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E-raamat: Seismic Inversion: Theory and Applications

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  • Ilmumisaeg: 15-Sep-2016
  • Kirjastus: Wiley-Blackwell
  • Keel: eng
  • ISBN-13: 9781119258049
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 15-Sep-2016
  • Kirjastus: Wiley-Blackwell
  • Keel: eng
  • ISBN-13: 9781119258049
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Seismic inversion aims to reconstruct a quantitative model of the Earth subsurface, by solving an inverse problem based on seismic measurements. There are at least three fundamental issues to be solved simultaneously: non-linearity, non-uniqueness, and instability. This book covers the basic theory and techniques used in seismic inversion, corresponding to these three issues, emphasising the physical interpretation of theoretical concepts and practical solutions.

This book is written for master and doctoral students who need to understand the mathematical tools and the engineering aspects of the inverse problem needed to obtain geophysically meaningful solutions. Building on the basic theory of linear inverse problems, the methodologies of seismic inversion are explained in detail, including ray-impedance inversion and waveform tomography etc. The application methodologies are categorised into convolutional and wave-equation based groups. This systematic presentation simplifies the subject and enables an in-depth understanding of seismic inversion.

This book also provides a practical guide to reservoir geophysicists who are attempting quantitative reservoir characterisation based on seismic data. Philosophically, the seismic inverse problem allows for a range of possible solutions, but the techniques described herein enable geophysicists to exclude models that cannot satisfy the available data. This book summarises the authors extensive experience in both industry and academia and includes innovative techniques not previously published.
Preface viii
1 Basics of seismic inversion 1(10)
1.1 The linear inverse problem
1(2)
1.2 Data, model and mapping
3(2)
1.3 General solutions
5(1)
1.4 Regularisation
6(5)
2 Linear systems for inversion 11(13)
2.1 The governing equation and its solution
11(4)
2.2 Seismic scattering
15(2)
2.3 Seismic imaging
17(1)
2.4 Seismic downward continuation
18(2)
2.5 Seismic data processing
20(4)
3 Least-squares solutions 24(18)
3.1 Determinant and rank
24(4)
3.2 The inverse of a square matrix
28(1)
3.3 LU decomposition and Cholesky factorisation
29(6)
3.4 Least-squares solutions of linear systems
35(3)
3.5 Least-squares solution for a nonlinear system
38(1)
3.6 Least-squares solution by QR decomposition
39(3)
4 Singular value analysis 42(11)
4.1 Eigenvalues and eigenvectors
42(3)
4.2 Singular value concept
45(2)
4.3 Generalised inverse solution by SVD
47(1)
4.4 SVD applications
48(5)
5 Gradient-based methods 53(15)
5.1 The step length
54(2)
5.2 The steepest descent method
56(3)
5.3 Conjugate gradient method
59(3)
5.4 Biconjugate gradient method
62(3)
5.5 The subspace gradient method
65(3)
6 Regularisation 68(16)
6.1 Regularisation versus conditional probability
68(3)
6.2 The 4, norm constraint
71(3)
6.3 The maximum entropy constraint
74(3)
6.4 The Cauchy constraint
77(3)
6.5 Comparison of various regularisations
80(4)
7 Localised average solutions 84(10)
7.1 The average solution
85(1)
7.2 The deltaness
86(1)
7.3 The spread criterion
86(3)
7.4 The Backus-Gilbert stable solution
89(5)
8 Seismic wavelet estimation 94(18)
8.1 Wavelet extraction from seismic-to-well correlation
95(4)
8.2 Generalised wavelet constructed from power spectrum
99(4)
8.3 Kurtosis matching for a constant-phase wavelet
103(4)
8.4 Cumulant matching for a mixed-phase wavelet
107(5)
9 Seismic reflectivity inversion 112(15)
9.1 The least-squares problem with a Gaussian constraint
112(2)
9.2 Reflectivity inversion with an Li, norm constraint
114(2)
9.3 Reflectivity inversion with the Cauchy constraint
116(3)
9.4 Multichannel reflectivity inversion
119(3)
9.5 Multichannel conjugate gradient method
122(5)
10 Seismic ray-impedance inversion 127(12)
10.1 Acoustic and elastic impedances
127(3)
10.2 Ray impedance
130(3)
10.3 Workflow of ray-impedance inversion
133(1)
10.4 Reflectivity inversion in the ray-parameter domain
134(2)
10.5 Ray-impedance inversion with a model constraint
136(3)
11 Seismic tomography based on ray theory 139(17)
11.1 Seismic tomography
139(1)
11.2 Velocity-depth ambiguity in reflection tomography
140(3)
11.3 Ray tracing by a path bending method
143(4)
11.4 Geometrical spreading of curved interfaces
147(2)
11.5 Joint inversion of traveltime and amplitude data
149(7)
12 Waveform tomography for the velocity model 156(17)
12.1 Inversion theory for waveform tomography
157(3)
12.2 The optimal step length
160(2)
12.3 Strategy for reflection seismic tomography
162(4)
12.4 Multiple attenuation and partial compensation
166(2)
12.5 Reflection waveform tomography
168(5)
13 Waveform tomography with irregular topography 173(14)
13.1 Body-fitted grids for finite-difference modelling
173(3)
13.2 Modification of boundary points
176(1)
13.3 Pseudo-orthogonality and smoothness
177(3)
13.4 Wave equation and absorbing boundary condition
180(4)
13.5 Waveform tomography with irregular topography
184(3)
14 Waveform tomography for seismic impedance 187(15)
14.1 Wave equation and model parameterisation
189(2)
14.2 The impedance inversion method
191(2)
14.3 Inversion strategies and the inversion flow
193(5)
14.4 Application to field seismic data
198(2)
14.5 Conclusions
200(2)
Appendices 202(13)
A Householder transform for QR decomposition
202(3)
B Singular value decomposition algorithm
205(5)
C Biconjugate gradient method for complex systems
210(1)
D Gradient calculation in waveform tomography
211(4)
Exercises and solutions 215(20)
References 235(7)
Author index 242(2)
Subject index 244
Yanghua Wang is a Professor at Imperial College London and has held the position of Director of the Centre for Reservoir Geophysics since 2004. He is a founding editor of the Journal of Geophysics and Engineering. He is also a Fellow of the Institute of Physics (FIntP) and a Fellow of the Royal Astronomical Society (FRAS).