Preface (First Edition) |
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xi | |
Preface (Second Edition) |
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xv | |
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1 Introduction to Multishooting: Challenges and Rewards |
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1.1 Dimensions and Notation Conventions |
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6 | (3) |
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6 | (1) |
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1.1.2 Dimensions of heterogeneous media |
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7 | (1) |
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1.1.3 Notation conventions |
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7 | (1) |
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1.1.4 The f-x and f-k domains |
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8 | (1) |
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1.2 Scattering Experiments in Petroleum Seismology |
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9 | (18) |
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1.2.1 Principles of seismic acquisition |
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11 | (6) |
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17 | (2) |
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1.2.3 Shot, receiver, midpoint, and offset gathers |
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19 | (4) |
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1.2.4 Multiazimuthal data |
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23 | (4) |
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1.3 Acquisition of Multishot Data |
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27 | (8) |
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1.3.1 Multiazimuth surveys |
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27 | (1) |
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1.3.2 Flip-flop acquisition |
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28 | (1) |
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1.3.3 Source encoding: the marine style |
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29 | (2) |
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1.3.4 Source encoding: the land-vibroseis style |
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31 | (2) |
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1.3.5 The challenges of multishooting acquisition |
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33 | (2) |
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1.4 Processing of Multishot Data |
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35 | (10) |
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1.4.1 Reciprocity theorems |
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35 | (3) |
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1.4.2 Cross-talk and challenges of the decoding process |
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38 | (5) |
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1.4.3 The challenges of imaging multishot data without decoding |
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43 | (2) |
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1.5 The Nonlinear Elasticity and the Superposition Principle |
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45 | (9) |
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1.5.1 Linear and nonlinear media |
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45 | (1) |
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1.5.2 Second-order nonlinear media |
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46 | (3) |
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49 | (5) |
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1.6 The Cocktail-Party Problem: A Multidisciplinary Problem |
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54 | (8) |
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1.6.1 A brief review of the cocktail-party problem |
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54 | (2) |
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1.6.2 Coding and decoding in communication theory |
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56 | (2) |
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1.6.3 Processing of multishot data without decoding |
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58 | (1) |
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1.6.4 Nearly simultaneous earthquakes |
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58 | (3) |
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1.6.5 Nearly simultaneous sources of volcanic activities |
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61 | (1) |
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1.7 Scope and Content of This Book |
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62 | (7) |
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63 | (6) |
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2 Decoding of Linear Instantaneous Mixtures |
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2.1 Seismic Data Representation as Random Variables |
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69 | (23) |
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2.1.1 Examples of random variables |
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69 | (7) |
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2.1.2 From seismic signals to seismic random variables |
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76 | (1) |
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2.1.3 Probability-density function (PDF) of seismic random variables |
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77 | (4) |
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2.1.4 Moments and cumulants of seismic random variables |
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81 | (6) |
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2.1.5 Negentropy: a measurement of non-Gaussianity |
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87 | (5) |
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2.2 Uncorrelatedness and Independence |
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92 | (35) |
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2.2.1 Joint probability-density functions and Kullback-Leibler divergence |
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93 | (8) |
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2.2.2 Joint moments and joint cumulants |
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101 | (5) |
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2.2.3 Uncorrelatedness and whiteness of random variables |
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106 | (1) |
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2.2.4 Independence of random variables |
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107 | (2) |
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2.2.5 Analysis of uncorrelatedness and independence with scatterplots |
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109 | (14) |
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123 | (4) |
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127 | (43) |
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2.3.1 Decoding by maximizing contrast functions |
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128 | (17) |
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2.3.2 Decoding by cumulant--tensor diagonalization |
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145 | (6) |
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2.3.3 ICA decoding by negentropy maximizing |
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151 | (7) |
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2.3.4 ICA decoding methods for noisy mixtures |
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158 | (6) |
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2.3.5 Decoding by joint diagonalization of the autocovariance matrices |
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164 | (6) |
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2.4 Constrained Independent Component Analysis (cICA) Decoding |
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170 | (28) |
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2.4.1 Negentropy maximization |
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171 | (9) |
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2.4.2 Cumulant-tensor diagonalization |
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180 | (4) |
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2.4.3 Nonorthogonal cICA, based on maximum likelihood |
