Geology Reference
In-Depth Information
Fig. 10.11
Far-field
components of
displacement in the
x
1
x
2
plane for a single force in
the
x
1
direction.
Left
:
P
wave field;
Right
:
S
wave
field
Fig. 10.12
Far-field components of displacement for a
double couple in the
x
1
x
2
plane.
Left
:
P
wave field;
Right
:
S
wave field. The orientation of the
arrows
shows the
direction of first motion and the length is proportional
to the displacement. In the red quadrants,
P
wave first
motion is outward, thereby they are called the
compres-
sional quadrants
. Conversely, in the
dilatational quad-
rants
(
white
regions)
P
wave first motion is inward.
Nodal
lines
of zero motion separate the
P
-wave polarities into
four quadrants. The
tension axis
(or
T
axis) is in the
middle of the compressional quadrant; the
pressure axis
(
P
axis) is in the middle of the dilatational quadrant
P
M.t
r='/
r
that the displacement field is four-lobed, but now
the lobes represent
first
-
motion
displacements,
not static dislocations.
So far, we have not discussed the meaning of
the near-field term in (
10.47
). This term com-
bines radial and tangential contributions and a
complete solution for double couple sources can
be found in Aki and Richards (
2002
). However,
the pattern of near-field displacement is important
only at short distances from an earthquake focus,
where it represents permanent static deformation.
In the next section, we shall use the double
couple description of seismic sources and the
x
i
x
j
x
k
r
3
1
2 ¡'
3
u
i
.r;t/
D
(10.48)
•
ij
r
2
P
M.t
r=“/
x
i
x
j
1
4
¡
“
3
x
k
r
u
i
.r;t/
D
r
(10.49)
where M is termed the
moment rate
function.
A three-dimensional view of the first-motion far-
field radiation pattern corresponding to a dou-
ble couple in the
x
1
x
2
plane is illustrated in
Fig.
10.12
. As in the elasto-static context, we note
