JOURNALOF PHYSICSOF THE EARTH, Vol. 19, No. 4, 1971
Source
Process
of Deep and
as Inferred
from
2.
Intermediate
Long-Period
Deep-focus
and
Earthquakes
P and
303
Earthquakes
S Waveforms
Intermediate-depth
around
Japan
By
Takeshi MIKUMO
DisasterPreventionResearchInstitute,Kyoto University
Abstract
The dynamical processes at the source of eleven deep-focus and intermediate-depth
earthquakes that occurred around Japan have been investigated from the analysis of long-period
P and S waveforms.
The recorded P waveforms have been equalized at some distance around the focal region
to get the source function, eliminating the combined effects of wave propagation in the
earth and of the seismograph characteristics.
It is found that the source process times
derived from the source function, as well as from the recorded first half-periods, indicate
some azimuthal dependence with respect to the orientation of one nodal plane and of the
null vector, in most of the earthquakes.
This dependence is interpreted
as a result of
shear faulting over a finite fault area, and used to determine the slip plane, slip direction,
fault length and width. The seismic moment and the average dislocation over the plane
are evaluated from P wave amplitudes together with the estimated fault dimension.
A close agreement in general features between the recorded and synthesized waveforms
including the absolute amplitudes of both P and S waves supports the above shear dislocation model. The overall distribution of the orientations of the slip planes and slip vectors
of these earthquakes
does not seem to be definitely related to the local dip or strike of
seismic zones in this region.
The calculated stress drops during these earthquakes, together with some available data,
appear to show a gradual increase with focal depths down to 400 km. A tentative interpretation of this increase is that the stress drop might be related, at least qualitatively,
to partial loss of the intrinsic (cohesive) shear strength of the material under increasing
hydrostatic pressures, if these earthquakes
are caused by brittle fractures in the lithosphere.
•˜1
.
Introduction
The
focus
focal
mechanism
and
intermediate-depth
around
Japan
gated
has
and
SYKES,
since
the
1969;
(HONDA
et
results
from
great
contributions
in
seismic
Recent
of
relation
the
and
investi1966;
KATSUMATA
MOLNAR,
of
al.,
the
in
the
this
seismological
deep-
1961,
HONDA
1952,
first
to
motion
clarify
1971),
and
1956),
tectonic
his
and
studies
the
earthquake-generating
to
zones
1967;
work
made
ses
et al.,
ISACKS
their
tribution
ICHIKAWA,
HONDA
pioneering
colleagues
extensively
1962;
1965;
of
earthquakes
been
(BALAKINA,
RITSEMA,
of a number
disstres-
features
of
deep
region.
approaches,
on
the
other hand, using the spectrum or waveform
of body and surface waves with the introduction of shear dislocation models have proved
effective to estimate not only the geometrical
orientation of a possible fault plane but also
more physical source parameters
including
the source dimension, the amount and direction of slip displacement,
its time function,
the fracture
velocity and the stress-strain
drop during deep earthquakes
(BERCKHEMER
and JACOB, 1968; MIKUMO,1969, 1971; FUKAO,
1970, 1971; ABE, 1971; WYSS, 1971).
It is the purpose of this paper to elucidate
such dynamical processes
at the source of
deep and intermediate
earthquakes
around
Takeshi
304
Japan,
and
ularly
to
plates
of
their
tectonic
deep
is
parameters
forms,
and
basis
of
into
the
direct
the
and
recording
the
observed
the
region.
and
S
P wave-
source
effects
waves
on
process,
of
wave
instruments,
Standardized
tions,
and
of
the
and
also
ing
the
the
Japan
from
3.
compare
Focal
Figs.
with
of
focus
and
that
this
around
from
greater
to
than
these
to
5.8.
The
and
P
tabulated
in
Table
are
of
the
northeastern
the
focal
Light
of
the
the
ponent
on
States
The
Fig.
and
lines
seismic
(1971).
long-period
seismograms
range
Data
vertical
of
140
these
respectively.
the
earthquakes
arc,
and
of
taken
from
mainly
and
recorded
Table
IsAms
used
1.
be
the
comWorld-
Information
that
for
tions.
of the
the
as
the
first
stations
shock
Since
earthquakes
small
and
mainly
the
from
these
source
5,
is
which
shock
from
the
second
WWSSN
pattern
be
includes
mainly
for
or
to
should
shock,
the
the
of
It
data
radiation
analyzed.
axes
from
double-couple
No.
of
tension
inferred
multiple
are
positions
faulting.
a
comones
mechanism
earthquake
Japanese
large
be
Open
the
and
focal
of
the
solid
denote
shear
regarded
data
are
is
on
through
indicate
and
may
the
equivalent
noted
and
here
horizontal
at
km.
depths
It
and
stations
hemisphere.
triangles)
T
the
Circles
hemisphere,
pressure
that
net.
projected
and
more
onto
near-by
motions
maximum
Japan,
510
lower
lower
eleven
includes
Wulff
to
pat-
the
projected
the
and
P
radiation
for
which
the
the
dilatations.
the
data
hemisphere
first
patterns
to
on
(circles
the
approximate
of
PKP
of
onto
cover
of
Ryukyu
from
indicate
zones
Sea
the
upper
the
arc,
the
of
incor-
mechanism.
motions
correspond
pressional
is
1, which
and
stations
symbols
the
National
locations
in
for
show
first
hemisphere
center
pertinent
Kurile-Kamchatka
depths
dotted
MOLNAR
1.
