GEOMAGNETIC INDUCTION STUDIES IN SOUTHERN SCOTLAND a by Alan George Jones Thesis presented for the degree of Doctor of Philosophy of the University of Edinburgh in the Faculty of Science 1977 DECLARATION I hereby declare that the work presented in this thesis is my own unless otherwise stated in the text, and that the thesis has been composed by myself. Alan George Jones C. ABSTRACT The Southern Uplands of Scotland: is at present a region of great interest to both geologists and geophysicists. The complex tectonic history associated with the closing of the proto-Atlantic ocean has yet to be determined. Previous geophysical studies have shown that the Southern Uplands is atypical of normal continent. Geomagnetic investi- gations have indicated a zone of anomalously high electrical conductivity underlying the Southern Uplands region at a depth of 12-30 km. In order to determine further the exact structure and spatial variation of this conductivity zone., two geomagnetic studies have been carried out in the region. A Geomagnetic Deep Sounding Array of 19 Gough-Reitzel variometers recorded the naturally varying Earth's magnetic field during December 1913 and January 1914. This was followed by • Magneto-Telluric observations on lines perpendicular and parallel to the strike of the supposed anomaly. • In this thesis, reviews of various regional MT studies, the geo- physical significance of conductivity measurements and the known geology and geophysics of the Southern Uplands region are given. The aims, and relevant theory, of induction studies are also presented. The observa-. • tional procedures for both the GDS and MT techniques, and the type and form of the MT activity, are described. Techniques for analysing the • MT data are developed in some detail. Methods are proposed, and examples given, for (a) estimating, the gross structural strike direction, • (b) averaging response function estimates, (c) estimating the confidence • intervals of the response functions, (d) estimating new forms of coherence functions, which exhibit many desirable properties, and (e) a frequency- time analysis for estimating the response functions for sub-intervals of the data set. a- The full MT and GDS estimates from analysis of the single station data - rotated major and rotated minor impedance estimates, azimuthal angles, skew factors and real and imaginary induction vectors - are presented and qualitatively discussed. A one-dimensional interpretation, of two-dimensional MT data is examined and shown to be valid for 'rotated major' impedance estimates from locations sufficiently distant from gross lateral inhomogeneity. Various methods for determining an 'optimum model' that best satisfies, in some manner, the observed MT responses are reviewed. A Monte-Carlo inversion procedure is developed and.applie& to the 'rotated major? data from six of the thirteen locations. It was considered,,for various reasons, unjustifiable to interpret an the data. The GDS and MT results agree on the complexity of the conductivity variations in the Midland Valley,- the Southern Uplands and Northern England. The simple 'Eskdalernuiranomaly' proposed by Edwards et al. ---- (1971) cannot explain the observations.. A conductive layer is required beneath the Midland Valley at a depth of no greater thaii 11 km. The conductive zone underlying the Southern Uplands is at a depth greater than 24 km. For the Northern England response, the top layer of highly conducting sediments 'screen' the possible effects of a 'lower crustal/ upper mantle' conductive layer. The geological and geophysical impli- cations of the acceptable MT models are discussed. In this work, the quantitative information, offered by the MT technique, is shown to be necessary fora full interpretation of the conductivity distribution. Also, estimation of the phase response, as well as the amplitude response, of the impedance tensor elements is shown to resolve the surface structure of the acceptable models. Various suggestions are made about further investigation of the region. ACKNOWLEDGEMENTS I gratefully acknowledge the help and direction given me by my supervisor, Dr. Rosemary Hutton. Dr. Hutton has not only encouraged me throughout my research but also has ensured that I was not too side- tracked by peripheral issues. I sin indebted to her for the years of preparation and organisation she spent on the project before I came to Edinburgh. I should like, to express my gratitude to the Geophysics Department of Edinburgh University for providing the wherewithal for my research. I wish to thank all members. of the Department for furnishing a refreshing and stimulating atmosphere in which to work. In particular, I would like to mention Drs. Jane Sik (co-supervisor), Dennis Rooney, Dave Summers and Bruce Hobbs, all of whom gave me much food for thought. Dennis Rooney is to be especially thanked for his guidance during the initial stages of data processing,-and Bruce Hobbs for theoretical assistance. The fieldwork and technical assistance -g4en