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E-raamat: Coding and Decoding: Seismic Data: The Concept of Multishooting

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(Faculty of Petroleum Geology, Texas A&M University, College Station, USA)
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Coding and Decoding: Seismic Data: The Concept of MultishootingSuurem pilt
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Currently, the acquisition of seismic surveys is performed as a sequential operation in which shots are computed separately, one after the other. The concept of the multishooting approach illustrates that several shots can be generated from several locations and at different time intervals simultaneously. 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.

This book investigates how to collect, stimulate, and process multishooting data, as well as address what improvements in seismic characterization and resolution one can expect.



  • 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

Muu info

Discusses how to collect, simulate, and process multishooting data, as well as how it improves seismic characterization and resolution
Preface ix
1 Introduction to Multishooting: Challenges and Rewards 1(54)
1.1 Dimensions and Notation Conventions
3(3)
1.1.1 Coordinate systems
3(1)
1.1.2 Dimensions of heterogeneous media
4(1)
1.1.3 Notation conventions
4(1)
1.1.4 The f-x and f-k domains
5(1)
1.2 Scattering Experiments in Petroleum Seismology
6(19)
1.2.1 Principles of seismic acquisition
8(8)
1.2.2 Seismic data
16(1)
1.2.3 Shot, receiver, midpoint, and offset gathers
17(5)
1.2.4 Multiazimuthal data
22(3)
1.3 An Illustration of the Concept of Multishooting
25(9)
1.3.1 An example of multishot data
25(7)
1.3.2 The principle of superposition in multishooting
32(2)
1.4 The Rewards of Multishooting
34(7)
1.4.1 Seismic acquisition
38(1)
1.4.2 Simulation of seismic surveys
39(1)
1.4.3 Seismic data processing
40(1)
1.4.4 Seismic data storage
41(1)
1.5 The Challenges of Multishooting
41(11)
1.5.1 Decoding of multishot data
42(5)
1.5.2 Source encoding
47(1)
1.5.3 Processing of multishot data without decoding
48(4)
1.6 Scope and Content of This Book
52(3)
2 Mathematics of Statistical Decoding: Instantaneous Mixtures 55(114)
2.1 Seismic Data Representation as Random Variables
57(26)
2.1.1 Examples of random variables
57(7)
2.1.2 From seismic signals to seismic random variables
64(1)
2.1.3 Probability-density function (PDF) of seismic random variables
65(5)
2.1.4 Moments and cumulants of seismic random variables
70(7)
2.1.5 Negentropy: A measurement of non-Gaussianity
77(6)
2.2 Uncorrelatedness and Independence
83(37)
2.2.1 Joint probability-density functions and Kullback–Leibler divergence
85(6)
2.2.2 Joint moments and joint cumulants
91(5)
2.2.3 Uncorrelatedness and whiteness of random variables
96(2)
2.2.4 Independence of random variables
98(3)
2.2.5 Analysis of uncorrelatedness and independence with scatterplots
101(12)
2.2.6 Whitening
113(7)
2.3 ICA Decoding
120(33)
2.3.1 Decoding by maximizing contrast functions
121(19)
2.3.2 Decoding by cumulant-tensor diagonalization
140(6)
2.3.3 ICA decoding by negentropy maximizing
146(7)
2.4 Decoding Methods of Noisy Mixtures
153(1)
2.4.1 Special cases
153(1)
2.4.2 General case
154(1)
Problems
154(15)
3 Mathematics of Statistical Decoding: Convolutive Mixtures 169(124)
3.1 Motivation and Foundation for Working in the T-F-X Domain
179(9)
3.1.1 Convolutive mixtures in the TX domain
180(4)
3.1.2 Convolutive mixtures in the F-X domain
184(2)
3.1.3 Convolutive mixtures in the T-F-X domain
186(2)
3.2 Statistics of Complex Random Variables and Vectors
188(45)
3.2.1 The complex-valued gradient and the Hessian matrix
189(6)
3.2.2 Statistics of complex random variables
195(16)
3.2.3 Statistics of complex random vectors
211(15)
3.2.4 An analysis of the statistical independence of seismic data in the T-F-X domain
226(7)
3.3 Decoding in the T-F-X Domain: The MICA Approach
233(40)