Hokkaido,
arc
magnitudes
(b)
wave
P
triangles
the
Administration,
shown
lower
four
based
United
Atmospheric
earthquakes
Izu-Bonin
with
are
focal
•˜
each
100
are
recent
information
the
deep-
earthquakes
mainly
of
and
part
eleven
in
1970
earthquakes,
Oceanic
are
Japan
1967
determinations
a
study
intermediate-depth
occurred
years
than
in
includ-
Report,
the
Mechanism
2 (a)
tern
•˜
Analyzed
Japan,
bulletins
Data
determine
inside
taking
records.
Data
from
Agency,
stations
seismological
earthquakes,
2.
sta-
information
Meteorological
Earthquake
to
(WWSSN)
available
university
porated
propagation
to
Network
other
high-sensitive
various
recorded
wide
stations
The
the
three-component
P
inferred
account
this
synthesize
of
descending
estimate
from
to
seismograms
to
partic-
or
around
approach
source
zones
lithosphere
present
implications
seismic
MIKUMO
does
stanot
Source
Fig. 1. Locations
Japan.
Process
and the fault-plane
of Deep
and
solutions
make much difference for these two shocks
(OIKE, 1971), the two kinds of data have been
superposed here, leaving some inconsistencies.
The focal mechanism solutions for the eleven
earthquakes
are also schematically shown in
Fig. 1, in which shaded parts indicate dilatational area.
The dip and dip directions of
two nodal planes are given in Table 1. The
tectonic implications of the mechanism,
together with distributions of the inferred slip
planes and slip directions will be discussed in
Intermediate
Earthquakes
of intermediate
a
later
and deep-focus earthquakes
Source
•˜
Functions,
and
In
at
this
Solid
in
Figs.
of
the
of
section,
the
apparent
the
Source
Inferences
obtain
the
around
section.
4.
to
305
we
source
time
source,
curves
3 (a)
vertical
on
the
the
and
shall
component
indicate
attempt
to
evaluate
energy
recorded
left-side
(b)
an
and
of
Times,
Parameters
make
functions
duration
from
Process
Source
release
P waveforms.
for
each
some
records
station
examples
of
P
waves
Takeshi
306
from
in
earthquakes
Figs.
for
6 (a)
No.
and
(b)
earthquakes
orded
in
mantle
structure
a
seismograph
BEN-MENAHEM,
The
the
recording
the
written
of
recorded
rec-
(ƒÖ),
the
system.
time
H(ƒÖ)
as
and
CM(ƒÖ) and
and
the
(TENG
and
h(t)
tion,
the
H(w)
in
overall
by
is
the
impulse
I
entire
effects
linear
response
of
waveforms
distance
following
tranfer
through
near
of
the
deconvolu-
wave
transmitting
the
some
system
H(ƒÖ)=Cm(ƒÖ)•EC(ƒÖ)•EP(ƒÖ)•E
eliminate,
the
to
the
the
we
here,
back
in
is
defined
If
sumed
crust-mantle
C(ƒÖ),
where
function
propagation
I(ƒÖ)
f(t)
be
The
region
MIKUMO,
those
source
of
characteristics
seismogram
therefore
the
wave
station
1965;
9.
effects
of
source
and
seismograms
No.
and
and
5,
the
the
effects
P(ƒÖ),
around
around
may
the
No.
and
S(ƒÖ)
U(ƒÖ),
the
2
include
finiteness
function
and
show
No.
waveforms
source
3
MIKUMO
distortion
system
can
the
be
source
as-
equalized
region
way,
1969).
at
(MIKUMO,
the
station
(2)
1969),
and
hence
source
(1)
F(ƒÖ)
transform
this
may
be
understood
as
the
function.
can
be
of
obtained
the
seismogram
from
the
f(t).
Fourier
CM(ƒÖ),
Source
Fig,
2.
