Haotian Xu, Caroline Beghein 

We present a method for measuring the dispersion of higher mode surface wave phase velocities from a single seismogram using a hierarchical transdimensional Bayesian approach. The 1-D shear velocity profiles down to 800km depth between sources and seismic stations are regarded as the controlling parameters to tune the phase velocities of fundamental and higher modes. The misfits between synthetics and real waveforms indicate whether the phase velocities are recovered well from the data. We use Monte Carlo Markov chains (MCMC) to approximate the posterior distribution of each model parameters, and assess the uncertainties from these probability density functions. These techniques can test models of varying dimensions while being parsimonious, thereby letting the data themselves control the complexity of the solution. Another advantage is that the algorithm can decide how much data noise is needed in order to explain the data without overfitting them. The data noise can be treated as an unknown and different noise levels can be applied to the different time windows considered. The posterior noise distributions can then be used as an indicator of the quality of the waveform fit within each frequency-time window. We considered phase velocities between 50s and 200s for each mode, and performed a reliability analysis to determine which modes and periods are reliably constrained. In this paper, we first present the method and demonstrate its feasibility with synthetic tests, which show that the technique is robust. We then illustrate it with applications to real data. We applied the method to two paths sampling Australia using earthquakes at regional distances, and obtained results that agree well with previous studies. The new method can be used in regional and global tomographic studies to obtain phase velocity maps and 3-D models of seismic velocities and anisotropy at depths that are not well resolved by fundamental mode surface waves or body waves.