Download Source Process of Deep and Intermediate Earthquakes as Inferred

JOURNAL OF PHYSICS OF THE EARTH, Vol.
Source
1.
Process
of Deep
from
Intermediate-depth
and
19, No.
Intermediate
1
1, 1971
Earthquakes
as Inferred
Long-Period
P and S Waveforms
Earthquakes
in the Southwest
Pacific
Region
By
Takeshi
Disaster
Prevention
MIKUMO
Research
Institute,
Kyoto University
Abstract
The source process of four intermediate earthquakes with magnitudes of 6.0-6.8 and focal
depths between 100 and 200km has been re-investigated from the analysis of long-period P
and S waveforms.
The source process times recovered from the times of the first half cycle of recorded P
waves or the group delay times derived from the slopes of equalized phase spectrum show
an azimuthal dependence with respect to the orientation of a nodal plane and of the null
vector.
If we assume shear dislocation models for these earthquakes,
the dependence
yields a solution to the problem of which of two nodal planes corresponds to the slip plane.
Various source parameters have also been estimated from the azimuthal dependence by least
squares technique.
The dimension of the slip plane or the fault length and width range in 25-40km and 8-18
km, respectively, and the rise time of dislocation is found to be about 1sec. The rupture
velocity might be as low as 3.2km/sec, if two-dimensional
propagation is assumed.
The theoretical seismograms of both direct P and S waves appropriate to each recording
station have been synthesized on the basis of the estimated source parameters, taking into
account the combined effects of wave propagation in the mantle and the crust and of the
seismograph response.
A good agreement of general features between the observed and
synthesized waveforms on the three component seismograms
gives support to the above
slip dislocation model.
Comparison of the amplitudes on the both kinds of seismograms
yields
of
seismic
exceed
also
§1.
moment
80-140cm.
170
estimated
The
bars
for
in
of
the
stress
drop
one
shock.
relation
to
order
at
of
The
the
1.6-3.0×1026
these
effective
frictional
stress
Introduction
quakes,
but also of deep-focus
and intermediate-depth
earthquakes
that occurred
between 100 and 600km
(TENG and BEN-MENAHEM, 1965; BOLLINGER, 1968; BERCKHEMER and
JACOB, 1968; MIKUMO, 1969; FUKAO, 1970). It
is expected
that
if the source
of all these
earthquakes
can be interpreted
in terms of
shear dislocations,
the stress-strain
drop at
the source, shear stresses
causing
these earth
their variations
with depth
and that
the
strength
will
and
and
ranges
initial
Recent seismic
observations
covering
a low
frequency
range and the introduction
of elastic
dislocation
models have provided
a powerful
approach
to clarify
the dynamical
process
at
the source not only of large
shallow
earth-
quakes,
and
be estimated,
dyne・cm
earthquakes
on
stress
the
slip
the
from
to
50
produce
amount of
to
90
shear
dislocation
bars
but
dislocations
might
is
plane.
thermal
state
of material
in the mantle
and
their implications
to the tectonic
structure
of
a deep seismic zone, such as descending
slabs
of the lithosphere
(ISACKS et al., 1968; MCKENZIE, 1969), and the cause
of deep and
intermediate
earthquakes
might
be brought
into the light.
It appears
that there still remain
unsolved
problems
on the observational
side in an application
of shear
dislocation
models to deep
earthquakes.
The
problems
are;
whether
the source is a moving dislocation,
or at what
velocity
dislocations
spread
out over a slip
plane formed
in the mantle
with
increased
temperature
and pressure;
and whether
the
radiation
pattern
of S waves
including
the
absolute
amplitudes
and waveforms
can be
Takeshi
2
explained
by a dislocation
source
with the
same parameters
as for P waves.
The purpose
of the present
paper
is to
elucidate
more clearly
the source process
of
intermediate-depth
earthquakes,
by making
direct approach
to the problems.
The first
step
is to make
an attempt
to estimate
the
source
parameters
including
the
dimension, the amount
of dislocation
and the rupture
velocity,
from azimuthal
variations
of
recorded
P waveforms.
The second approach
is to synthesize
theoretical
seismograms
of
both P and S waves from dislocation
sources
with
the estimated
parameters,
taking
into
account
the combined
effects
of wave pro-
MIKUMO
meters
through
a linear
filter
system
com-
posed of the earth
and instrument,
and compared with the corresponding
records.
The
comparison
has shown that the average
waveform on the records
is similar
to that from
a double-couple
point
source
with a ramp
function
time
dependence
with
τ<3sec,
and
yielded the seismic moment
and probable
ranges for some other parameters.
Closer
examinations reveal, however, some difference
in the recorded P waveforms
for the first
half-period as well as in the slope of the
equalized phase spectrum
(MIKUMO 1969),
depending on the location of recording stations
with respect to the source.
For this reason,
an attempt is made here to evaluate the pospagation
in the earth and a recording
instrument,
and to compare
them
with their obsible azimuthal dependence of the above two
served
waveforms
on the three-component
quantities.
Although
the waveforms
are
records,
in order to test the appropriateness
predominantly
controlled
by the seismoof the assumed
model.
The stress
drop at
graph characteristics,
we assume that there
the time of these earthquakes
and the initial
are no serious differences in its frequency
stress
to produce
shear
dislocations
are disresponse among the stations. This assumption
cussed
in some detail.
may be justified by the fact that the shape
of calibration pulses placed on seismograms
§2. Data
is almost identical at these stations.
The earthquakes
analyzed
here are four
(1) The slope of the phase spectrum (or the
intermediate shocks that occurred along island
group delay time)
arcs from New Guinea to the Fuji Islands
The equalized source phase spectrum of
at depths between
100 and 200km, which
direct P waves has been given in Fig. 19 in
have been treated in a previous paper (MIKUMO, the previous paper, for all stations in the
four earthquakes
mentioned.
It can be seen
1969). Relevant
information
is again listed
in Table 1. Data used are the long-period
that there are appreciable differences in the
slope of the spectrum, and a possibility has
vertical and two horizontal component seismobeen suggested
that the source dimension
grams recorded at the WWSSN stations.
could in principle be evaluated from the slopes
§3.
Analysis
if the initial phase correction
is made for a
In the previous study (MIKUMO, 1969), theospherical earth.
