Simulated Annealing Inversion of Multi-mode Rayleigh Waves

Rayleigh-wave velocity dispersion curves provide important constraints on the shear-wave velocity structure from the surface. Most Rayleigh wave studies assume the propagating surface-wave packet is composed solely of the primary Rayleigh mode. However, in near-surface studies higher order Rayleigh wave modes contain a sizable fraction of the propagating surface wave energy; and interference of the various modes complicates analysis. Inversion of Rayleigh wave dispersion curves for structure is further complicated by the inherent nonlinearity of the problem. Simulated annealing is a popular method for solving such problems but has not before been applied to the inversion of multi-mode Rayleigh wave dispersion curves. We applied this method to a near-surface set of Rayleigh waves produced by hammer blows onto the surface of a thick clay layer and recorded by an array 3-component geophones offset from the source from 7-m to 38-m at a 0.5-m spacing. Three strong Rayleigh wave modes were detected over the frequencies from 10-Hz to 80-Hz from the observed traces using a modified slant-stack method. Inversion of the three resulting dispersion curves provided a stable inversion that agreed well with the geologic stratification known from wellbore measurements and coring. In contrast, use of only the primary Rayleigh-wave dispersion curve provided a solution in poorer agreement with the geology despite matching the dispersion curve well. This study suggests that incorporating higher order Rayleigh wave modes yields a more reliable solution for geologic interpretation of near surface structure.