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Informationen zum Autor 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). Klappentext 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. Zusammenfassung 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. Inhaltsverzeichnis 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 s...