The correction gives a conretical seismograms
of direct P waves have
stant term independent
on frequency on the
been synthesized
from moving
dislocation
standpoint
of normal modes (BRUNE, 1964;
models with variously assumed source paraSATO, 1969), and hence yields no effects on the
Table
1.
Information
of the earthquakes
analyzed.
Source
slope
of
source
the
phase
phase
faulting
spectrum.
φ(ω)
may
Process
be
in
The
the
written
of Deep
case
and Intermediate
(2)
unilateral
1969),
The
τ/2+ω(TL+TW)
left-hand
and
L
and
slip
W
are
plane,
wave
the
the
null
phase
is
group
station
following
ad
to
slip
the
to
source
and
the
The
the
the
the
group
azimuth
parameters
relevant
or
slope
the
be determined
that
evaluated
times
There
of
of
slip
part
at
from
L/υp,
W/υp
directly
from
than
three
more
range
direction
in
large
be
the
might
in
the
Crustal
to
with
delay
phase
be
the
are
station
(the
first half-periods,
spectra
and source
linear
a
earthquakes,
for;
not
slopes
the
0.15c/s.
dependence
to
The
are
over
and
azimuth
accounted
15)
determined
0.01
some
the
structures
each
times
scattering.
be
(earthquake
No.
between
plots
rather
Figs. 1(a)
(earthquake
equalized
appears
the
of
1(b)
group
the
of
Group delay times, observed
(b) No. 23
and
frequency
for
(a) No. 15
upper
plotted
to
delay
form,
Fig. 1.
the
from
αj and
direction
respectively.
or
of
be
delay
23)
No.
compressional
velocity,
the
related
dislocation,
width
cosines of
to
spectrum dφ/4ω
then
the
rupture
either
vector,
of
ad
υ are
and
direction
relative
time
length
υp and
ray
the
the
velocity
αk are
constant
may
can
(2) indicates
stations.
In
time
Eq.
τ±L/υ
the
(1)
τ is the
side
observations.
and
where
3
corrected
of
(MIKUMO,
φ(ω)=φU(ω)+φS(ω)=ω
Earthquakes
possible
but
reason
i) The
always
have
process times.
with
for
this
assumed
appropriate
been
cor-
4
Takeshi
MIKUMO
rected for a standard structure of HASKELL
(1960).). A difference of 10km in the crustal
thickness
yields the change of about 1.5sec
in the group delay time.
ii) The corrected
phase spectra do not change monotonously
with frequency;
and iii) The initial time of
digitization might not exactly agree with the
arrival time of first P waves when they have
a blunt beginning.
It would therefore
be
rather difficult to rely on the group delay
times in a precision
determination
of the
source parameters.
(b) Source process time
Another method is to infer from observed
records the apparent time duration of energy
release at the source region or the total time
of faulting process, which is specified by the
source finiteness and the rise time of dislocation. The displacement
of P waves ur0(t) at
great distances from dislocation sources may
be expressed by (MIKUMO, 1969),
(3)
Fig. 2.
Relation
between
the source process times.
first
half-periods
and
The width of the base of the pulse, hereafter
termed
as the source process time T0, is
specified by,
(4)
(8)
where
As
the
a
the
(5)
next
time
lower
times t
(7)
It
is clear
the
from
eqs.
deconvolved
SW(t)
is
of
a
rectangular
τ, 2TL
convolved
form
and
pulse
s(t),
so
tically
that
shown
that
each
of
with
a
the
such
lower
a
is
having
time
part
a
as
of
but
schema-
to
2.
Figs.
been
1 (a)
solid
parallel
and
half-cycle
read
circles.
alignments
on
each
We
1 (b),
of
directly
at
T0
in
records.In
P
the
vertical
station,
notice
between t
the
waves,
that
and
are
there
dφ/dω,
and hence this shows that t can be used as a
measure of T0. It is now necessary to find
a relationshipbetween t and T0. The procedure emloyed here is similarto that used
by BOLMNGER (1968,1970).An empiricalrelation is establishedhere on a number of
hypotheticalseismograms, which have been
constructedby the convolutionof ur0(t)for
variouslyassumed values of T0 with the impulse response h(t) of the earth-instrument
quely
with
Fig.
by
system.
STAUDER,
of Δu(t)
form
a
interval
and
convolution
has
in
width
s(t)
at the
(HIRASAWA
this
the
and SW(t),
specified
is
and
respectively.
of SL(t)
(TL+TW)
1965). ur0(t)
(7)
pulse
2TW
of trapezoid
0〓t〓2
(5) and
functions, Δu(t), SL(t),
of
determine
observed
seismograms
plotted
are
shall
the first
have
component
(6)
we
from
half
of
which
step,
domain
been
Since the form of ur0(t)is not uni-
specified
depends
τ, 2TL
made
only
also
and
on
2TW,
for
by
the
the
so
various
total
partition
that
time
of
of the
computations
combinations
T0
time
have
of
the
Source
three
parameters
Fig.
2 shows
station
HKC
No.
15),
an
average
ble
attenuation
this
each
kind
the
of
station,
hatched
for
an
relation
the
above
in
of
in
part
input
has
be
2.
with
conventional
of T0.
to
Table
crust,
and
indicates
example
for
earthquake
T/Q=1.5
the
and
ranges.
relation
single-layered
constants
of t
of Deep
probable
of
a standard
The
range
their
example
(Δ〓40°, Φ=314°
with
instrumental
system.
within
an
Process
a possiAlthough
derived
may
Source
for
be
ap-
process
Intermediate
Earthquakes
5
plied,as a first
approximation,to most of the
stations,
to recover T0 from t since differences
in crustalstructuresand attenuationsdo not
yield significantdiscrepanciesin the waveform. Two broken linesB-B and B-S show
the relationsderived by BOLLINGER (1970)for
an incidentbox-car pulseand half-cosinepulse
respectively.However, his relations,do not
include the effectsof attenuationsand of the
partitionof the total time duration,and are
times
and direction
cosines
6
Takeshi
MIKUMO
Fig. 3. Source processtimes plottedagainstthe directionsof one nodal planeand of the
null vector. (a)No. 12
(b)No. 15
(c)No.6
(d) No. 23
Source
Process
of Deep
and Intermediate
not used here.