Fault-plane
tions
on the
solutions,
lower
Process
open
hemisphere,
of Deep
symbols:
triangles:
and Intermediate
compression,
stations
on the
Earthquakes
solid
upper
symbols:
307
dilatation,
hemisphere.
circles:
sta-
Takeshi
308
which
does
deep
not
of
metrical
on
a
and
the
Q
KURITA
effects
the
each
of
used
the
at
were
the
with
a
between
quency
an
range,
a
computed
To
made
convolution
to
recover
of
c/s
and
the
in
the
0.1
c/s,
of
the
filter
functions,
technique.
0.005
For
has
check
the
synthesis
increment
high-cut
source
from
system
0.005
c/s.
uni-
computations
of
amplification
F(ƒÖ)H-1(ƒÖ).
for
structure
Fourier
interval
1.0
been
appro-
taken
All
and
logarithmic
and
has
the
was
between
0.1
decreasing
been
at
dispersive
but
when
WWSSN.
range
MIKUM0
seismograph
functions
made
frequency
and
site,
Haskell
long-period
transfer
profile
of
structure
known. I(ƒÖ)
conventional
11)
the
layered
geowere
C(ƒÖ)
recording
model
of
velocity
1962).
well
effects
(Model
including
to
not
model
(1968)
for
layered
the
here.
attenuations
(FUTTERMAN,
computed
priate
for
and
for
omitted
Jeffreys-Bullen
mantle
effects
been
P(ƒÖ)
spreading
based
and
important
has
Computations
is
provide
earthquakes,
applied
reliability
seen
to
of
attempts
from
fre-
linearly
been
It is
Fig. 3. Recorded (full line) and synthesized (broken line) P waveforms and their equalized source
functions.
(a) No. 3 (b) No. 5. (c) R: record,
S: source function, T: recovered seismogram.
1.10
latter
with
f(t)
MIKUMO
u0(t)
in
the
have
Fig.
by
a
3(c)
that the agreement
between the original and
recovered waveforms appears satisfactory.
The traces in the right-side in Figs. 3 (a)
and (b) are the source functions equalized at
a distance of 50 km, all of which have a
Source
Process
of Deep
and
Intermediate
plotted
Earthquakes
in
Figs.
5 (a)
directions ƒ¿1,2,3;
seismic
with
nodal
and
as
T0
for
To
four
as
cess
times
of
between
and
P waves
on
wedge-like
As
source
functions
preceded
directly
these
the
was
(1968)
that
by
the
5
process
of
are
process
the
time
P
relations
Fig.
and
t
thetical,
4
T0,
location
may
also
be
shows
the
established
the
tion
effects.
A
show
that
allowance
constants,
for
Ts=13-17
in
been
confirmed
thus
estimated
t
on
order
dependence
for
less
the
from
to
the
T0
of
u0(t)
with
the
of
attenua-
the
to
examine
of
the
source
earthquakes,
hs
yield
has
process
recorded
a
with
finite
source
the
source
by
a
shear
dimension.
function
can
In
be
written
1971),
where
(3)
and hence
the source
process
time or
breadth
of the base of the function
is,
also
times
first
accuracy,
possible
average
is
and
width
rise
time
apparent
of
source
to
L
our
the
and
the
of
slip
nodal
are
of
the
P
wave
the
is
Fig.
and
compression
first
5,
slip
we
its
the
and
motions.
direction
to
pole
of
be
the
the
norother
determined
dilatation
The
vector
dependence
The
can
the
conclude
null
parallel
sense
the
relation
can
the
plane.
the
the
are
above
to
oriented
through
Ą
and ƒËw
around
the
is
surface,
and ƒËs
including
are
D
along
velocities
relevant
to
plane,
from
in
motion
passing
and ƒËp
shear
plane
normal
corresponds
estit
nodal
W
fault
velocities
Applying
observations
the
the
and
plane,
dislocation, ƒËL
W,
and
slip
on
of
and
L
the
fracture
region.
that
of
dislocation
the
the
with
azimuthal
and
the
mal
times
To
length
half-
functions.
process
S0=(LW/2ƒÎƒËp)(ƒËs/ƒËp)2ƒ¿1ƒ¿2,
the
compressional
sec,
It
source
the
directions
instrumental
source
this
are
calculations
sec.
a satisfactory
calculated
eight
0.4
model
where
have
Tg=90-100
than
magnitudes.
of
(4)
hypo-
and ƒÐ2=0.0-0.1,
that
agree,
of
the
sec,
hg=0.8-1.5
differences
of
trial
for
esti-
which
of
dislocation
depend-
between
a variety
number
smaller
interpreted
but
this
MIKUMO,
number
values
h(t)
find
be
but
recognized,
following
1968;
convolution
assumed
response
periods
a
with
other
similar
half-cycle
the
relations
on
by
variously
first
seismograms,
constructed
impulse
the
to
the
11,
be
also
between
For
and
To
and
bears
the
using
6
possible
may
9,
and
5.
