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Book
ix, 246 pages : illustrations (some color) ; 25 cm
  • Preface viii Chapter 1 Basics of seismic inversion 1 1.1 The linear inverse problem 1 1.2 Data, model and mapping 3 1.3 General solutions 4 1.4 Regularisation 5 Chapter 2 Linear systems for inversion 11 2.1 A governing equation and its solution 11 2.2 Seismic scattering 14 2.3 Seismic imaging 16 2.4 Seismic downward continuation 18 2.5 Seismic data processing 20 Chapter 3 Least-squares solutions 23 3.1 Determinant and rank 23 3.2 The inverse of a square matrix 27 3.3 LU decomposition and Cholesky factorisation 28 3.4 Least-squares solutions 34 3.5 Least-squares solution for a nonlinear system 37 3.6 Least-squares solution by QR decomposition 37 Chapter 4 Singular value analysis 41 4.1 Eigenvalues and eigenvectors 41 4.2 Singular value concept 44 4.3 Generalised inverse solution by SVD 46 4.4 SVD applications 48 Chapter 5 Gradient-based methods 53 5.1 The step length 54 5.2 The steepest descent method 55 5.3 Conjugate gradient method 59 5.4 Biconjugate gradient method 61 5.5 The subspace gradient method 64 Chapter 6 Regularisation 67 6.1 Regularisation versus conditional probability 67 6.2 The Lp-norm constraint 70 6.3 The maximum entropy constraint 73 6.4 The Cauchy constraint 76 6.5 Comparison of various regularisations 79 Chapter 7 Localised average solutions 83 7.1 The average solution 84 7.2 The deltaness 85 7.3 The spread criterion 86 7.4 The Backus-Gilbert stable solution 88 Chapter 8 Seismic wavelet estimation 93 8.1 Wavelet extraction from seismic-to-well correlation 94 8.2 Constant-phase wavelet by kurtosis matching 98 8.3 Mixed-phase wavelet by cumulant matching 102 8.4 Generalised seismic wavelets 106 Chapter 9 Seismic reflectivity inversion 111 9.1 The least-squares problem with a Gaussian constraint 111 9.2 Reflectivity inversion with an Lp-norm constraint 113 9.3 Reflectivity inversion with the Cauchy constraint 115 9.4 Multichannel inversion scheme 118 9.5 Multichannel conjugate gradient method 121 Chapter 10 Seismic ray-impedance inversion 125 10.1 Acoustic and elastic impedances 125 10.2 Ray impedance 129 10.3 Workflow of ray-impedance inversion 132 10.4 Ray-impedance inversion with a model constraint 136 Chapter 11 Seismic tomography based on ray theory 137 11.1 Seismic tomography 137 11.2 Velocity-depth ambiguity in tomography 138 11.3 Ray tracing by a path bending method 141 11.4 Geometrical spreading of curved interfaces 144 11.5 Joint inversion of traveltime and amplitude data 147 Chapter 12 Waveform tomography for the velocity model 153 12.1 Inverse theory for seismic waveform tomography 154 12.2 The optimal step length 157 12.3 Strategy for reflection seismic tomography 159 12.4 Multiple attenuation and partial compensation 162 12.5 Waveform tomography 166 Chapter 13 Waveform tomography with irregular topography 169 13.1 Body-fitted grids for finite-difference modelling 169 13.2 Modification of boundary points 172 13.3 Pseudo-orthogonality and smoothness 173 13.4 Wave equation and absorbing boundary condition 176 13.5 Waveform tomography with irregular topography 180 Chapter 14 Waveform tomography for seismic impedance 183 14.1 Wave equation and model parameterisation 185 14.2 The impedance inversion method 187 14.3 Inversion strategies and the inversion flow 188 14.4 Application to field seismic data 193 14.5 Conclusions 196 Appendices 197 A Householder transform for QR decomposition 197 B Singular value decomposition 200 C Iterative methods for solving a linear system 206 D Biconjugate gradient method for complex systems 209 Exercises and solutions 211 References 231 Author index 238 Subject index 240.
  • (source: Nielsen Book Data)9781119257981 20161213
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 author s extensive experience in both industry and academia and includes innovative techniques not previously published.
(source: Nielsen Book Data)9781119257981 20161213
Earth Sciences Library (Branner)
Book
ix, 238 p. : ill. (some col.) ; 24 cm.