The open circles plotted in the lower part
of Figs. 1(a) and 1(b) are the source process
times T0 thus estimated
from t on the indivisual records.
It can be seen that the
plotted points show a good consistency with
24φ/dω
the
with
above
less
scattering.
stated
reasons,
For
we
this
use the
and
tern of P wave first motions.
The next step is to evaluate
source
parameters
do
know
not
gation
assume
and
process
times obtained
from this time domain
analysis,
rather
than
the group
delay times
from the frequency
domain analysis
to evaluate the source parameters.
the
the
sionally
in
at
Estimation
The
a
source
number
are
of Source
Fig.
4(a).
stood
as
process
of
stations
tabulated
to
and
to
the
the
of
surement
the
between t
It
zero
to
sec,
and
is
as
2-3
in
local
sec
only
uncertainty,
the
from
a
muthal
been
mine
sponds
for
to
each
the
of
Figs.
to
the
the
plane
is the
plane
nodal
can
less
the
It
there
T0
as
along
the linear
υk are
defined
the
by
the j-
source
rupture
υj=υ/sinφ
and
dimen-
apparent
and
k-directions,
υk=υ/
either
of
result
also
null
vector.
some
found
can
as
shown
are
some
linear
of
Eq.
to
(9)
different
be
seen
between
direction
of
(α1 or α2)
the
T0
We
the
and
con-
nodal
directions
on
radiation
2)
In
T0∼
slope
or
moving
the
υj,k>υp;
for
the
slope
should
in
positive
αj,k<1,
being
this
αj,k=υp/υj,k.
pat-
either
positive
and
In
as
negative
as
case
be
positive
positive
for
direction.
with
be
symmetric
intercept
be
should
the
stations
stations
or
could
opposite
for
The
there
to
k-axis,
to
and
the null
αj,k diagram,
moves
of
but
of
∂T0/∂ αj,k
rupture
the j-
direction
3(a)∼3(d).1)
υp/υj,k<1,
1),
case
that
of
Figs.
the
slip
orientation
indicates
in
υj,k<υp,
rupture
the
the
types
if the
between
to
does
negative
vector.
the
other
corre-
been
direction
corresponds
the
deter-
has
relevant
from
which
three
to
that
slip
azi-
planes
scatter
two
inferred
are
dimen-
the
directions
dependence
The
Lk
υj and
the
dependence
table,
nodal
two
the
plane.
a
6
possible
above
and
in
0.5-
than
earthquakes,
the
rewritten
estimated
to
(α3) to the
be
almost
The
considerable
of
including
slip
from
of
T0.
that
the
plane.
Fig. 4(a). Geometry for an assumed rupture process.
plane.
planes
from
of
source
two
four
with
direction
clude
slip
the
either
cosφ,
respect
the
the
3(a)•`3(d),
relations
and
in
of
be
slip
interpretation
the
of
given
which
velocities,
rela-
order
variations
with
the
attenuations
the
examine
tested
directions
mea-
propagation.
now
rupture
along
differences
in
asymmetric
dependence
has
T0
large
rupture
shall
to
reaches
To
take
and
the
Since
of
we
the
of
may
private
form,
and
sions,
in
been
and
difference
rather
and
We
in
1969).
azimuthally
sion
has
structures
above
the
where Lj
planes
due
sometimes
average
(MIKUMO,
crustal
of
T0 ranges
and
the
make
that
that
4sec
although
is
which
sides
(8)
1964;
FUKAO,
(9)
The
allowance
T0
found
about
nodal
times
to
eq.
under-
with
respectively.
process
and
case,
general
be
velocities
shorter
a
illustrated
(OTSUKA,
1965;
in
we
two-dimenas
may
different
also
propa-
the
azimuth
two
this
travels
STAUDER,
and
We
reason,
starts
from
velocity ƒÒ
1970)
and
this
faulting
with
more
with
station
to
In
at
earthquakes
together
vector
errors
1.0sec.
the
estimated
four
2,
normals
null
uncertainty
tion
of
thus
the
Table
cosines
respect
for
in
direction
times
it
unknown
υ.
rupture
assumption
communication,
longer
of
bidirectional
and
of
For
rupture
front
four
τ and
direction
This
HIRASAWA
Parameters
W,
a constant
propagates
§4.
L,
at
this
stage.
here
that
the
point
source
7
Earthquakes
αj,k<
negative
with
to
time
values.
as
υp/υj,k<
the
can
axis of
take
Takeshi
8
Taking
and
into
tions,
we
where
the jdirection
and
δT0
From
and
and
shows
be
the
one
the
slip
its
width
Lk)
is
of
an
plane
ranges
W
about
1/2•`1/4
12.
the
a
for
earthquake
results
longer
direction
Nos.
6
and
No.
12,
the
two
the
the
null
23.
In
dimension
42
in
15,
vector
for
case
has
slip
it
and
order
of
plane
in
the
of
earthquake
order
directions.
dimensions
Fig. 4(b).
were
Relation between
determined,
the apparent
the
in
is
and
1970)
is
for
other
ranges
of
the
suppose
two
the
rupture
is
L
case
(B)
the
Fig.
4(b)
υL,W
in
velocity
the
shorter
shows
the
respectively,
earthquake
of
two
three
slip
No.
cannot
least
squares.
from
It
probable
ts.
in
Here
case
the
(A),
longer
plane(φ=π/2, υw=∞);
is
direction
the
15.
uniquely
the
along
rupture
cases
recorded
estimated
earthquakes
cases:
propagated
the
the
The
parameters
extreme
(1969;
comparison
to estimate
two
we
the
has
paper
of
we
by
however,
estimated
which
earthquake
hand,
τ and υ
possible,
in
for
140cm
be
from
waves.
least
computed
DLW,
previous
70•`100cm
the
also
or
amplitudes
P
reaches
On
can
the
double
synthesized
amount
rupture
D
linear
The
moment
Corrections,
the
along
earthquakes
a comparable
also
direction
direction
does
seismic
determine
while
Lj
slip
See
of
earthquake
the
the
but
the
the
for
that
Lk)
km,
determined
by
earthquake.
dislocation
been
and
the
of
being
except
dimension
of
to
of
the
value
(the
each
from
between
L
and
one
show
No.
