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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 800 km 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 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 50 and 200 s 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. [ABSTRACT FROM AUTHOR]

Seismic full waveform inversion (FWI) is a state-of-the-art technique for estimating subsurface physical models from recorded seismic waveform, but its application requires care because of high non-linearity and non-uniqueness. The final outcome of global convergence from conventional FWI using local gradient information relies on an informative starting model. Bayesian inference using Markov chain Monte Carlo (MCMC) sampling is able to remove such dependence, by a direct extensive search of the model space. We use a Bayesian trans-dimensional MCMC seismic FWI method with a parsimonious dipping layer parametrization, to invert for subsurface velocity models from pre-stack seismic shot gathers that contain mainly reflections. For the synthetic study, we use a simple four-layer model and a modified Marmousi model. A recently collected multichannel off-shore seismic reflection data set, from the Lord Howe Rise (LHR) in the east of Australia, is used for the field data test. The trans-dimensional FWI method is able to provide model ensembles for describing posterior distribution, when the dipping-layer model assumption satisfies the observed data. The model assumption requires narrow models, thus only near-offset data to be used. We use model stitching with lateral and depth constraints to create larger 2-D models from many adjacent overlapping submodel inversions. The inverted 2-D velocity model from the Bayesian inference can then be used as a starting model for the gradient-based FWI, from which we are able to obtain high-resolution subsurface velocity models, as demonstrated using the synthetic data. However, lacking far-offset data limits the constraints for the low-wavenumber part of the velocity model, making the inversion highly non-unique. We found it challenging to apply the dipping-layer based Bayesian FWI to the field data. The approximations in the source wavelet and forward modelling physics increase the multimodality of the posterior distribution; the sampled velocity models clearly show the trade-off between interface depth and velocity. Numerical examples using the synthetic and field data indicate that trans-dimensional FWI has the potential for inverting earth models from reflection waveform. However, a sparse model parametrization and far offset constraints are required, especially for field application. [ABSTRACT FROM AUTHOR]