Other than commonly assumed in seismology, the phase velocity of Rayleigh waves is not
necessarily a single-valued function of frequency. In fact, a single Rayleigh mode can exist
with three different values of phase velocity at one frequency. We demonstrate this for the first
higher mode on a realistic shallow seismic structure of a homogeneous layer of unconsolidated
sediments on top of a half-space of solid rock (LOH). In the case of LOH a significant
contrast to the half-space is required to produce the phenomenon. In a simpler structure
of a homogeneous layer with fixed (rigid) bottom (LFB) the phenomenon exists for values
of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-wave velocity being
three times S-wave velocity (Poisson’s ratio of 0.4375). A pavement-like structure (PAV)
of two layers on top of a half-space produces the multivaluedness for the fundamental mode.
Programs for the computation of synthetic dispersion curves are prone to trouble in such cases.
Many of them use mode-follower algorithms which loose track of the dispersion curve and
miss the multivalued section. We show results for well established programs. ... mehr