Lj
25
20km,
length,
The
has
to
length
Lj
amount
large
around
length
shorter
the
of T0.
appropriate
from
(the
6
of
two
are:
as
rather
estimated
the
results
dimensions
velocity
The
Lj/υ ρ,
respectively,
with
ts=τ ±Lj/υj±Lk/υk
for
vector
source
compressional
longer
the
the
and
squares
taken
deviation
Lk/υp
sta-
all
quantities
standard
assigning
region.
Once
null
situations
αj,k for
were
estimated
by
source
No.
the
the
can
above
of
and k-axes
uncertainty
to
sign
three
the above,
Lk
the
the
determined
slip
in
account
re-arranging
MIKUMO
W
relation
for
assumed
the
where
two
give the upper
to
move
(φ=0, υL=∞).
between
four
τ and
earthquakes
curves
from
one
and lower bounds
and the rise time of dislocation.
Source
Intermediate
Earthquakes
that come from probable
errors in the adopted
dimension.
If all the four earthquakes
occur
through
the dynamical
process
with similar
the
velocity
time
<24°
constants
υL,W
would
by
the
shows
the lowest
Case
(A),
a
region
earthquake
the
relation
go
these
for
the
hatched
and
measured
Plane.
If
and
we
the
further
does
but υW
cases,
from
the
tan φ=υW/υL,
shorter
impose
not
Using
we
have
relations
of the
a limitation
Fig.
of
5.
φ
slip
that
Fault-plane
cannot
(MANSINHA,
exceed
1964),
the
their
3.2<υ<υ8〓4.5km/sec
shear
possible
and
13°<φ
The stress
drop during
these earthquakes
has also been estimated
by using the obtained
source
parameters.
For a dip-slip
displacealong
(16/3π)μ)D/W
long
vertical
ment, Δ
would
where
side
3.3
bound
are
9
respectively.
ment
except
1.7sec.
two
we
in
and
earthquake
13°<φ<29°
from
If
lowest
region,
the
a
estimated
bounded,
if τ exceeds
for
1/υ2=1/υL2+1/υW2
is
last
values
be
The
the
estimates
3.2<υ<5.1
will
No.12.
similar
range.
τ as
of 0.7<τ<1.8sec
sec
through
take
of
velocity
values
bounded
indicates
rupture
wave
10<υL<14km/sec.
wide
value
<υW<5.5km/sec
for
and
(A)
and
τ and
region
Case
rather
of Deep
velocities,
hatched
curves.
of 0.7<τ<1.4sec
(B)
take
rupture
fall in the
above
region
Case
and
Process
) as
an
(AKI,
fault
infinitely long
1966),
with
while
fault, Δ
for
strike-slip
σ=(2/π)μD/W=(KNOPOFF,
defined
by D=(π/4)Dm
an
displace1958),
is the
σ=
infinitely
where
average D
dis-
placement
over the entire fault surface.
Earthquake No.15
would correspond
to the former
case, and the latter may be applied
to earthquakes Nos. 6, 12 and 23. The above equations
assume,
however,
an infinitely
long fault.
It
may be more appropriate
to consider
a circular
type
crack
with
of dislocation, Δ
solutions.
a finite
radius
σ=(7π/16)μD/a
a.
For
(ESHELBY,
this
Takeshi
10
Table
1957;
KEYLIS-BOROK,
based
on
the
here
as
The
stress
reach
All
170bar,
the
the
estimated
in
for
fault-plane
lower
hemisphere
§5.
and
slip
four
Comparison
thesized
in
W
is
the
have
between
of
onto
net,
in
the
which
arrows.
Observed
P
similar
5 illustrates
projected
by
the
The
reduced
take
Wulff
of
3.
been
Fig.
indicated
Seismograms
3.
15
three
Table
τ and υ
solutions
direction
other
parameters
shocks.
of
Table
No.
the
given
that
the
their
the
L
in
taken
values.
source
are
condition
values
while
drop
was
earthquake
similar
earthquakes
Estimated
stress
(a
included
during
show
uncertainties
on
are
drop
earthquakes
The
assumption
a=√A/π)
might
four
1959).
last
3.
and
and
S
SynWaves
In the previous study, the synthesized
seismograms of P waves have been compared
with the vertical component
records at 15
stations in each of the four earthquakes analyzed here. There remains, however, an
important problem whether observed S waveforms including the absolute amplitudes could
also be explained by the dislocation sources
derived from P waves.
It has long been
recognized from observations that predominant
periods of S waves are usually longer than
those of P waves, but it does not always
appear from theoreticalwork (HASKELL, 1964;
HIRASAWA
and STAUDER, 1965) that moving
dislocation models could fully account for
the observational results. In this section,
theoretical seismograms of S waves, as well
as of P waves, are synthesized on the basis
MIKUMO
source
parameters.
of the source parameters estimated in the
preceding section, taking into account the
effects of attenuation, and compared with
their recorded waveforms on the three components.
The general solutions for the displacement
of P and S waves from moving dislocation
sources have been given by MARUYAMA
(1963),
HASKELL (1964),and BURRIDGE and KNOPOFF
(1964), and treated in detail for the far field
solutions by HIRASAWA
and STAUDER (1965)
and SAVAGE (1965). It is more convenient for
practical purposes here to write the solutions
referring to the geographical coordinate at the
source. The m-component of the displacement
of P and S waves in an infinitehomogeneous
medium may be written as, from their solutions,
(10)
where the suffixes p and s denotes the quantitiesfor P and S waves.The
1- and 2-axes
are taken to be perpendicular to the slipplane
and parallel to the slipdirection respectively.
Using the notations in the previous study
(MIKUMO, 1969),
(11)
where
SD(ω)=S1(ω)・S2(ω)
and
UD(ω)=U(ω)/D.
Source
Here
we
nate
with
X=sinΘ
introduce
the
origin at
・sinΦ,
Φ are
measured
from
the
from
ponents,
and
2-,
and
be
(uX, uY, uZ)
the
3-axes,
Then
we
geographical coordi-
the
center of
・cosΦ,
the
Let
the
and
cosines
to
the
(lm, mm, nm),
11
(14)
clockwise
comof
new
Earthquakes
(Θ and
displacement
direction
and Intermediate
source:
Z=cosΘ
zenith
the
relative
and
of Deep
the
Y=sinΘ
north).
