Modeling and inversion of dispersion curves of surface waves in shallow site investigations

The shallow S-wave velocity structure is very important for the seismic design of engineered structures and facilities, seismic hazard evaluation of a region, comprehensive earthquake preparedness, development of the national seismic hazard map, and seismic-resistant design of buildings. The use of surface waves for the characterization of the shallow subsurface involves three steps: (a) acquisition of high-frequency broadband seismic surface wave records generated either by active sources or passive ambient noise (microtremors or microseisms), (b) extraction of phase dispersion curves from the recorded seismic signals, and (c) derivation of S-wave velocity profiles either using inversion algorithms or manually error and trial forward modeling. The first two steps have been successfully achieved by several techniques. However, the third step (inversion) needs more improvements. An accurate and automatic inversion method is needed to generate shallow S-wave velocity profiles.; With the achievement of a fast forward modeling method, this study focuses on the inversion of phase velocity dispersion curves of surface waves contained in ambient seismic noise for a one dimensional, flat-layered S-wave velocity structure.; For the forward modeling, we present a new more efficient algorithm, called the fast generalized R/T (reflection and transmission) coefficient method, to calculate the phase velocity of surface waves for a layered earth model. The fast method is based on but is more efficient than the traditional ones. The improvements by this study include (1) computation of the generalized reflection and transmission coefficients without calculation of the modified reflection and transmission coefficients; (2) presenting an analytic solution for the inverse of the 4X4 layer matrix E. Compared with traditional R/T methods, the fast generalized R/T coefficient method, when applied on Rayleigh waves, significantly improves the speed of computation, cutting the computational time at least by half while keeping the stability of the traditional R/T method.; On inversion study, the dissertation explored a linear inversion technique, a non-linear inversion method, and a joint method on the dispersion data of surface waves. Chapter 3 explores the Occam's linear inversion technique with a higher-order Tikhonov regulization. The blind tests on a suite of nine synthetic models and two field data sets show that the final model is heavily influenced by (a) the initial model (in terms of the number of layers and the initial S-wave velocity of each layer); (b) the minimum and the maximum depth of profiles; (c) the number of dispersion picks; (d) the frequency density of dispersion picks; and (e) other noise.; To minimize this initial-model-dependence of the Occam's inversion, the nonlinear simulated annealing (SA) inversion technique is proposed in Chapter 4. Following previous developments I modified the SA inversion yielding one-dimensional shallow S-wave velocity profiles from high frequency fundamental-mode Rayleigh dispersion curves and validated the inversion with blind tests. Unlike previous applications of SA, this study draws random numbers from a standard Gaussian distribution. The numbers simultaneously perturb both S-wave velocities and layer thickness of models. The annealing temperature is gradually decreased following a polynomial-time cooling schedule. Phase velocities are calculated using the reflectivity-transmission method. The reliability of the model resulting from our implementation is evaluated by statistically calculating the expected values of model parameters and their covariance matrices. Blind tests on the same data sets as these in Chapter 3 show that the SA implementation works well for S-wave velocity inversion of dispersion curves from high-frequency fundamental-mode Rayleigh waves. Blind estimates of layer S-wave velocities fall within one standard deviation of the velocities of the original synthetic models in 78...