Geology Reference
In-Depth Information
Fig. 9.21 Near field
phases from a seismic
source A to a receiver B .
For clarity, S wave arrivals
( dashed lines )areshown
separately
phase. The first arrival at a seismic station can be
either a Pg phase or a Pn phase, depending on the
epicentral distance , the Moho depth, z m ,and
the focal depth z f . Close to the epicenter, the first
arrival is always Pg .
However, at a certain angular distance c the
Pn phase takes over Pg . The distance where the
first arrival changes from Pg to Pn is called the
crossover point . This location clearly depends
from the crustal thickness and is 0.27 ı from
the epicenter in the oceans and 1.35 ı from the
epicenter on the continents. In general, for shal-
low earthquakes it results c 900 z m R ,where
R is the Earth's radius, which corresponds to a
great circle distance X c 5 z m km. The reflection
PmP always arrives after Pg and Pn , although
its amplitude can be dominant in the coda. This
phase follows very closely Pg , with delay less
than 2 s beyond the crossover point. As shown in
Fig. 9.21 , an equivalent nomenclature exists for
the S wave arrivals. Furthermore, it is possible to
have converted phases ,suchas PmS , SmP ,or PS ,
which arise from the conversion of a P wave into
an S wave or vice versa after a reflection at the
Moho discontinuity or at the Earth's surface.
The last high-amplitude arrival is represented
by surface waves travelling near the Earth's
surface. In the case of spherical body waves,
we know that the energy density decays as
1/ r 2 , because it depends from the squared wave
amplitude (Eq. 8.59 ) , which decreases as 1/ r
(Eq. 8.40 ) . Conversely, geometrical spreading
of surface waves determines a two-dimensional
spread of energy, thereby energy in this instance
decays as 1/ r and not as 1/ r 2 . Consequently, at
large distances from the source, surface waves
dominate the seismograms. These phases, which
are easily recognized in the case of shallow
earthquakes, are of two kinds. Rayleigh waves
are
Fig. 9.22 Multiple reflections of S waves at the Earth's
surface
superposition of P and SV waves, with period
less than 3 s, group velocity 3.0 km/s, which
are absent if the focal depth exceeds 3 km.
They determine retrograde elliptical trajectories
of ground in the radial vertical plane. It can
be shown that at the top of a homogeneous
Poisson solid their velocity is 0.92“, slightly
less than the S wave velocity (e.g., Stein and
Wysession 2003 ; Shearer 2009 ). Love waves
are transversely polarized surface waves that
form by constructive interference of high-order
SH multiples, that is SH wave reflections at the
Earth's surface (Fig. 9.22 ). The multiples are
usually indicated as SS , SSS , SSSS , SSSSS ,etc.,
as illustrated in Fig. 9.22 . Love waves, just as
Rayleigh waves, do not form an independent
class of seismic waves, because they represent
an interference phenomena of normal S waves.
Therefore, in principle it is possible to build them
by superposition of body waves. A simplified
model of formation for Love waves considers
the propagation of monochromatic plane waves
through a homogeneous layer overlying a ho-
mogeneous half-space with different mechanical
properties (Fig. 9.23 ). It is assumed that the
interference is associated with the superposition
of multiple reflections trapped between the
discontinuity plane and the Earth's surface. In
fact, if the incidence angle of the SH waves
exceeds the critical angle ™ c D arcsin(“ 1 /“ 2 )
(Eq. 9.47 ), then the waves are totally reflected
both at the interface and at the Earth's surface.
Therefore, they are trapped in the upper layer.
radially
polarized
phases
resulting
from
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