Process
the
where
1-,
coordinate
respectively.
have
(5)
(12)
cp, cSV,
the
and CSH
source
relevant
The
displacements
ponents,
and
SH
which
waves,
for
the
corresponds
(γ, Θ, Φ)-comto
those
of
P,
case
SV
are
(13)
where
in the
these
components
are taken
positive
directions
away from the origin, away
M0
as
downwards
tively.
we
for
Putting
θ<π/2,
eqs.
and
(10)
clockwise,
and
(12)
respecinto
(13),
since
have
been
cSV
Fig, 6.
the
of
and cSH
together
seismic
(b) No. 15
by
of
those
the
in
the
(MIKUMO,
source
the
from
orientation
moment
from
P waves.
Figs.
of
for
the
first
three
their
Nos.
12
6(a)
kinds
nodal
and
nodal
the
motion
P,
SV
and
eqs.(14)
of two
determined
with
of
evaluated
Nodal curves of P, SV and SH waves,
(a) No. 12
to
source
distribution
be
distribution
earthquakes
obtain,
equal
location
M0=μDLW.
can
(15),
the
is
specified
the
point
amplitude,
waves
pattern
constants
and
double-couple
defined
The
the
and
station,
of
1962).
SH
are
mechanism
and
and
planes
first motion
6(b)
shows
sings of cp,
of body
waves,
curves, in,
15,
according
two
to
the
Takeshi
12
MIKUMO
for the
sake
of comparison.
C(ω) has
method of KEYLIS-BOROK (1957). SV waves model
emitted downward from the source changes also been computed
for the vertical
and
horicomponents
of
P
and
SV
waves
and
the sign during propagation to the station. zontal
(HASKELL,
This effectis included in the above figures. for SH waves by the matrix method
structure
approThe above figuresWill be useful forthe syn- 1960, 1962), for the layered
thesisof the three components.
priate
to each
station
and
for
the
pertinent
angle.
when
the
structure
is not
The body waves radiated from the source incident
are sufferedfrom the effectsof propagation known,
the
unilayered
model
of HASKELL
has
to the
stations.
through the mantle and crust and of the been applied
seismograph. The waveforms that would be
Now
we
have
the synthesized
seismograms
components
of
recorded on seismograms at the earth'ssur- of the Vertical and horizontal
face should be derivedfrom the superposition P)and
SV
waves
fPu(t), fPw(t),
fSVu(t)
and
of normal modes in a gravitatingspherical fSVw(t), and of SH waves,
fSH(t),
through
eq.
earth (forexample, SATO et al.,1967;USAMI (16).
Fig.
7 shows
the
observed(full
line)
(broken
line)
waveforms
on
et al.,1968). It has been shown (SATO, 1969), and synthesized
seismograms
for five
however, that for direct body waves with the Vertical component
periods probably up to about 40sec, the divergence effectfor a limited but ratherwide
range of epicentraldistancesmay be approximated With errors less than 5% by the geometrical spreading expected from the ray
theory. For this reason,the waveforms may
be expressed, to a good approximation, by
(MIKUMO, 1969)
(16)
where
and
Hp,8(ω)=Pp,8(ω)・Cp,8(ω)・I(ω)
P(ω),
C(ω),
transfer
I(ω)
mental
and
respectively.
for
by
spreading
models,
waves.
mainly
and
For
to
a
Q
as
KURITA
by
a constant
rate
to
a
Qα/Qβ=9/4
SON
relation
et
al.
(1968)
(1965),
S
by
of 4/9
and
response,
waves
product
profile
in
the
geo-
from
and
the
probable
case
of
direct
effect,
we
refer
11)
reducing
of
the
suggested
to
MIKUMO
Q
at all depths
also
has
of
attenuation
(Model
and
mantle
instru-
system
the
attenuation
model
the
direct
Velocity
dissipative
are
response,
total
here
Jeffreys-Bullen
P
the
P(ω)
computed
metrical
H(ω)
crustal
response
been
and
function,
Values
according
by
their
ANDERMM8-Qβ
Fig. 7. Observed and syntllesizedseismograms of
earthquake No. 23. (vertical component of P
and SV waves)
Source
Process
of Deep
and
Intermediate
Earthquakes
Fig. 8. Observed and synthesized seismograms (three components of P and S waves)
(a) earthquake No. 12.
13
Takeshi
14
Fig. 8. Observed
(b) earthquake
and synthesized
No. 15.
MIKUMO
seismograms
(three components
of P and S waves)
Source
Process
of Deep
and Intermediate
selected stationsin earthquake No. 23. It
appears that general features of the waveforms are in good agreement between the
two kinds of seismograms. The S waves
recorded at MUN
and SPA show rather
shorterperiods than those predicted. If the
short-period
oscillations
are removed by a
proper filtering,
the agreement
would be
much improved.
It is more appropriate to make such a comparison on the three component seismograms,
since a different kind of information
is involved in the horizontal records, particularly
of S waves.
It is, however, usually difficult
to see well-isolated
direct S waves on all of
the three components at many stations.
This
is because they are often contaminated
by
preceding motion of P wave group and later
phases such as sS and ScS over a wide range
of epicentral
distances, and partly because
SV waves are sometimes distorted by the crust
due to large incident angles.
For this reason,
the comparison can be made only for a limited
number of stations,
whereas
FUKAO (1970)
estimated the fault parameters
directly from
S waveforms at many stations.
Two horizontal components
fN(t) and fE(t)
on the synthesized seismograms
are derived
by the rotation of axis,
Earthquakes
waveforms.
An introduction
model
did
instead
of
make
much
not
amplitudes.
It
trary
assumption
tical
S-wave
than the
able
is
reconcile
most
the
S-wave
are
sensitive
plane
the
Fig.
5
tudes
said that
waveforms
of
amplitudes,
8(a)and
and
8(b)
depict
synthesized
stations
the
of
for
both
line
P
waves,
higher
and
by
longer
be
seen
between
tical
predictions
that
the
there
for
most
line)
may
and
four
15.
All
to
and
the
of P
observed
for
the
the
concluded
mainly
mantle
and
times due
fault
from
the
the
observed
S
absolute
amplitudes
dislocation
§6.
to
length
and
sources
above
com-
waveforms
ingive
support
inferred
from
P
Discussion
a
this
P
paper,
parameters
models.
