of 20
Geophys.
J.
R.
astr.
SOC.
(1975)
43,
307-326
Tidal
Triggering
of
Earthquakes*
Thomas
H.
Heaton
(Received
1975
April
14)t
Summary
Analysis
of
the tidal stress tensor
at
the
time
of
moderate
to
large
earth-
quakes strongly
suggests
that
shallow
(<
30
km)
larger magnitude oblique-
slip
and
dip-slip
earthquakes are
triggered
by
tidal
stresses.
No
corre-
sponding
triggering
effect
is seen
for
shallow
strike-slip
earthquakes
or
for
any type
of
intermediate
or
deep focus earthquakes
which have been
studied. Tidal triggering
is
also
discussed
from the
viewpoint of
the
'
dilatancy-diffusion
'
model.
Specifically,
the
model
as
usually
stated,
excludes
the
possibility
of
small earthquakes
being tidally
triggered.
Introduction
The
study
of
tides
provides a unique opportunity
to
view
the
response
of
the Earth
to
known
changes
in stress (known in
the
sense
of
an
assumed
model). The
response
of
the
Earth
to
these known stresses
must
limit
our
ideas
of
how
the
Earth
responds
to
the much larger and
generally
unknown tectonic
stresses which
are
ultimately
responsible
for
earthquakes.
The fact
that
practically any ultra-long period strain
measurements
of the
Earth are
dominated
by
the luni-solar tide indicates
that
although
tidal
stresses
are
probably
at
least three orders
of
magnitude smaller
than
the
tectonic
stresses
upon
which
they
are
superimposed,
tidal
streys rates
may
be
comparable
to
tectonic stress
rates.
Before
discussing
the
possible
effects
of
tides
on
earthquakes, a
few
basic
facts
about
tides
will be reviewed.
Also
included is
a brief
review
of
a few
previous
tidal
triggering
studies.
There
are
two types
of
tides
which
produce observable
strains
in
the Earth's crust:
solid
earth
tides
and oceanic
tides.
Solid
earth tides
On
a global
scale,
differential gravitational
forces
exerted
by
the Sun
and Moon
cause the surface
of
the
Earth
to
yield
radially
by
up
to
40
cm.
Since
tidal
periodicities
are
an
order
of
magnitude longer
than the
longest
period free oscillations
of
the
Earth,
the deformations
caused by
tides
are
usually
modelled by
equilibrium elasticity
theory. Strains
in the Earth's crust
caused
by
tides
can
be
directly computed from the
vertical deformations and
dimensionless
constants
of
proportionality
called
Love
and
Shida numbers.
The
boundary condition
of
no
traction acting
on
the Earth's surface
*
Contribution
No.
2566,
Division
of
Geological
and Planetary
Sciences,
California Institute
of
Technology, Pasadena,
California
91
125.
t
Received
in
original
foml
1975
February
21.
307
308
T.
H.
Heston
Horizontal
compression
I
3
(Gravitational
force
at
point
1
-
(Gravitational force
on
centre
of
earth)
FIG
1.
Schematic
for
tidal
forces
and
deformation
along
any
great
circle passing
directly
beneath
the
mass.
Gm
a2
2
r3
Tidal potential
=
W,
=
-
-
(3
cosz
0-1)
h
u,
=
-
w,
g
au,
err
=
-
ar
1
aUe
U,
eee=-
-+-
r
ae
r
G
=
universal gravitation
constant,
6.67
x
lo-'
dyne
cm2
g-,
g
=
acceleration
of
gravity,
980
cm
s-
h
x
0.6
1
s
0.07
Love
numbers
yields
the
conclusion
that
tidal
stresses
normal
to
the
free surface (provided
the
observer is
at
a sufficiently shallow
depth)
are
zero.
Thus for
an
observer
near the
Earth's
surface,
the
minimum
absolute principal
stress
axis
is always
vertical.
There-
fore, the remaining principal
stress
axes
are in
the
horizontal
plane
and
change
their
orientation as
the
tidal
bulge moves
around
the
Earth.
A
fairly
involved
argument
is
necessary
to
show
that
when
the tide producing
body is directly overhead,
the Earth
is stretched
upward and
the
horizontal tidal
stresses
are
tensile. When
the tide pro-
ducing
body
is on
the
horizon, horizontal tidal
stresses
are
compressional
(see
Fig.