scat-
between
the
on
(BOLLINGER,
synthetic
been
of
waves,
large
dependence
times
model,
are
and ƒ¿2
4,
earthquakes
re-
there
3. and
may
azimuthal
vector,
termed
time
times
1,
to
are
now
breadth
Nos.
null
that
also
No.
a
normal
the
will
which
T0
shock
longer
(MIKUMO,
ground
No.
for
process
3 (b),
It
depending
from
1971).
mated
the
Fig.
shock.
source
recorded
empirical
In
for
earthquake
functions,
source
the
those
half-cycle
obtained
in
no
The
stations.
mated
for
those
seen
for
differences
The
T0
small
the
some
of
a
noticed
of
hereafter
of
be
first
pro-
seismograms.
to
JACOB
source
the
synthesized
can
by
base
of
similar
and
motion.
times
the
form
BERCKHEMER
be
the
the assumed
2,
dependence
ence
Relation
for
shocks,
weaker
4.
Nos.
of
the
rather
and
between
and
the
al
three
cosines
seen
with
and
shocks
dependence
Fig.
be
but
between
against
to
to
can
dependence,
ter,
it
and
It
(b)
direction
respect
planes
spectively.
some
and
the
ray
two
309
pattern
slip
vector
310
Fig. 5. Azimuthal dependence of the source process times (open circles) and the first half-periods (s
Takeshi
MIKUMO
) Nos. 2, 3, 5, and 9 (b) Nos. 1, 4, 6, and 11.
Source
thus
determined
Figs.
1
W
have
eq.
(4),
ing
an
2.
been
values
are
is
and
evaluated
value
of
fracture
the
be
the
intercept
type)
ing
If
do
(Mumma,
of
not
45•‹
travelling
five
5.8
for
earthquake
The
large
r
might
also
be
shall
them
as
of
In
No.
3
the
P
the
3 (a)
of
No.
wave
the
ical
and
and
the
and
(b)
synthe-
component
No.
2
also
and
No.
9.
displayed
for
the
earthquakes
Comparison
the
time
of
domain
of seismograms
provides
Mo
the
assigns
and
hence
the
absolute
amplitudes.
relationship
observed
earthquakes.
vertical
in
Figs.
between
double
Most
the
amplitudes
of the
P
way
constant
observed
are
a
estimated
time
6 (a)
the
test
of
such
the
respectively.
moment
to
Figs.
amplitudes
theoretical
show
with
seismograms
This
compare
models
in
assumed
(b)
kinds
seismo-
and
seismograms
the
and
two
D.
the
blunt
Seismograms
earthquakes
5
seismic
(b)
three
a
records,
(1),
of
for
and
location
eight
of
kinds
between
to
eq.
seismograms
two
last
dislocation
velocities.
waves
Figs.
and
6 respec-
from
waves
shear
and
examples
P
and
the
synthesized
in
fracture
sized
S
the
dimensions
show
for
0.13.6
synthesized
and
been
expressed
and
values
Theoretical
have
source
(4.9-4.8
1.9,
4, 3
corresponding
of
here.
waves
direction
between
Synthesized
P
the
validity
assumed
faulta
and
calculate
both
with
the
values
understood
and
next
of
earth-
waveforms.
Observed •˜
We
the
in
Nos.
shocks
grams
of
bidirectional
earthquakes,
tively.
5.
(stepvalues
and ƒË=0.9 ƒËs
take
for
P
yield
most
1971)
would
of
fur-
squares
reasonable
for
here
0.5 sec
onset
plane
without
and Ą=0
to
assume
(ƒËL=ƒËw=ƒË/0.7)
km/sec), Ą
sec
least
lead
velocity
we
velocity
slip
time ts=ƒÑ•}L/ƒËL•}W/ƒËL.
fracture
quakes.
constant
the
of ƒËL=ƒËw=ƒË
function
estimated
and
determined
the
and
assign-
time
direction
since
Assumptions
the
The
311
earthquakes
along
uniquely
assumptions,
of
2.
in Table
and
propagation
cannot
only
eight
Earthquakes
from
k and
The
for
Intermediate
in
L
squares
of ƒ¿j,
to ƒËp.
uncertainty
summarized
dislocation
least
signs
and
arrows
dimensions
by
appropriate
of Deep
by
source
the
of
ther
indicated
The
rearranging
with
Process
plotted
dis-
values
7(a)
and
theoretfor
the
points
Fig. 6. Examples of the recorded (full line) and
synthesized
(broken line) vertical
component
seismograms of P waves. (a) No. 2 (b) No. 9.
fall along a straight
line, indicating
that the
P wave amplitudes
as well as their waveforms
may be well explained
by the inferred
model.
Theoretical
seismograms
of SV and
SH
waves
can be synthesized
in a similar way,
with the parameters
estimated
from P waves
mograms. (a
312
Takeshi
MIKUMOFig. 7. Relation between the double amplitudes of P waves on the reco
) Nos. 2, 3, 5, and 9 (b) Nos. 1, 4, 6, and 11.
