Geophysical data analysis: discrete inverse theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
San Diego
Academic Press
c1989
|
| Ausgabe: | Rev. ed |
| Schriftenreihe: | International geophysics series
v. 45 |
| Schlagworte: | |
| Online-Zugang: | DE-1046 DE-1047 Volltext |
| Beschreibung: | Includes bibliographical references (p. 277-280) and index Preface. -- Introduction. -- DESCRIBING INVERSE PROBLEMS -- Formulating Inverse Problems. -- The Linear Inverse Problem. -- Examples of Formulating Inverse Problems. -- Solutions to Inverse Problems. -- SOME COMMENTS ON PROBABILITY THEORY -- Noise and Random Variables. -- Correlated Data. -- Functions of Random Variables. -- Gaussian Distributions. -- Testing the Assumption of Gaussian Statistics -- Confidence Intervals. -- SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 1:THE LENGTH METHOD -- The Lengths of Estimates. -- Measures of Length. -- Least Squares for a Straight Line. -- The Least Squares Solution of the Linear Inverse Problem. -- Some Examples. -- The Existence of the Least Squares Solution. -- The Purely Underdetermined Problem. -- Mixed-b1Determined Problems. -- Weighted Measures of Length as a Type of A Priori Information. -- Other Types of A Priori Information. -- The Variance of the Model Parameter Estimates. -- - Variance and Prediction Error of the Least Squares Solution. -- SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 2: GENERALIZED INVERSES -- Solutions versus Operators. -- The Data Resolution Matrix. -- The Model Resolution Matrix. -- The Unit Covariance Matrix. -- Resolution and Covariance of Some Generalized Inverses. -- Measures of Goodness of Resolution and Covariance. -- Generalized Inverses with Good Resolution and Covariance. -- Sidelobes and the Backus-Gilbert Spread Function. -- The Backus-Gilbert Generalized Inverse for the Underdetermined Problem. -- Including the Covariance Size. -- The Trade-off of Resolution and Variance. -- SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 3: MAXIMUM LIKELIHOOD METHODS -- The Mean of a Group of Measurements. -- Maximum Likelihood Solution of the Linear Inverse Problem. -- A Priori Distributions. -- Maximum Likelihood for an Exact Theory. -- Inexact Theories. -- The Simple Gaussian Case with a Linear Theory. -- - The General Linear, Gaussian Case. -- Equivalence of the Three Viewpoints. -- The F Test of Error Improvement Significance. -- Derivation of the Formulas of Section 5.7. -- NONUNIQUENESS AND LOCALIZED AVERAGES -- Null Vectors and Nonuniqueness. -- Null Vectors of a Simple Inverse Problem. -- Localized Averages of Model Parameters. -- Relationship to the Resolution Matrix. -- Averages versus Estimates. -- Nonunique Averaging Vectors and A Priori Information. -- APPLICATIONS OF VECTOR SPACES -- Model and Data Spaces. -- Householder Transformations. -- Designing Householder Transformations. -- Transformations That Do Not Preserve Length. -- The Solution of the Mixed-Determined Problem. -- Singular-Value Decomposition and the Natural Generalized Inverse. -- Derivation of the Singular-Value Decomposition. -- Simplifying Linear Equality and Inequality Constraints. -- Inequality Constraints. -- LINEAR INVERSE PROBLEMS AND NON-GAUSSIAN DISTRIBUTIONS -- L1 Norms and Exponential Distributions Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies |
| Beschreibung: | 1 Online-Ressource (xii, 289 p.) |
| ISBN: | 0080507328 0124909213 9780080507323 9780124909212 |
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| 245 | 1 | 0 | |a Geophysical data analysis |b discrete inverse theory |c William Menke |
| 250 | |a Rev. ed | ||
| 264 | 1 | |a San Diego |b Academic Press |c c1989 | |
| 300 | |a 1 Online-Ressource (xii, 289 p.) | ||
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| 490 | 0 | |a International geophysics series |v v. 45 | |
| 500 | |a Includes bibliographical references (p. 277-280) and index | ||
