Probabilistic inversion of shear wave velocity profile based on the dispersion curve from multichannel analysis of surface waves and inequality constraints on layer thicknesses

Abstract

Multichannel analysis of surface waves (MASW) method is one of commonly-used geophysical methods for site investigation in geological and geotechnical engineering. This study proposes a new Bayesian framework for probabilistic inversion of Rayleigh wave dispersion curve (DC) from MASW to obtain the shear wave velocity (v_s) profile along the depth. The proposed framework considers inequality constraints (IC) on layer thicknesses as additional data complementary to limited DC data in likelihood function for probabilistic DC inversion, rather than prior knowledge in prior distribution as done in previous studies. This study discusses different ways of using IC information for probabilistic DC inversion from a theoretical perspective and highlights proper treatment of IC. The proposed approach is illustrated and verified using synthetic and real-life data. Results show that the proposed framework not only properly identifies the most probable v_s profile, but also reflects its identifiability by quantifying the identification uncertainty. Using IC indeed improves the identifiability of results. However, using IC as prior knowledge for identifying the v_s profile, e.g., like existing methods, assigns an insufficient penalty on stratification model complexity. As a result, the selected stratification model class can be unnecessarily complex, i.e., with a layer number more than the actual stratigraphy.