# Coding and Decoding: Seismic Data

, by Ikelle**Note:**Supplemental materials are not guaranteed with Rental or Used book purchases.

- ISBN: 9780080451596 | 0080451594
- Cover: Hardcover
- Copyright: 5/11/2010

This cutting-edge handbook and guide on surveying techniques on Coding and Decoding: Seimic Date investigates how to collect, stimulate, and process multishooting data, as well as address what improvements in seismic characterzation and resolution one can expect.

Preface | p. ix |

Introduction to Multishooting: Challenges and Rewards | p. 1 |

Dimensions and Notation Conventions | p. 3 |

Coordinate systems | p. 3 |

Dimensions of heterogeneous media | p. 4 |

Notation conventions | p. 4 |

The f-x and f-k domains | p. 5 |

Scattering Experiments in Petroleum Seismology | p. 6 |

Principles of seismic acquisition | p. 8 |

Seismic data | p. 16 |

Shot, receiver, midpoint, and offset gathers | p. 17 |

Multiazimuthal data | p. 22 |

An Illustration of the Concept of Multishooting | p. 25 |

An example of multishot data | p. 25 |

The principle of superposition in multishooting | p. 32 |

The Rewards of Multishooting | p. 34 |

Seismic acquisition | p. 38 |

Simulation of seismic surveys | p. 39 |

Seismic data processing | p. 40 |

Seismic data storage | p. 41 |

The Challenges of Multishooting | p. 41 |

Decoding of Multishot data | p. 42 |

Source encoding | p. 47 |

Processing of muitishot data without decoding | p. 48 |

Scope and Content of This Book | p. 52 |

Mathematics of Statistical Decoding: Instantaneous Mixtures | p. 55 |

Seismic Data Representation as Random Variables | p. 57 |

Examples of random variables | p. 57 |

From seismic signals to seismic random variables | p. 64 |

Probability-density function (PDF) of seismic random variables | p. 65 |

Moments and cumulants of seismic random variables | p. 70 |

Negentropy: A measurement of non-Gaussianity | p. 77 |

Uncorrelatedness and Independence | p. 83 |

Joint probability-density functions and Kullback-Leibler divergence | p. 85 |

Joint moments and joint cumulants | p. 91 |

Uncorrelatedness and whiteness of random variables | p. 96 |

Independence of random variables | p. 98 |

Analysis of uncorrelatedness and independence with scatterplots | p. 101 |

Whitening | p. 113 |

ICA Decoding | p. 120 |

Decoding by maximizing contrast functions | p. 121 |

Decoding by cumulant-tensor diagonalization | p. 140 |

ICA decoding by negentropy maximizing | p. 146 |

Decoding Methods of Noisy Mixtures | p. 153 |

Special cases | p. 153 |

General case | p. 154 |

Problems | p. 154 |

Mathematics of Statistical Decoding: Convolutive Mixtures | p. 169 |

Motivation and Foundation for Working in the T-F-X Domain | p. 179 |

Convolutive mixtures in the T-X domain | p. 180 |

Convolutive mixtures in the F-X domain | p. 184 |

Convolutive mixtures in the T-F-X domain | p. 186 |

Statistics of Complex Random Variables and Vectors | p. 188 |

The complex-valued gradient and the Hessian matrix | p. 189 |

Statistics of complex random variables | p. 195 |

Statistics of complex random vectors | p. 211 |

An analysis of the statistical independence of seismic data in the T-F-X domain | p. 226 |

