5–50 26.29 ± 4.02

q3(Ωm) 10 1–20 10.15 ± 1.14

q4(Ωm) 7500 350–10,000 7496 ± 25

h1(m) 0.5 0.1–2 0.55 ± 0.15

h2(m) 3.5 1–10 3.17 ± 1.75

h3(m) 25 5–50 25.53 ± 3.64

Misfit error – – 2.00 � 10−5


Schlumberger sounding data nor AMT data give any indication that observed datacorresponds to more than 4 layers. Therefore, initially joint inversion was carriedout assuming a 4-layer model. We can see that optimization of a 4-layer modelgives erroneous model parameters (actual model is not within the estimateduncertainties) as well as it shows poor fitting between the observed and model data(Table 1.3; Fig. 1.5). Figure 1.5 reveals that AMT phase data shows the worstfitting. This is because phase in EM methods is more sensitive than apparentresistivity. Any deviation in the subsurface model parameters with respect to theiractual value will cause more deviation in phase response than apparent resistivityresponse. The above discrepancy gives an indication that observed data does notcorrespond to a 4-layer structure and 6-layer or 8-layer model optimization isrequired.

Table 1.3 Model parameters after joint inversion of DC resistivity and AMT data over 6-layerstructure using 4-layer and 6-layer models

Model parameters Search range Interpreted models using

4-layer model 6-layer model

q1(Ωm) 5.0 1–10 3.28 ± 1.07 4.56 ± 1.90

q2(Ωm) 25 5–50 37.34 ± 5.67 24.51 ± 7.70

q3(Ωm) 10 1–20 13.23 ± 0.24 8.53 ± 1.92

q4(Ωm) 7500 350–10,000 6911 ± 89 6550 ± 1635

q5(Ωm) 10 1–20 – 11.32 – 4.20q6(Ωm) 7500 350–10,000 – 7481.24 – 22h1(m) 0.5 0.1–2 0.35 ± 0.12 0.45 ± 0.23

h2(m) 3.5 1–10 1.21 ± 0.34 5.36 ± 2.44

h3(m) 25 5–50 45.41 ± 0.98 20.42 ± 5.96

h4(m) 70 10–100 – 70.32 – 3.22h5(m) 10 5–50 – 11.69 – 4.15Misfit error 1.22 � 10−2 5.98410−4

Fig. 1.5 Fitting between the observed and model data for DC resistivity and AMT data when4-layer model is optimized using data recorded over 6-layer structure


After observing the limitations of a 4-layer model to fit the observed data inFig. 1.5, joint inversion has been performed for the same data assuming 6-layermodel. The corresponding results are presented in Fig. 1.6 and Table 1.3.Figure 1.6 reveals that fitting between the observed and model data is perfect now.Interpreted model parameter, specially for the 5th layer, which represents theimportant aquifer in the area has been resolved very well. Even though this layer isnot seen anywhere in either DC resistivity or AMT sounding data, the systematicjoint inversion considered in this study is able to resolve this layer very well.Further, we can see that resistivity of the fourth layer has a large uncertainty but itsthickness is well resolved. This is because of in general insensitivity of EMmethods towards the resistivity of a highly resistive layer. Moreover, the depth tothe top for second aquifer (5th layer) has been estimated correctly. Therefore, suchjoint inversion study is helpful in predicting the depth of the aquifer accurately insimilar geological conditions.

(iii) Joint inversion of data measured over 8-layer structure considering4-layer, 6-layer and 8-layer models

Next, the observed synthetic data corresponding to an 8-layer model (Fig. 1.2;Table 1.1) is optimized. Since apparent resistivity data shown in Fig. 1.2 reflectsonly 4-layer structure and AMT data in Fig. 1.3 is uncertain about the number oflayers in the subsurface, we started joint inversion with the assumption that sub-surface consists of only 4-layer structure. However, joint inversion considering only4-layer model has resulted in very poor fitting of all the observed data sets. Further,the final model is also inappropriate (Table 1.4). Figure 1.7 depicts a poor fittingbetween the observed and model data for DC resistivity and AMT data. We can seethat fitting in this case becomes further poor in comparison to the 6-layer structureoptimized using a 4-layer model presented in previous section (Fig. 1.5).Obviously, when data observed for a 6-layer structure could not be modeledproperly using a 4-layer model, then the data observed corresponding to an 8-layerstructure will be more difficult to optimize using a 4-layer model. However, wehave to proceed in this way as the measured data reflects only a 4-layer structure. It



is important to highlight that we have kept search ranges same for various modelsfor comparison.