Source
Process
of Deep
and Intermediate
Earthquakes
Fig. 8. Examples of the recorded (full line) and synthesized (broken line) three-component seismo- grasms of P and S waves. (a) No. 2 (b) No. 5.
313
Takeshi
314
and
the
the
focal
S
wave
mantle
The
into
the
NS
directly
(a)
and
sized
S
(b)
the
ment
of
5,
and
and
6.
the
to
of
It
may
be
there
are
be
in
sized
the
shear
least
however,
to
to
wave
The
focal
Nos.
consistent
ISACKS
for
10
to
and
the
double1970),
of
addi
double-couple
force
1970).
Slip
Nos.
general
MOLNAR
modulus
fraction
and
and
be
generate
RANDALL,
No.
the
to
source
also
earthquakes
11,
deep
is
shear
solutions
and
and
in
mechanism
with
these
volumetric
the
Stresses
waves,
approximation,
could
KNOPOFF,
of
syntheS
It
small
the
absolute
of
for
change
to
and
obtained
a
be
component
Orientation
first
equivalent
could
(RANDALL
some
Japan.
(KNOPOFF
there
tional
the
a
wave
agree-
and
transitions
type
P
of
observed
models
sudden
radiations
couple
and
to
that
phase
foregoing
of
satisfactory
and
around
subjected
due
P
dislocation
earthquakes
the
including
the
of
at
noted,
solulater
dependence
waveforms
seismograms
favor,
partly
attenuations.
pattern
and
between
all
from
radiation
times,
the
amplitudes
and
due
from
of
azimuthal
process
ment
appre-
mechanism
variations
exFor
computed
may
concluded
the
motions,
source
2,
•˜
that
first
of
No.
the
focal
and
agree-
contamination
lateral
P
station.
Discussion
results
synthe8
features
a
however,
in
Figs.
and
at
This
for
difficulty
satisfactory
between
partly
phases,
to
earthquake
amplitudes.
al-
only
S waves.
general
component
uncertainty
tion
due
show
differences
observed
made
observed
that
case
one
compare
seismograms
No.
ciable
by
the
appears
the
for
earthquake
5,
stations
components
in
cept
be
direct
depict
It
three
to
of
resolved
to
records,
can
three-component
waves.
(MIKUMO,
are
components
well-isolated
and
crustal
waves
corresponding
number
selecting
to
the
the
waves
comparison
limited
S
SH
EW
the
this
Qƒ¿) and
to
and
and
with
though
of
SV
due
account
(divergence
QƒÀ=4/9
appropriate
1971).
into
function
with
response
factors
taking
transfer
attenuation
a
amplification
mechanism,
(1971)
Planes
in
1,
9
Nos.
and
pattern
in
regions
Fig.
7
1
and
3 appears
described
of
the
MIKUMO
Kamchatka-Kurile
arc, North Honshu, the
junction between the Izu-Boinin arc and North
Honshu, and of the Izu-Bonin arc, respectively. The mechanism for earthquake
No. 1
and No. 10 has also been reported independently by them, indicating a good agreement
with our solutions,
although
ours include
much more data from near stations.
The
above solutions suggest that the pressure axis
(down-dip compression)
tends to be parallel
to the dip of seismic zones or descending
lithosphere plate in the last three regions, as
has been pointed out by ICHIKAWA(1961, 1966)
and ISACKSand MOLNAR (1971), and that the
parallelism holds for the tension axis (downdip extension) in the first region.
Solutions
for Nos. 4 and 6 in the Hokkaido corner and
for No. 2 in the Ryukyu arc show, however,
somewhat different patterns from ISACKSand
MOLNAR (1971), and consistent rather with the
solutions by HONDA et al. (1956) and ICHIKAWA
(1966), and by KATSUMATAand SYKES (1969),
respectively.
These exceptions might be associated with complicated tectonic structures
such as oblique-angled junctions, contortions
of the lithosphere
and so on (ISACKS and
MOLNAR, 1971).
In Fig. 1 are indicated by arrows the possible slip planes and the slip directions of the
upper block relative to the lower one, which
have been inferred from the present analysis.
Broken arrows means somewhat questionable
choice of the fault plane because of weak
azimuthal
variations
of the source process
times, and there could be another choice in
these cases. It is to be noted that the slip
plane of earthquake
No. 5 agrees with that
determined
by OIKE (1971) from the travel
time differences of first P waves from the
double shocks of this earthquake.
It appears
that there is no systematic
trend in the
overall distribution of the inferred slip planes
and slip directions related to tectonic structures such as local dip or strike of seismic
zones around this region.
