A niching particle swarm optimization strategy for the multimodal inversion of surface waves

Abstract

SUMMARY In practice, near-surface structures with shear wave velocity inversions or strong shear wave velocity contrasts may cause the phase velocity spectra of surface waves to be complex. Hence, it is sometimes difficult to identify mode numbers in the phase velocity spectrum. To avoid numbering different modes, the determinant misfit function has been applied to invert multimodal dispersion curves with a very limited computational cost due to the absence of the root-seeking procedure. However, this function presents a complicated relation with modal parameters and thus has multiple minima, resulting in an increase in model ambiguity. Therefore, it is more appropriate to adopt a multimodal optimization algorithm to find multiple minima instead of obtaining one optimal solution. In this study, we use a niching particle swarm optimization to find multiple minima with an enhanced fine search ability. Subsequently, we performed cluster analysis to distinguish different clusters in the inverted solutions and find the best-fitting profiles from multiple minima based on the Euclidean distance between the measured and inverted dispersion curves. Moreover, a modified Thomson–Haskell transfer matrix method is used to calculate the determinant misfit function for a better constraint on inversion because it can only resolve the surface wave modes possessing energy at the free surface, where both the sources and geophones are commonly deployed for active and passive surface wave exploration. Tests of synthetic and field data demonstrate that our inversion method is both effective and robust and emphasize its great potential in urban subsurface exploration and geotechnical characterization applications.