ALBERT

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: TABLE OF CONTENTS FOREWORD 1 INTRODUCTION AND SURVEY OF RADIOANALYSIS 1.1 Introduction 1.2 Principles of radioanalysis 1.2.1 General 1.2.2 Glossary of basic terms and concepts 1.3 Scope and contents References 2 SAMPLING AND PRECONCENTRATION 2.1 Survey and principles 2.1.1 Sampling 2.1.2 From sample to aliquot 2.1.2 .1 General 2.1.2.2 Granular material 2.1.2.3 Water 2.2 Sampling procedures 2.2.1 Rocks 2.2.2 Sediments and pore water 2.2.2.1 Sediments 2.2.2.2 Pore water 2.2.3 Fresh and ground water and related particulate matter 2.2.3.1 Fresh water 2.2.3.2 Ground water 2.2.4 Sea- and estuarine water and related particulate matter and sediments 2.2.4.1 Water 2.2.4.2 Particulate matter 2.2.4.3 Sediment cores 2.2.5 Rainwater and dry deposition 2.2.5.1 Rainwater 2.2.5.2 Dry deposition 2.3 Preconcentration 2.3.1 General 2.3.2 Fresh water and rainwater 2.3.3 Seawater 2.3.3.1 Survey 2.3.3.2 Scavenging procedures 2.3.3.3 Ion-exchange and solvent extraction procedures for Th, U and Pu 2.4 Reference materials 2.4.1 Principle 2.4.2 Survey of reference materials and SRM's 2.4.3 Use of reference materials and SRM's 2.4.3.1 Reference materials 2.4.3.2 SRM's 2.4.4 Reference materials for environmental radioactivity and isotopic ratio measurements References 3 INSTRUMENTAL RADIOANALYSIS OF GEOLOGICAL MATERIALS 3.1 Survey 3.1.1 Activation analysis 3.1.2 Photon activation analysis 3.1.3 Charged particle activation analysis (CPAA and HIAA) 3.1.4 Prompt techniques 3.1.4.1 Neutron induced prompt capture y-ray measurement (PGAA) 3.1.4.2 Proton induced X-ray emission (PIXE) 3.2 Principles 3.2.1 Principles of instrumental neutron activation analysis (INAA) 3.2.1.1 Activation 3.2.1.2 Standardization and flux monitoring 3.2.1.3 Count rate 3.2.1.4 Counting result 3.2.1.5 Sensitivity 3.2.1.6 Characteristic parameters of the three types of neutron activation 3.2.2 Delayed neutron counting 3.2.3 Activation analysis with high-energy photons 3.2.4 Principles of charged particle activation analysis (CPAA) 3.2.5 Principles of prompt techniques 3.2.5.1 Prompt capture gamma-ray measurements (PGAA) 3.2.5.2 Proton induced X-ray emission (PIXE) 3.3 Practical aspects of INAA, IPAA and PIXE 3.3.1 The radioanalytical laboratory 3.3.2 Irradiation facilities for NAA 3.3.2.1 Nuclear reactors 3.3.2.2 Rabbit systems 3.3.2.3 Epithermal activation 3.3.2.4 Neutron generators 3.3.2.5 Delayed neutron counting 3.3.3 Routing of INAA 3.3.4 Practical aspects of IPAA 3.3.5 Practical aspects of CPAA 3.3.6 Practical aspects of PGAA 3.3.7 Practical aspects of PIXE and PIGE 3.3.7.1 Proton induced X-ray emission (PIXE) 3.3.7.2 Proton induced prompt gamma emission (PIGE) 3.3.8 The error-budget 3.4 Multielement determination by INAA based on gamma-ray spectrometry 3.4.1 General 3.4.2 A practical procedure for INAA of silicates based on thermal neutrons 3.4.2.1 Preparation of sample and standards for irradiation 3.4.2.2 Irradiation and measurements 3.4.2.3 Conclusion 3.4.3 Rocks and ores 3.4.4 Meteorites 3.4.5 Sediments 3.4.6 Air-dust 3.4.7 Coal and ash 3.5 Instrumental neutron activation analysis of the lanthanides 3.6 Instrumental neutron activation analysis of uranium 3.7 Applications of instrumental neutron activation analysis with an isotopic neutron source and a 14.5 MeV neutron generator 3.7.1 Survey 3.7.2 INAA with isotopic neutron sources in the radiochemical laboratory 3.7.3 INAA with the neutron generator in the radiochemical laboratory 3.7.4. Conclusion 3.8 Applications of IPAA to silicates 3.9 Applications of IPAA to silicates 3.10 Applications of prompt techniques 3.10.1 Applications of PGAA and PIGE 3.10.2 Applications of PIXE References 4 NEUTRON ACTIVATION ANALYSIS INCLUDING CHEMICAL SEPARATION OF GEOLOGICAL SAMPLES 4.1 Introduction 4.2 Dissolution procedures and separation schemes 4.3 Lanthanides 4.3.1 General 4.3.2 Present procedures 4.4 Noble metals 4.4.1 General 4.4.2 