Close examinations of the five reliable solutions show, however, that the slip planes or slip
directions of earthquakes No. 4 and No. 5 in
the northern
Honshu, with a predominant
Source
Process
of Deep
and
Fig. 9. Schematic representation of the orientation of slip planes and the local dip of seismic
zones.
strike-slip
component,
are oriented
almost
parallel to the strike of the seismic zones,
but that earthquake
No. 9, 3 and 2 in the
south of Honshu, which are characterized by
predominant
dip-slip component, have a slip
direction nearly normal to the strike of the
seismic zones. In order to examine possible
relations between the orientation
of the slip
plane or the slip direction and the local dip
of the presumed
lithospher plate, the five
fault-plane solutions are schematically shown
in Fig. 9, on the cross section of the seismic
zones. Small solid circles and wings on the
rear end of arrows indicate strike-slip motion
towards up and away down seen from this
paper sheet respectively.
This may also be
understood from Fig. 1. Broken oblique lines
at the left side of each shock show the
local clip of seismic zone in the respective
regions (ISACKS and MOLNAR, 1971), but do
not indicate the periphery of the zone. This
figure suggests that the orientation
of the
slip plane and slip directions relative to the
seismic zone appreciably differ for these earthquakes, indicating almost pure strike-slip (No.
5), reverse faulting (No. 4), underthrusting
(No. 2) and normal faulting (Nos. 3 and 9),
respectively.
This variety of slip motions would be explained neither by the hypothesis of SUGIMURA
and UYEDA (1967), who associate the formation of a fault plane with a preferred orien-
Table 2. Estimated source parameters.
Intermediate
Earthquakes
315
Takeshi
316
tation
of
nor
by
olivine
generation
plane
Table
2
that
with
the
the
fault
crack
weakness
5.8
10
and
to
fault
30 km,
is
about
order
circular
rather
be
for
4
is
(MOLNAR
and
as
found
to
having
larger
with
WYSS,
1-7
than
comparable
plot
plot
m,
that
are
ex-
amount
of
which
for
apshal-
moments.
fault
width
No.
4,
we
length
The
see
that
a
twice
fault.
In
probable
ranges
assumption
10.
Estimated
stress
drops
together
against
focal
of
drops
in
from
the
are
with
depths.
the
a
plotted
those
and
larger
fault
area.
the
2,
two
where
we
yields
rectangular
values
stress
are
2
fault
under
center
of
the
assumption
values
10 the
ac-
smal-
smaller
Table
fault
the
be
the
No.
the
bounds
fault
to
squares
here
by
circular
uncerthe
may
least
take
given
the
large
Since
by
stress
Fig.
Although
earthquakes
multiplied
almost
first
ones.
are
sake
the
of
reliable
calculated
case,
for
data.
dimensions
lower
appro-
corresponding
for
also
plane
present
rather
evaluated
the
and
most
precision
tentatively
as
is
the
fault
except
width
It
used
have
bounds
most
reliable
depths,
1972).
Fig.
ler
as
assumptions
azimuthal
which
lower
earth-
r,
in
been
to
largest
cepted
fault
would
T0•`ƒ¿2
The
be
or
T0•`ƒ¿1
and
faulting.
considerably
earthquakes
the
to ƒ¿j=0,
bilateral
faulting
It
the
which
these
fault
available
according
circular
from ƒ¢ƒÐ=(2M0/3ƒÎ)
latter
has
values
to
a rectangular
the
estimated
a
radius
1969)
with
less
bilateral
unilateral.
interpret
for
to
former
possible
1, 2 and
that
be
earthquakes
No.
dislocation
length
Nos.
apply
equivalent
comparison
area,
reaches
to
with
refer
the
tainty
average
it
fault
possibility
symmetric
pected
the
pure
to
two
earthquake
variations
but
could
than
first
The
an
by ƒ¢ƒÐ
with
KEYLIS-BOROK),
able
(CHINNERY,
to
the
southwest
calculated
(4/L2+3/W2)/(L2+W2)1/2.
of
smaller
the
km,
with
a
possible
the
in
1971).
earthquakes
length
be
dislocations
but
earthquakes
earthquakes,
suggests
these
fault
1957;
to
with
been
dislocations
(ESHELEY,
priate
magni-
somewhat
8-10
intermediate
This
The
moments
comparable
three
6.4.
(MIKUMO,
width
with
ap-
has
for
(L•~W)
differ
intermediate-depth
region
source
moment
drop
assumed
for
earthquakes
earthquakes
comparable
Pacific
larger
seismic
these
for
estimated
eight
The
from
than
pears
horizontal
stress
=(7/16)M0/r3
quakes
between
ranges
for
The
mantle,
pre-existing
summarizes
for
tudes
for
upper
is
here.
preciably
also
a nearly
to
for
analyzed
for
the
Parameters
parameters
4.
in
1969).
