Joint multizonal transdimensional Bayesian inversion of surface wave dispersion and ellipticity curves for local near-surface imaging

• Published in: Geophysical journal international 2021-07, Vol.226 (1), p.627-659
• Main Authors: Hallo, Miroslav, Imperatori, Walter, Panzera, Francesco, Fäh, Donat
• Format: Article
• Language: English
• ISSN: 0956-540X; 1365-246X
• DOI: 10.1093/gji/ggab116

Summary Physical properties of near-surface soil and rock layers play a fundamental role in the seismic site effects analysis, being an essential element of seismic hazard assessment. Site-specific mechanical properties (i.e. shear- and compressional-wave velocities and mass density) can be inferred from surface wave dispersion and horizontal-to-vertical or ellipticity data by non-linear inversion techniques. Nevertheless, results typically exhibit significant inherent non-uniqueness as different models may fit the data equally well. Standard optimization inversion techniques minimize data misfit, resulting in a single representative model, rejecting other models providing similar misfit values. An alternative inversion technique can be formulated in the Bayesian framework, where the posterior probability density on the model space is inferred. This paper introduces an inversion approach of surface wave dispersion and ellipticity data based on a novel multizonal transdimensional Bayesian formulation. In particular, we parametrize 1-D layered velocity models by the varying number of Voronoi nuclei, allowing us to treat the number of layers as an unknown parameter of the inverse problem. The chosen parametrization leads to the transdimensional formulation of the model space, sampled by a reversible jump Markov chain Monte Carlo algorithm to provide an ensemble of random samples following the posterior probability density of model parameters. The used type of the sampling algorithm controls a model complexity (i.e. the number of layers) self-adaptively based on the measured data's information content. The method novelty lies in the parsimonious selection of sampling models and in the multizonal formulation of prior assumptions on model parameters, the latter allows including additional site-specific constraints in the inversion. These assumptions may be based on, e.g. stratigraphic logs, standard penetration tests, known water table, and bedrock depth. The multizonal formulation fully preserves the validity of the transdimensional one, as demonstrated analytically. The resultant ensemble of model samples is a discrete approximation of the posterior probability density function of model parameters and associated properties (e.g. VS30, quarter-wavelength average velocity profile and theoretical SH-wave amplification function). Although the ultimate result is the posterior probability density function, some representative models are selected according to data fi