Separation schemes 4.4.3 Single element determinations 4.5 Uranium and thorium 4.5.1 General 4.5.2 Procedures 4.5.2.1 Uranium 4.5.2.2 Thorium 4.6 Other elements 4.6.1 General 4.6.2 Alkali metals 4.6.3 Earth alkali metals 4.6.4 Copper and zinc 4.6.5 Mercury 4.6.6 Indium 4.6.7 Thallium 4.6.8 Tin 4.6.9 Elements with volatile halides and hydrides: Ga, Ge, As, Se, Sb, Te 4.6.9.1 Survey 4.6.9.2 Procedures 4.6.10 Vanadium and tantalum 4.6.11 Chromium 4.6.12 Molybdenum andtungsten 4.6.13 Halogens References 5 RADIOANALYSIS OF WATER 5.1 Survey 5.2 Elemental analysis of fresh water 5.2.1 Survey 5.2.2 Routine elemental analysis of rainwater 5.2.2.1 Sampling and sample treatment 5.2.2.2 Irradiation and processing of aliquots 5.2.2.3 Results 5.2.3 Special elemental analysis of rainwater 5.2.3.1 Bromine and iodine by isotopic exchange 5.2.3.2 Iodate by anion-exchange 5,2.3.3 Silver by cation-exchange and subsequent INAA 5.2.4 Routine elemental analysis of surface and ground water 5.2.4,1 General 5.2.4.2 Routine procedures 5.3 Elemental analysis of seawater 5.3.1 Survey 5.3.2 Routine elemental analysis of seawater by preconcentration on a "Chelex"-column and INAA 5.3.3 Routine elemental analysis of seawater by preconcentration on active carbon 5.3.3,1 General 5.3.3.2 Arsenic and antimony 5,3.3.3 Vanadium, iodine, tellurium and uranium 5.3.3.4 Total antimony, molybdenum and tungsten 5,3.3.5 Chromate, cobalt, nickel and tetravalent selenium 5.3.3,6 Mercury 5.3.4 Special elemental analysis of seawater 5.3.4.1 General 5.3.4.2 Rubidium and cesium 5.3.4.3 Strontium 5.3.4.4 Manganese and zinc 5,3,4.5 Tin 5.3.4.6 Nickel 5.3.4.7 Noble metals 5.3.4.8 Mercury References 6 RADIOTRACER EXPERIMENTS IN THE LABORATORY 6.1 Survey 6.2 Basic equations of radiotracer experiments in closed systems 6.3 Isotopic exchange in solution 6.4 Isotopic exchange between a solution and a solid 6.5 Reactions in solution 6.6 Reaction between a solution and a solid 6.6.1 Dissolution 6.6. 2 Leaching 6.6.3 Diffusion from solids 6.6.4 Sorption 6.7 Migration studies in solid-liquid systems 6.7.1 General 6.7.2 The determina tion of distribution coefficients in seawater 6.7.3 Radioecological column experiments in the laboratory 6.7.4 Laboratory experiments on very slow migration; the case of the actinides References 7 RADIOTRACER EXPERIMENTS IN THE FIELD 7.1 Survey 7.2 Principles of (radio)tracer experiments in open systems with flow in one direction 7.2.1 Basic concepts 7.2.2 Measurement of linear velocity and flow rate 7.2.3 Measurement of axial dispersion 7.2.4 Measurement of sedimentation rates 7.2.4.1 General 7.2.4.2 Lead-210 7.2.4.3 Cesium-137 7.2.5 Measurement of the degree of sediment mixing 7.2.6 Measurement of filtration velocity in case of horizontal groundwater flow 7.2.7 Measurement of groundwater flow in the unsaturated zone by radiocarbon 7.3 Principles of (radio)tracer experiments in open systems with flow in various directions 7.3.1 Survey 7.3.2 Measurement of sand or silt flow rates on the sea floor 7.3.3 Radiotracer measurements in water movement in the saturated zone 7.3.4 Radiotracer measurement on water movement in the unsaturated zone 7.4 Practical aspects of radiotracer experiments in the field 7.4.1 Preparation 7.4.2 Performance 7.4.3 Calculations References 8 MEASUREMENT OF NATURAL RADIOACTIVITY 8.1 General 8.1.1 Survey 8.1.2 Concentrations 8.1.3 Detection by direct measurement ofradiation 8.1.3.1 In situ measurements of uranium and thorium 8.1.3.2 Laboratory measurements 8.1.4 Detection by secundary effects 8.2 Measurement of low-level gamma-activities 8.2.1 General 8.2.2 A low background system (LBS) 8.2.2.1 Set-up 8.2.2.2 Limits of detection and determination 8.2.2.3 Processing of data 8.2.3. Anti-coincidence (AC)-counting 8.3 Measurements in rocks and sediments 8.3.1 General 8.3.2 Radon measurements (emanometry) 8.3.3 Age dating by measurement of disequilibrium in the natural decay-series 8.3.3.1 General 8.3.3.2 234U-230Th 8.3.3.3 235U-231Pa 8.3.3.4 232Th-230Th 8.3.3.5 230Th-231Pa 8.3.4 Environmental laboratory measurements on naturally occurring radionucl

