Maximum Likelihood Parameter Estimation for Surface Waves: Application to Ambient Vibrations

The analysis of ambient vibrations represents a valuable tool in seismic microzonation, engineering seismology, and other fields. An extensively used approach for the study of ambient vibrations is the use of array processing techniques. We have developed a novel technique for the analysis of the seismic wave field and show an application to the analysis of ambient vibrations. We derived maximum likelihood estimators for the parameters of the different wave types, considering all the measurements simultaneously. Our method allows us to separate the contribution of Love and Rayleigh waves as well as fundamental and higher modes. We assess the performance on SESAME synthetic models. We show that the proposed approach allows to detect weaker signals from higher modes, even when they are not visible with traditional techniques. This leads to a more accurate estimation of the dispersion curves, potentially over a broader frequency range and including larger portion of higher modes. In addition, we estimate Rayleigh wave ellipticity with a maximum likelihood estimator and estimate the retrograde vs. prograde behavior of the particle motion. INTRODUCTION The analysis of ambient vibrations represents a valuable tool in seismic microzonation, engineering seismology, and other fields. An extensively used approach for the study of ambient vibrations is the use of array processing techniques (Fäh et al. 2008, Cornou et al. 2003). Array processing techniques currently in use present several limitations, such as: measurements from different components of the seismometer are processed separately; wave field parameters are not estimated jointly; superposition of different wave phenomena is not accounted for. We have developed a novel technique for the analysis of the seismic wave field and show an application to the analysis of ambient vibrations (Maranò et al. 2011b, submitted). The proposed technique relies on a particular type of probabilistic graphical model called factor graph. We derived maximum likelihood estimators for the parameters of the different wave types, considering all the measurements simultaneously. Our method works in the time domain and addresses wave superposition. This enables us to separate the contribution of Love and Rayleigh waves as well as fundamental and higher modes. We assess the performance of the described technique on the SESAME synthetic dataset (Bonnefoy-Claudet et al. 2006). We show that the proposed approach allows to detect weaker signals from higher modes, even when they are not visible with traditional techniques. This leads to a more accurate estimation of the dispersion curves, potentially over a broader frequency range and including larger portion of higher modes. In addition, we estimate Rayleigh wave ellipticity with a maximum likelihood estimator and estimate the retrograde vs. prograde behavior of the particle motion. 1 4 IASPEI / IAEE International Symposium: Effects of Surface Geology on Seismic Motion August 23–26, 2011 ∙ University of California Santa Barbara