Geology Reference
In-Depth Information
Fig. 9.23
Multiple reflections of
S
waves in a flat Earth model. The upper layer is homogeneous with slowness
s
1
.The
underlying half-space has slowness
s
2
<
s
1
. Wavefronts are shown as
dashed lines
Let us consider the three points
A
,
B
,and
C
in
Fig.
9.23
. The downgoing wavefronts at
A
and
C
are in phase and are subject to constructive
interference only if the phase of the
SH
wave
changes by 2
n
(for some integer
n
)afterthetwo
reflections. Such phase variation includes two
contributions, one associated with the reflections,
•ª
R
, and one due to propagation, •ª
P
:
Table 9.1
Main symbols for building mantle and core
phases in the IASPEI standard
Phase symbol
Description
P
P
wave travelling through the mantle
K
P
wave travelling through the outer core
I
P
wave travelling through the inner core
S
S
wave travelling through the mantle
J
S
wave travelling through the inner core
c
Reflection at the CMB
i
Reflection at the ICB
•ª
D
•ª
R
C
•ª
P
(9.75)
It is possible to prove (e.g., Stein and
Wysession
2003
) that reflection at postcritical in-
cidence angle determines a phase shift given by:
•ª
R
D
2 arctan
"
2
1
or, equivalently,
p
2
1=2
s
2
s
1
p
2
2
1
D
tan .hk cos ™/ (9.79)
1=2
#
p
2
s
2
s
1
p
2
(9.76)
Phases associated with Rayleigh and Love
waves are indicated respectively by the symbols
LR
and
LQ
.At
teleseismic distance
(>20
ı
)it
is possible to observe either the
mantle phases
or the
whole Earth phases
.Table
9.1
lists the
basic symbols used to build mantle and core
phase names, according to the
IASPEI Standard
(Storchak et al.
2003
).
Phase names are built considering reflections,
refractions, and conversions along raypaths. For
each transformation, a new symbol is added to the
phase name. For example, a raypath starting in
the mantle, refracted at the CMB and bottoming
in the external core will be indicated as
PKP
(Fig.
9.24
). Similarly, the phase
PKJKP
indicates
a
P
wave that penetrates the outer core, converts
to an
S
wave at the ICB, and has a turning point
in the inner core.
In the case of deep focus earthquakes, up-
going rays reflected at the Earth's surface are
termed
depth phases
and are indicated by
pP
,
where
1
and
2
are the rigidity moduli of the
upper layer and the half-space, respectively. Re-
garding •
ª
P
,
it
is de
termined by the path length,
which is AB
C
BC, and by the wavenumber
k
:
ª
P
D
AB
C
BC
k
BC cos 2ª
C
k
h
cos™
D
hk
cos™
.1
C
cos2ª/
D
2hk cos ™
(9.77)
D
Therefore, the condition of constructive inter-
ference assumes the form:
arctan
"
2
1
1=2
#
p
2
s
2
s
1
p
2
2hk cos™
D
2n
(9.78)
