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Information-based inversion and processing with applications [[electronic resource] /] / Tadeusz J. Ulrych, Mauricio D. Sacchi
| Information-based inversion and processing with applications [[electronic resource] /] / Tadeusz J. Ulrych, Mauricio D. Sacchi |
| Autore | Ulrych Tadeusz J |
| Pubbl/distr/stampa | Amsterdam ; ; London, : Elsevier, 2005 |
| Descrizione fisica | 1 online resource (437 p.) |
| Disciplina | 550 |
| Altri autori (Persone) | SacchiMauricio D |
| Collana | Handbook of geophysical exploration. Seismic exploration |
| Soggetto topico |
Inversion (Geophysics)
Prospecting - Geophysical methods - Mathematical models |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-64104-5
9786610641048 0-08-046134-4 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Contents; Some Basic Concepts; Introduction; Probability Distributions, Stationarity & Ensemble Statistics; Essentials of Probability Distributions; Ensembles, Expectations etc; The Ergodic Hypothesis; The Chebychev Inequality; Time Averages and Ergodidty; Properties of Estimators; Bias of an Estimator; An Example; Variance of an Estimator; An Example; Mean Square Error of an Estimator; Orthogonality; Orthogonal Functions and Vectors; Orthogonal Vector Space; Gram-Schmidt Orthogonalization; Remarks; Orthogonality and Correlation; Orthogonality and Eigenvectors; Fourier Analysis
IntroductionOrthogonal Functions; Fourier Series; The Fourier Transform; Properties of the Fourier Transform; The FT of Some Functions; Truncation in Time; Symmetries; Living in a Discrete World; Aliasing and the Poisson Sum Formula; Some Theoretical Details; Limits of Infinite Scries; Remarks; The z Transform; Relationship Between z and Fourier Transforms; Discrete Fourier Transform; Inverse DFT; Zero Padding; The Fast Fourier Transform (FFT); Linearity and Time Invariance; Causal Systems; Discrete Convolution; Convolution and the z Transform; Dcconvolution; Dipole Filters Invertibility of Dipole FiltersProperties of Polynomial Filters; Some Toy Examples for Clarity; Least Squares Inversion of Minimum Phase Dipoles; Inversion of Minimum Phase Sequences; Inversion of Nonminimum Phase Wavelets: Optimum Lag SpikingFilters; Discrete Convolution and Circulant Matrices; Discrete and Circular Convolution; Matrix Notation for Circular Convolution; Diagonalization of the Circulant Matrix; Applications of the Circulant; Convolution; Deconvolution; Efficient Computation of Large Problems; Polynomial and FT Wavelet Inversion; Expectations etc.,; The Covariance Matrix Lagrange MultipliersLinear Time Series Modelling; Introduction; The Wold Decomposition Theorem; The Moving Average. MA, Model; Determining the Coefficients of the MA Model; Computing the Minimum Phase Wavelet via the FFT; The Autoregressive, AR, Model; Autocovariance of the AR Process; Estimating the AR Parameters; The Levinson Recursion; Initialization; The Prediction Error Operator, PEO; Phase Properties of the PEO; Proof of the Minimum Delay Property of the PEO; The Autoregressive Moving Average, ARMA, Model; A Very Special ARMA Process MA, AR and ARMA Models in Seismic Modelling and ProcessingExtended AR Models and Applications; A Little Predictive Deconvolution Theory; The Output of Predictive Deconvolution; Remarks; Summary; A Few Words About Nonlinear Time Series; The Principle of Embedding; Summary; Levinson's Recursion and Reflection Coefficients; Theoretical Summary; Summary and Remarks; Minimum Phase Property of the PEO; PROOF I; Eigenvectors of Doubly Symmetric Matrices; Spectral decomposition; Minimum phase property; PROOF II; Discussion; Information Theory and Relevant Issues; Introduction Entropy in Time Series Analysis |
| Record Nr. | UNINA-9910458822303321 |
Ulrych Tadeusz J
|
||
