Using examples and case studies directly drawn from the authors’ experience, Surface Wave Methods for Near-Surface Site Characterization addresses both the experimental and theoretical aspects of surface wave propagation in both forward and inverse modeling. This book accents the key facets associated with surface wave testing for near-surface site characterization. It clearly outlines the basic principles, the theoretical framework and the practical implementation of surface wave analysis. In addition, it also describes in detail the equipment and measuring devices, acquisition techniques, signal processing, forward and inverse modeling theories, and testing protocols that form the basis of modern surface wave techniques.

Preface xiii

Acknowledgments xvii

Authors xix

1 Overview of surface wave methods 1

1.1 Seismic waves 2

      1.1.1 Seismic tests for site characterization 3

1.2 Surface waves 5

      1.2.1 Geometric dispersion 6

1.3 Test methodology 8

      1.3.1 Acquisition 10

      1.3.2 Processing 12

      1.3.3 Inversion 13

1.4 Historical perspective 15

      1.4.1 Global seismology 15

      1.4.2 Exploration geophysics 17

      1.4.3 Near-surface applications 18

      1.4.3.1 Pioneering applications 18

      1.4.3.2 Spectral analysis of surface waves 19

      1.4.3.3 Multistation approaches 20

      1.4.3.4 Microtremor surveys 20

1.5 Challenges of surface wave methods 21

      1.5.1 Sampling in space: Apparent phase velocity (mode superposition) 21

      1.5.2 Near-feld effects 23

      1.5.3 Model errors 24

      1.5.4 Resolution and depth of investigation 26

1.6 Typical applications 29

      1.6.1 Site characterization 29

      1.6.2 Soil improvement 31

      1.6.3 Nondestructive testing of pavements 31

      1.6.4 Offshore and near-shore site characterization 32

      1.6.5 Near-surface characterization in seismic exploration 32

      1.6.6 Anomaly detection 34

1.7 Advantages and limitations 34

2 Linear wave propagation in vertically inhomogeneous continua 37

2.1 Basic notions of wave propagation 38

      2.1.1 Two categories of wave motion 38

      2.1.2 Group velocity 41

      2.1.3 Body waves in unbounded, homogeneous, linear elastic, isotropic continua 43

2.2 Rayleigh waves in homogeneous elastic half-spaces 51

      2.2.1 Overview 51

      2.2.2 Dispersion relation of Rayleigh waves 53

2.3 Existence of love waves 60

2.4 Surface waves in vertically inhomogeneous elastic continua 65

      2.4.1 Eigenvalue problem associated with free surface waves 66

      2.4.1.1 Solutions by numerical techniques 72

      2.4.2 The source problem: Surface waves generated by a vertical point load 78

      2.4.2.1 Lamb’s problem for time- harmonic, vertical point load 78

      2.4.2.2 Features of wave propagation in two dimensions 83

      2.4.2.3 Geometric spreading function for surface Rayleigh waves 84

      2.4.2.4 Apparent phase velocity of surface waves 90

2.5 Surface waves in vertically inhomogeneous, inelastic continua 96

      2.5.1 Constitutive modeling of linear dissipative materials 96

      2.5.2 Viscoelastic waves in unbounded homogeneous media 106

      2.5.3 Surface Rayleigh waves in dissipative half-spaces 113

      2.5.3.1 Surface Rayleigh waves in weakly dissipative half-spaces 116

3 Measurement of surface waves 121

3.1 Seismic data acquisition 122

      3.1.1 Seismic data 122

      3.1.2 Surface wave acquisition 125

3.2 The wave feld as a signal in time and space 126

3.3 Acquisition of digital seismic signals 130

      3.3.1 Spectral analysis and wave feld transforms 130

      3.3.2 Fourier series and Fourier transform 131

      3.3.2.1 Properties of the Fourier transform 133

      3.3.3 Sampling 134

      3.3.4 Interpolation and aliasing 136

      3.3.5 Windowing 137

      3.3.6 Quantization and analog-to-digital conversion 140

      3.3.7 Acquisition of 2D signals 141

      3.3.7.1 Effects of fnite sampling 143

3.4 Acquisition of surface waves 148

      3.4.1 Noise 149

      3.4.1.1 Incoherent noise 150

      3.4.1.2 Increasing the SNR for incoherent noise 154

      3.4.1.3 Coherent noise 158

      3.4.1.4 Body waves 159

      3.4.1.5 Air blast 160

      3.4.1.6 Near-feld 160

      3.4.1.7 Lateral variations 162

      3.4.1.8 Higher modes 162

      3.4.2 Sampling 165

      3.4.2.1 Spatial and temporal discrete and fnite sampling 165

      3.4.2.2 Maximum wavenumber and spatial aliasing 168

      3.4.2.3 Spectral resolution and aperture 169

      3.4.2.4 Effects of side lobes 173

      3.4.3 Survey design 174

      3.4.3.1 Acquisition layout for active tests 174

      3.4.3.2 The two-station method 178

      3.4.3.3 Acquisition of passive surface wave data 179

3.5 Equipment 182

      3.5.1 Sources 183

      3.5.1.1 Impulsive sources 184

      3.5.1.2 Vibrating sources 186

      3.5.1.3 Sweep signals 189

      3.5.2 Receivers 191

      3.5.2.1 Geophones 193

      3.5.2.2 Accelerometers and MEMS 197

      3.5.2.3 Receiver coupling and land streamers 198