After getting an unsatisfactory fitting between the observed and model datawhile optimizing a 4-layer model to fit observed data over 8-layer structure, next wemoved to optimize this data using a 6-layer model. Surprisingly, the theoretical data

Table 1.4 Model parameters after joint inversion of DC resistivity and AMT data over 8-layerstructure using 4-layer, 6-layer and 8-layer models

Model parameters

Search range

Interpreted models using

4-layer model 6-layer model 8-layer model5.0 1–10 2.60 ± 1.00 4.70 ± 1.51 5.20 ± 1.5825 5–50 15.20 ± 0.71 26.26 ± 7.07 26.14 ± 6.94 10 1–20 13.40 ± 0.62 9.27 ± 1.61

7500 350–10,000 5890 ± 274 7181 ± 919

9.25 ± 1.486991 ± 1922

10 1–20 – 12.91 ± 4.71 13.37 ± 4.44

7500 350–10,000 – 7437 ± 28 4599 ± 3324

10 1–20 – – 10.84 ± 3.777500 350–10,000 – – 7462 ± 40

0.5 0.1–2 0.17 ± 0.007 0.48 ± 0.19 0.54 ± 0.193.5 1–10 9.54 ± 0.44 4.47 ± 2.39 4.31 ± 2.0525 5–50 47.72 ± 2.22 23.04 ± 5.28 22.55 ± 4.8570 10–100 – 91 ± 3.97 62.24 ± 1510 5–50 – 25.44 ± 9.29 11.78 ± 6.2070 10–100 – – 64.21 ± 1510 5–50 – 12.51 ± 6.24

Misfit error

–

4.85 × 10−2 7.27 × 10−4 5.12 × 10−5



generated for an 8-layer subsurface structure fits very well with the model dataobtained after optimizing a 6-layer structure only. The corresponding results havebeen presented in Fig. 1.8 and Table 1.4. If we compare the interpreted modelparameters obtained after optimizing 6-layer structure shown in Table 1.4 with theactual model parameters, then we can see that the interpreted thickness h4 and h5 aremore than their actual values while resistivity of these layers is resolved very well.Since data observed over an 8-layer model fits well with model data optimizedusing a 6-layer model only, therefore, how to identify the 3rd aquifer layer (7thlayer in Table 1.1) present at a larger depth? This is another challenging situation.The solution of this problem requires additional a priori information in the studyarea. If we know by some apriori information that third aquifer is present in thesubsurface or the interpreted thickness of the 2nd aquifer using 6-layer model ismore than the expected thickness of aquifer in the area, then we can always interpretthis data to optimize an 8-layer structure. This could be the possible solution toidentify and locate the third aquifer layer in the area.

While interpreting observed data over 8-layer structure using 6 layer model weget a higher estimate of h5 which is incorrect according to aprori information fromthe area. It is important to highlight that we restricted the higher bound of the searchrange for thickness as 15 m and lower bound of its resistivity at 8 Ωm. If we keepthe restriction of the resistivity and thickness of the target layer then the optimizedmodel parameter reveals that resistivity lies at the lower boundary and thickness atthe higher boundary. This means optimization technique is trying to find theequivalent physical model in order to fit the response. But this physical model doesnot obey the geological information of the area. Thus restricting the search rangeaccording to the local geology we can still find alternate way to detect the presenceof third aquifer hidden at depth in the resistivity and AMT sounding data.Therefore, it can be concluded that we may get good fitting model in the area using6-layer optimization, however, it is important to analyze whether the obtainedmodel is geologically reliable. If not, we can increase the number of layers to getgeologically meaningful results.



Next, after getting geologically incorrect model while optimizing a 6-layermodel for synthetic data generated for 8-layer subsurface structure, we performedoptimization for 8-layer model in the same wide search range. Table 1.4 reveals thateven though the search range is wide, interpreted model parameters are appropriateand geologically correct. Fittings between the observed and model data are shownin Fig. 1.9. Table 1.4 depicts the interpreted model parameters which shows thatmisfit error has improved when optimizing an 8 layer model compared to a 6-layermodel.

1.5 Discussions

Now, we know very well that recorded DC resistivity sounding data in the area willshow only a 4-layer structure whether the subsurface is 4-layer, 6-layer or 8-layerstructure. Therefore, first we should interpret only Schlumberger sounding datausing a 4-layer model. Next, we should vary the search ranges for q1, q2, q3, h1, h2,h3 within the estimated uncertainty obtained after the individual inversion of DCresistivity data and proceed systematically to perform joint inversion of DC resis-tivity and AMT data mentioned in the results section above to get the best fitted andgeologically correct model. When all the observed data fits very well with 4-layermodel then the subsurface structure is 4-layer only. If not, we will perform 6-layerinversion. Now responses will definitely fit. When the observed responses are fittedwell with the model data and also estimated model is geologically correct then thesubsurface structure is 6-layer. However, when the observed data and model dataare fitted well but interpreted models are not geologically correct, then we shouldoptimized 8-layer model. Table 1.5 presents the results obtained after such kind ofinversion and these are the most correct and reliable results.



Arkoprovo Biswas Shashi Prakash Sharma Advances in Modeling … · 2020. 1. 2. · the last few years, on “Advances in Modeling and Interpretation in Near Surface Geophysics.”

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