LEADER 05623nam 2200685Ia 450 001 9910458822303321 005 20200520144314.0 010 $a1-280-64104-5 010 $a9786610641048 010 $a0-08-046134-4 024 3 $z9780080447216 035 $a(CKB)1000000000383945 035 $a(EBL)270301 035 $a(SSID)ssj0000072350 035 $a(PQKBManifestationID)11110307 035 $a(PQKBTitleCode)TC0000072350 035 $a(PQKBWorkID)10095783 035 $a(PQKB)10725062 035 $a(MiAaPQ)EBC270301 035 $a(Au-PeEL)EBL270301 035 $a(CaPaEBR)ebr10137949 035 $a(CaONFJC)MIL64104 035 $a(OCoLC)74850405 035 $a(EXLCZ)991000000000383945 100 $a20060124d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInformation-based inversion and processing with applications$b[electronic resource] /$fTadeusz J. Ulrych, Mauricio D. Sacchi 210 $aAmsterdam ;$aLondon $cElsevier$d2005 215 $a1 online resource (437 p.) 225 0 $aHandbook of geophysical exploration. Seismic exploration ;$vv.36 300 $aDescription based upon print version of record. 311 $a0-08-044721-X 320 $aIncludes bibliographical references and index. 327 $aCover; 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 327 $aIntroductionOrthogonal 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 327 $aInvertibility 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 327 $aLagrange 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 327 $aMA, 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 327 $aEntropy in Time Series Analysis 330 $aThis book examines different classical and modern aspects of geophysical data processing and inversion with emphasis on the processing of seismic records in applied seismology. Chapter 1 introduces basic concepts including: probability theory (expectation operator and ensemble statistics), elementary principles of parameter estimation, Fourier and z-transform essentials, and issues of orthogonality. In Chapter 2, the linear treatment of time series is provided. Particular attention is paid to Wold decomposition theorem and time series models (AR, MA, and ARMA) and their connection t 410 0$aHandbook of geophysical exploration.$nSection I,$pSeismic exploration ;$vv. 36. 606 $aInversion (Geophysics) 606 $aProspecting$xGeophysical methods$xMathematical models 608 $aElectronic books. 615 0$aInversion (Geophysics) 615 0$aProspecting$xGeophysical methods$xMathematical models. 676 $a550 700 $aUlrych$b Tadeusz J$0880202 701 $aSacchi$b Mauricio D$0880203 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910458822303321 996 $aInformation-based inversion and processing with applications$91965321 997 $aUNINA