Bulletin
of
the
Seismological
Society
of
America,
Vol.
75,
No.
4,
pp.
965-1004,
August
1985
TELESEISMIC
TIME
FUNCTIONS
FOR
LARGE,
SHALLOW
SUBDUCTION
ZONE
EARTHQUAKES
BY
STEPHEN
H.
HARTZELL
AND
THOMAS
H.
HEATON
ABSTRACT
Broadband
vertical
P-wave
records
are
analyzed
from
63
of
the
largest
shallow
subduction
zone
earthquakes
which
have
occurred
in
the
circum-Pacific
in
the
last
45
yr.
Most
of
the
records
studied
come
from
a
common
instrument,
the
Pasadena,
California,
Benioff
1-90
seismometer.
Propagation
and
instrument
effects
are
deconvolved
from
the
P-wave
records
using
a
damped
least-squares
inversion
to
obtain
the
teleseismic
source
time
function.
The
inversion
has
the
additional
constraint
that
the
time
function
be
positive
everywhere.
The
period
band
over
which
the
time
functions
are
considered
reliable
is
from
2.5
to
50
sec.
Fourier
displacement
amplitude
spectra
computed
for
each
of
the
1-90
P-wave
trains
indicate
spectral
slopes
measured
between
2
and
50
sec
of
00
-1°
to
o~
-=-=s
with
an
average
value
of
o~
-l's.
These
values
assume
an
average
attenuation
of
t*
=
1.0.
The
seismic
moments
derived
from
the
P-wave
time
functions
compare
well
with
other
published
values
for
earthquakes
having
moments
smaller
than
2.5
x
10
=8
dyne-cm
(M,,
=
8.2).
Because
the
1-90
seismometer
has
little
response
at
very
long
periods,
this
technique
underestimates
the
moments
of
the
very
largest
events.
The
time
functions
are
characterized
using
five
parameters:
(1)
spectral
slope
between
2
and
50
sec;
(2)
roughness
of
the
time
function;
(3)
multiplicity
of
sources;
(4)
pulse
widths
of
individual
sources;
and
(5)
overall
signal
duration.
The
63
earthquakes
studied
come
from
15
subduction
zones
with
a
wide
range
in
the
ages
of
subducted
lithosphere,
convergence
rates,
and
maximum
size
of
earthquakes.
Comparing
the
time
function
parameters
with
age,
rate,
and
M,,
of
the
subduction
zone
does
not
yield
obvious
global
trends.
However,
most
of
the
subduction
zones
do
behave
characteristically
and
can
be
grouped
accordingly.
INTRODUCTION
In
terms
of
the
details
of
fault
rupture
or
source
complexity,
our
knowledge
of
the
very
largest
earthquakes
is
limited.
Until
very
recently,
most
of
what
was
known
about
major
earthquakes
consisted
of
estimates
of
their
focal
mechanism
and
moment.
Although
this
information
is
of
fundamental
interest,
it
is
desirable
to
know
more
about
the
spatial
and
temporal
distribution
of
moment
release.
The
very
largest
earthquakes
have
been
shallow
thrust
events
at
convergent
plate
boundaries.
In
this
paper,
we
present
the
results
of
a
survey
study
of
teleseismic
source
time
functions
for
major
shallow
thrust
earthquakes.
Sixty-three
of
the
largest
shallow
subduction
zone
earthquakes
that
have
occurred
in
the
circum-Pacific
in
the
last
45
yr
are
studied.
Earthquakes
from
15
different
subduction
zones
with
very
different
ages
of
subducted
lithosphere
and
plate
convergence
rates
are
included.
The
source
complexity
of
the
earthquakes
is
appraised
by
the
physical
features
of
the
teleseismic
source
time
functions.
These
features
include
the
overall
duration,
multiple
or
single
event
character,
individual
source
pulse
widths,
and
roughness
of
the
time
function.
The
above
measures
of
source
size
and
complexity
can
then
be
compared
with
the
age
of
subducted
lithosphere,
plate
convergence
rate,
and
other
physical
parameters
of
the
subduction
zone.
Such
comparisons
are
important
for
increasing
our
understanding
of
the
worldwide
distribution
of
the
largest
earth-
965
966
STEPHEN
H.