There
for
deep-focus
due
agree-
1963;
DENNIS
theore-
1966;
EVISON,
and
S
we
source
changes
is general
of
be
that
the
the
In
at
1,500.
observations
of
the
process
S
those
width.
component
normalized
of
source
effects
with
in
the
synthesized
than
accounted
attenuations
their
Figs.
waves
12
been
magnification
ment
S
be
may
synthesized
Also,
the
agree
may
ampliit
including
longer
generally
This
Although
the
troughs,
and
of
located
(Compare
agreement.
apparently
and
are
in
waves,
fault
waves.
azimuth
(full
three
Nos.
have
seismograph
back
epicenter.
recorded
earthquakes
seismograms
It may
the
broken
seismograms
the
to
S
the
6(b)).
or
in good
periods
are
and
that
stations
waves
recorded
P and
are
predominant
waves
stations
peaks
the
be
two
of
SV
6(a)
that
waves
However,
the
the
of
great
SH
would
some differences
specific
the
and
accuracy
Figs.
also
for
SV
at
15.
from
possibility
discrepancy.
since
NS-
No.
from
a
for
plane
the
comes
deviating
is also
to the
nodal
are
in
earthquake
amplitudes
with
there
to
φ is
in
larger
appreci-
in earthquake
explanations
solutions,
near
arbi-
theore-
An
discrepancy
the
acceptable
parison
cluding
station
the
wave
an
the
however,
attenuations
could
It
where
COL
There
combined
from
at
S
that
makes
at BAG
incidence
partly
measured
lies,
path.
different
found
the
significantly
waves
that
here
in
amplitudes.
S
and
wave
circle
be
also
amplitude
likely
the
by
respectively,
was
MM8-Qβ
model assumed
of Qα=Qβ
of
12
It
of
Qβ
difference
discrepancy
periods.
(17)
the
recorded
component
No.
15
extentional
have
for
are
estimated
shear
alternative
earthquakes,
to
and
transitions
WALKER,
1967)
dislocation)
hypotheses
such
phase
and
1965;
tensile
models
various
dislocation
as
volume
(BENIOFF,
RANDALL,
fracture
(SAVAGR,
(or
1965;
16
Takeshi
MIKUMO
BURRIDGE, 1968). It appears, however, that infinite distance
could
move
at
a uniform
azimuthal dependence of the source process supersonic
velocity
on
a slip or
fault
plane,
with
increastimes as well as the radiationpatternsof the if the frictional stress decreases
double-coupletype, which were found here, ing displacement
velocity
across
the
slip
favor the shear dislocationmodels for the plane.
four earthquakes analyzed. This does not
If we
assume
bilateral
faulting,
the
total
necessarilymean that the source process of process
time
is the superposition
of the width
all deep earthquakes can be relatedto shear of two pulses from two unilateral faulting in
dislocations.More deep earthquakes in dif- opposite
directions.
Since
a
predominant
ferent regions need be analyzed to testthe portion with large amplitude
usually
lies in
validityof this model.
the first-arrived
pulse,
the synthesized
waveWe have so far assumed bidirectional
type form
is between
those
from
the
two
uni(MIKUMO,
1969).
It would
be
of faulting rather than pure unilateraland lateral faulting
to
discriminate
bilateral
bilateral,since it may be more realisticto difficult, therefore,
from
unilateral
one on the azimuthal
considerthat faultingwould initiate
near the faulting
of the
source
process
times.
center of the stressed region (SAVAGE, 1966) dependence
The
concept
of
bidirectional
faulting
has
and proceed rapidlyon the faultsurfacealong
been
introduced
by
FUKAO
(private
communiand across the slip directions,in view of a
analysis
of a
number of evidence that aftershocksof large cation, 1970) in the time domain
deep-focus
shock
in South
America.
shallow earthquakes occur frequentlyin an multiple
It has
been
demonstrated
that
this type
of
area with the main shock at the edge.
could
account
for our
results,
partiIf we suppose that unilateralfaultingpro- faulting
velocity.
It appears
pagates along the longeraxis of the slipplane cularly for the rupture
has
propagated
at
veloci(Case (A)),it would follow that the rupture that the rupture
ties
between
3.2
and
a
shear
velocity
of 4.5
velocitytakes unusuallyhigh values. FUKAO
km/sec
in
the
present
case,
as
has
been
sug(1970)also obtained an extremely high rupby
a
theoretical
work
(MANSINHA,
ture velocityfor a deep-focus earthquake of gested
a number
of
observations.
Banda Sea from the analysisof S waveforms. 1964) and from
propagating
direction
makes
a
small
In these cases,we would have to take the The
following interpretations. One would be angle to the shorter axis of the fault plane.
are
correct,
earthsimultaneous faulting; the source process If these interpretations
will be such that body waves-are radiated quakes
Nos.
6
and
23
with
predominant
would
be approximated
almost simultaneously over the entirefault strike slip component
while
earthquake
No.
surface within the rise time of dislocation by edge dislocations,
12
having
strike-slip
with
a
fraction
of
dip(FUKAO, 1970). The source process time in
earthquake
No. 15 characthis case is interpretedas the time difference slip component, and
terized
by
thrust
faulting
could
be associated
between the arrivaltime of body waves from
with
screw
dislocations.
the nearest point on the faultsurface at the
initiationof the rupture process and that
We
shall
next
estimate
the
effective
stress
slip dislocations
from the farthest point at the termination at the initial state to produce
sections.
(FUKAO, 1970). Another interpretation
would from the results in the preceding
(1960)
has
stated
that
during
the
be supersonic dislocations,
in which the rup- OROWAN
ture velocity exceeds elasticwave veloci- fault
rupture
a
frictional
stress
σf
acts
and
the
initial
ties. The possibilityhas been suggestedby to resist the fault slippage,
ESHELBY (1956)for a part of screw dislocation shear stress σa decreases
to σf when
the slipon a slipplane in crystals,and by WEERTMAN
page
will.
cease.
Since,
in
this
case,
an
of the
energy
σfDA
will
be lost as
(1969) for slippage for earthquake faults. amount
WEERTMAN (1969)has proved that both screw frictional
heating,
while
an
energy 1/2
(σadislocationsand edge dislocationsover an σf)DA will go into the generation
of seismic
Source
waves,
the
is the
stress
average
1970).
deduced
stresses
observations,
from
stress.