me by Mr. Alex Jackson and Mr. Hugh Muir did not go unnoticed. It was much S appreciated. The fieldwork for the GDS Array study was more amusing because of the companionship of Mr. Surrinder Chita, whose help is thankfully acknowledged. Also, I an grateful to my two colleagues, Mr. Dave 14cKirdy and Ms. Sheila Kirkwood, for their patience and assistance during the last six months.. Sheila Kirkwood is also thanked for proof-reading the typescript of this thesis. I an pleased to extend warm thanks to Dr. Ian Gough for his invitation to process the GDS Array data initially at the Department of Physics of the University of Alberta, Edmonton, Canada. During my two-month visit to that Department, Dr. Remi Alabi gave up much of his time both to train me in the data reduction procedure and to entertain me during the weekends - for which I am very grateful. F I wish to thank most sincerely all the people on whose land the instruments were located, many of whom gave up garages, outbuildings and even houses to provide shelter for the MT filtering and recording equipment. Their overwhelming generosity and hospitality made the fieldwork for the MT project very enjoyable. I should like to thank all the staff of the Edinburgh Regional Computing Centre who have helped me at the data processing stage of my research. I express appreciation especially to Ms. Beth Egan for digitising some of the MT data sections. My financial support for this research was by a Natural Environment Research Council studentship, for the initial two years, and a University of Edinburgh studentship for the final 18 months. The Royal Society of London provided.the funds for the purchase and construction of the MT equipment. I express gratitude to all three bodies. Finally, I wish to thank,Ms. Fiona Train for aiding me in inumerable ways, and Ms. Kathy Dodds who gave up many hours to type this thesis - an achievement for which I mn indebted to her. CONTENTS Page CHAPTER I INTRODUCTION 1.1 General Comments 1 • 1.2 Natural Source Field Characteristics 3 1.3 Regional Magneto-Telluric Studies 5 • 1.4 Geophysical Significance of Conductivity Measurements . 17 1.5 Geology and Geophysics of the Southern Uplands Region ••. 21 1.5.1 Geology .• 21 1.5.2 Geophysics . 45 1.6 The Purpose of the Induction Studies 30 CHAPTER 2 THEORY 2.1 Brief Historical Review 32 2.2 Relationships from Maxwell's Equations 37 2.3 General Geomagnetic Induction over One- Dimensional Structures •. 140 2.3.1 Homogeneous half-space . 140 2.3.2 N-layered isotropic half-space 142 2.14 General Geomagnetic Induction over Two- Dimensional Structures 145 • 145 - 2.14.1 General considerations 2.14.2 Typical two-dimensional models 46 a. Fault 146 b. Dyke 148 C. General body . 148 2.4..3 Dimensionality and directionality indicators . 53 Page CHAPTER 3 DATA ACQUISITION 3.1 The GDS Array 61 3.2 The MT Project 64 3.3 MT Instrumentation 68 The telluric systems 68 The magnetic systems 71 C. The recorders lit d. Calibration 75. 3.4 Discussion of MT Data Collected 77 Data quality and quantity 77 Type and. form of activity recorded 17 C. Site problems 79 CHAPTER 4 DATA PROCESSING 4.1 General Considerations 4.2 Processing of Fourier Transient Events from the GDS Array 4.2.1 Data selecticn 4.2.2 Data reduction 4.2.3 Time domain analysis - .. 4.2.4 Frequency domain analysis 4.3 Processing of Fourier Intransient Record Sections for Single Station MT and GDS Data 4.3.1 Data selection 4.3.2 Data reduction 4.3.3 Data conditioning 4.3.4 Spectral estimation and band averaging Page 4.3.5 Correction for instrument response 100 14.3.6 Digital filtering 1014 4.3.7 Frequency-time analysis io6 4.3.8 Polarisation analysis 109 14 • 14 Linear System Parameter Evaluation 110 14.4.1 Single input/single output system 111 4.4.2 Two input/single output system 116 4.14.3 Bias associated with coherence function estimation 119 - 4.4.4 Normalised transformed coherence • functions 121 4.5 Magneto-Telluric Impedance Estimation 128 • 14.5.1 Cagniard impedance estimation • 128 4.5.2 Tensor impedance estimation 129 • 4.5.3 Rotation of the tensor impedances 131 4.5.14 Minimum-maximum analysis 133 4.6 GDS Transfer Function Estimation • 1314 4.7 Station Data' Averaging 134 4..1 Acceptance criteria and averaging of algorithms for GDS data • 135 Acceptance criteria • 135 Averaging algorithms 136 14.7.2 Acceptance criteria and averaging algorithms for MT data 138 a. Acceptance criteria 138 b. Averaging algorithms 139 14.8 Confidence Limit Estimation 1141 14.8.1 For GDS data 142 Page 5.8.2 For MT data 155 5.8.3 For azimuthal data 152 4.8.5 For skew data 155 CHAPTER 5 RESULTS 5.1 GDS Array Data 155 5.2 Synopsis of MT and GDS Single-Station Data 157 5.3 Midland Valley Response 160 5.4 Southern Uplands Response 161 5.5 Northern England Response 166 5.6 Unreliable and Anomalous Responses 167 CHAPTER 6 AND CONCLUSIONS 6.1 Introduction 169 6.2 One-Dimensional Interpretation Techniques 171 6.2.1 Validity 171 6.2.2 First approximation inversion schemes 176 6.2.3 Curve, fitting procedures 179 6.2.5.