HARTZELL
AND
THOMAS
H.
HEATON
quakes
and
their
radiated
energy.
The
teleseismic
source
time
function
gives
information
about
source
complexity
which
can
be
used
in
the
estimation
of
strong
ground
motions.
Studies
of
source
complexity
are
also
important
to
evaluate
the
validity
of
recent
asperity
models
of
faulting,
where
the
fault
is
characterized
by
localized
regions
of
higher
strength.
In
subduction
zone
regimes,
the
maximum
earthquake
magnitude
has
been
related
to
asperity
size
and
to
the
mechanical
coupling
between
the
plates
(Uyeda
and
Kanamori,
1979;
Ruff
and
Kanamori,
1980,
1983;
Lay
et
al.,
1982).
The
earthquake
time
functions
in
this
paper
will,
we
hope,
add
insight
to
these
interpretations.
For
the
period
range
of
interest,
about
1
to
60
sec,
P-wave
radiation
is
the
natural
choice
for
study
of
source
complexity.
It
is
useful
for
later
discussion
to
briefly
review
the
most
common
techniques
which
have
been
used
to
estimate
teleseismic
body-wave,
source
time
functions.
The
techniques
can
be
grouped
into
two
general
types:
(1)
division
of
the
record
by
the
theoretical
point
impulse
response
in
the
frequency
domain;
and
(2)
parameterization
of
the
time
function.
With
the
second
approach,
the
optimum
values
of
the
parameters
are
obtained
by
various
methods
including
cross-correlation,
linear
least-squares,
and
maximum
likelihood.
Boat-
wright
(1980)
utilizes
a
direct
deconvolution
approach.
The
source
time
function
is
obtained
by
a
recursive
deconvolution
in
the
time
domain
of
the
seismogram
by
a
bandpass-filtered
theoretical
impulse
response
of
the
earth.
The
effect
of
the
filtering
on
the
low-frequency
baseline
of
the
time
function
is
approximately
removed
by
subtracting
the
effect
of
the
same
processing
performed
on
an
idealized
functional
form
of
the
seismogram.
Source
finiteness
is
neglected.
Burdick
and
Mellman
(1976)
invert
P
waveforms
from
WWSSN
stations
forthe
1968
Borrego
Mountain
earthquake.
In
their
approach,
the
source
time
function
is
parameterized
by
a
few
variables
whose
optimum
values
are
obtained
by
a
numerical
correlation
between
the
synthetics
and
the
observations.
Care
should
be
exercised
in
applying
such
a
technique,
since
the
time
function
can
only
reflect
that
amount
of
complexity
that
is
allowed
for
by
the
particular
parameterization
used.
Kanamori
and
Stewart
(1978)
and
Stewart
and
Kanamori
(1982)
use
a
forward
modeling
procedure
to
examine
the
complexity
of
WWSSN
P
waveforms.
In
their
technique,
a
single
point
source,
having
a
trapezoidal
far-field
time
function,
is
chosen
such
that
it
simulates
the
very
beginning
of
the
P
wave
train.
The
synthetic
for
this
point
source
is
then
subtracted
from
the
observations.
This
process
is
repeated
using
the
remaining
waveform
until
all
significant
arrivals
are
accounted
for.
Depending
on
the
com-
plexity
of
the
waveforms,
this
procedure
can
be
quite
tedious.
Kikuchi
and
Kanamori
(1982)
extend
the
method
of
Kanamori
and
Stewart
(1978)
so
that
complex
body
waves
can
be
formally
inverted
for
the
source
time
function.
The
synthetic
seismogram
for
an
initial
source
with
a
ramp
dislocation
function,
rise
time
r,
and
rupture
duration
T
is
subtracted
from
the
observations.
The
strength
and
arrival
time
of
this
source
are
determined
by
cross-correlation
of
the
synthetic
and
data
records.
The
process
is
continued
for
N
iterations
until
an
acceptable
fit,
measured
in
a
least-squares
sense,
is
obtained
to
the
data.
The
best
value
of
r
is
obtained
by
trial
and
error.
