ALBERT

Note: Mike Coward and Dorothee Dietrich: Alpine tectonics — an overview / Geological Society, London, Special Publications, 45:1-29, doi:10.1144/GSL.SP.1989.045.01.01 --- Tectonic Evolution of the External Zones of the Alps --- J. G. Ramsay: Fold and fault geometry in the western Helvetic nappes of Switzerland and France and its implication for the evolution of the arc of the western Alps / Geological Society, London, Special Publications, 45:33-45, doi:10.1144/GSL.SP.1989.045.01.02 --- D. Dietrich and M. Casey: A new tectonic model for the Helvetic nappes / Geological Society, London, Special Publications, 45:47-63, doi:10.1144/GSL.SP.1989.045.01.03 --- J.-P. Gratier, G. Ménard, and R. Arpin: Strain-displacement compatibility and restoration of the Chaînes Subalpines of the western Alps / Geological Society, London, Special Publications, 45:65-81, doi:10.1144/GSL.SP.1989.045.01.04 --- N. Fry: Southwestward thrusting and tectonics of the western Alps / Geological Society, London, Special Publications, 45:83-109, doi:10.1144/GSL.SP.1989.045.01.05 --- Tectonic Evolution of the Internal and Southern Zones of the Alps --- O. Merle, P. R. Cobbold, and S. Schmid: Tertiary kinematics in the Lepontine dome / Geological Society, London, Special Publications, 45:113-134, doi:10.1144/GSL.SP.1989.045.01.06 --- J. P. Platt, P. C. Cunningham, P. Weston, G. S. Lister, F. Peel, T. Baudin, and H. Dondey: Thrusting and backthrusting in the Briançonnais domain of the western Alps / Geological Society, London, Special Publications, 45:135-152, doi:10.1144/GSL.SP.1989.045.01.07 --- S. M. Schmid, H. R. Aebli, F. Heller, and A. Zingg: The role of the Periadriatic Line in the tectonic evolution of the Alps / Geological Society, London, Special Publications, 45:153-171, doi:10.1144/GSL.SP.1989.045.01.08 --- A. C. Ellis, A. C. Barnicoat, and N. Fry: Structural and metamorphic constraints on the tectonic evolution of the upper Pennine Alps / Geological Society, London, Special Publications, 45:173-188, doi:10.1144/GSL.SP.1989.045.01.09 --- J. Ridley: Structural and metamorphic history of a segment of the Sesia-Lanzo zone, and its bearing on the kinematics of Alpine deformation in the western Alps / Geological Society, London, Special Publications, 45:189-201, doi:10.1144/GSL.SP.1989.045.01.10 --- K. H. Brodie, E. H. Rutter, and D. Rex: On the age of deep crustal extensional faulting in the Ivrea zone, northern Italy / Geological Society, London, Special Publications, 45:203-210, doi:10.1144/GSL.SP.1989.045.01.11 --- D. Roeder: South-Alpine thrusting and trans-Alpine convergence / Geological Society, London, Special Publications, 45:211-227, doi:10.1144/GSL.SP.1989.045.01.12 --- H. P. Laubscher: The tectonics of the southern Alps and the Austro-Alpine nappes: a comparison / Geological Society, London, Special Publications, 45:229-241, doi:10.1144/GSL.SP.1989.045.01.13 --- L. Ratschbacher and F. Neubauer: West-directed décollement of Austro-Alpine cover nappes in the eastern Alps: geometrical and rheological considerations / Geological Society, London, Special Publications, 45:243-262, doi:10.1144/GSL.SP.1989.045.01.14 --- Models of the Development of the Alpine Chain --- J. F. Dewey, M. L. Helman, S. D. Knott, E. Turco, and D. H. W. Hutton: Kinematics of the western Mediterranean / Geological Society, London, Special Publications, 45:265-283, doi:10.1144/GSL.SP.1989.045.01.15 --- J. E. T. Channell and J. C. Mareschal: Delamination and asymmetric lithospheric thickening in the development of the Tyrrhenian Rift / Geological Society, London, Special Publications, 45:285-302, doi:10.1144/GSL.SP.1989.045.01.16 --- St. Mueller: Deep-reaching geodynamic processes in the Alps / Geological