1).
Tides
are
computed
separately
for
the Moon
and
Sun
and then
combined;
the lunar
tides being
about
twice
the amplitude
of
solar
tides.
Oceanic
tides
The
effects of
oceanic tides
on crustal
stresses
are
generally difficult
to
model.
The
free
period
of
oceanic
waves
can
be
comparable
to
tidal
periodicities
and
thus
resonance phenomena
cause oceanic tides
to
differ
significantly
from
static equilibrium
in
both phase and amplitude.
Oceanic
tides sometimes
depart
from
equilibrium
by
Tidal
triggering
of
earthquakes
309
several metres,
and
are
therefore capable
of
generating
significant
vertical and hori-
zontal
stresses
(up
to
0-3
bars
on
some
coastal
shelves).
To
model
oceanic tidal
effects
on
crustal stress then,
one
must first
model oceanic
tides
and
then
model
the
response
of
the
Earth
to
a complicated distribution
of
vertical forces. Modelling
of
this
sort
has
been
done
(see
Langdon
&
Thomas
(33)),
but due
to
the
complexity
of
the
problem, oceanic
tides have been
ignored for this study.
In
many
instances one
could argue
that
crustal shear
stresses
due
to
oceanic tides
are
small compared
to
the
solid
earth
tides. These
arguments
are
not
always
satisfactory
and it
seems
clear
that
loading
stresses
from oceanic tides should
be
modelled
to
fully
evaluate
the
effects
of
tides
on
earthquakes.
Earthquakes
and
tides
Suppose
that
earthquakes result from stress accumulations
on
the
order
of
150
bars. Suppose further
that
in
active
areas
a fault
would
break once
every
100
years.
Although
it is conceivable
that
the tectonic stress rate prior
to
failure
is quite
high,
the
tectonic stress
rate
averaged over
the
recurrence
interval
for
such
a region
would
be
about
0.001
bars/6 hr. Tidal stress rates
which
can
be
0.1
bars/6
hr
are
two orders
of
magnitude
larger
than
this. Despite many attempts
to
solve
the problem though,
the
question
of
whether tides
trigger earthquakes
is
still
unresolved.
It
is
very
difficult
to
disprove tidal
triggering since
it can always
be
contended
that
the wrong parameter
or
data
set
were
used.
Knopoff
(30)
cross correlated
9000
Southern California earth-
quakes
of
magnitude
greater
than
2
with
the tidal potential.
He
found
that
the
occurrence
of
earthquakes appeared random
with respect
to
the tides. Studies
of
triggering
of
earthquakes
on
a worldwide basis have
been
done
by
Shlien
(58)
and
Dix
(16)
among others.
These
studies appear
to
be
inconclusive
at
best.
There
are
also many papers supporting tidal
triggering.
Unfortunately,
not
all
of
these reports
are
consistent.
Some have
found
that
large earthquakes
are
more
likely
to
be
triggered
than
small ones
(see
Allen
('7,
also Tamrazyan
(64)),
and
yet
there
have been
several
positive
correlations noted
for
microearthquake
swarms.
Ryall,
Van
Wormer
&
Jones
(52)
report
a cross
correlation
coefficient
which is
significant
at
the
99
per
cent
confidence
level
for a
swarm
near Truckee, California.
Willis
&
Taylor
(71)
reported
correlations
between
Nevada
microseismicity
and
tides.
Caution
is necessary
using
microearthquakes
since
the
seismic noise
level
and
hence
the threshold
for
measuring
microearthquakes often
has
a diurnal period
due
to
manmade
noise
(32).
There
have
also
been
reports
of
correlations
between
tides
and
volcanoes.
Hamil-
ton
(24)
and Mauk
&
Johnston
(38)
found tidal
periodicities
in
volcanic
eruptions.
Some
investigators
have
found
that
earthquakes
are
triggered
during
the
maximum
amplitude
for
tidal potential; others
have
found
that
earthquakes
are
triggered
during
maximum
rate
of
change
of
amplitude;
and
still
others
have
found
that
tides have
nothing
to
do
with
earthquakes.
In
general,
things
seem
confused.
We
are
faced
with the question:
How
might tides trigger earthquakes
anyway? To
answer this
question,
we
must
decide
what might
be
important
in determining
when
a rock
breaks,
and
then
decide
how
tides
enter
into
our
hypothetical fracture criteria.