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184 | (2) |
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186 | (12) |
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3 Decoding of Linear Convolutive Mixtures |
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3.1 Motivation and Foundation for Working in the T-F-X Domain |
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198 | (16) |
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3.1.1 Convolutive mixtures in the T-X domain |
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205 | (5) |
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3.1.2 Convolutive mixtures in the F-X domain |
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210 | (2) |
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3.1.3 Convolutive mixtures in the T-F-X domain |
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212 | (2) |
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3.2 Statistics of Complex Random Variables and Vectors |
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214 | (44) |
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3.2.1 The complex-valued gradient and the Hessian matrix |
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214 | (6) |
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3.2.2 Statistics of complex random variables |
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220 | (14) |
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3.2.3 Statistics of complex random vectors |
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234 | (15) |
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3.2.4 An analysis of the statistical independence of seismic data in the T-F-X domain |
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249 | (9) |
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3.3 Decoding in the T-F-X Domain |
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258 | (39) |
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3.3.1 Whiteness of complex random variables |
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258 | (1) |
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3.3.2 Decoding by negentropy maximization of complex random vectors |
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259 | (10) |
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3.3.3 Permutation inconsistency problem |
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269 | (2) |
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3.3.4 Cascaded and constrained ICA approaches |
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271 | (2) |
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273 | (24) |
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3.4 Decoding In other Domains and Nonlinear Mixtures |
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297 | (21) |
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3.4.1 Decoding in the F-X domain |
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297 | (1) |
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3.4.2 Decoding in the T-X domain |
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298 | (7) |
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3.4.3 Decoding of convolutive post-nonlinear mixtures |
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305 | (1) |
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306 | (12) |
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4 Decoding of Underdetermined Mixtures |
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4.1 Estimation of the Mixing Matrix |
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318 | (33) |
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4.1.1 Histograms of data-concentration directions |
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321 | (7) |
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4.1.2 Expectation maximization |
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328 | (11) |
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4.1.3 Histogram approach in the T-F-X domain |
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339 | (1) |
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4.1.4 Isolated single-shot estimation in the T-F-X domain |
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340 | (8) |
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4.1.5 Isolated single-shot estimation in the T-F domain |
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348 | (3) |
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4.2 ICA- and Sparsity-Based Decoding: 2M3S |
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351 | (12) |
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351 | (3) |
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4.2.2 ICA-based decoding: formulation |
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354 | (1) |
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4.2.3 ICA-based decoding: examples |
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355 | (3) |
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4.2.4 The compressive sensing relationship with multishooting |
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358 | (5) |
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4.3 Decoding Using Denoising Tools: 1M2S and 1M4S |
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363 | (40) |
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4.3.1 Phase encoding and cross-talk |
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363 | (8) |
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4.3.2 Basic formulation of phase encoding |
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371 | (2) |
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373 | (4) |
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4.3.4 Denoising-based decoding: C1-norm and total variations |
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377 | (4) |
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4.3.5 Compressive sensing and phase decoding data |
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381 | (5) |
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4.3.6 Denoising-based decoding: dictionary filtering |
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386 | (8) |
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4.3.7 Denoising-based decoding: median filtering |
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394 | (4) |
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4.3.8 Decoding with reference shots |
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398 | (5) |
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4.4 Multicomponent-Based Decoding: 1M2S, 1MS4, and 1M8S |
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403 | (4) |
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4.4.1 Simultaneous deghosting and decoding of multishot data |
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403 | (2) |
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4.4.2 Decoding of deghosted multishot data |
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405 | (2) |
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407 | (7) |
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4.6 ICA-Based Decoding: 1M16S |
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414 | (15) |
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4.6.1 Decoding in the T-F-X domain with a known mixing matrix |
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414 | (1) |
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4.6.2 Decoding based on isolated single-shot estimations |
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415 | (2) |
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4.6.3 Decoding in the T-F-X domain with an unknown mixing matrix |
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417 | (5) |
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422 | (7) |
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5 Decoding of Nonlinear Mixtures |
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5.1 Models of Nonlinear Mixtures |
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429 | (5) |
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5.1.1 The general nonlinear mixing model |
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429 | (2) |
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5.1.2 Post-nonlinear (PNL) mixtures |
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431 | (1) |
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5.1.3 Multilayer perceptron model |
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432 | (2) |
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5.1.4 Convolutive nonlinear mixtures |