Source
low
of
parallel
(SAVAGE,
a
crystals
MIKUMO
with
drop
from
against
obtained
their
the
focal
by
Source
Process
of Deep
and
Intermediate
BERCKHEMER
and JACOB(1968) and FUKAO(1970,
1971) for deep-focus earthquakes, by MIKUMO
(1971) and ABE (1971) for intermediatedepth earthquakes,
and those compiled by
BRUNE and ALLEN (1967) for shallow earthquakes.
The values by the first authors,
which are unfortunately
based on an erroneously replaced divergence factor, have been
corrected here, and we take the values only
for five shocks with more than seven data.
Tabulated values by the last authors (marked
by small open circles) which are from an indefinitely long vertical or horizontal fault,
have also been corrected (the right end of
lines) for circular cracks to compare with the
other observations.
Although the stress drop
might be a function of seismic moment and
could be subjected to regional differences as
suggested by MOLNAR and WYSS (1972) for
shallow earthquakes,
we notice here that the
estimated
values for deep earthquakes
are
several times larger than those for shallow
earthquakes,
and that they tend to increase
with depth down to about 400 km.
If they
are plotted against hydrostatic pressures at appropriate depths, a linear relation with rather
large scatter apply. This is the case even if
we refer to CHINNERY (1969) for stress drop
calculation
for all the earthquakes.
WYSS
(1971) recently calculated the source parameters
of deep earthquakes in the Tonga arc from the
corner frequency of body wave spectra using
BRUNE's theory (1970), and also found larger
stress drop at intermediate
depths than at
shallow crust.
show,
A Consideration
on the apparent increase in
stress drop with depth
Larger stress drops for deep earthquakes
result apparently from smaller fault dimension
and/or larger displacements on the slip plane,
but there might be more substantial
significance. A tentative interpretation
is described
here.
One would expect that the stress drop during seismic faulting may be directly associated
with the average shear strength
of rock
material in the earth's crust and mantle (e.g.
CHINNERY, 1964). Laboratory
experiments
(e.g. GRIGGSand HANDIN, 1960; MOGI, 1966)
ternal
however,
rocks
that
under
high
sponding
to
crust
This
released
fraction
evidence
of
rock
around
This
would
that
be
dry
would
brittle
not
and
increase
of
al.,
yield
HEARD,
the
PATTERSON
brittle
fractures
1960).
due
minerals.
This
plained
by
the
where
ing
a
pressure
pore
of
have
and
ISACKS
focus
lithosphere
stress
on
resulted
the
p
case
zero
in-
MCKENZIE
(1969,
by
1971)
deep-
brittle
cold
frac-
slabs
or
the
of
and
caused
the
shear
of
(1968),
of
the
extensional
gravitational
exceeds
confin-
coefficient
compressional
from
slab
RUBEY,
the
in
descending
when
in
or
MOLNAR
are
within
and
intermediate
earthquakes
tures
of
failure
plane,
the
et al.
and
that
role
expressed
fracture
is
ISACKS
suggested
stress
the
stress
material
and ƒÊ
friction.
to
p=ƒÉƒÐ(0<ƒÉ<1), ƒÑ0
the
stress,
(1969),
shear
normal
the
ex-
strength
(HUBBERT
with
strength
been
shear
Coulomb-Mohr
the
across
pressure
normal
is
such
hydrous
has
the
as
condition, ƒÑ=ƒÑ0+ƒÊ(ƒÐ-p)
1959),
of
due
the
and
that
under
principal
of
hand,
possibility
pressures,
form
other
even
failure
an
(GRIGGS
RALEIGH
dehydration
of
cause
fluid
modified
the
phenomenon
of
to
interstitial
On
occur
to
rather
flow
the
weakening
decrease
required
earthquakes
but
of
could
environments
do
Coulomb-type
uniform
suggest
and
mantle
(OROWAN,1960),
experiments
(1965)
pointed
pressures
shallow
or
and
been
upper
1960)
ductility
the
1966).
intermediate
ordinary
in
small
by
it has
the
HANDIN,
stress
a
BRACE,
sliding
as
1960;
however,
a
in
frictional
the
only
hydrostatic
fracture
(GRIGGS
or
for
but
increased
of
stress
that
and
case
temperatures
lower
supported
(PRESS
the
the
orders
estimated
is
stress
faults
allow
et
the
earthquakes,
elevated
in
suggests
total
of
corre-
two
earthquakes
the
deep-focus
and
than
during
strength
pressures
kilobars,
larger
drops.
shear
pressures
several
magnitudes
not
the
confining
hydrostatic
reaches
out
317
Earthquakes
force
acting
strength
of
the
material.