Tidal
stress
and
fault orientation
Although the parameters relevant
to
fracture
may
be
a function
of
stress, time and
constitutive
law (which
in
the failure region
may itself
be
a function
of
position and
time), it
seems
clear
that
a complete time
history
of
stress
in
the
region
of
an
earth-
quake
would
be
a useful
piece
of
information.
This,
of
course,
is
not obtainable.
However,
variations
in
stress due
to
tides can
be
calculated.
In
most tidal
triggering
310
T.
H.
Heaton
nsion
axis
FIG.
2.
Definition
of
co-ordinates systems
(el,
e2,
e3)
and
(el’,
ez‘,
e3’)
for
a
thrust
fault.
studies, only
tidal potential has
been
considered.
The relation
between
potential and
stress
state
(and therefore earthquakes)
is not
always clear.
Since
the
Sun
and
Moon
traverse
approximately
the
same
trajectories each
day,
tidal stress
cycles
may essentially
repeat themselves
from
one
day
to
the
next.
If we
confine ourselves
to
one
nearly
homogeneous local
tectonic
stress
system
and
season,
then earthquakes might occur
at
a consistent phase
of
the
tides
which
can
be
characterized
by
the
single
parameter,
tidal potential.
When considering
several
different
tectonic
stress
systems
or
seasons,
special
care must
be
taken
to
calculate
how
the
tidal
stresses
relate
to
tectonic
stresses.
Six
independent
variables
are
necessary
to
characterize the
symmetric
stress tensor
at any
point
in
the Earth.
Assume
the stress
in
the
region
of
an
earthquake
to
be
the
sum
of
the
tectonic stress
tensor,
Q
and the tidal
stress tensor,
t.
A
fixed
co-ordinate
frame
should
be
chosen
in order
to
sum the tectonic
and
tidal
stresses.
For
earthquake
studies,
the fault plane
and
slip vector
of
an
earthquake
can
be
utilized
to
define
the
most
useful
co-ordinate
frames.
First consider the
frame
(el,
e,,
e3)
defined by
the
maximum,
intermediate, and
minimum
principal
stress
axes,
respectively,
which can
be
calculated
from the
known
fault
plane
and
slip
vector
(see
Fig.
2).
The tectonic
stress
tensor,
u,
is very
nearly
diagonal
in
this frame
and
for
this
study
assume
that
u
is diagonal in
the
(el,
e,,
e3)
frame. This frame
is very
convenient
since
most fracture
criteria
for
the
fixed
fault are
easily expressed
as functions
of
all,
cr,,,
and
c33.
The
shear
stress
causing
the
earthquake
is simply
(al
-
033)/2.
Unfortunately,
the
tidal
stress
tensor has
no
knowledge
of
the tectonic co-ordinate
frame
and
in general it
is
not
diagonal
in
the
frame
(el,
e2,
e3).
Yet by
rotating the tidal
stress
tensor,
t,
into
this frame,
some idea
of how
tides
affect
parameters such as deviatoric stress
and
confining
pressure
can
be
obtained in a co-ordinate
system
natural
to
the
earthquake.
Since
z
is not
diagonal
in
the
(el,
e,,
e3)
frame,
the
tidal shear stress acting
on
the
rupture surface
is not
generally
equal
to
(zll
-233)/2.
For
this reason
it
is
convenient
to
introduce a
second
co-ordinate
frame
(el’,
e2’,
e3‘)
(see
Fig.
2),
where
el’
is parallel
to
the slip vector and
e3’
is perpendicular
to
the
fault
plane.
In this frame,
r;
is the
actual tidal shear
stress sympathetic
to
failure,
Tidal
triggering
of
earthquakes
311
Taking
the
epicentral location,
the
directions and
distances
of
the
Sun
and
Moon
were
computed
as
a function
of
time
using
standard theory
of
planetary motion
and
the
Ile
lunar
theory.
Computer programs written
by
Henry
Fliegel
of
the Jet
Pro-
pulsion
Laboratory
were used
to
make
these calculations. Takeuchi’s
(63)
work
was
then
used
in
a computer program written
by
Hewitt
Dix
to
calculate the
Sun
and
Moon
tidal
stress
tensors at
the
hypocentral location. The
stress
tensors
were
given
relative
to
spherical
polar co-ordinates with
axes
centred
at
the
Earth’s centre
and
polar
axis
towards the Sun
or
Moon. The stress tensors
thus
found
were
then
referred
to
rectangular co-ordinates (up, south, east)
with
origins
at
the
focus.