Decoding in the T-F-X Domain: The MICA Approach | p. 233 |

Whiteness of complex random variables | p. 235 |

Decoding by negentropy maximization of complex random vectors | p. 236 |

Permutation inconsistency problem | p. 245 |

A cascaded ICA approach | p. 251 |

Numerical examples | p. 251 |

Decoding in Other Domains | p. 273 |

Decoding in the F-X domain | p. 273 |

Decoding in the T-X domain | p. 277 |

Problems | p. 283 |

Decoding Methods for Underdetermined Mixtures | p. 293 |

Identification: Estimation of the Mixing Matrix | p. 294 |

Histograms of data-concentration directions | p. 297 |

Expectation maximization | p. 306 |

Cumulant matching methods | p. 318 |

Some Background on Sparsity Optimization | p. 322 |

Sparsity regularization methods: $_{0}norm | p. 322 |

Sparsity regularization methods: $_{1}norm | p. 339 |

Separation Based on ICA Decomposition | p. 350 |

Data-driven transform | p. 353 |

Single-shot separation | p. 363 |

Separation Based on Phase Encoding | p. 369 |

Decoding with reference single shots | p. 373 |

Window-by-window decoding | p. 382 |

A combination of phase encoding and reciprocity | p. 385 |

Array-processing Decoding Methods | p. 394 |

Simultaneous shooting of monopole and dipole sources | p. 394 |

Beamforming-based decoding | p. 397 |

MUSIC decoding | p. 401 |

Decoding with Known Source Signatures | p. 403 |

Decoding of single-mixture data in the F-X domain | p. 405 |

Decoding of single- and multiple-mixture data in the T-F-X domain | p. 406 |

Decoding with Unknown Source Signatures | p. 408 |

Decoding of single-mixture data in the F-X domain | p. 408 |

Decoding of single- and multiple-mixture data in the T-F-X domain | p. 409 |

Problems | p. 414 |

Modeling and Imaging of Multishot Data | p. 419 |

Introduction to Multiple Attenuation | p. 420 |

Some background on free-surface demultiple methods | p. 420 |

Radon free-surface-multiple attenuation | p. 425 |

Kirchhoff-Scattering Demultiple of Multishot Data | p. 432 |

A brief review of Kirchhoff-based free-surface multiple attenuation | p. 432 |

A reformulation of the Kirchhoff demultiple for multishot data | p. 442 |

Denoising of the vertical component of the particle velocity | p. 454 |

A reconstruction of primaries | p. 466 |

The Sea-Level-Based Demultiple | p. 477 |

The phenomenon of low and high tides in demultiples | p. 477 |

Demultiples | p. 478 |

Migration and Velocity Analysis | p. 488 |

Formulation of migration of multishot data | p. 490 |

Velocity-migration analysis | p. 494 |

ICA for seismic imaging and monitoring | p. 513 |

Numerical Modeling Using the Multishooting Concept | p. 518 |

Perturbation theory in data decoding | p. 522 |

Array-processing-based decoding of FDM data | p. 527 |

The source-signature-based decoding of FDM data | p. 528 |

Problems | p. 533 |

Nonnegative Matrix Factorization | p. 539 |

Lee-Seung Matrix Factorization Algorithm | p. 540 |

Mathematical formulation | p. 540 |

Numerical illustrations of the forward and inverse transform | p. 547 |

Selecting the number of elements of a dictionary | p. 551 |

Nonnegative matrix factorization with auxiliary constraints | p. 553 |

Other Nonnegative Matrix Factorization Algorithms | p. 556 |

Project-gradient algorithm | p. 556 |

Alternating least-squares algorithm | p. 559 |

Decoding Challenges | p. 567 |

Nonnegative Tensor Factorization | p. 569 |

Parafac Decomposition Model | p. 569 |

Tucker Tensor Factorization | p. 575 |

A Review of _{3} D Finite-difference Modelling | p. 579 |

Basic Equations for Elastodynamic Wave Motion | p. 579 |

Discretization in Both Time and Space | p. 581 |

Staggered-grid Implementation | p. 582 |

Stability of the Staggered-grid Finite-difference Modelling | p. 587 |

Grid Dispersion in Finite-difference Modelling | p. 587 |

Boundary Conditions | p. 588 |

Bibliography | p. 589 |

Author Index | p. 597 |

Subject Index | p. 601 |

Table of Contents provided by Ingram. All Rights Reserved. |