S U M M A R YThis paper applies a general trans-dimensional Bayesian inference methodology and hierarchical autoregressive data-error models to the inversion of microtremor array dispersion data for shear wave velocity (v s ) structure. This approach accounts for the limited knowledge of the optimal earth model parametrization (e.g. the number of layers in the v s profile) and of the dataerror statistics in the resulting v s parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A transdimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the indexing parameter) are considered in the results. The earth model is parametrized in terms of a partition model with interfaces given over a depth-range of interest. In this work, the number of interfaces (layers) in the partition model represents the trans-dimensional model indexing.In addition, serial data-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate data-error statistics, and have no requirement for computing the inverse or determinant of a data-error covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the state space that spans multiple subspaces of different dimensionalities. The order of the autoregressive process required to fit the data is determined here by posterior residual-sample examination and statistical tests. Inference for earth model parameters is carried out on the trans-dimensional posterior probability distribution by considering ensembles of parameter vectors. In particular, v s uncertainty estimates are obtained by marginalizing the trans-dimensional posterior distribution in terms of v s -profile marginal distributions. The methodology is applied to microtremor array dispersion data collected at two sites with significantly different geology in British Columbia, Canada. At both sites, results show excellent agreement with estimates from invasive measurements.
S U M M A R YThis paper applies Bayesian inversion, with evaluation of data errors and model parametrization, to produce the most-probable shear-wave velocity profile together with quantitative uncertainty estimates from microtremor array dispersion data. Generally, the most important property for characterizing earthquake site response is the shear-wave velocity (V S ) profile. The microtremor array method determines phase velocity dispersion of Rayleigh surface waves from multi-instrument recordings of urban noise. Inversion of dispersion curves for V S structure is a non-unique and non-linear problem such that meaningful evaluation of confidence intervals is required. Quantitative uncertainty estimation requires not only a non-linear inversion approach that samples models proportional to their probability, but also rigorous estimation of the data error statistics and an appropriate model parametrization. This paper applies a Bayesian formulation that represents the solution of the inverse problem in terms of the posterior probability density (PPD) of the geophysical model parameters. Markov-chain Monte Carlo methods are used with an efficient implementation of Metropolis-Hastings sampling to provide an unbiased sample from the PPD to compute parameter uncertainties and inter-relationships. Nonparametric estimation of a data error covariance matrix from residual analysis is applied with rigorous a posteriori statistical tests to validate the covariance estimate and the assumption of a Gaussian error distribution. The most appropriate model parametrization is determined using the Bayesian information criterion, which provides the simplest model consistent with the resolving power of the data. Parametrizations considered vary in the number of layers, and include layers with uniform, linear and power-law gradients. Parameter uncertainties are found to be underestimated when data error correlations are neglected and when compressional-wave velocity and/or density (nuisance) parameters are fixed in the inversion.Bayesian inversion of microtremor array data is applied at two sites in British Columbia, the area of highest seismic risk in Canada, to study the ability to recover an accurate V S profile in relatively deep and shallow geological settings on the Fraser River delta in Greater Vancouver and in Victoria, respectively. A well-resolved V S profile to at least 110 m depth is determined at the Fraser River delta site for a power-law gradient parametrization. At the Victoria site, a layer with low V S and a weak linear gradient is indicated to 15-18 m depth, above much higher velocity material. Invasive V S measurements from seismic cone penetration testing and/or surface-to-downhole methods are used to assess the reliability of the Bayesian microtremor inversion results, with excellent agreement obtained at both sites.
Finite-difference modeling of 3D long-period (> 2 s) ground motions for large (M w 6.8) scenario earthquakes is conducted to investigate effects of the Georgia basin structure on ground shaking in Greater Vancouver, British Columbia, Canada. Scenario earthquakes include deep (> 40 km) subducting Juan de Fuca (JdF) plate earthquakes, simulated in locations congruent with known seismicity. Two sets of simulations are performed for a given scenario earthquake using models with and without Georgia basin sediments. The chosen peak motion metric is the geometric mean of the two orthogonal horizontal components of motion. The ratio between predicted peak ground velocity (PGV) for the two simulations is applied here as a quantitative measure of amplification due to 3D basin structure.
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