Geoscience Reference
In-Depth Information
Love wave
Rayleigh wave
Figure 4.4.
The particle motion for surface waves. (After Bolt (1976).)
Rayleigh waves are denoted by LR or R, and Love waves are denoted by LQ or Q
(L for long; R for Rayleigh; Q for
Querwellen
, German, 'transverse waves';
Section 4.2.7). Rayleigh waves occur close to the surface of a semi-infinite
medium. The particle motion for these waves is confined to a vertical plane
containing the direction of propagation (Fig. 4.4). Near the surface of a uniform
half-space it is a retrograde (anticlockwise for a wave travelling to the right)
vertical ellipse. Rayleigh waves can therefore be recorded both by the vertical
component and by the horizontal component of a seismometer. In contrast, Love
waves occur when there is a general increase of S-wave velocity with depth. They
propagate by multiple internal reflections of horizontally polarized S-waves (SH-
waves) in this near-surface medium and thus propagate in a waveguide. The
Love-wave particle motion is transverse and horizontal, so they can be recorded
only by horizontal seismometers (Fig. 4.4).
The amplitude of Rayleigh waves decays exponentially with depth beneath
the surface. The amplitude of any particular frequency component is dependent
upon the following ratio:
depth beneath the surface
wavelength
Thus, for each frequency, the amplitude decreases by the same factor when
the depth increases by a wavelength. This means that the longer-wavelength
(longer-period or lower-frequency) surface waves contain more information
about the deep velocity structure, and the shorter-wavelength (shorter-period or
higher-frequency) surface waves yield information about the shallow structure.
A good rule of thumb is that surface waves sample to a depth of their wave-
length divided by three. Surface waves with periods less than about 50 s are used
to determine gross crustal shear-wave velocity structures. However, even the
highest-frequency (shortest-wavelength) surface waves cannot resolve the fine
structure of the crust because their wavelength (velocity/frequency) is too great.
Surface waves with longer periods are used to determine the mantle shear-wave
velocity structure. For details of the mathematics of surface waves refer to a
text such as officer (1974), Lay and Wallace (1995), Aki Richards (2001), Udıas
(1999), or Seth and Wysession (2003).
