Application of the Coupled Local Minimizers Method to the Optimization Problem in the Spectral Analysis of Surface Waves Method

Abstract

The spectral analysis of surface waves (SASW) method aims to determine the small strain dynamic soil characteristics of shallow soil layers. The method involves an in situ experiment, the determination of an experimental dispersion curve, and the solution of an inverse problem, formulated as a nonlinear least squares problem. The latter is usually solved with a gradient-based local optimization method, which converges fast, but does not guarantee to find the global minimum of the objective function. The method of coupled local minimizers (CLM) combines the advantage of gradient-based local algorithms with the global approach of genetic algorithms. A cooperative search mechanism is set up by simultaneously performing a number of local optimization runs that are coupled by pairs of synchronization constraints. A synthetic example with two design variables (the shear wave velocity of two top layers of a layered half-space consisting of three layers on a half-space), demonstrates that the CLM method succeeds in finding the global minimum of an objective function with multiple minima and can successfully be used to solve the inverse problem in the SASW method. This is further illustrated by a complete inversion of the shear wave velocity profile accounting for seven design variables (the thickness and shear wave velocity of the three layers and the shear wave velocity of the underlying half-space). The inversion algorithm based on the CLM method is subsequently applied to invert the experimental dispersion curve derived from in situ data collected at a test site in Saluggia, Italy, consisting mainly of alluvial sediments. Up to a depth of about