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  • 1
    Monograph available for loan
    Monograph available for loan
    San Diego : Academic Press
    Associated volumes
    Call number: 5/M 92.0428 ; AWI S2-95-0210
    In: International geophysics series, Volume 45
    Type of Medium: Monograph available for loan
    Pages: xii, 289 Seiten , Illustrationen
    Edition: revised edition
    ISBN: 0124909213 , 0-12-490921-3
    Series Statement: International geophysics series 45
    Classification:
    A.2.1.
    Language: English
    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
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  • 2
    Call number: AWI A5-93-0227 ; MOP 29824(28)
    In: Advances in geophysics, 28B
    Type of Medium: Monograph available for loan
    Pages: XVI, 432 Seiten , Illustrationen
    ISBN: 012018849X
    Series Statement: Advances in geophysics 28B
    Language: English
    Note: Contents: Contributors. - Foreword. - Preface. - PART 1. NUMERICAL WEATHER PREDICTION. - Medium-range forecasting at the ECMWF / Lennart Bengtsson. - 1. Introduction. - 2. The physical and mathematical basis for medium-range forecasting. - 3. Numerical methods and modeling techniques. - 4. Observations, their use and importance. - 5. Operational application and results. - 6. Problems and prospects in numerical weather prediction. - 7. Concluding remarks. - References. - Extended range forecasting / K. Miyakoda and J. Sirutis. - 1. Introduction. - 2. An evolution of 10-day forecast performance. - 3. Examples of monthly forecasts. - 4. A projection of seasonal forecasts. - 5. Postscript. - References. - Predictability / J. Shukla. - 1. Introduction. - 2. Classical predictability studies. - 3. Predictability of space-time averages. - 4. Some outstanding problems. - 5. Concluding remarks. - References. - Data Assimilation / W. Bourke, R. Seaman, and K. Puri. - 1. Introduction. - 2. Evolution of assimilation and the FGGE. - 3. Components of four-dimensional assimilation systems. - 4. Characteristics of some current Assimilation schemes. - 5. Role of four-dimensional assimilation in research and operations. - 6. Conclusion. - References. - PART 2. MESOSCALE DYNAMICS. - Predictability of mesoscale atmospheric motions / Richard A. Anthes, Ying-Hwa Kuo, David P. Baumhefner, Ronald M. Errico, and Thomas W. Bettge. - 1. Introduction. - 2. Classic predictability experiments and their relationship to mesoscale predictability. - 3. Preliminary predictability study with a mesoscale model. - 4. Discussion and comparison with a predictability study using a global model. - 5. Summary and conclusions. - References. - Thermal and orographic mesoscale atmospheric systems - an essay / Roger A. Pielke. - 1. Introduction. - 2. Summary of major research accomplishments. - 3. Research areas. - 4. Eventual goals. - References. - Advances in the theory of atmospheric fronts / I. Orlanski, B. Ross, L. Polinsky, and R. Shaginaw. - 1. Introduction. - 2. Baroclinic waves and fronts. - 3. Mature front. - 4. What observed features can be explained by theory?. - 5. What other processes are important in Frontogenesis?. - References. - PART 3. TROPICAL DYNAMICS. - Numerical modeling of tropical cyclones / Yoshio Kurihara. - 1. Introduction. - 2. Numerical models of hurricanes. - 3. Numerical simulation of tropcial cyclones. - 4. Some challenging issues in the future. - Appendix. GFDL Hurricane Model. - References. - Numerical weather prediction in low latitudes / T. N. Krishnamurti. - 1. Introduction. - 2. Initialization: dynamic, normal mode, and physical. - 3. Parameterization of physical processes. - 4. Medium-range prediction of monsoon disturbances. - 5. On the prediction of the quasi-Stationary component. - 6. Scope of future research. - References. - PART 4. TURBULENCE AND CONVECTION. - Sub-grid-scale turbulence modeling / J. W. Deardorff. - 1. Introduction: the need for grid-scale Reynolds averaging. - 2. The effect of grid-volume Reynolds averaging. - 3. The sub-grid scale Eddy Coefficient. - 4. Recent developments. - 5. Future outlook. - References. - Ensemble average, turbulence closure / George L. Mellor. - 1. Introduction. - 2. The turbulence macroscale and turbulence closure. - 3.Averaging distance for measurements in the atmosphere and oceans and for numerical models. - 4. Numerical modeling applications and horizontal diffusion. - 5. Concluding remarks. - References. - The planetary boundary layer / H. A. Panofsky. - 1. General characteristics. - 2. The equations in the PBL. - 3. The surface layer. - 4. First- and second-order closures. - 5. Boundary-layer models. - 6. Boundary-layer parameterization. - References. - Modeling studies and convection / Yoshi Ogura. - 1. Introduction. - 2. Bénard-Rayleigh Convection. - 3. Complexity of convection in the atmosphere. - 4. Shallow moist convection. - 5. Deep moist convection. - 6. Feedback effects of cumulus clouds on larger-scale environments. - 7. Concluding remarks. - References. - Index.
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