      3.5.2.4 Use of two-component receivers 199

      3.5.2.5 Receivers for marine surveys 199

      3.5.3 Data acquisition systems 202

4 Dispersion analysis 205

4.1 Phase and group velocity 206

4.2 Steady-state method 208

4.3 Spectral analysis of surface waves 211

4.4 Multi-offset phase analysis 220

4.5 Spatial autocorrelation 231

      4.5.1 Single source 231

      4.5.2 Isotropic wave feld 232

4.6 Transform-based methods 235

      4.6.1 Frequency–wavenumber domain 236

      4.6.2 Frequency–slowness analysis (MASW) 241

      4.6.3 Refraction microtremor method 244

4.7 Group velocity analysis 251

4.8 Errors and uncertainties in dispersion analyses 253

5 Attenuation analysis 255

5.1 Attenuation of surface waves 255

5.2 Univariate regression of amplitude versus offset data 258

5.3 Transfer function technique and complex wavenumbers 261

5.4 Multichannel multimode complex wavenumber estimation 265

5.5 Other simplifed approaches 268

      5.5.1 Half-power bandwidth method 268

      5.5.2 Spatial decay of the Arias intensity 270

5.6 Uncertainty in the attenuation measurement 270

6 Inversion 273

6.1 Conceptual issues 275

      6.1.1 Forward and inverse problems in geophysics 275

      6.1.2 Ill-posedness of inverse problems 277

      6.1.3 Inversion strategies: Local versus global methods 280

6.2 Forward modeling 282

6.3 Surface wave inversion by empirical methods 286

      6.3.1 Numerical example 287

      6.3.2 Manual inversion 289

6.4 Surface wave inversion by analytical methods 289

      6.4.1 Measures of ftting goodness 289

      6.4.2 Linear inverse problem 292

      6.4.2.1 Singular-value decomposition and Moore–Penrose generalized inverse 292

      6.4.2.2 Instability of the solution and condition number 296

      6.4.2.3 Tikhonov regularization methods 298

      6.4.2.4 Other regularization methods 301

      6.4.2.5 Accuracy and resolution 302

      6.4.3 Nonlinear inverse problem 303

      6.4.3.1 Linearization by transformation of variables 303

      6.4.3.2 LS iterative methods and GS techniques 306

      6.4.3.3 Analytical versus numerical Jacobian 310

      6.4.3.4 An example of a LS iterative method: Occam’s algorithm 312

      6.4.4 A priori information in surface wave inversion 320

      6.4.4.1 Borehole logs 321

      6.4.4.2 P-wave refraction survey 321

      6.4.4.3 Joint inversion of geophysical data 323

6.5 Uncertainty 324

      6.5.1 Inverse problems and measurement errors 324

      6.5.1.1 Linear problems with Gaussian data errors 324

      6.5.1.2 Normality assessment 325

      6.5.1.3 Nonlinear problems with Gaussian data errors 327

      ]6.5.2 Uncertainty in surface wave measurements 329

      6.5.2.1 Experimental dispersion curve 330

      6.5.2.2 Experimental attenuation curve 333

      6.5.2.3 Joint experimental dispersion and attenuation curves 336

      6.5.3 Estimate of variance of model parameters 339

      6.5.4 Trade-off between model resolution and uncertainty 344

      6.5.5 Bayesian approach 349

7 Case histories 351

7.1 Comparison among processing techniques with active-source methods 352

      7.1.1 Two-station (spectral analysis of surface waves) 352

      7.1.2 Frequency–wavenumber analysis 355

7.2 Comparison among inversion strategies 363

      7.2.1 Experimental dataset 363

      7.2.2 Empirical inversion 368

      7.2.3 Deterministic approach (least squares) 369

      7.2.4 Stochastic approach (Monte Carlo) 370

      7.2.5 Deterministic approach with vertically heterogeneous medium 374

7.3 Examples for determining V s and D s profles 375

      7.3.1 Memphis 376

      7.3.2 Pisa 377

7.4 Dealing with higher modes 380

7.5 Surface wave inversion of seismic refection data 384

      7.5.1 Application with engineering data in 2D 385

      7.5.2 Application with exploration data in 3D 388

8 Advanced surface wave methods 393

8.1 Love waves 393

      8.1.1 The nature of Love waves 394

      8.1.2 Experimental confgurations 396

      8.1.3 Real data example 400

8.2 Offshore and nearshore surface wave testing 402

      8.2.1 Scholte waves 404

      8.2.2 Guided waves 408

      8.2.3 Example 410

8.3 Joint inversion with other geophysical data 413

      8.3.1 Joint inversion 413

      8.3.1.1 Geometrical joint inversion 415

      8.3.1.2 Petrophysical joint inversion 416

      8.3.2 Surface wave joint inversion 416

      8.3.2.1 Joint inversion with electrical and electromagnetic measurements 417

      8.3.2.2 Joint inversion with other seismic data 419

      8.3.2.3 Joint inversion of refracted and surface wave 420

8.4 Passive seismic interferometry 426

8.5 Multicomponent surface wave analysis, polarization studies, and horizontal-to-vertical spectral ratio 430

      8.5.1 Mode identifcation in the case of high velocity contrasts 433

      8.5.2 Passive H/V 433

      8.5.3 How to compute the H/V 437

      8.5.4 Interpretation of H/V 438

References 441

Index 459

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