TY  - JOUR
A1  - Forbriger, Thomas
A1  - Gao, Lingli
A1  - Malischewsky, Peter
A1  - Ohrnberger, Matthias
A1  - Pan, Yudi
T1  - A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency
JF  - Geophysical journal international
N2  - 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. Their 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 lth Rayleigh mode to be a single-valued function of frequency.. 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.
KW  - Surface waves and free oscillations
KW  - Theoretical seismology
KW  - Wave
KW  - propagation
Y1  - 2020
U6  - https://doi.org/10.1093/gji/ggaa123
SN  - 0956-540X
SN  - 1365-246X
VL  - 222
IS  - 1
SP  - 582
EP  - 594
PB  - Oxford Univ. Press
CY  - Oxford
ER  -