| 500 | |a Preface. -- Introduction. -- DESCRIBING INVERSE PROBLEMS -- Formulating Inverse Problems. -- The Linear Inverse Problem. -- Examples of Formulating Inverse Problems. -- Solutions to Inverse Problems. -- SOME COMMENTS ON PROBABILITY THEORY -- Noise and Random Variables. -- Correlated Data. -- Functions of Random Variables. -- Gaussian Distributions. -- Testing the Assumption of Gaussian Statistics -- Confidence Intervals. -- SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 1:THE LENGTH METHOD -- The Lengths of Estimates. -- Measures of Length. -- Least Squares for a Straight Line. -- The Least Squares Solution of the Linear Inverse Problem. -- Some Examples. -- The Existence of the Least Squares Solution. -- The Purely Underdetermined Problem. -- Mixed-b1Determined Problems. -- Weighted Measures of Length as a Type of A Priori Information. -- Other Types of A Priori Information. -- The Variance of the Model Parameter Estimates. -- | ||
| 500 | |a - Variance and Prediction Error of the Least Squares Solution. -- SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 2: GENERALIZED INVERSES -- Solutions versus Operators. -- The Data Resolution Matrix. -- The Model Resolution Matrix. -- The Unit Covariance Matrix. -- Resolution and Covariance of Some Generalized Inverses. -- Measures of Goodness of Resolution and Covariance. -- Generalized Inverses with Good Resolution and Covariance. -- Sidelobes and the Backus-Gilbert Spread Function. -- The Backus-Gilbert Generalized Inverse for the Underdetermined Problem. -- Including the Covariance Size. -- The Trade-off of Resolution and Variance. -- SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 3: MAXIMUM LIKELIHOOD METHODS -- The Mean of a Group of Measurements. -- Maximum Likelihood Solution of the Linear Inverse Problem. -- A Priori Distributions. -- Maximum Likelihood for an Exact Theory. -- Inexact Theories. -- The Simple Gaussian Case with a Linear Theory. -- | ||
| 500 | |a - The General Linear, Gaussian Case. -- Equivalence of the Three Viewpoints. -- The F Test of Error Improvement Significance. -- Derivation of the Formulas of Section 5.7. -- NONUNIQUENESS AND LOCALIZED AVERAGES -- Null Vectors and Nonuniqueness. -- Null Vectors of a Simple Inverse Problem. -- Localized Averages of Model Parameters. -- Relationship to the Resolution Matrix. -- Averages versus Estimates. -- Nonunique Averaging Vectors and A Priori Information. -- APPLICATIONS OF VECTOR SPACES -- Model and Data Spaces. -- Householder Transformations. -- Designing Householder Transformations. -- Transformations That Do Not Preserve Length. -- The Solution of the Mixed-Determined Problem. -- Singular-Value Decomposition and the Natural Generalized Inverse. -- Derivation of the Singular-Value Decomposition. -- Simplifying Linear Equality and Inequality Constraints. -- Inequality Constraints. -- LINEAR INVERSE PROBLEMS AND NON-GAUSSIAN DISTRIBUTIONS -- L1 Norms and Exponential Distributions | ||
| 500 | |a Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Menke, William |
| author_facet | Menke, William |
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| dewey-ones | 551 - Geology, hydrology, meteorology |
| dewey-raw | 551 |
| dewey-search | 551 |
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| dewey-tens | 550 - Earth sciences |
| discipline | Geologie / Paläontologie |
| edition | Rev. ed |
| format | Electronic eBook |
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| id | DE-604.BV043045147 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-08T00:10:31Z |
| institution | BVB |
| isbn | 0080507328 0124909213 9780080507323 9780124909212 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028469685 |
| oclc_num | 427403877 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xii, 289 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Academic Press |
| record_format | marc |
| series2 | International geophysics series |
