Computation, Optimization, and Machine Learning in Seismology - Subhashis Mallick

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Auteur(s) : Subhashis Mallick

Editeur : John Wiley & Sons Inc

Langue : Anglais

Parution : 01/10/2025

Format : Moyen, de 350g à 1kg

Nombre de pages : 416.0

ISBN : 9781119654469

Résumé :

A textbook applying fundamental seismology theories to the latest computational tools

The goal of computational seismology is to digitally simulate seismic waves, create subsurface models, and match these models with observations to identify subsurface rock properties. With recent advances in computing technology, including machine learning, it is now possible to automate matching procedures and use waveform inversion or optimization to create large-scale models.

Computation, Optimization, and Machine Learning in Seismology provides students with a detailed understanding of seismic wave theory, optimization theory, and how to use machine learning to interpret seismic data.

Volume highlights include:

• Mathematical foundations and key equations for computational seismology
• Essential theories, including wave propagation and elastic wave theory
• Processing, mapping, and interpretation of prestack data
• Model-based optimization and artificial intelligence methods
• Applications for earthquakes, exploration seismology, depth imaging, and multi-objective geophysics problems
• Exercises applying the main concepts of each chapter

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Biographie:

Subhashis Mallick, University of Wyoming, USA...

Sommaire:

Preface xiii

Availability Statement xv

About the Companion Website xvii

1 Introduction to Key Concepts in Seismic Inversion and Elastic Wave Theory 1

1.1 Background 1

1.2 Seismology-A Historical Perspective 1

1.2.1 Earthquake Seismology 1

1.2.2 Exploration Seismology 2

1.3 Mathematical Foundations of Seismology 3

1.4 Seismic Inversion 3

1.4.1 The Meaning of Inversion 3

1.4.2 Seismic Problems 4

1.4.3 Operator-Based and Model-Based Inversions-The Concept of Optimization 9

1.4.4 Fundamental Concepts of the Optimization Method (Model-Based Inversion) 10

1.5 Model, Data, and Objective Spaces 11

1.6 Different Flavors of Optimization 11

1.6.1 Local (Gradient-Based) Optimization 12

1.6.2 Global Optimization 12

1.6.3 Machine-Learning-Based Optimization 14

1.6.4 Single and Multi-objective Optimization 15

1.7 Bayesian Approach to Inversion/Optimization 16

1.8 Summary and Organization of the Book 16

1.9 Exercises 17

References 18

2 Mathematical Background 23

2.1 Fourier Series and Fourier Integrals 23

2.1.1 Fourier Series 23

2.1.2 Fourier Integrals 26

2.1.3 Fourier Transforms 27

2.2 Partial Differential Equations 33

2.2.1 How Do the Simplest Partial Differential Equations Arise? 33

2.2.2 Elliptic, Hyperbolic, and Parabolic Partial Differential Equations: Theory of Characteristics 35

2.2.3 Simple Examples of the Partial Differential Equations 36

2.2.4 Adjoint Differential Forms 40

2.3 Fundamentals of Tensor Algebra and Tensor Calculus 40

2.3.1 System of Coordinates 41

2.3.2 What Are Tensors? 41

2.3.3 Basis Vectors 42

2.3.4 The Gradient Operator and the Covariant and Contravariant Basis Vectors 43

2.3.5 Concept of Tensors 44

2.3.6 The Identity Tensor 44

2.3.7 Elements of Tensor Algebra 45

2.3.8 Elements of Tensor Calculus 49

2.3.9 Useful Theorems in Tensor Calculus 55

2.4 Chapter Summary 56

2.5 Exercises 56

References 57

3 Fundamentals of the Linearized Elastic Wave Theory 59

3.1 Introduction 59

3.2 The Stress Tensor and Traction 59

3.3 Strain (Deformation) Tensor 60

3.4 Static Relation-The First Fundamental Equation in Elasticity 62

3.4.1 Orthogonal Transformation of the Elastic Stiffness Matrix 63

3.4.2 Elastic Symmetries 68

3.4.3 Geological Interpretation of the Elastic Symmetries-The Concept of an Equivalent Medium 71

3.5 Strain Energy Function and the Positive-Definite Conditions 74

3.6 Dynamic Relation-Second Fundamental Equation in Elasticity 75

3.7 Elastodynamic Equation 75

3.8 Solution of the Elastodynamic Equation in Homogeneous Elastic Medium 76

3.8.1 Solution of the Christoffel Equation for a Hexagonally Symmetric Medium 77

3.8.2 Solution of the Christoffel Equation for an Orthorhombically Symmetric Medium 80

3.9 Ray (Group) Angle and Ray (Group) Velocity 83

3.9.1 Mathematical Formulation of the Group and Phase Directions for an Elastic Medium with Arbitrary Anisotropy 83

3.9.2 Analytical Expressions for Group Velocity and Angle for Specific Symmetries 85

3.9.3 Importance of the Group and Phase-An Optimization Problem of Practical Importance 88

3.10 Radiation Patterns from Seismic Sources 92

3.10.1 The Laplacian Operator and Its Inverse 92

3.10.2 Helmholtz Representation Theorem 93

3.10.3 Momentum Equation for Isotropic Elastic System 94

3.10.4 Green's Function for Hyperbolic Partial Differential Equations 94

3.10.5 Radiation Pa...