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Geomagnetic Impulses and the Electrical Conductivity of the Lower This copy has been supplied on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. The right of Douglas Norman Stewart to be identified as Author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. © 1991 The University of Leeds and Douglas Norman Stewart Geomagnetic Impulses and the Electrical Conductivity of the Lower Mantle by Douglas Norman Stewart Submitted in accordance with the requirements for the degree of Doctor of Philosophy The University of Leeds, Department of Earth Sciences, December, 1991 The candidate confirms that the work submittedis his own and that appropriate credit has been given where reference has been made to the work of others. 11 Abstract This thesis is an investigation of the changes in the magnetic field as measured at the surface of the Earth on the time-scale of months to decades. In particular the phenomena of geomagnetic "impulses" or "jerks" are investigated. Vigorous discussion has surrounded these phenomena since they were first suggested to have been of global scale, of short duration and originating within the core (Courtillot et a/, 1978), primarily because of their implications for lower mantle conductivity. A major point of discussion has been whether they were of internal or external origin, and to what extent external fields determine their apparent time-scale. A large quantity of monthly means of the geomagnetic field is analysed here to investigate the contribution from external and induced fields. A model of the disturbance fields on the time-scale of months and years is derived. Using the oa geomagnetic index to represent the temporal dependence, the spatial morphology is found to be primarily dipolar aligned with the Earth's main dipole. This model allows a better representation of the core field to be obtained. Seasonal fluctuations in the field are also quantified. The results are found to be consistent with an insulating mantle down to about 600fcm and a conductivity of about 0.15m-1 to 15m"1 below that. A new method is developed to analyse the time-dependence of the improved repre sentation of the core-field and is applied to a large set of geomagnetic annual means. This method determines the periods oftime for which the field, as measured at different locations, can be represented by a quadratic time-dependence. Such a representation is found to be valid typically for 10 years at a time and valid for 93% of the data. Dates at which the changes from one quadratic time-dependence to another occur are found, to a certain extent, to be globally synchronous. Particular dates when this occurs are found to be 1970, 1978 and 1983, the latter events being similar in character to the 1970 jerk, and are thought to arise from impulses in the third time-derivative of the core field. Spherical harmonic models ofthe main field with a quadratic time-dependence are thenderived for epochs 1965.5,1974.5, 1981.5 and 1986.5 using thetechnique ofstochas tic inversion. These models are then used to map the changes in secular acceleration associated with the 1970, 1978 and 1983 jerks. The global extent of the 1978 and 1983 jerks have not previously beeninvestigated. The 1983 jerk is found to be much weaker Ill than the others and the 1978 jerk appears anti-correlated with the 1970 jerk. The role of electromagnetic coupling between the core and mantle is considered in the presence of a thin conducting layer at the base of the mantle. Time-dependent torques are computed for the period 1900 to 1980 and found to correlate closely with the torque required to explain the decade fluctuations in the length of day. If electro magnetic coupling is solely responsible for the decade fluctuations then this implies the conductance of the layer must be ~ 7 x 1085. Various other pieces of evidence relating to lower mantle conductivity are also discussed. IV Contents 1 Introduction 1 1.1 The Earth's magnetic field 1 1.1.1 The origin of the geomagnetic field 1 1.1.2 The mantle and the geomagnetic field 3 1.1.3 Observing the geomagnetic field 3 1.2 Geomagnetic jerks 5 1.2.1 At what dates have jerks occurred? 