  • Preface.1. Introduction to inverse Q filtering.1.1 The earth Q effect on seismic waves.1.2 Inverse Q filters.1.3 The effectiveness of inverse Q filtering.Part I: Mathematical Q models.2. Kolsky's model for seismic attenuation and dispersion.2.1 Kolsky's attenuation-dispersion model.2.2 Modification to the Kolsky model.2.3 Accurate velocity dispersion correction.2.4 Comparison with different Q models.3. Mathematical definition of the earth Q models.3.1 Mathematical definition of Q.3.2 Kolsky's Q model and the complex wavenumber.3.3 The Strick-Azimi Q model.3.4 Kjartansson's constant-Q model.3.5 Azimi's second and third Q models.3.6 Muller's Q model.3.7 The Zener or standard linear solid model.3.8 The Cole-Cole Q model.3.9 A general linear model.Part II: Inverse Q filters.4. Stabilized inverse Q filtering algorithm.4.1 Basics of inverse Q filtering.4.2 Numerical instability of inverse Q filtering.4.3 Stabilized inverse Q filter.4.4 Comparison with gain-limited inverse Q filter.4.5 Comparison with a conventional inverse Q filter.4.6 Synthetic and real data examples.5. Inverse Q filtering for phase and amplitude separately.5.1 Phase-only inverse Q filtering.5.2 Amplitude-only inverse Q filtering.5.3 Forward Q filtering.5.4 Summary of inverse and forward Q filters by downward.continuation.5.5 Different stabilization schemes.6. Layered implementation of inverse Q filters.6.1 The layered approach to inverse Q filtering.6.2 Inverse Q filtering within a constant-Q layer.6.3 Phase- or amplitude-only inverse Q filtering.6.4 Forward Q filtering.6.5 Application of layered inverse Q filtering.7. Inverse Q filtering in the Gabor transform domain.7.1 Stabilized inverse Q filter.7.2 The Gabor transform.7.3 Inverse Q filtering by Gabor transform.7.4 Forward Q filtering by Gabor transform.7.5 An empirical formula for the stabilization factor.8. The effectiveness of stabilized inverse Q filtering.8.1 Inverse Q filtering of a land seismic section.8.2 Flattening the amplitude spectrum and strengthening.the relative amplitude.8.3 Increasing the spectral bandwidth.8.4 Improving the signal-to-noise ratio.8.5 Enhancing seismic resolution.8.6 Sensitivity of the resolution enhancement to Q values.9. Migration with inverse Q filtering.9.1 Inverse Q filtered migration in the wavenumberfrequency.domain.9.2 Stabilized migration with lateral variation in velocity.and Q models.9.3 The implicit finite-difference extrapolator in the spacefrequency.domain.9.4 Migration examples.Part III: Q estimation.10. Q estimation from vertical seismic profiling data.10.1 The attenuation effect on VSP waveform.10.2 Spectral ratio method for Q estimation.10.3 The multitaper technique for spectral estimation.10.4 Robust Q estimation from real VSP data.11. Q analysis from reflection seismic data.11.1 Q analysis based on amplitude attenuation.11.2 Q analysis based on amplitude compensation.11.3 Interval-Q calculation by linear inversion.11.4 Q analyses on the P-P and P-SV wave sections.12. Crosshole seismic tomography for the Q model.12.1 Inverse theory for waveform tomography.12.2 Issues in real data application.12.3 Waveform inversion for the velocity model.12.4 Waveform tomography for the attenuation model.References.Author index.Subject index.
  • (source: Nielsen Book Data)9781405185400 20160528
Seismic inverse Q filtering is a data processing technology for enhancing the resolution of seismic images. It employs a wave propagation reversal procedure that compensates for energy absorption and corrects wavelet distortion due to velocity dispersion. By compensating for amplitude attenuation, seismic data can provide true relative-amplitude information for amplitude inversion and subsequent reservoir characterization. By correcting the phase distortion, seismic data with enhanced vertical resolution can yield correct timings for lithological identification. This monograph presents the theory of inverse Q filtering and a series of algorithms, collected with the following selection criteria in mind: robustness, effectiveness and practicality. The book is written for processing geophysicists who are attempting to improve the quality of seismic data in terms of resolution and signal-to-noise ratio, as well as for reservoir geophysicists who are concerned about seismic fidelity in terms of true amplitudes, true timings and true frequencies. It will also be particularly valuable as a guide for seasoned geophysicists who are attempting to develop seismic software for various research settings. Finally, it can be used as a reference work or textbook for postgraduate students in seismic and reservoir geophysics.