| Amsterdam ; ; London, : Elsevier, 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Information-based inversion and processing with applications [[electronic resource] /] / Tadeusz J. Ulrych, Mauricio D. Sacchi
| Information-based inversion and processing with applications [[electronic resource] /] / Tadeusz J. Ulrych, Mauricio D. Sacchi |
| Autore | Ulrych Tadeusz J |
| Pubbl/distr/stampa | Amsterdam ; ; London, : Elsevier, 2005 |
| Descrizione fisica | 1 online resource (437 p.) |
| Disciplina | 550 |
| Altri autori (Persone) | SacchiMauricio D |
| Collana | Handbook of geophysical exploration. Seismic exploration |
| Soggetto topico |
Inversion (Geophysics)
Prospecting - Geophysical methods - Mathematical models |
| ISBN |
1-280-64104-5
9786610641048 0-08-046134-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover; Contents; Some Basic Concepts; Introduction; Probability Distributions, Stationarity & Ensemble Statistics; Essentials of Probability Distributions; Ensembles, Expectations etc; The Ergodic Hypothesis; The Chebychev Inequality; Time Averages and Ergodidty; Properties of Estimators; Bias of an Estimator; An Example; Variance of an Estimator; An Example; Mean Square Error of an Estimator; Orthogonality; Orthogonal Functions and Vectors; Orthogonal Vector Space; Gram-Schmidt Orthogonalization; Remarks; Orthogonality and Correlation; Orthogonality and Eigenvectors; Fourier Analysis
IntroductionOrthogonal Functions; Fourier Series; The Fourier Transform; Properties of the Fourier Transform; The FT of Some Functions; Truncation in Time; Symmetries; Living in a Discrete World; Aliasing and the Poisson Sum Formula; Some Theoretical Details; Limits of Infinite Scries; Remarks; The z Transform; Relationship Between z and Fourier Transforms; Discrete Fourier Transform; Inverse DFT; Zero Padding; The Fast Fourier Transform (FFT); Linearity and Time Invariance; Causal Systems; Discrete Convolution; Convolution and the z Transform; Dcconvolution; Dipole Filters Invertibility of Dipole FiltersProperties of Polynomial Filters; Some Toy Examples for Clarity; Least Squares Inversion of Minimum Phase Dipoles; Inversion of Minimum Phase Sequences; Inversion of Nonminimum Phase Wavelets: Optimum Lag SpikingFilters; Discrete Convolution and Circulant Matrices; Discrete and Circular Convolution; Matrix Notation for Circular Convolution; Diagonalization of the Circulant Matrix; Applications of the Circulant; Convolution; Deconvolution; Efficient Computation of Large Problems; Polynomial and FT Wavelet Inversion; Expectations etc.,; The Covariance Matrix Lagrange MultipliersLinear Time Series Modelling; Introduction; The Wold Decomposition Theorem; The Moving Average. MA, Model; Determining the Coefficients of the MA Model; Computing the Minimum Phase Wavelet via the FFT; The Autoregressive, AR, Model; Autocovariance of the AR Process; Estimating the AR Parameters; The Levinson Recursion; Initialization; The Prediction Error Operator, PEO; Phase Properties of the PEO; Proof of the Minimum Delay Property of the PEO; The Autoregressive Moving Average, ARMA, Model; A Very Special ARMA Process MA, AR and ARMA Models in Seismic Modelling and ProcessingExtended AR Models and Applications; A Little Predictive Deconvolution Theory; The Output of Predictive Deconvolution; Remarks; Summary; A Few Words About Nonlinear Time Series; The Principle of Embedding; Summary; Levinson's Recursion and Reflection Coefficients; Theoretical Summary; Summary and Remarks; Minimum Phase Property of the PEO; PROOF I; Eigenvectors of Doubly Symmetric Matrices; Spectral decomposition; Minimum phase property; PROOF II; Discussion; Information Theory and Relevant Issues; Introduction Entropy in Time Series Analysis |
| Record Nr. | UNINA-9910784533103321 |
|
Ulrych Tadeusz J
|
||
| Amsterdam ; ; London, : Elsevier, 2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