(AKI,
of
the
leased
stress
where
energy
ησmeans
stress.
E8
and
energy
release
and
it follows
The
have
is
drop
stress
to
The
BRUNE,
sphere
δ (aver-
The
σ2), the
re-
stress
of
on
age
stress
and
of
the
and
deep-focus
1968;
270
with
lower
were
other
bars
the
while
at
Tonga-Kermadec
such
apparent
it may
sider
that
effective
the
intermediate
than
mantle.
depths
those
at
These
and
(1970)
stated,
the
and
be
not
crust
high
BRUNE,
inter150km
that
in
stress.
initial
the
From
to
shear
be
and
stresses
con-
stress
appreciably
the
of
σf,
at
a
this
tional
stress
tions
that
is
from
is
the
to
be
should
more
deep
need
be
analyzed.
occur
with
time
derived
the
regarded
slip
plane
1969),
for
be
intermediate
The
the
about
four
30∼120
relation.
above
as
and
fric-
dislocations.
to
that
high
material
dynamic
σ1-σf
estimated
and
a
the
of
stress
the
of
BAKER,
decrease
the
relatemperature
on
and
above
and
1969).
would
melting
state
noted
be
be
litho-
(MCKENZIE,
stress
probably
GRIGGS
would
at
could
of the
increasing
partial
initial
that
slabs
zones
depths
1960:
hence
It
stresses
well-lubricated
(OROWAN;
it
esti-
temperature-pressure
likely
produce
associated
although
MCKENZIE's
frictional
the
intermediate
or
the
seismic
to
It is
reach
descending
low
be
mater-al,
only
interpretatentative,
earthquakes
Acknowledgments
I have benefited
from stimulate
discussions
with Drs. Yoshio Fukao and Katsuyuki
Abe
of the Earthquake
Research
Institute,
and
Mr. Kazuo Oike at our Institute.
I wish to
thank
Dr. Michio Otsuka
of Kumamoto
University
for valuable
suggestions
at an early
stage
of this
study.
My thanks
are also
extended
to Mrs. Ritsuko
Koizumi
for assistance in the present work.
Computations
were
made on a FACOM
230-60 at the Data Processing
Center,
Kyoto University.
obtained
characterized
reasonable
will
values
shallow
however,
depths
are
between
for 10
45
average
evidence,
for
(WYSS
intermediate
these
larger
those
value
Trench
a high
from
aver-
lies
between
He
their
apparent
These
WYSS
mean
America.
earthquakes
for
and
different
shocks
with
earthquakes
South
that
although
197O).
order
the
magniBRUNE,
than
the
four
(MIKUMO,
as
mediate
hand,
1970),
that
(BERCKHEMER
earthquakes
WYSS,
1967;
of
values
given
than
similar
tion.
bars
time
as
ALLEN,
1970),
same
the
in deep
relation
we
initial
low
would
of
for
possible
in
stress
to
in
earthquakes
process
larger
FUKAO,
bars
are
at
initial
appear
effective
relations,
effective
drop
slightly
ησ for
37
the
et al.,1969).
the
estimates
the
of
earthquakes,
and
1968;
sum
dislocations.
considerably
methods
and
average
the
total
faulting
earthquakes
JACOB,
ours.
for
earthquakes
and
seismic
of σ1, or
strength
2.5kb
stresses
ie. E0=E8+Ef,
these
shear
(BRUNE
deep-focus
the
the
σ/2+ησ
seems
shallow
tudes
1968),
to
(BRUNE
intermediate
3,
the
actual
that
energies,
during
estimated
Table
most
of
accumulated
respectively
equal
produce
four
at
mate
relation
energy
η are
Combing
σ1-σf=Δ
the
and
that σ=ησ+σf
stress
by
average
and
for the
further
frictional
is Δ σ=σ1-σ2<σ1.
in
strain
efficiency
a lower
bound
If we
assume
seismic
8
stress
the
not
E0; σ=(σ1+σ2)/2=E0/DA=μE0/M0,
wave
for
σ1 and final
and
does
in-
17
values
high
high
be
and
stress
M0,
ησ=μE8/M0,
in
WYss
acting
high
with
may
Earthquakes
both.
The
seismic
the
to
or
determine
following
1968;
Intermediate
due
(BRUNE,
from
and
the
average
moment
to
stress
drop
have
BRUNE,
initial
seismic
stress
We
among
age
effective
the
1966;
1968)
difficult
and
waves
σa-σf
σf separately
the
acting
is
of Deep
seismic
stress
it
σa and
ferred
from
effective
Although
the
Process
uppermay
be
References
Aki, K., Generation and propagation of G wave
from the Niigata earthquake
of June 16, 1964,
Part 2.
Estimation
of earthquake
moment,
released energy and stress-strain
drop from the
G wave spectrum, Bull. Earthq. Res. Inst., 44,
73-88, 1966.
Anderson, D.L., A. Ben-Menahem and C.B. Archambeau, Attenuation of seismic energy in the mantle,
J. Geophys. Res., 70, 1441-1448, 1965.
Benioff, H., Source wave form of three earthquakes,
Bull. Seism. Soc. Amer., 53, 893-904, 1963.
18
Takeshi
Berckhemer, H. and K.H. Jacob, Investigation
of
the dynamical process in earthquake foci by analyzing the pulse shape of body waves, Proc. of the
X Assembly of the ESC, Sept., 1968, II, 253-352,
1970.
Bollinger, G.A., Determination of earthquake fault
parameters from long-period P waves, J. Geophys.
Res., 73, 785-807, 1968.
Bollinger, G.A., Fault length and fracture velocity
for the Kyushu, Japan, earthquake of October 3,
1963, J. Geophys. Res., 75, 955-964, 1970.
Brune, J., Travel times, body waves and normal
modes of the earth, Bull. Seism. Soc. Amer., 54,
2099-2127, 1964.
Brune, J., Seismic moment, seismicity, and rate of
slip along major fault zones, J. Geophys. Res., 73,
777-784, 1968.
Brune, J., Tectonic stress and the spectra of seismic
shear waves from earthquakes, J. Geophys. Res.,
75, 4997-5009, 1970.