The
stress
tensors
were
then
added
and
the resultant rotated
into
the primed and
unprimed
co-ordinate
systems defined by
the
fault plane
and
slip vector
of
the
earthquake.
Due
to
the
symmetry
of the stress tensor, either
of the
two complementary
fault
planes
and
slip
vectors
which
are obtained from the fault plane solution
give sufficient
information
to
rotate the tidal stress tensor into the co-ordinate
systems defined
above. Various
functions
of
z(t)
and
z’(t)
were
investigated
(i.e.
different failure
criteria),
to
discover whether
the
origin
times
of
earthquakes had any
simple depen-
dence
upon tidal
stresses.
Choice
of
earthquake
sample
The major
purpose
of
this study
is
to
determine
if
the time
at which an
earthquake
occurs depends
upon
tidal
stresses.
It seems
clear
that
to
optimize
any
possible
tidal
effects,
only
earthquakes
whose
origin time
is independent
of
other obvious factors
should
be
chosen.
For
instance,
the
origin times
for
earthquakes
which
belong
to
a
closely-spaced sequence
(e.g.
foreshock-aftershock sequence)
are probably
not
independent
of
one
another. There
was
an attempt made then
to
use
only large
mainshocks
which were
not
preceded
by
foreshocks.
The fault plane
and
slip
vector
for
each quake
should
be
known and
well
constrained.
These
parameters
were
obtained from either
observed
surface
rupture
or
seismically
determined fault
plane
solutions.
Because of
the
free surface boundary condition
on
earth
tides,
zil
(the
shear stress sympathetic
to
failure)
for
dip-slip earthquakes on
vertical
faults
is always
nearly
zero.
Thus the polarity
of
the tidal
shear
stress
for
such an earthquake
is
always sensitive
to
minor errors in the
fault
plane
solution.
For
this
reason,
vertically
Time,
hours
FIG.
3.
Example showing
how
earthquakes
were
assigned
a
phase relative
to
the
tides.
312
T.
H.
Heaton
I
I
I
I
I
I
I
I
3
FIG.
4.
Geometric interpretation
of
PR.
PR
is the probability
that
a random
walk
consisting
of
rn
unit
steps
will
walk
a
distance
of
R
or greater.
faulted
dip-slip earthquakes
were
not
considered. Earthquakes
which
appeared
to
meet
the
specifications
given
above
were
rather
randomly
chosen
from
many
different
sources.
The earthquakes
were
then
classified
according
to
depth,
type
of
mechanism,
location,
etc.
Clearly,
judgment
was
required in
deciding
which
earthquakes
to
include
and
how
to
classify
them.
To protect against
systematic
error
due
to
my own
prejudices,
the
decisions
were
made
about the
earthquakes
before
any
tides
were
computed and furthermore
the decisions
were
final.
Data analysis
Various
components and
combinations of
components
of
z
and
z'
were
plotted
as
a function
of
time.
Each
earthquake
was assigned
a phase on
a linear
scale
from
0"
to
360°,
where
0"
was
maximum
tidal stress directly before the
earthquake
and
360"
was
the
maximum
tidal stress
directly
after
the
earthquake
(see
Fig.
3).
These
phases were
then plotted
on
rose
diagrams.
A
clustering
of
earthquake
phases
on
the
rose
diagrams
indicates
a possible
relation
between
tidal-stress
and
earthquakes.
If
earthquake
origin
times
and
tides
are
independent then
the distribution
of
phases
on
the
rose
diagrams
should
appear
uniform.
A
simple
method
for determining the
degree of
order
in
a rose diagram
was
developed
by
Rayleigh
(49).
Consider
a two-
dimensional vector
in
polar
co-ordinates
u
=
(r,
$)
(see
Fig.
4).
If
the magnitude
of
Tidal
triggering
of
earthquakes
313
the
vector sum
of
n
unit 2-dimensional vectors
(1,4;),
is denoted
by
R
and
the
4i
correspond
to
earthquake
phases
then the probability,
PRY
that
a random
set
of
n
phases
will
produce
a sum vector
whose
magnitude
exceeds
R
is approximately
equal
to
exp
(-
RZ/n).