Society, London, Special Publications, 45:303-328, doi:10.1144/GSL.SP.1989.045.01.17 --- P. Vialon, P. Rochette, and G. Ménard: Indentation and rotation in the western Alpine arc / Geological Society, London, Special Publications, 45:329-338, doi:10.1144/GSL.SP.1989.045.01.18 --- R. Lacassin: Plate-scale kinematics and compatibility of crustal shear zones in the Alps / Geological Society, London, Special Publications, 45:339-352, doi:10.1144/GSL.SP.1989.045.01.19 --- J. C. Hunziker, J. Desmons, and G. Martinotti: Alpine thermal evolution in the central and the western Alps / Geological Society, London, Special Publications, 45:353-367, doi:10.1144/GSL.SP.1989.045.01.20 --- A. J. Hurford, M. Flisch, and E. Jäger: Unravelling the thermo-tectonic evolution of the Alps: a contribution from fission track analysis and mica dating / Geological Society, London, Special Publications, 45:369-398, doi:10.1144/GSL.SP.1989.045.01.21 --- F. Heller, W. Lowrie, and A. M. Hirt: A review of palaeomagnetic and magnetic anisotropy results from the Alps / Geological Society, London, Special Publications, 45:399-420, doi:10.1144/GSL.SP.1989.045.01.22 --- K. J. Hsü: Time and place in Alpine orogenesis — the Fermor Lecture / Geological Society, London, Special Publications, 45:421-443, doi:10.1144/GSL.SP.1989.045.01.23

Note: CONTENTS: PREFACE. - INTRODUCTION. - 1 DESCRIBING INVERSE PROBLEMS. - 1.1 Formulating Inverse Problems. - 1.2 The Linear Inverse Problem. - 1.3 Examples of Formulating Inverse Problems. - 1.4 Solutions to Inverse Problems. - 2 SOME COMMENTS ON PROBABILITY THEORY. - 2.1 Noise and Random Variables. - 2.2 Correlated Data. - 2.3 Functions of Random Variables. - 2.4 Gaussian Distributions. - 2.5 Testing the Assumption of Gaussian Statistics. - 2.6 Confidence Intervals. - 3 SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 1: THE LENGTH METHOD. - 3.1 The Lengths of Estimates. - 3.2 Measures of Length. - 3.3 Least Squares for a Straight Line. - 3.4 The Least Squares Solution of the Linear Inverse Problem. - 3.5 Some Examples. - 3.6 The Existence of the Least Squares Solution. - 3.7 The Purely Underdetermined Problem. - 3.8 Mixed-Determined Problems. - 3.9 Weighted Measures of Length as a Type of A Priori Information. - 3.10 Other Types of A Priori Information. - 3.11 The Variance of the Model Parameter Estimates. - 3.12 Variance and Prediction Error of the Least Squares Solution. - 4 SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 2: GENERALIZED INVERSES. - 4.1 Solutions versus Operators. - 4.2 The Data Resolution Matrix. - 4.3 The Model Resolution Matrix. - 4.4 The Unit Covariance Matrix. - 4.5 Resolution and Covariance of Some Generalized Inverses. - 4.6 Measures of Goodness of Resolution and Covariance. - 4.7 Generalized Inverses with Good Resolution and Covariance. - 4.8 Sidelobes and the Backus-Gilbert Spread Function. - 4.9 The Backus-Gilbert Generalized Inverse for the Underdetermined Problem. - 4.10 Including the Covariance Size. - 4.11 The Trade-off of Resolution and Variance. - 5 SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 3: MAXIMUM LIKELIHOOD METHODS. - 5.1 The Mean of a Group of Measurements. - 5.2 Maximum Likelihood Solution of the Linear Inverse Problem. - 5.3 A Priori Distributions. - 5.4 Maximum Likelihood for an Exact Theory. - 5.5 Inexact Theories. - 5.6 The Simple Gaussian Case with a Linear Theory. - 5.7 The General Linear, Gaussian Case. - 5.8 Equivalence of the Three Viewpoints. - 5.9 The F Test of Error Improvement Significance. - 5.10 Derivation of the Formulas of Section 5.7. - 6 NONUNIQUENESS AND LOCALIZED AVERAGES. - 6.1 Null Vectors and Nonuniqueness. - 6.2 Null Vectors of a Simple Inverse Problem. - 6.3 