| spelling | Menke, William Verfasser aut Geophysical data analysis discrete inverse theory William Menke Rev. ed San Diego Academic Press c1989 1 Online-Ressource (xii, 289 p.) txt rdacontent c rdamedia cr rdacarrier International geophysics series v. 45 Includes bibliographical references (p. 277-280) and index Preface. -- Introduction. -- DESCRIBING INVERSE PROBLEMS -- Formulating Inverse Problems. -- The Linear Inverse Problem. -- Examples of Formulating Inverse Problems. -- Solutions to Inverse Problems. -- SOME COMMENTS ON PROBABILITY THEORY -- Noise and Random Variables. -- Correlated Data. -- Functions of Random Variables. -- Gaussian Distributions. -- Testing the Assumption of Gaussian Statistics -- Confidence Intervals. -- SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 1:THE LENGTH METHOD -- The Lengths of Estimates. -- Measures of Length. -- Least Squares for a Straight Line. -- The Least Squares Solution of the Linear Inverse Problem. -- Some Examples. -- The Existence of the Least Squares Solution. -- The Purely Underdetermined Problem. -- Mixed-b1Determined Problems. -- Weighted Measures of Length as a Type of A Priori Information. -- Other Types of A Priori Information. -- The Variance of the Model Parameter Estimates. -- - Variance and Prediction Error of the Least Squares Solution. -- SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 2: GENERALIZED INVERSES -- Solutions versus Operators. -- The Data Resolution Matrix. -- The Model Resolution Matrix. -- The Unit Covariance Matrix. -- Resolution and Covariance of Some Generalized Inverses. -- Measures of Goodness of Resolution and Covariance. -- Generalized Inverses with Good Resolution and Covariance. -- Sidelobes and the Backus-Gilbert Spread Function. -- The Backus-Gilbert Generalized Inverse for the Underdetermined Problem. -- Including the Covariance Size. -- The Trade-off of Resolution and Variance. -- SOLUTION OF THE LINEAR, GAUSSIAN INVERSE PROBLEM, VIEWPOINT 3: MAXIMUM LIKELIHOOD METHODS -- The Mean of a Group of Measurements. -- Maximum Likelihood Solution of the Linear Inverse Problem. -- A Priori Distributions. -- Maximum Likelihood for an Exact Theory. -- Inexact Theories. -- The Simple Gaussian Case with a Linear Theory. -- - The General Linear, Gaussian Case. -- Equivalence of the Three Viewpoints. -- The F Test of Error Improvement Significance. -- Derivation of the Formulas of Section 5.7. -- NONUNIQUENESS AND LOCALIZED AVERAGES -- Null Vectors and Nonuniqueness. -- Null Vectors of a Simple Inverse Problem. -- Localized Averages of Model Parameters. -- Relationship to the Resolution Matrix. -- Averages versus Estimates. -- Nonunique Averaging Vectors and A Priori Information. -- APPLICATIONS OF VECTOR SPACES -- Model and Data Spaces. -- Householder Transformations. -- Designing Householder Transformations. -- Transformations That Do Not Preserve Length. -- The Solution of the Mixed-Determined Problem. -- Singular-Value Decomposition and the Natural Generalized Inverse. -- Derivation of the Singular-Value Decomposition. -- Simplifying Linear Equality and Inequality Constraints. -- Inequality Constraints. -- LINEAR INVERSE PROBLEMS AND NON-GAUSSIAN DISTRIBUTIONS -- L1 Norms and Exponential Distributions Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies SCIENCE / Earth Sciences / Geography bisacsh SCIENCE / Earth Sciences / Geology bisacsh Geophysics / Measurement fast Inverse problems (Differential equations) / Numerical solutions fast Oceanography / Measurement fast Geografie Geologie Geowissenschaften Geophysics Measurement Oceanography Measurement Inverse problems (Differential equations) Numerical solutions Inversion Mathematik (DE-588)4162235-2 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Daten (DE-588)4135391-2 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Messung (DE-588)4038852-9 gnd rswk-swf Matrixinversion (DE-588)4374244-0 