This approximation
is sufficient
when
n
is larger
than
10.
Thus the
smaller
PR
gets,
the
higher
our
confidence
in
tidal
triggering
becomes. Some
caution
should
be
used
in interpreting
PR.
Since
the
data
sample
has
been
grouped in
many
ways,
the probability
of
finding
a random
sample
with
a small
PR
is significant.
For
example,
the probability
of
being
dealt
a flush
in poker
is small
for any
individual
deal,
but
the probability
of
achieving
a flush
at
some
point during
a
long
evening
of
poker
is not
so
bad.
Results
A
total
of
107
earthquakes
were
included
in
the data
sample
and
they
appear
in
Table
1.
They
are
grouped
according
to
depth and
focal
mechanism. Earthquakes
with
depths
listed
as
33
km
may
have
had the depth constrained.
Rake
is defined
to
be
such
that
0"
is left-lateral movement
and
+90"
indicates
thrusting.
Listed
are the
phases
of
both the
tidal hydrostatic
stress and
tidal
shear stress
sympathetic
to
failure.
Other stress parameters
were
investigated,
but the best
correlation obtained
was
with
the
shear stress,
zi3.
The
hydrostatic
stress
(T~~
+222+233)/3,
is proportional to the
magnitude
of
the tidal potential
and
is
independent
of
the co-ordinate frame.
A
comparison
of
the
phases
of
the
tidal hydrostatic
stress
and
the
phases
of
the tidal
shear
stress,
zi3,
thus
gives
an
indication
of
the importance of orienting the tidal
stress tensor
relative
to
the motion
of
the earthquake.
Figs
5
and
6 summarize the
correlation
of
the
phases
of
tidal
stress with
several
different
groupings
of
the earth-
quake
sample. Fig. 5(a)
shows
no
apparent correlation
(PR
=
0.56)
between
the
phase
of
the tidal hydrostatic stress and
the
occurrence time
of
the earthquake.
The
correlation
improved
(PR
=
0.059)
when
the
phases
of
the sympathetic tidal
shear
stress
were
considered
as
is
shown
in
Fig.
5(b).
The
possible
correlation
shown in
Fig.
5(b)
is
evidently
not due
to
earthquakes
deeper
than
30
km
as
Fig.
5(c)
and
(d)
indicate
no
significant
correlation
of
either hydrostatic
(PR
=
0.26) or
shear stress
(PR
=
0.15)
with origin time. Fig.
6(a) shows
no
significant
correlation
(PR
=
0-76)
between
tidal
shear stress
and
shallow strike-slip
earthquakes. Fig.
6(b)
and
(c)
illustrate
that
most
of
the
possible
correlation
between
a11
107
earthquakes and tidal
shear stress is due
to
that portion
of
the sample consisting
of
shallow
(less
than
30
km)
dip-slip or
oblique-slip
earthquakes (greater
than
30
per cent vertical
motion).
The
phases
of
the hydrostatic stress
for
shallow dip-slip
or
oblique-slip events
appear
to
be
random
(PR
=
0*77), but
the
phases
of
the
shear stress show
a rather
impressive
correlation
with
origin times
(PR
=
1
.O
x
Apparently,
depth
is an
important
parameter
since
dip-slip events
in the
30km
to
50
km
(PR
=
0.26)
region
(see
Fig.
6(d))
do
not
reflect
the
correlation
seen
for
shallow events.
This
classification
may
be
somewhat misleading,
though,
as
earthquakes
which
are
assigned
depths
of
33
km
niay
well
have
been
shallower.
Discussion
Although
a larger
data
sample
is desirable, some
preliminary conclusions can
be
drawn from the
results
given above.
Origin
times
for
shallow
dip-slip
or
oblique-slip
earthquakes
with magnitude
greater
than
five
appear
to
correlate strongly
with
tidal
shear
stresses
acting
sympathetic
to
failure.
No
corresponding correlation
is found for
shallow strike-slip
earthquakes or for
any
earthquakes
deeper
than
30
km.
Obviously,
these conclusions
do not
give
sufficient information
to
construct
a model
of
failure.
They
do,
however,
provide
constraints
on
any
models which
might
be
proposed.
