Wavefield Analysis of Rayleigh Waves for Near-Surface Shear-Wave Velocity

Shear (S)-wave velocity is a key property of near-surface materials and is the fundamental parameter for many environmental and engineering geophysical studies. Directly acquiring accurate S-wave velocities from a seismic shot gather is usually difficult due to the poor signal-to-noise ratio. The relationship between Rayleigh-wave phase velocity and frequency has been widely utilized to estimate the S-wave velocities in shallow layers using the multichannel analysis of surface waves (MASW) technique. Hence, Rayleigh wave is a main focus of most near-surface seismic studies. Conventional dispersion analysis of Rayleigh waves assumes that the earth is laterally homogeneous and the free surface is horizontally flat, which limits the application of surface-wave methods to only 1D earth models or very smooth 2D models. In this study I extend the analysis of Rayleigh waves to a 2D domain by employing the 2D full elastic wave equation so as to address the lateral heterogeneity problem. I first discuss the accurate simulation of Rayleigh waves through finite-difference method and the boundary absorbing problems in the numerical modeling with a high Poisson's ratio ( 0.4), which is a unique near-surface problem. Then I develop an improved vacuum formulation to generate accurate synthetic seismograms focusing on Rayleigh waves in presence of surface topography and internal discontinuities. With these solutions to forward modeling of Rayleigh waves, I evaluate the influence of surface topography to conventional dispersion analysis in 2D and 3D domains by numerical investigations. At last I examine the feasibility of inverting waveforms of Rayleigh waves for shallow S-wave velocities using a genetic algorithm. Results of the study show that Rayleigh waves can be accurately simulated in near surface using the improved vacuum formulation. Spurious reflections during the numerical modeling can be efficiently suppressed by the simplified multiaxial perfectly matched layers. The conventional MASW method can tolerate gentle topography changes with insignificant errors. Finally, many near-surface features with strong lateral heterogeneity such as dipping interfaces, faults, and tunnels can be imaged by the waveform inversion of Rayleigh waves for shallow S-wave velocities. This thesis consists of four papers that are either published (chapter 1) or in review (chapter 2, 3, and 4) for consideration of publication to peer-refereed journals. Each chapter represents a paper, and therefore inadvertently there will be a certain degree of overlap between chapters (particularly for the introduction parts, where references to many common papers occur)