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Meereskunde (DE-588)4074685-9 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Geophysik (DE-588)4020252-5 gnd rswk-swf Datenauswertung (DE-588)4131193-0 gnd rswk-swf Geophysik (DE-588)4020252-5 s Daten (DE-588)4135391-2 s Inversion Mathematik (DE-588)4162235-2 s Datenauswertung (DE-588)4131193-0 s MATLAB (DE-588)4329066-8 s 1\p DE-604 Meereskunde (DE-588)4074685-9 s Messung (DE-588)4038852-9 s Inverses Problem (DE-588)4125161-1 s 2\p DE-604 3\p DE-604 Datenanalyse (DE-588)4123037-1 s 4\p DE-604 Matrixinversion (DE-588)4374244-0 s 5\p DE-604 Datenverarbeitung (DE-588)4011152-0 s 6\p DE-604 7\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=279574 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 6\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 7\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Menke, William Geophysical data analysis discrete inverse theory SCIENCE / Earth Sciences / Geography bisacsh SCIENCE / Earth Sciences / Geology bisacsh Geophysics / Measurement fast Inverse problems (Differential equations) / Numerical solutions fast Oceanography / Measurement fast Geografie Geologie Geowissenschaften Geophysics Measurement Oceanography Measurement Inverse problems (Differential equations) Numerical solutions Inversion Mathematik (DE-588)4162235-2 gnd Datenanalyse (DE-588)4123037-1 gnd Daten (DE-588)4135391-2 gnd Datenverarbeitung (DE-588)4011152-0 gnd Messung (DE-588)4038852-9 gnd Matrixinversion (DE-588)4374244-0 gnd Inverses Problem (DE-588)4125161-1 gnd Meereskunde (DE-588)4074685-9 gnd MATLAB (DE-588)4329066-8 gnd Geophysik (DE-588)4020252-5 gnd Datenauswertung (DE-588)4131193-0 gnd |
| subject_GND | (DE-588)4162235-2 (DE-588)4123037-1 (DE-588)4135391-2 (DE-588)4011152-0 (DE-588)4038852-9 (DE-588)4374244-0 (DE-588)4125161-1 (DE-588)4074685-9 (DE-588)4329066-8 (DE-588)4020252-5 (DE-588)4131193-0 |
| title | Geophysical data analysis discrete inverse theory |
| title_auth | Geophysical data analysis discrete inverse theory |
| title_exact_search | Geophysical data analysis discrete inverse theory |
| title_full | Geophysical data analysis discrete inverse theory William Menke |
| title_fullStr | Geophysical data analysis discrete inverse theory William Menke |
| title_full_unstemmed | Geophysical data analysis discrete inverse theory William Menke |
| title_short | Geophysical data analysis |
| title_sort | geophysical data analysis discrete inverse theory |
| title_sub | discrete inverse theory |
| topic | SCIENCE / Earth Sciences / Geography bisacsh SCIENCE / Earth Sciences / Geology bisacsh Geophysics / Measurement fast Inverse problems (Differential equations) / Numerical solutions fast Oceanography / Measurement fast Geografie Geologie Geowissenschaften Geophysics Measurement Oceanography Measurement Inverse problems (Differential equations) Numerical solutions Inversion Mathematik (DE-588)4162235-2 gnd Datenanalyse (DE-588)4123037-1 gnd Daten (DE-588)4135391-2 gnd Datenverarbeitung (DE-588)4011152-0 gnd Messung (DE-588)4038852-9 gnd Matrixinversion (DE-588)4374244-0 gnd Inverses Problem (DE-588)4125161-1 gnd Meereskunde (DE-588)4074685-9 gnd MATLAB (DE-588)4329066-8 gnd Geophysik (DE-588)4020252-5 gnd Datenauswertung (DE-588)4131193-0 gnd |
| topic_facet | SCIENCE / Earth Sciences / Geography SCIENCE / Earth Sciences / Geology Geophysics / Measurement Inverse problems (Differential equations) / Numerical solutions Oceanography / Measurement Geografie Geologie Geowissenschaften Geophysics Measurement Oceanography Measurement Inverse problems (Differential equations) Numerical solutions Inversion Mathematik Datenanalyse Daten Datenverarbeitung Messung Matrixinversion Inverses Problem Meereskunde MATLAB Geophysik Datenauswertung |
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| work_keys_str_mv | AT menkewilliam geophysicaldataanalysisdiscreteinversetheory |