Let
Ref.
Date
Earthquakes
deeper
than
50
km
1963
September
17
1963
September
24
1964
November 2
1964
November
28
1964
December 9
1965
March
5
1965
June
12
1965
November 3
1966
May 1
1966
December
20
1967
January 17
1967
February 15
1967
May
11
1967
December
25
1967
December
27
1968
August
23
197OJune11
1970
June 19
1970
July
31
1964
July
9
1966June13
1966
December
1
1966
December
21
1967
January 19
1967
March
31
1964
January
14
1964
August 13
1966
Auguqt
5
1966
December 14
1968
January
7
1965
April
29
Origin
time
GCT
05:54
16:30
0650
16:41
13:35
14:32
18:50
01 :39
16:22
12:26
01
:08
16:ll
15:05
10:41
09:17
22:36
06:02
10:56
17:08
16:39
18 :08
04:56
08:52
12:38
20:05
15:58
00:31
04:33
21 :07
#:56
15:28
Comments
Peru-Chile
Peru-Chile
Peru-Chile
Peru-Chile
Chile
Peru-Chile
Peru Chile
Peru-Chile
Peru-Chile
Peru-Chile
Peru-Chile
Peru-Chile
Chile
Peru-Chile
Peru-Chile
Chile
Chile
Chile
Columbia
New
Hebrides
New
Hebrides
New
Hebrides
New
Hebrides
New
Hebrides
New
Hebrides
Solomons
Solomons
Solomons
Solomons
Solomons
NW
United States
Table
1
Magni-
Depth
tude
(km)
6-314
76
6-314
91
5-9
586
5-6
573
5.8
102
6.2
593
5.8
154
5.7
586
6.2
597
6.1
115
5.8
135
6.4
135
5.8
537
6.0
112
6.3
52
7.1
651
6
259
6
132
5.8
249
5-5
156
5.3
132
5-6
169
6-112
392
5.5
52
5.7
80
5.1
118
6-112
60
5-112
650
5-112
590
7-1/2
121
GlIZ
59
Long.
(deg)
78.2
W
78.3
W
76.9
W
71.3
W
63.2
W
63.3
W
69.3
W
71.4
W
74.3
w
63.3
W
63.3
W
71.3
W
68.5
W
68-3
W
68.3
W
63.5
W
68-5
W
70.5
W
72-6
W
167.6
E
167.1
E
167.1
E
169.7
E
166.4
E
167.5
E
150.8
E
154.3
E
162.6
E
144.1
E
153.9 E
122.3
W
Lat.
(ded
10.6
S
10-7
S
4.1
S
7.9
s
27.5
S
27
S
20-5
S
9.1
S
8.4
S
26.2
S
27.4
S
9s
20.3
S
21.2s
21.2
s
22
s
24-5
s
22.2
s
1.5
S
15.5
S
12.2
s
14
S
20
s
11-8
S
15.4
S
5.2
S
5.5
s
11.1
s
4.9
s
N5W
35W
N50 W
18
W
N30 W
30
W
N25 W
45
W
NlO
W
80
W
N10 W
70
W
N30W
7W
N10
W
50
W
N15E
70E
N20W
70
W
N25
W
65
W
N10
W
45
W
N30 W
70
E
N20
W
25
W
N20 W
25
W
N5E
30W
N10
W
25
W
N5W
70E
N20
W
30
E
N5W
53W
N10E
45
W
N15
W
45
W
N15E
65E
NO
60E
N15 W
45
W
N55E
80SE
N45
W
30
NW
N50 W
45
NW
N50 W
60
NE
5-1
S
N35W
45NW
47.4N
N10W
70E
-
75
Rake
(deg)
-
75
-
90
-
90
-
85
-
120
-110
-
90
-
90
-115
-
75
-
115
-
90
-
100
-
85
-
85
-
80
-
80
-90
-
80
90
55
95
-40
100
90
90
-
100
100
90
80
Phase
of
static
hydro-
26
216
68
115
172
273
83
4
31
52
145
238
283
334
218
180
241
189
35
109
256
70
3
158
107
52
220
38
150
72
246
z
P
Phase
of
shear
(deg)
26
208
75
115
250
339
61
27
39
229
x
349
8
g
3:
265
212
141
230
178
60
309
64
260
346
316
308
210
210
220
327
260
197