Localized Averages of Model Parameters. - 6.4 Relationship to the Resolution Matrix. - 6.5 Averages versus Estimates. - 6.6 Nonunique Averaging Vectors and A Priori Information. - 7 APPLICATIONS OF VECTOR SPACES. - 7.1 Model and Data Spaces. - 7.2 Householder Transformations. - 7.3 Designing Householder Transformations. - 7.4 Transformations That Do Not Preserve Length. - 7.5 The Solution of the Mixed-Determined Problem. - 7.6 Singular-Value Decomposition and the Natural Generalized Inverse. - 7.7 Derivation of the Singular-Value Decomposition. - 7.8 Simplifying Linear Equality and Inequality Constraints. - 7.9 Inequality Constraints. - 8 LINEAR INVERSE PROBLEMS AND NON-GAUSSIAN DISTRIBUTIONS. - 8.1 L1 Norms and Exponential Distributions. - 8.2 Maximum Likelihood Estimate of the Mean of an Exponential Distribution. - 8.3 The General Linear Problem. - 8.4 Solving L1 Norm Problems. - 8.5 The L [Infinity symbol] Norm. - 9 NONLINEAR INVERSE PROBLEMS. - 9.1 Parameterizations. - 9.2 Linearizing Parameterizations. - 9.3 The Nonlinear Inverse Problem with Gaussian Data. - 9.4 Special Cases. - 9.5 Convergence and Nonuniqueness of Nonlinear L2 Problems. - 9.6 Non-Gaussian Distributions. - 9.7 Maximum Entropy Methods. - 10 FACTOR ANALYSIS. - 10.1 The Factor Analysis Problem. - 10.2 Normalization and Physicality Constraints. - 10.3 Q-Mode and R-Mode Factor Analysis. - 10.4 Empirical Orthogonal Function Analysis. - 11 CONTINUOUS INVERSE THEORY AND TOMOGRAPHY. - 11.1 The Backus-Gilbert Inverse Problem. - 11.2 Resolution and Variance Trade-off. - 11.3 Approximating Continuous Inverse Problems as Discrete Problems. - 11.4 Tomography and Continuous Inverse Theory. - 11.5 Tomography and the Radon Transform. - 11.6 The Fourier Slice Theorem. - 11.7 Backprojection. - 12 SAMPLE INVERSE PROBLEMS. - 12.1 An Image Enhancement Problem. - 12.2 Digital Filter Design. - 12.3 Adjustment of Crossover Errors. - 12.4 An Acoustic Tomography Problem. - 12.5 Temperature Distribution in an Igneous Intrusion. - 12.6 L1, L2, and L [infinity symbol] Fitting of a Straight Line. - 12.7 Finding the Mean of a Set of Unit Vectors. - 12.8 Gaussian Curve Fitting. - 12.9 Earthquake Location. - 12.10 Vibrational Problems. - 13 NUMERICAL ALGORITHMS. - 13.1 Solving Even-Determined Problems. - 13.2 Inverting a Square Matrix. - 13.3 Solving Underdetermined and Overdetermined Problems. - 13.4 L2 Problems with Inequality Constraints. - 13.5 Finding the Eigenvalues and Eigenvectors of a Real Symmetric Matrix. - 13.6 The Singular-Value Decomposition of a Matrix. - 13.7 The Simplex Method and the Linear Programming Problem. - 14 APPLICATIONS OF INVERSE THEORY TO GEOPHYSICS. - 14.1 Earthquake Location and the Determination of the Velocity Structure of the Earth from Travel Time Data. - 14.2 Velocity Structure from Free Oscillations and Seismic Surface Waves. - 14.3 Seismic Attenuation. - 14.4 Signal Correlation. - 14.5 Tectonic Plate Motions. - 14.6 Gravity and Geomagnetism. - 14.7 Electromagnetic Induction and the Magnetotelluric Method. - 14.8 Ocean Circulation. - APPENDIX A: Implementing Constraints with Lagrange Multipliers. - APPENDIX B: L2 Inverse Theory with Complex Quantities. - REFERENCES. - INDEX