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434 | (1) |
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5.2 Scatterplots of Nonlinear Mixtures |
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434 | (12) |
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434 | (6) |
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440 | (6) |
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5.3 Decoding of Post-Nonlinear Mixtures |
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446 | (44) |
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5.3.1 Alternating conditional expectations (ACE) |
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446 | (30) |
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5.3.2 Inverse of a specified cumulative distribution function (ICDF) |
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476 | (7) |
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5.3.3 Geometrical-transformation approach |
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483 | (7) |
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5.4 Kernel-Based Decoding of Nonlinear Mixtures |
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490 | (28) |
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5.4.1 The making of nonlinear mixtures |
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491 | (1) |
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5.4.2 A brief background on linear principal component analysis |
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491 | (3) |
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5.4.3 A nonlinear form of principal component analysis |
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494 | (10) |
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5.4.4 Construction of linearized mixtures and decoding |
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504 | (14) |
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5.5 Kernel Canonical Correlation Analysis |
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518 | (18) |
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5.5.1 Canonical correlation analysis |
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518 | (7) |
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5.5.2 Kernel canonical correlation analysis |
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525 | (7) |
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532 | (4) |
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6 Imaging of Multishot Data Without Decoding |
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536 | (54) |
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6.1.1 The NMF-based demultiple |
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537 | (20) |
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6.1.2 The sea-level-based demultiple |
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557 | (9) |
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6.1.3 Migration/inversion |
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566 | (8) |
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6.1.4 Velocity estimation |
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574 | (8) |
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582 | (8) |
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590 | (11) |
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590 | (8) |
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6.2.2 Seismic imaging machine |
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598 | (3) |
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6.3 Modeling. Decoding, and Imaging in Snapshot Domain |
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601 | (8) |
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6.3.1 Multicomponent recordings |
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601 | (1) |
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6.3.2 Alternating conditional expectations (ACE) |
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602 | (2) |
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604 | (5) |
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A Some Background on Sparsity Optimization |
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609 | (4) |
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609 | (2) |
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A.1.2 C0-minimization: definition |
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611 | (1) |
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A.1.3 Various ways of measuring sparsity |
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611 | (1) |
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A.1.4 C0-minimization: uniqueness |
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612 | (1) |
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613 | (21) |
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A.2.1 An example of a linear system |
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613 | (1) |
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A.2.2 Convex and nonconvex optimization problems |
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614 | (4) |
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A.2.3 A practical implementation of the C1-minimization |
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618 | (2) |
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A.2.4 C1-optimization of complex-valued data |
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620 | (14) |
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C Nonnegative Matrix Factorization |
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C.1 Lee-Seung Matrix Factorization Algorithm |
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634 | (14) |
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C.1.1 Mathematical formulation |
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634 | (4) |
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C.1.2 Numerical illustrations of the forward and inverse transform |
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638 | (4) |
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C.1.3 Selecting the number of elements of a dictionary |
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642 | (2) |
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C.1 4 Nonnegative matrix factorization with auxiliary constraints |
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644 | (3) |
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C.1.5 NMF optimization criteria |
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647 | (1) |
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C.2 Other Nonnegative Matrix Factorization Algorithms |
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648 | (11) |
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C.2.1 Project-gradient algorithm |
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649 | (4) |
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C.2.2 Alternating least-squares algorithm |
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653 | (6) |
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659 | (2) |
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D Nonnegative Tensor Factorization |
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D.1 PARAFAC Decomposition Model |
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661 | (6) |
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D.2 Tucker Tensor Factorization |
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667 | (4) |
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E A Review of 3D Finite-Difference Modeling |
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E.1 Basic Equations for Elastodynamic Wave Motion |
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671 | (1) |
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E.2 Discretization In Both Time and Space |
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672 | (2) |
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E.3 Staggered-Grid Implementation |
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674 | (4) |
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E.4 Stability of the Staggered-Grid Finite-Difference Modeling |
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678 | (1) |
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E.5 Grid Dispersion in Finite-Difference Modeling |
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678 | (1) |
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679 | (2) |
Bibliography |
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681 | (12) |
Index |
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693 | |