Forward modeling of steady-state surface wave test

The forward modeling of the dispersion curve of a layered medium calculated from the spectral characteristics of Rayleigh waves requires an efficient algorithm for predicting the surface displacements of the medium under a dynamic load. The usual methods for solving the wave equation are based on matrix methods prone to numerical problem or yielding to the determination of complex modes that are difficult to interpret. A modified linearized stiffness matrix method is proposed in this technical note to solve the discrete stiffness matrix. The developed algorithm is based on a finite element equation associating each surface wave mode to the resonant frequency of a structure with a stiffness depending on the wavelength. The filtering, of complex wave modes to keep only suitable surface waves is avoided. Furthermore, the mesh design is based on the actual wavelength of each mode providing a better representation of higher modes. The new algorithm is validated with two irregular stiffness profiles.