Note: Table of Contents: Copyright; Additional copies. - Foreword and acknowledgements. - Chapter 1. Cosmochemistry of the Rare Earth Elements: Condensation and Evaporation Processes / by William V. Boynton. - Introduction. - Meteorites. - Astrophysical context for interpretation of cosmochemical data. - Solar nebula. - Solar abundances. - Cosmochemical properties of the REE. - REE condensation reactions. - Activity coefficients. - Partial pressures. - Solid / gas distribution coefficients. - Why are the REE volatilities so different?. - Calculated REE patterns. - Early condensates. - Removing REE in the gas. - Comparison with meteoritic data. - Ultra-refractory component. - Group II inclusions. - FUN inclusions. - REE condensation as a function of oxygen fugacity. - Rims on CAI. - What have we learned from the REE?. - High temperatures were achieved in the solar nebula. - A very efficient mechanism for gas/dust separation existed in the solar nebula. - The high nebular temperatures existed for a long time. - A very intense, very brief, heat source also existed. - The solar nebula was a chaotic environment. - Summary. - Acknowledgements. - References. - Chapter 2. Radiogenic Isotope Geochemistry of Rare Earth Elements / by P. Jonathan Patchett. - Introduction. - Long-lived radioactive isotopes of Rare Earth Elements. - 138La-138Ce decay. - 147Sm-143Nd decay. - 176Lu-176Hf decay. - Cemical variations of La/Ce, Sm/Nd and Lu/Hf ratios. - Geochronological studies. - La-Ce and Lu-Hf chronology. - Sm-Nd chronology. - Defining bulk planetary isotopic evolution. - Isotopic study of planetary interiors. - The Moon. - The Earth. - Nd isotopes in studies of terrestrial crustal evolution. - Model Nd ages of continental crust. - Growth curves for the continental crust. - Origin of granitoids. - Nd isotopes and the sedimentary system. - Characterization of whole crustal terranes. - Crustal Lu-Hf isotopic studies. - Major unsolved problems. - Continental crustal growth curve. - Abundance of Archean continental crust. - Origin of mantle isotopic variations. - References. - Chapter 3. Partitioning of Rare Earth Elements between Major Silicate Minerals and Basaltic Melts / by Gordon A. McKay. - Introduction. - Usefulness of the REE for petrogenetic modelling. - Scope of this chapter. - Caveat. - How partition coefficients are measured. - Phenocryst/matrix studies of natural samples. - Experimental measurement of partition coefficients. - Basic experimental approach. - Equilibrium. - Percent level doping technique. - Beta-track mapping technique. - Other experimental approaches. - Henry's law: The applicability of percent-level doping results. - Factors governing mineral/melt partitioning. - Ionic size and charge of trace element. - Crystal field effects. - Cristallographic versus defect sites: The Henry's law question. - Phase compositions. - Oxidation state. - Thermodynamic relationships: Dependence of partitioning on temperature and composition. - Other predictive approaches. - Special applications. - Eu as an oxygen fugacity indicator. - Origin of the Eu anomaly in lunar mare basalts. - REE partition coefficient patterns for the major minerals. - Plagioclase. - Olivine. - Pyroxene. - Low-Ca pyroxene. - High-Ca pyroxene. - Garnet. - Future directions. - Acknowledgements. - References. - Chapter 4. An Approach to Trace Element Modeling Using a Simple Igneous System as an Example / by Gilbert N. Hanson. - Introduction. - Review of trace element equations. - Melting. - Fractional crystallization. - Melting versus fractional crystallization. - Essential structural constituents. - Example of petrogenetic approach. - Discussion and summary. - Acknowledgements. - References. - Chapter 5. Rare Earth Elements in Upper Mantle Rocks / by W. F. McDonough and Fredrick