7 1.2.2 The internal nature of jerks 8 1.2.3 The characteristic time-scale of jerks 8 1.2.4 Related topics 9 1.3 Outline of this thesis 9 2 Solar related phenomena of the geomagnetic field 12 2.1 Introduction 12 2.2 Data selection and validation 15 2.3 Method: a time-series model 18 2.3.1 Accounting for the core field and its variation 18 2.3.2 Seasonal effects 19 2.3.3 Disturbance fields 20 2.3.4 Form of the model 22 2.3.5 Parameter estimation and errors 23 2.4 Results 26 2.4.1 Disturbance field results 26 2.4.2 Annual and biannual variations 26 2.5 Discussion 30 2.5.1 The disturbance fields 30 2.5.2 Annual and biannual variations 33 2.6 The core field revealed 35 2.7 Conclusions 38 3 Spatial analysis of the external and induced fields 40 3.1 Introduction 40 3.2 Spherical harmonic analysis 40 3.3 Results 42 3.3.1 Average disturbance field model 42 3.3.2 The annual and biannual variations 49 3.4 Discussion 49 3.4.1 Disturbance phenomena 49 3.4.2 Annual and biannual variations 53 3.5 Response of the upper Earth to the external fields 54 3.5.1 Empirical response estimates 54 3.5.2 Theoretical hmitations — an example from magnetotellurics. ... 58 3.6 Conclusions 60 4 A new method for secular variation analysis 62 4.1 Introduction 62 4.2 Optimal piecewise regression algorithm 64 4.2.1 Formulation 66 4.2.2 Segment confidence regions 67 4.2.3 Piecewise regression algorithm 68 4.2.4 Information criteria and optimisation 69 4.3 Application to synthetic data , 71 4.4 Geomagnetic data analysis 72 4.4.1 Selection and validation of data 72 4.4.2 Correction for the effects of external fields 74 VI 4.4.3 Prior values for the standard deviation 75 4.4.4 Results 79 4.4.5 Analysis of residuals 86 4.5 Summary and Conclusions 89 5 Geomagnetic jerks of 1970, 1978 and 1983 91 5.1 Introduction 91 5.2 Global, simultaneous geomagnetic jerks 91 5.3 Models of the main field, secular variation and secular acceleration .... 98 5.3.1 Stochastic inversion 99 5.3.2 Data 100 5.3.3 Structure of the data covariance matrix 103 5.3.4 Parameter covariance matrix: model norms 105 5.3.5 Results 106 5.3.6 A note on computational efficiency and accuracy 114 5.4 Models of the geomagnetic jerks of 1969, 1978 and 1983 117 5.5 Discussion 118 5.6 Conclusions 124 6 Geomagnetism and the rotation of the Earth 126 6.1 Introduction 126 6.2 Electromagnetic core-mantle coupling 127 6.2.1 A thin conducting layer at the base of the mantle 129 6.2.2 Formulation of the torque integral 131 6.2.3 Field and flow at the core-mantle boundary 135 6.3 Results 136 6.4 Discussion 136 6.4.1 Astronomical observations of Earth rotation 136 6.4.2 The case for electromagnetic coupling 138 6.4.3 Alternative coupling mechanisms 141 6.4.4 Angular momentum budget 143 6.5 Conclusions 145 Vll 7 The electrical conductivity of the lower mantle 146 7.1 Introduction 146 7.2 Electromagnetic core-mantle coupling 149 7.3 Locating the core-mantle boundary geomagnetically 152 7.4 Geomagnetic impulses and mantle conductivity 155 7.4.1 Geomagnetic jerks: the core impulse hypothesis 156 7.4.2 Impulse constants from the 1970, 1978 and 1983 jerks 158 7.5 Propagation times 161 7.6 Conclusions 162 8 Concluding remarks 165 8.1 Summary 165 8.2 Conclusions and future work 167 8.2.1 External and induced fields 167 8.2.2 The time-dependent magnetic field and core flows 168 8.2.3 Mantle conductivity 170 8.2.4 Endpiece 171 References 173 A Summary of data used in field models 187 Vlll List of Tables 2.1 List of 59 observatories analysed in Chapter 2 17 2.2 Statistics demonstrating stationarity of model parameters 26 2.3 Relative amplitudes of disturbance 27 2.4 Amplitudes and phases of the annual variation 28 2.5 Amplitudes and phases of the biannual variation 29 2.6 Relative amplitudes of disturbance for UK, Japan and N. America .... 32 3.1 Power spectra and misfit, degree 3 disturbance model, geomagnetic refer ence frame, no damping 44 3.2 Power spectra and misfit, AVDF91 model 44 3.3 Power spectra and misfit, degree 4 disturbance model, geographic refer ence frame, no damping 44 3.4 Power spectra and misfit, degree 4 model, geographic reference frame, with damping 44 3.5 Spherical harmonic coefficients of model AVDF91 48 3.6 Power spectra of the amplitudes of the annual and biannual variations. 50 3.7 Estimated response to the annual and biannual variations 57 4.1 Details of the 89 single site observatories of Chapter 4 76 4.2 Details of the 30 composite observatories of Chapter 4 78 4.3 OPRA prior values of standard deviations compared to r.m.s. residuals. 85 5.1 Statistics of the stable secular acceleration models 113 5.2 Comparison of mean residuals to different time-dependent models .
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