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. ... mehrTheir inability
to properly handle these cases might be one reason why the phenomenon of multivaluedness
went unnoticed in seismological Rayleigh wave research for so long. For the very same
reason methods of dispersion analysis must fail if they imply wave number $k_l(\omega)$ for the $l$-th
Rayleigh mode to be a single-valued function of frequency $\omega$. This applies in particular to
deconvolution methods like phase-matched filters. We demonstrate that a slant-stack analysis
fails in the multivalued section, while a Fourier–Bessel transformation captures the complete
Rayleigh-wave signal. Waves of finite bandwidth in the multivalued section propagate with
positive group-velocity and negative phase-velocity. Their eigenfunctions appear conventional
and contain no conspicuous feature.