(source: Nielsen Book Data)9781405185400 20160528
Earth Sciences Library (Branner)
Book
xvi, 252 p. : ill. ; 25 cm.
  • Preface. Introduction (Professor G.A. Houseman). 1. Introduction to amplitude inversion. Introduction. Velocity-depth ambiguity in traveltime inversion. Resolving ambiguity by using amplitude information. Overview of amplitude inversion. Analytical expression for the geometrical spreading function for layered structures. 2. Traveltime and ray-amplitude in heterogeneous media. Introduction. Bending ray tracing method. Traveltime and its perturbations. Propagator of paraxial rays and geometrical spreading. Ray perturbations due to model perturbations. Ray amplitude. 3. Amplitude coefficients and approximations. Introduction. The Zoeppritz equations. The pseudo-p2 expressions. Quadratic expressions in terms of elastic contrasts. Accuracy of the quadratic approximations. Amplitude coefficients represented as a function of three elastic parameters. Three elastic parameters from amplitude inversion. Implication for fluid substitution modelling. 4. Amplitude inversion for interface geometry. Introduction. Parameterization and forward modelling. Subspace gradient inversion method. A simple example of reflection amplitude inversion. Inversion for an interface represented as a sum of harmonic functions. Stability of the amplitude inversion. Strategy for the choice of &Dgr--k and M. Discussion. 5. Amplitude inversion for velocity variation. Introduction. Amplitude dependence on slowness perturbation. Inversion algorithm. Inversion example of 1-D slowness distribution. Constraining higher wavenumber components. Robustness of the inversion in the presence of model error or data noise. Inversion of arbitrary smooth velocity anomalies. Discussion. 6. Sensitivities of traveltimes and amplitudes in joint inversion. Introduction. The Hessian and the norm in model space. Sensitivities to interface geometry. Sensitivities to 2-D slowness variation. Inversion formula. Joint inversion for an interface. Joint inversion for slowness. Discussion. 7. Amplitude inversion of a multi-layered structure. Introduction. Forward calculation and inverse method. Preliminary inversion test. Damped subspace method. Multi-scale scheme. Multi-stage damped subspace method. 8. Practical approach to application. Introduction. Amplitudes estimated from migrated gathers. Demigration of reflection amplitudes. Winnowing amplitudes by LOESS. Inversion procedure. Inversion results. 9. Simultaneous inversion for model geometry and elastic parameters. Introduction. Ray-amplitude and its approximation. Inversion method. Inversion example. Measurements for lithological interpretation. Structural effects on amplitude variation. 10. Decomposition of structural effect and AVO attributes. Introduction. Decomposition of ray-amplitude. The inverse problem. Sample dataset of gas-water contact. Inversion results. The Chebyshev spectra of the AVO attributes. 11. Amplitude tomography in practice. Introduction. Estimate of amplitudes, traveltimes and data uncertainties. Tomographic inversion incorporating more information and using an improved forward calculation. Consideration of factors influencing amplitudes. Turning-ray tomography for near-surface velocity structure and attenuation. Prestack seismic trace inversion for ray elastic impedance. Appendices. Derivation of the geometrical spreading function. Derivation of reflection amplitude demigration. References. Author Index. Topic Index.
  • (source: Nielsen Book Data)9780080442433 20160528
This is the first book of its kind on seismic amplitude inversion in the context of reflection tomography. The aim of the monograph is to advocate the use of ray-amplitude data, separately or jointly with traveltime data, in reflection seismic tomography. The emphasis of seismic exploration is on imaging techniques, so that seismic section can be interpreted directly as a geological section. In contrast, it is perhaps ironic that, in decades of industrial seismology, one major aspect of waveform data that potentially is easier to measure and analyse has generally been ignored. That is, the information content of seismic amplitudes. Perhaps the potential complexity has deterred most researchers from a more thorough investigation of the practical use of seismic amplitude data. The author of this volume presents an authoritative and detailed study of amplitude data, as used in conjunction with traveltime data, to provide better constraints on the variation of seismic wave speed in the subsurface. One of the fundamental problems in conventional reflection seismic tomography using only traveltime data is the possible ambiguity between the velocity variation and the reflector depth. The inclusion of amplitude data in the inversion may help to resolve this problem because the amplitudes and traveltimes are sensitive to different features of the subsurface model, and thereby provide more accurate information about the subsurface structure and the velocity distribution. An essential goal of this monograph is to make the amplitude inversion method work with real reflection seismic data.
(source: Nielsen Book Data)9780080442433 20160528
Earth Sciences Library (Branner)

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