We
tentatively
stress
may
ified
sibility
to
be
assume
produce
approximately
failure
that
here
faulting
in
that
the
the
specified
condition,
since
released
water
shear
lithosphere
by
there
from
the
is
moda pos-
hydrous
Takeshi
318
minerals,
partially
vapour
from
portion
of
them
the
temperature
than
in
against
this
BAKER,
1969).
a
the
sphere.
Once
cohesive
1959;
1968),
and
hence
further
follow
and
<1)
is
the
fraction
regarded
cients
as
of
the
internal
for
a
killobars
1959;
greater
hundreds
(e.g.
HANDIN
1966),
than
might
be
and
cohesive
and
by
the
and
which
would
flaws
HAGER,
a
regime
RIECKER,
of 10-1
two
Thus,
least
on
condition.
some
experimental
real
the
difference
of
400
magnitude
that
of
is
The
brittle
pressures
of
the
and
order
tƒÊ1-ƒÊ2 would
lower
than ƒÊ1
apparent
drops
with
with
focal
accounted
for,
hence
may
results
in
the
by
This
micro-
stress
and
km
MOGI,
(TOWLE
values
the
1960),
earth.
confining
takes
qualitatively,
failure
existence
the
estimated
to
(e.g.
of
mechanics),
friction ƒÊ1
pressures
down
loss
material
the
appears
the
hydrostatic
depths
but
with
1961;
HANDIN,
be
the
not
in-
experimental
inconsistent
(e.g..
1966) that the ratio of stress drop to applied
initial stress becomes smaller for stronger
medium, since the absolute values of applied
stress or hydrostatic pressures in the present
case increase with depth.
Alternative
hypotheses such as shear melting instability
(GRIGGS and HANDIN, 1960;
GRIGGS and BAKER, 1969), or lubrication due
to partial melting (SAVAGE, 1969), and creep
instability (OROWAN,1960) have been presented
to account for the physical properties of deep
earthquakes.
In those cases, the stress drop
would be associated with the cohesive strength
of partially molten material between fault
faces, as that of soil-like materials in shallow
earthquakes
(BERG, 1968), or creep strength
of material there.
Since the order of the
strengths
seems plausible to compare with
seismic stress drops, these possibilities cannot
be rule out at this stage.
It should be emphasized
that the above
interpretations
involving many assumptions
are only tentative,
and it is undoubtedly
necessary to analyze much more deep earthquakes, to examine and regional and depth
variations of stress drops as well as of slip
vectors of fault planes.
Acknowledgments
of Ą0
material
in
orders
it
of
discrepancies
temperatures
100, so that
or
crease
from
and
1968),
to
one
of
weakly
1966)
our ĢĄ-hydro-
partial
and
in
internal
depends
(MOGI,
few
magnitude
decrease
1968),
rocks
of
a
JAEGER,
(MATSUSHIMA,
effect
in
of
of
to
ranges
1957;
order
(GRIGGS
come
labora-
about
The
references
coefficient
may
coeffi-
from
to
one
partly
size
scopic
at
rocks
bars
RIEGKER,
and
be,
ĢĄ
and ƒÊ2
kinetic
temperatures
intercept
strength
1966b;
.
and
temperatures
TOWLE
required
would
then
where ƒÁ(0<ƒÁ
loss, ƒÊ1
relation.
due
increasing
and
BERG,
as, ƒÑ2=(1-ƒÁ)ƒÑ0
of the
still
the
pressure
some
intrinsic
1960;
static
room
few
static
be
at
MOGI,
at
stress
drop
Ą0
various
experiments
from
litho-
friction.
estimated
tory
over-
the
(HUBBERT
shear
will
first
the
HANDIN,
the
faulting
of
and
initiate
started
+ƒÊ2(ƒÐ-p).
The
stress
drop
=ƒÑ1-ƒÑ2=ƒÁƒÑ0+(ƒÊ1-ƒÊ2)(1-ƒÉ)ƒÐ,
be
GRIGGS
of
loss
will
GRIGGS
(e.g.
arguments
stress
has
partial
500•Ž
will
strength
strength Ą0
RUBEY,
are
shear
fracture
or
about
(e.g.
the
lower
possible
mantle
process
shear
some
the
a
by
there
Faulting
complete
in
lower
although
local
or
under
surrounding
where
the
for
even
interpretation
point
point,
exist
lithosphere,
1970),
come
magma,
distribution
that
HASEBE,
at
molten
MISUMO
with
MATSUSHIMA,
I wish to thank Dr. Peter Molnar for comments on this study,
Drs. Kazuo Oike,
Katsuyuki
Abe, Michio Otsuka and Shogo
Matsushima
for discussions on many problems. My thanks are also due Mrs. Ritsuko
Koizumi for assistance in the present work.
Seismograms
were supplied by the United
States National
Oceanic and Atmospheric
Administration,
and computations were made
on a FACOM 230-60 at the Data Processing
Center, Kyoto University.
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