Note: J.S. Daly, R.A. Cliff, and B.W.D. Yardley: Preface / Geological Society, London, Special Publications, 43:vii-viii, doi:10.1144/GSL.SP.1989.043.01.01 --- E. J. Essene: The current status of thermobarometry in metamorphic rocks / Geological Society, London, Special Publications, 43:1-44, doi:10.1144/GSL.SP.1989.043.01.02 --- L. Ya. Aranovich and K. K. Podlesskii: Geothermobarometry of high-grade metapelites: simultaneously operating reactions / Geological Society, London, Special Publications, 43:45-61, doi:10.1144/GSL.SP.1989.043.01.03 --- Frank S. Spear: Relative thermobarometry and metamorphic P-T, paths / Geological Society, London, Special Publications, 43:63-81, doi:10.1144/GSL.SP.1989.043.01.04 --- R. H. Vernon: Porphyroblast-matrix microstructural relationships: recent approaches and problems / Geological Society, London, Special Publications, 43:83-102, doi:10.1144/GSL.SP.1989.043.01.05 --- John Ridley: Vertical movement in orogenic belts and the timing of metamorphism relative to deformation / Geological Society, London, Special Publications, 43:103-115, doi:10.1144/GSL.SP.1989.043.01.06 --- R. A. Jamieson and C. Beaumont: Deformation and metamorphism in convergent orogens: a model for uplift and exhumation of metamorphic terrains / Geological Society, London, Special Publications, 43:117-129, doi:10.1144/GSL.SP.1989.043.01.07 --- Peter K. Zeitler: The geochronology of metamorphic processes / Geological Society, London, Special Publications, 43:131-147, doi:10.1144/GSL.SP.1989.043.01.08 --- James J. Irwin, Charles Kirschbaum, Tek. H. Lim, Derek Powell, and William E. Glassley: A laser-microprobe study of argon isotopes in deformed pegmatites from the Northern Highlands of Scotland / Geological Society, London, Special Publications, 43:149-160, doi:10.1144/GSL.SP.1989.043.01.09 --- A. Reuter and R. D. Dallmeyer: K-Ar and 40Ar/39Ar dating of cleavage formed during very low-grade metamorphism: a review / Geological Society, London, Special Publications, 43:161-171, doi:10.1144/GSL.SP.1989.043.01.10 --- Hanan J. Kisch: Discordant relationship between degree of very low-grade metamorphism and the development of slaty cleavage / Geological Society, London, Special Publications, 43:173-185, doi:10.1144/GSL.SP.1989.043.01.11 --- J. J. De Yoreo, D. R. Lux, and C. V. Guidotti: The role of crustal anatexis and magma migration in the thermal evolution of regions of thickened continental crust / Geological Society, London, Special Publications, 43:187-202, doi:10.1144/GSL.SP.1989.043.01.12 --- C. P. Chamberlain and Douglas Rumble III: The influence of fluids on the thermal history of a metamorphic terrain: New Hampshire, USA / Geological Society, London, Special Publications, 43:203-213, doi:10.1144/GSL.SP.1989.043.01.13 --- Howard W. Day and C. Page Chamberlain: Implications of thermal and baric structure for controls on metamorphism: northern New England, USA / Geological Society, London, Special Publications, 43:215-222, doi:10.1144/GSL.SP.1989.043.01.14 --- L. Aguirre, B. Levi, and J. O. Nyström: The link between metamorphism, volcanism and geotectonic setting during the evolution of the Andes / Geological Society, London, Special Publications, 43:223-232, doi:10.1144/GSL.SP.1989.043.01.15 --- T. M. Gordon: Thermal evolution of the Kisseynew sedimentary gneiss belt, Manitoba: metamorphism at an early Proterozoic accretionary margin / Geological Society, London, Special Publications, 43:233-243, doi:10.1144/GSL.SP.1989.043.01.16 --- Peter H. Thompson: An empirical model for metamorphic evolution of the Archaean Slave Province and adjacent Thelon Tectonic Zone, north-western Canadian Shield / Geological Society, London, Special Publications, 43:245-263, doi:10.1144/GSL.SP.1989.043.01.17 --- Amalbikash Mukherjee: P-T-time history and thermal modelling of an anorthosite-granulite interface, Eastern Ghats metamorphic belt, India / Geological Society, London, Special Publications, 43:265-274, doi:10.1144/GSL.SP.1989.043.01.18 --- Leonid L. Perchuk: P-T-fluid regimes of metamorphism and related magmatism with specific reference to the granulite-facies Sharyzhalgay complex of Lake Baikal / Geological Society, London, Special Publications, 43:275-291, doi:10.1144/GSL.SP.1989.043.01.19 --- D. Ackermand, B. F. Windley, and A. Razafiniparany: The Precambrian mobile belt of southern Madagascar / Geological Society, London, Special Publications, 43:293-296, doi:10.1144/GSL.SP.1989.043.01.20 --- I. Cartwright and A. C. Barnicoat: Evolution of the Scourian complex / Geological Society, London, Special Publications, 43:297-301, doi:10.1144/GSL.SP.1989.043.01.21 --- M. A. H. Maboko, I. McDougall, and P. K. Zeitler: Metamorphic P-T path of granulites in the Musgrave Ranges, central Australia / Geological Society, London, Special Publications, 43:303-307, doi:10.1144/GSL.SP.1989.043.01.22 --- Eileen McLellan, Daniel Linder, and Jenny Thomas: Multiple granulite-facies events in the southern Appalachians, USA / Geological Society, London, Special Publications, 43:309-314, doi:10.1144/GSL.SP.1989.043.01.23 --- James M. McLelland: Pre-granulite-facies metamorphism in the Adirondack Mountains, New York / Geological Society, London, Special Publications, 43:315-317, doi:10.1144/GSL.SP.1989.043.01.24 --- F. Mengel and T. Rivers: Thermotectonic evolution of proterozoic and reworked Archaean terranes along the Nain-Churchill boundary in the Saglek Area, northern Labrador / Geological Society, London, Special Publications, 43:319-324, doi:10.1144/GSL.SP.1989.043.01.25 --- Motoyoshi Yoichi, Satoshi Matsubara, and Hiroharu Matsueda: P-T evolution of the granulite-facies rocks of the Lützow-Holm Bay region, East Antarctica / Geological Society, London, Special Publications, 43:325-329, doi:10.1144/GSL.SP.1989.043.01.26 --- H. R. Rollinson: Garnet—orthopyroxene thermobarometry of granulites from the north marginal zone of the Limpopo belt, Zimbabwe / Geological Society, London, Special Publications, 43:331-335, doi:10.1144/GSL.SP.1989.043.01.27 --- Volker Schenk: P-T-t path of the lower crust in The Hercynian fold belt of southern Calabria / Geological Society, London, Special Publications, 43:337-342, doi:10.1144/GSL.SP.1989.043.01.28 --- Daniel Vielzeuf and Christian Pin: Geodynamic implications of granulitic rocks in the Hercynian belt / Geological Society, London, Special Publications, 43:343-348, doi:10.1144/GSL.SP.1989.043.01.29 --- R. G. Warren and B. J. Hensen: The P-T evolution of the Proterozoic Arunta Block, central Australia, and Implications for tectonic evolution / Geological Society, London, Special Publications, 43:349-355, doi:10.1144/GSL.SP.1989.043.01.30 --- D. J. Waters: Metamorphic evidence for the heating and cooling path of Namaqualand granulites / Geological Society, London, Special Publications, 43:357-363, doi:10.1144/GSL.SP.1989.043.01.31 --- I. S. Buick and T. J. B. Holland: The P-T-t path associated with crustal extension, Naxos, Cyclades, Greece / Geological Society, London, Special Publications, 43:365-369, doi:10.1144/GSL.SP.1989.043.01.32 --- M. Franceschelli, I. Memmi, F. Pannuti, and C. A. Ricci: Diachronous metamorphic equilibria in the Hercynian basement of northern Sardinia, Italy / Geological Society, London, Special Publications, 43:371-375, doi:10.1144/GSL.SP.1989.043.01.33 --- P. K. Verma: The Himalayan metamorphism / Geological Society, London, Special Publications, 43:377-383, doi:10.1144/GSL.SP.1989.043.01.34 --- A. J. Barker and M. W. Anderson: The Caledonian structural—metamorphic evolution of south Troms, Norway / Geological Society, London, Special Publications, 43:385-390, doi:10.1144/GSL.SP.1989.043.01.35 --- Kevin W. Burton, Alan P. Boyle, Wendy L. Kirk, and Roger Mason: Pressure, temperature and structural evolution of the Sulitjelma fold-nappe, central Scandinavian Caledonides / Geological Society, London, Special Publications, 43:391-411, doi:10.1144/GSL.SP.1989.043.01.36 --- A. H. N. Rice, R.