3.3.1 Whiteness of complex random variables
235(1)
3.3.2 Decoding by negentropy maximization of complex random vectors
236(9)
3.3.3 Permutation inconsistency problem
245(6)
3.3.4 A cascaded ICA approach
251(1)
3.3.5 Numerical examples
251(22)
3.4 Decoding in Other Domains
273(10)
3.4.1 Decoding in the F-X domain
273(4)
3.4.2 Decoding in the T-X domain
277(6)
Problems
283(10)
4 Decoding Methods for Underdetermined Mixtures 293(126)
4.1 Identification: Estimation of the Mixing Matrix
294(28)
4.1.1 Histograms of data-concentration directions
297(9)
4.1.2 Expectation maximization
306(12)
4.1.3 Cumulant matching methods
318(4)
4.2 Some Background on Sparsity Optimization
322(28)
4.2.1 Sparsity regularization methods: to norm
322(17)
4.2.2 Sparsity regularization methods: Li norm
339(11)
4.3 Separation Based on ICA Decomposition
350(19)
4.3.1 Data-driven transform
353(10)
4.3.2 Single-shot separation
363(6)
4.4 Separation Based on Phase Encoding
369(25)
4.4.1 Decoding with reference single shots
373(9)
4.4.2 Window-by-window decoding
382(3)
4.4.3 A combination of phase encoding and reciprocity
385(9)
4.5 Array-processing Decoding Methods
394(9)
4.5.1 Simultaneous shooting of monopole and dipole sources
394(3)
4.5.2 Beamforming-based decoding
397(4)
4.5.3 MUSIC decoding
401(2)
4.6 Decoding with Known Source Signatures
403(5)
4.6.1 Decoding of single-mixture data in the F-X domain
405(1)
4.6.2 Decoding of single- and multiple-mixture data in the T-F-X domain
406(2)
4.7 Decoding with Unknown Source Signatures
408(6)
4.7.1 Decoding of single-mixture data in the F-X domain
408(1)
4.7.2 Decoding of single- and multiple-mixture data in the T-F-X domain
409(5)
Problems
414(5)
5 Modeling and Imaging of Multishot Data 419(120)
5.1 Introduction to Multiple Attenuation
420(12)
5.1.1 Some background on free-surface demultiple methods
420(5)
5.1.2 Radon free-surface-multiple attenuation
425(7)
5.2 Kirchhoff–Scattering Demultiple of Multishot Data
432(45)
5.2.1 A brief review of Kirchhoff-based free-surface multiple attenuation
432(10)
5.2.2 A reformulation of the Kirchhoff demultiple for multishot data
442(12)
5.2.3 Denoising of the vertical component of the particle velocity
454(12)
5.2.4 A reconstruction of primaries
466(11)
5.3 The Sea-Level-Based Demultiple
477(11)
5.3.1 The phenomenon of low and high tides in demultiples
477(1)
5.3.2 Demultiples
478(10)
5.4 Migration and Velocity Analysis
488(30)
5.4.1 Formulation of migration of multishot data
490(4)
5.4.2 Velocity-migration analysis
494(19)
5.4.3 ICA for seismic imaging and monitoring
513(5)
5.5 Numerical Modeling Using the Multishooting Concept
518(15)
5.5.1 Perturbation theory in data decoding
522(5)
5.5.2 Array-processing-based decoding of FDM data
527(1)
5.5.3 The source-signature-based decoding of FDM data
528(5)
Problems
533(6)
Appendix A Nonnegative Matrix Factorization 539(30)
A.1 Lee-Seung Matrix Factorization Algorithm
540(16)
A.1.1 Mathematical formulation
540(7)
A.1.2 Numerical illustrations of the forward and inverse transform
547(4)
A.1.3 Selecting the number of elements of a dictionary
551(2)
A.1.4 Nonnegative matrix factorization with auxiliary constraints
553(3)
A.2 Other Nonnegative Matrix Factorization Algorithms
556(11)
A.2.1 Project-gradient algorithm
556(3)
A.2.2 Alternating least-squares algorithm
559(8)
A.3 Decoding Challenges
567(2)
Appendix B Nonnegative Tensor Factorization 569(10)
B.1 Parafac Decomposition Model
569(6)
B.2 Tucker Tensor Factorization
575(4)
Appendix C A Review of 3D Finite-difference Modelling 579(10)
C.1 Basic Equations for Elastodynamic Wave Motion
579(2)
C.2 Discretization in Both Time and Space
581(1)
C.3 Staggered-grid Implementation
582(5)
C.4 Stability of the Staggered-grid Finite-difference Modelling
587(1)
C.5 Grid Dispersion in Finite-difference Modelling
587(1)
C.6 Boundary Conditions
588(1)
Bibliography 589(8)
Author Index 597(4)
Subject Index 601
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.
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