Brune, J. and C.R. Allen, A low stress-drop, lowmagnitude earthquake with surface faulting:
The
Imperial, California, earthquake of March 4, 1966,
Bull. Seism. Soc. Amer., 57, 501-514, 1967.
Brune, J.N., T.L. Henrey and R.F. Roy, Heat flow,
stress and rate of slip along the San Andreas
Fault, California, J. Geophys. Res., 74, 38213827, 1969.
Burridge, R. and L. Knopoff, Body force equivalents
for seismic dislocations, Bull. Seism. Soc. Amer.,
54, 1875-1888, 1964.
Burridge, R., Theoretical seismic sources and propagating brittle cracks, J. Phys. Earth,
16,
Special Issue, 83-92, 1968.
Dennis, J.G. and C.T. Walker, Earthquakes resulting from metastable phase transitions, Tectonophysics, 2, 401-405, 1965.
Eshelby, J.D., Supersonic dislocations and dislocations in dipersive media, Proc. Phys. Soc. London,
B 69, 1013-1019, 1956.
Eshelby, J.D., The determination
of the elastic
field of an ellipsoidal inclusion and related problems, Proc. Roy Soc. London, A 241, 376-396,
1957.
Evison, F.F., On the occurrence of volume change
at the earthquake
source,
Bull.
Seism. Soc.
Amer., 57, 9-26, 1967.
Fukao, Y., Focal process of a deep focus earthquake as deduced from long-period P and S waves,
Bull. Earthq. Res. Inst., 48, 707-727, 1970.
Griggs, D.T. and D.W. Baker, The origin of deepfocus earthquakes,
in Properties
of Matter, pp.
23-42, John Wiley & Sons, New York, 1969.
Haskell, N.A., Crustal reflection of plane SH waves,
MIKUMO
J. Geophys. Res., 65, 4147-4150, 1960.
Haskell, N.A., Crustal reflection of P and SV waves,
J. Geophys. Res., 67, 4751-4767, 1962.
Haskell, N.A., Total energy and spectral density
of elastic wave radiation from propagating fault,
Bull. Seism. Soc. Amer., 54, 1811-1841, 1964.
Hirasawa, T. and W. Stauder, On the seismic body
waves from a finite moving source, Bull. Seism.
Soc. Amer., 55, 237-262, 1965.
Isacks, B,J. Oliver and L.R. Sykes, Seismology
and the new global tectonics, J. Geophys. Res.,
73, 5855-5899, 1968.
Keylis-Borok, V.I., The determination of earthquake
mechanism, using both longitudinal and transverse
waves, Ann. Geofis., 10, 105-128, 1957.
Keylis-Borok, V.I., On estimation of the displacement in an earthquake source and of source dimensions, Ann. Geofis., 12, 205-214, 1959.
Knopoff, L., Energy release in earthquakes, Geophys.
J., 1, 44-52, 1958.
Maruyama, T., On the force quivalents of dynamical
elastic dislocations with reference to the earthquake mechanism, Bull. Earthq. Res. Inst., 41,
467-486, 1963.
Mansinha, L., The velocity of shear fracture, Bull.
Seism. Soc. Amer., 54, 369-376, 1964.
McKenzie, D.P, Speculations on the consequences
and causes of plate motions, Geophys. J., 18,
1-32, 1969.
Mikumo, T., Mechanism of local earthquakes
in
Kwanto region, Japan, derived from the amplitude
relation of P and S waves, Bull. Earthq. Res.
Inst., 40, 399-424, 1962.
Mikumo, T. and T. Kurita, Q distribution for longperiod P waves in the mantle, J. Phys. Earth,
16, 11-29, 1968.
Mikumo, T., Long-period P waveforms and the
source mechanism of intermediate
earthquakes,
J. Phys. Earth,
17, 169-192, 1969; Correction,
ibid., 18, 313, 1970.
Orowan, E., Mechanism of seismic faulting in rock
deformation,
A Symposium, Geol. Soc. Amer.
Mem., 79, 323-345, 1960.
Otsuka, M., Study on focal mechanism by the analysis of seismic waves of S-type, Spec. Contr.
Geophys. Inst., Kyoto Univ., 4, 37-49, 1964.
Randall, M.J., Seismic radiation from a sudden
phase transition, J. Geophys. Res., 71, 5297-5302,
1966.
Sato, Y.,T. Usami and M. Landisman, Theoretical
seismograms of spheroidal type on the surface of
a gravitating elastic sphere, II. Case of Gutenberg-Bullen A' earth model, Bull. Earthq, Res.
Inst., 45, 601-624, 1967.
Source
Sato,
R.,
Amplitude
of
body
geneous
sphere,
comparison
ray theory,
Geophys.
J., 17,
Savage,
J. C., The effect
seismic
first motions,
55,
263-275,
Process
waves
of wave
527-544,
in
of Deep
and Intermediate
a heterotheory
1969.
and
of rupture
velocity upon
Bull.
Seism.
Soc. Amer.,
1965.
Savage,
J. C., Radiation
faulting,
Bull.
Seism.
1966.
Teng, T. L. and
deep earthquakes
from
Soc.
a realistic
model of
Amer.,
56, 577-592,
A. Ben-Menahem,
from spectrums
Mechanism
of
of isolated body-
wave signals,
1. Banda Sea earthquake
of March
21, 1964, J. Geophys.
Res., 70, 5157-5170,
1965.
Usami,
T., Y. Sat6 and M. Landisman
and T. Odaka,
Theoretical
seismograms
of spheroidal
type
on
the
surface
of
a gravitating
elastic
sphere,
III.
Earthquakes
19
Case of a homogeneous mantle with a liquid core,
Bull. Earthq. Res. Inst., 46, 791-819, 1968.
Weertman,
J., Dislocation motion on an interface
with friction that is dependent on sliding velocity,
J. Geophys. Res., 74, 6617-6622, 1969.
Wyss, M., and J. N. Brune, Seismic moment, stress,
and source dimensions from earthquakes
in the
California-Nevada
region, J. Geophys, Res., 73,
4681-4694, 1968.
Wyss, M., Stress estimates for South American
shallow and deep earthquakes,
J. Geophys. Res.,
75, 1529-1544, 1970.
(Received
revised
September 29., 1970;
December 26, 1970)