Seismic Interferometry Book

Preface ix

1 Introduction 1

1.1 Seismic interferometry 1

1.2 Benefits and liabilities 12

1.3 Historical development of seismic interferometry 15

1.4 Organization of the book 18

1.5 Exercises 19

1.6 Appendix 1: Basics of exploration seismology 23

1.7 Appendix 2: Fourier identities 27

1.8 Appendix 3: Glossary 28

1.9 Appendix 4: MATLAB codes 29

2 Reciprocity equations of convolution and correlation types 30

2.1 Green's functions 31

2.2 Reciprocity equation of convolution type 32

2.3 Reciprocity equation of correlation type 36

2.4 Stationary phase integration 40

2.5 Seismic migration 44

2.6 Interferometric migration 49

2.7 Summary 49

2.8 Exercises 50

2.9 Appendix 1: Causal and acausal Green's functions 53

2.10 Appendix 2: Principal value contribution of dipoles 54

2.11 Appendix 3: Sommerfeld radiation conditions 56

2.12 Appendix 4: Adjoint operator 57

2.13 Appendix 5: Forward and backward wave propagation 58

2.14 Appendix 6: MATLAB codes 60

3 VSP SWP correlation transform 61

3.1 Introduction 61

3.2 VSP $$ SWP correlation transform 62

3.3 Stationary phase analysis 63

3.4 Benefits 67

3.5 Liabilities 70

3.6 Numerical implementation 72

3.7 Numerical results 75

3.8 Summary 77

3.9 Exercises 79

3.10 Appendix 1: MATLAB codes 80

3.11 Appendix 2: Interferometric imaging = RTM 80

3.12 Appendix 3: Source wavefield deconvolution 82

3.13 Appendix 4: 3D reciprocity equation by quadrature 83

4 VSP $$ SSP correlation transform 86

4.1 VSP $$ SSP correlation transform 86

4.2 Benefits and limitations of the VSP $$ SSP transform 93

4.3 Truncation artifacts, VSP geometry,and model illumination 95

4.4 Numerical examples 98

4.5 Summary 105

4.6 Exercises 106

4.7 Appendix 1: Computer codes 108

5 VSP $$ SSP convolution transform 109

5.1 Introduction 109

5.2 VSP $$ SSP convolution transform 110

5.3 Transforming VSP travel times into SSP travel times 113

5.4 Numerical results 114

5.5 Summary 120

5.6 Exercises 120

5.7 Appendix 1: MATLAB codes 123

6 SSP $$ SSP correlation transform 124

6.1 Transforming SSP multiples into SSP primaries 125

6.2 Benefits 128

6.3 Interferometric interpolation of seismic data 131

6.4 Numerical examples 132

6.5 Summary 143

6.6 Exercises 144

6.7 Appendix 1: Computer codes 145

6.8 Appendix 2: Surface wave prediction by the SSP $$ SSP transform 146

7 VSP $$ VSP correlation transform 147

7.1 VSP $$ SSP $$ VSP correlation transform 147

7.2 VSP $$ SWP $$ VSP correlation transform 150

7.3 Interpolation and extrapolation of VSP and OBS data 152

7.4 Numerical results 156

7.5 Summary 160

7.6 Exercises 161

7.7 Appendix 1: Computer codes 161

8 SSP $$ VSP $$ SWP transforms 162

8.1 SSP $$ VSP correlation transform 162

8.2 SSP $$ SWP correlation transform 164

8.3 Natural Green's functions 165

8.4 Numerical examples 166

8.5 Summary 174

8.6 Exercises 176

9 Traveltime interferometry 177

9.1 Introduction 177

9.2 Theory 178

9.3 Numerical results 184

9.4 Summary 187

9.5 Exercises 187

10 Stochastic interferometry 189

10.1 Theory 190

10.2 Numerical examples 194

10.3 Summary 204

10.4 Exercises 205

10.5 Appendix 1: Processing steps for drill-bit data 208

10.6 Appendix 2: MATLAB codes 210

11 Interferometric source estimation 211

11.1 Source imaging condition 211

11.2 Summation imaging condition 215

11.3 Validation of super-resolution and super-stacking 221

11.4 Summation imaging condition and correlated traces 226

11.5 Summary 227

11.6 Exercises 228

12 Body wave earthquake interferometry 229

12.1 Introduction 229

12.2 Theory 234

12.3 Numerical tests 242

12.4 Summary 248

12.5 Exercises 248

References 250

Index 259