A. Frey. - Introduction. - Massive peridotites. - Massive peridotites: dominantly lherzolite Western Alps - Lanzo. - Western Alps -Baldissero, Balmuccia. - Eastern Liguria, Italy. - Western Liguria, Italy. - Eastern Pyrenees - France. - Ronda, Spain Effects of late stage alteration on REE. - What can be inferred about the melting process and the segregated melts?. - Massive peridotites: pyroxenite layers and veins and their wall rocks. - Amphibole-bearing pyroxenite veins. - Anhydrous pyroxenite layers. - How were the pyroxenite layers created? Evidence for multistage processes. - Implications for mantle enrichment processes (metasomatism). - Massive peridotites: dominantly harzburgite. - Oceanic peridotites. - Ultramafic xenoliths. - Group I spinel peridotites. - Garnet peridotites. - Pyroxenite and related xenoliths. - Models for REE abundance trends in peridotite xenoliths. - Megacrysts, minerals in xenoliths and damong inclusions. - Megacrysts. - Minerals in peridotites and pyroxenites. - Inclusions in diamonds. - Summary: comparison of peridotites from massifs and xenoliths and implications of REE data for Upper Mantle composition. - Acknowledgements. - References. - Chapter 6. Rare Earth Elements in Metamorphic Rocks / by Richard I. Grauch. - Introduction. - REE residence in metamorphic rocks. - REE mobility during metamorphism. - REE content of metamorphic rocks. - Suggestions for future work. - Acknowledgements. - References. - Chapter 7. Rare Earth Elements in Sedimentary Rocks: Influence of Provenance and Sedimentary Processes / by Scott M. McLennan. - Introduction. - Rare earth element properties and sedimentary rocks. - Cosmochemical considerations. - Geochemical considerations. - Aqueous geochemistry. - Normalizing and notation. - Sedimentary processes. - Weathering. - Diagenesis. - Sedimentary sorting. - REE and provenance studies. - Sedimentary rocks and crustal abundances. - Sedimentation and plate tectonics. - Archean sedimentary rocks and the Archean crust. - Archean greenstone belts. - REE in sedimentary rocks and crustal evolution. - Acknowledgements. - References. - Chapter 8. Aqueous Geochemistry of Rare Earth Elements / by Douglas G. Brookins. - Introduction. - The trivalent lanthanides (Ln III). - Types of complexes in solution. - Hydrolysis products. - Phosphate complexes. - Carbonate complexes. - Halide complexes. - Complexes with total dissolved sulfur. - Gadolinium-Terbium fractionation?. - Scandium and Yttrium. - Europium (II). - Cerium (IV). - Eh-pH diagrams. - Cerium. - Europium. - Other lanthanides. - Lanthanides in ocean waters. - Lanthanides and actinides. - Concluding remarks. - Acknowledgements. - References. - Chapter 9. Rare Earth Elements in Lunar Materials / by Larry A. Haskin. - Introduction. - The nature of planet moon. - The magma ocean hypothesis and its presumed products. - Lunar REE patterns. - Highland plutonic rocks. - Anorthosites. - Durâtes, troctolites, norites, and gabbros. - Lunar felsite (granite). - Highland volcanic rocks: KREEP. - Mare basalts. - Mare basalt sources as magma ocean products. - Assimilation of crusted material during basalt petrogenesis. - Glassy spherules. - Soils and breccias. - Caveat. - Acknowledgements. - References. - Chapter 10. Compositional and Phase Relations among Rare Earth Element Minerals / by Donald M. Burt. - Introduction. - Geochemical background. - Minerals. - Coupled substitutions. - Vector treatment. - Application to selected mineral groups. - Fluorides. - Carbonates. - Fluorocarbonates. - Monazite, xenotime, zircon, and related phases. - Apatites. - Florencite and related phases. - A-B oxides (niobates, tantalates, titanates, ferrites). - Fergusonitelbetafergusonite, ABO4. - Perovskite, ABO3. - Aeschyniteleuxenite, AB2O6. - Pyrochlore, A1-2B2O6(O,F,OH). - Allanite. - Titanite. - Garnet. - Gadolinite. - Chevkinite/perrierite. - Element distributions: acid-base relations. - Summary. - Acknowledgemen