Subsurface structure across the Tacoma Basin, Washington State, using trans-dimensional Bayesian inversion of fundamental mode spatial autocorrelation data

Spatial autocorrelation (SPAC), the azimuthal average of the normalized cross-correlation between equidistant station pairs deployed in a 2-D array, is widely used to image the subsurface structure. However, the rigorous estimate of subsurface structure and its uncertainties as a function of depth using SPAC data is challenging due to the nonlinear relation between the SPAC data and Earth structure as well as the trade-off between depth and velocity. Additionally, data noise is strongly correlated due to data processing (e.g. filtering, stacking from multiple time segments and azimuthal averaging). Most studies do not account for the correlated noise and fix the ratio of compressional-wave velocity ( V_P ) to shear-wave velocity ( V_s ) (i.e. V_P / V_s ratio) and the number of layers, both of which are typically unknown. To address these challenges, we develop a hierarchical trans-dimensional Bayesian inversion of fundamental mode of SPAC data that properly accounts for the correlated data noise, samples the V_P / V_s ratio and relaxes the number of layers (i.e. model parametrization) to be unknown in the inversion. We further examine the limitation of using only fundamental modes in the inversion. Our synthetic experiments show that the inversion recovers an incorrect model unless we sample the correlated noise and V_P / V_s ratio in the inversion. The inversion is then applied to SPAC data acquired at 19 sites across the Tacoma basin in Washington State to characterize the V_s and the time-averaged V_s over 30-m depth ( V_s30 ). Our results show that the V_s30 varies from ∼200 to 800 m s⁻¹ . The V_s30 within the basin is higher in the middle and lower on the east and west sides. We find that these V_s30 values vary with geologic unit. The uncertainties for V_s30 are within 20 m s⁻¹ in average except for the most eastern site TB28. Additionally, the uncertainties are greater for deeper depths beneath most of the sites as the sensitivity decreases as a function of depth. The Vs structure as a function of depth is also complex beneath some sites, possibly because the SPAC curves are affected by higher order Rayleigh modes that are not considered in the inversion. To better constrain the deeper V_s structure, V_s30 and/or other average measures of V_s over depth, additional constraints from complementary data, such as ellipticity or geologic data are needed. Moreover, our synthetic experiments show that higher order modes can have significant effect in the inversion results, particularly when there is a low-velocity layer.