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SUMMARY We propose a new Bayesian method to reveal the Vs structure of the near surface of the earth using spatial autocorrelation (SPAC) functions and apply this new method to synthetic, broad-band and geophone data sets. The principle of SPAC is introduced, and an implementation of the Bayesian Monte Carlo inversion (BMCI) for modelling SPAC coherency functions is described. To demonstrate its effectiveness, BMCI is applied to synthetic tests, data from 14 SPAC array sites in the Salt Lake Valley (SLV), Utah, and two arrays (one broad-band and one geophone) located in south central Utah. The Vs models derived from previous SPAC analysis of the 14 SLV sites differ by 10 per cent at most from those determined by BMCI and lie within uncertainties determined for the BMCI models. These agreements demonstrate the effectiveness of the BMCI method. The synthetic tests and applications to the SLV SPAC data show BMCI has great potential to resolve Vs structure down to at least 400 m. To achieve resolution for deeper Vs structure, longer duration deployments, wider array apertures, and additional seismometers or geophones can be used. Additionally, when the target frequencies are greater than 0.1 Hz, there is no apparent disadvantage in using geophone data for BMCI compared to broad-band data. Most significantly, BMCI places a quantifiable constraint on the uncertainties of the Vs models as well as Vs30.

A Bayesian Monte Carlo inversion of spatial auto-correlation (SPAC) for near-surface Vs structure applied to both broad-band and geophone data