ISBN-10:
0080451594
ISBN-13:
9780080451596
Pub. Date:
05/01/2010
Publisher:
Elsevier Science
Coding and Decoding: Seismic Data: The concept of multishooting

Coding and Decoding: Seismic Data: The concept of multishooting

by Luc T. Ikelle

Hardcover

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Overview

Currently, the acquisition of seismic surveys is performed as a sequential operation in which shots are computed separately, one after the other. This approach is similar to that of multiple-access technology, which is widely used in cellular communications to allow several subscribers to share the same telephone line.

The cost of performing various shots simultaneously is almost identical to that of one shot; thus, the savings in time and money expected from using the multishooting approach for computing seismic surveys compared to the current approach are enormous. By using this approach, the long-standing problem of simulating a three-dimensional seismic survey can be reduced to a matter of weeks and not years, as is currently the case.




  • Investigates how to collect, stimulate, and process multishooting data
  • Addresses the improvements in seismic characterization and resolution one can expect from multishooting data
  • Aims to educate the oil and gas exploration and production business of the benefits of multishooting data, and to influence their day-to-day surveying techniques

Product Details

ISBN-13: 9780080451596
Publisher: Elsevier Science
Publication date: 05/01/2010
Series: Handbook of Geophysical Exploration: Seismic Exploration Series , #39
Pages: 618
Product dimensions: 6.30(w) x 9.10(h) x 1.60(d)

About the Author

Dr. Luc Ikelle is a Professor in Geology and Geophysics at Texas A&M University. He received his PhD in Geophysics from Paris 7 University in 1986 and has sense cultivated expertise in: seismic data acquisition, modeling, processing, and interpretation for conventional and unconventional energy production; inverse problem theory, signal processing, linear and nonlinear elastic wave propagation, linear and nonlinear optics, and continuum and fracture mechanics. His research interests include a combined analysis of petroleum systems, earthquakes, and volcanic eruptions based on geology, geophysics, statistical modeling, and control theory.

He is a founding member of Geoscientists Without Borders, for which he received an award from SEG in 2010. He is a member of the editorial board of the Journal of Seismic Exploration and has published 107 refereed publications in international journals.

Table of Contents

Preface ix

1 Introduction to Multishooting: Challenges and Rewards 1

1.1 Dimensions and Notation Conventions 3

1.1.1 Coordinate systems 3

1.1.2 Dimensions of heterogeneous media 4

1.1.3 Notation conventions 4

1.1.4 The f-x and f-k domains 5

1.2 Scattering Experiments in Petroleum Seismology 6

1.2.1 Principles of seismic acquisition 8

1.2.2 Seismic data 16

1.2.3 Shot, receiver, midpoint, and offset gathers 17

1.2.4 Multiazimuthal data 22

1.3 An Illustration of the Concept of Multishooting 25

1.3.1 An example of multishot data 25

1.3.2 The principle of superposition in multishooting 32

1.4 The Rewards of Multishooting 34

1.4.1 Seismic acquisition 38

1.4.2 Simulation of seismic surveys 39

1.4.3 Seismic data processing 40

1.4.4 Seismic data storage 41

1.5 The Challenges of Multishooting 41

1.5.1 Decoding of Multishot data 42

1.5.2 Source encoding 47

1.5.3 Processing of muitishot data without decoding 48

1.6 Scope and Content of This Book 52

2 Mathematics of Statistical Decoding: Instantaneous Mixtures 55

2.1 Seismic Data Representation as Random Variables 57

2.1.1 Examples of random variables 57

2.1.2 From seismic signals to seismic random variables 64

2.1.3 Probability-density function (PDF) of seismic random variables 65

2.1.4 Moments and cumulants of seismic random variables 70

2.1.5 Negentropy: A measurement of non-Gaussianity 77

2.2 Uncorrelatedness and Independence 83

2.2.1 Joint probability-density functions and Kullback-Leibler divergence 85

2.2.2 Joint moments and joint cumulants 91

2.2.3 Uncorrelatedness and whiteness of random variables 96

2.2.4 Independence of random variables 98

2.2.5 Analysis of uncorrelatedness and independence with scatterplots 101

2.2.6 Whitening 113

2.3 ICA Decoding 120

2.3.1 Decoding by maximizing contrast functions 121

2.3.2 Decoding by cumulant-tensor diagonalization 140

2.3.3 ICA decoding by negentropy maximizing 146

2.4 Decoding Methods of Noisy Mixtures 153

2.4.1 Special cases 153

2.4.2 General case 154

Problems 154

3 Mathematics of Statistical Decoding: Convolutive Mixtures 169

3.1 Motivation and Foundation for Working in the T-F-X Domain 179

3.1.1 Convolutive mixtures in the T-X domain 180

3.1.2 Convolutive mixtures in the F-X domain 184

3.1.3 Convolutive mixtures in the T-F-X domain 186

3.2 Statistics of Complex Random Variables and Vectors 188

3.2.1 The complex-valued gradient and the Hessian matrix 189

3.2.2 Statistics of complex random variables 195

3.2.3 Statistics of complex random vectors 211

3.2.4 An analysis of the statistical independence of seismic data in the T-F-X domain 226

3.3 Decoding in the T-F-X Domain: The MICA Approach 233

3.3.1 Whiteness of complex random variables 235

3.3.2 Decoding by negentropy maximization of complex random vectors 236

3.3.3 Permutation inconsistency problem 245

3.3.4 A cascaded ICA approach 251

3.3.5 Numerical examples 251

3.4 Decoding in Other Domains 273

3.4.1 Decoding in the F-X domain 273

3.4.2 Decoding in the T-X domain 277

Problems 283

4 Decoding Methods for Underdetermined Mixtures 293

4.1 Identification: Estimation of the Mixing Matrix 294

4.1.1 Histograms of data-concentration directions 297

4.1.2 Expectation maximization 306

4.1.3 Cumulant matching methods 318

4.2 Some Background on Sparsity Optimization 322

4.2.1 Sparsity regularization methods: $0norm 322

4.2.2 Sparsity regularization methods: $1norm 339

4.3 Separation Based on ICA Decomposition 350

4.3.1 Data-driven transform 353

4.3.2 Single-shot separation 363

4.4 Separation Based on Phase Encoding 369

4.4.1 Decoding with reference single shots 373

4.4.2 Window-by-window decoding 382

4.4.3 A combination of phase encoding and reciprocity 385

4.5 Array-processing Decoding Methods 394

4.5.1 Simultaneous shooting of monopole and dipole sources 394

4.5.2 Beamforming-based decoding 397

4.5.3 MUSIC decoding 401

4.6 Decoding with Known Source Signatures 403

4.6.1 Decoding of single-mixture data in the F-X domain 405

4.6.2 Decoding of single- and multiple-mixture data in the T-F-X domain 406

4.7 Decoding with Unknown Source Signatures 408

4.7.1 Decoding of single-mixture data in the F-X domain 408

4.7.2 Decoding of single- and multiple-mixture data in the T-F-X domain 409

Problems 414

5 Modeling and Imaging of Multishot Data 419

5.1 Introduction to Multiple Attenuation 420

5.1.1 Some background on free-surface demultiple methods 420

5.1.2 Radon free-surface-multiple attenuation 425

5.2 Kirchhoff-Scattering Demultiple of Multishot Data 432

5.2.1 A brief review of Kirchhoff-based free-surface multiple attenuation 432

5.2.2 A reformulation of the Kirchhoff demultiple for multishot data 442

5.2.3 Denoising of the vertical component of the particle velocity 454

5.2.4 A reconstruction of primaries 466

5.3 The Sea-Level-Based Demultiple 477

5.3.1 The phenomenon of low and high tides in demultiples 477

5.3.2 Demultiples 478

5.4 Migration and Velocity Analysis 488

5.4.1 Formulation of migration of multishot data 490

5.4.2 Velocity-migration analysis 494

5.4.3 ICA for seismic imaging and monitoring 513

5.5 Numerical Modeling Using the Multishooting Concept 518

5.5.1 Perturbation theory in data decoding 522

5.5.2 Array-processing-based decoding of FDM data 527

5.5.3 The source-signature-based decoding of FDM data 528

Problems 533

Appendix A Nonnegative Matrix Factorization 539

A.1 Lee-Seung Matrix Factorization Algorithm 540

A.l.l Mathematical formulation 540

A.1.2 Numerical illustrations of the forward and inverse transform 547

A.1.3 Selecting the number of elements of a dictionary 551

A.1.4 Nonnegative matrix factorization with auxiliary constraints 553

A.2 Other Nonnegative Matrix Factorization Algorithms 556

A.2.1 Project-gradient algorithm 556

A.2.2 Alternating least-squares algorithm 559

A.3 Decoding Challenges 567

Appendix B Nonnegative Tensor Factorization 569

B.l Parafac Decomposition Model 569

B.2 Tucker Tensor Factorization 575

Appendix C A Review of 3 D Finite-difference Modelling 579

C.1 Basic Equations for Elastodynamic Wave Motion 579

C.2 Discretization in Both Time and Space 581

C.3 Staggered-grid Implementation 582

C.4 Stability of the Staggered-grid Finite-difference Modelling 587

C.5 Grid Dispersion in Finite-difference Modelling 587

C.6 Boundary Conditions 588

Bibliography 589

Author Index 597

Subject Index 601

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