A
linear
baseline
trend,
which
is
a
result
of
the
band-limited
nature
of
the
data,
is
removed
from
the
source
time
function.
For
multiple-station
data,
the
relative
timing
of
sources
between
stations
can
be
used
to
locate
each
source
with
respect
to
a
given
hypocenter.
Ruff
and
Kanamori
(1983)
estimate
the
source
time
function
for
several
great
earthquakes
by
solving
the
least-
squares
problem
[A/~I]X
~-
[b/0].
Here,
A
is
a
matrix
of
phase
shifted
Green's
functions
for
the
earth
with
narrow
source
time
histories,
I
is
the
identity
matrix,
TELESEISMIC
TIME
FUNCTIONS
FOR
LARGE
EARTHQUAKES
967
~,
is
a
damping
or
moment
minimization
parameter,
X
is
the
discretized
source
time
function,
and
b
is
the
observation
vector.
A
long-period,
half-sine
function
is
added
to
the
time
function
to
shift
the
baseline.
This
adjustment
is
done
to
approximately
compensate
for
the
band-limited
nature
of
the
data
and
to
obtain
a
mostly
positive
time
function.
Nabelek
(1984a,
b)
parameterizes
the
teleseismic
source
time
function
either
as
a
series
of
overlapping
isosceles
triangles
for
a
point
source,
or
overlapping
trapezoids
for
a
line
source.
The
number
of
elementary
sources,
N,
the
rise
time
of
each
source,
7,
and
the
duration
of
each
source
as
seen
at
different
azimuths
(for
the
line
source
problem)
are
all
set
a
priori.
An
iterative
maximum
likelihood
inverse
is
used
to
find
the
best-fitting
weight
to
be
applied
to
each
of
the
N
sources.
All
of
the
above
techniques
share
the
common
limitations
of
the
bandwidth
of
the
data
and
the
accuracy
of
the
computed
impulse
response
of
the
earth
for
the
earthquake
mechanism.
DATA
SET
Rather
than
study
a
few
earthquakes
in
detail,
we
considered
a
survey
study
of
a
larger
number
of
events
in
order
to
characterize
the
overall
nature
of
shallow
subduction
zone
earthquakes.
The
objective
is
to
compare
as
many
earthquakes
of
this
type
as
possible
by
using
body-wave
records
that
have
all
been
recorded
on
the
same
instrument.
Although
the
full
effect
of
the
receiver
structure
may
not
be
known,
by
using
a
common
site
and
instrument,
comparison
studies
between
earthquakes
are
possible.
The
determination
of
the
spatial
and
temporal
rupture
history
of
a
three-dimensional
source
requires
good
azimuthal
coverage
of
the
radiated
energy.
In
this
study,
only
one
station
is
used.
Therefore,
we
obtain
an
estimate
of
the
teleseismic
source
time
function
as
viewed
from
one
particular
azimuth.
The
desirable
characteristics
of
the
recording
instrument
for
this
study
are:
(1)
a
long
time
period
of
continuous
operation;
(2)
a
well-calibrated,
broadband
frequency
response;
and
(3)
a
location
such
that
most
of
the
circum-Pacific
lies
at
a
distance
between
30
°
and
90
°,
the
distance
range
where
direct
P
waves
bottom
in
the
lower
mantle.
The
first
two
requirements
rule
out
WWSSN
stations.
The
instruments
which
do
the
best
job
of
meeting
the
above
requirements
are
the
southern
California
array
of
Benioff
1-90
seismometers
operated
by
the
California
Institute
of
Tech-
nology.
These
instruments
have
a
1-sec
natural
period
seismometer,
a
90-sec
natural
period
galvanometer,
and
a
peak
gain
of
3000
at
1
sec.
Benioff
1-90
seismometers
have
operated
at
four
sites
in
southern
California:
Pasadena;
Riverside;
Barrett;
and
Tinemaha.
The
Pasadena
instrument
was
chosen
because
of
its
longer
period
of
operation
and
because
the
records
are
free
from
obvious
site
reverberations.
In
a
few
cases,
when
Pasadena
records
could
not
be
found,
the
Barrett
record
is
used.
The
Barrett
station
writes
seismograms
very
similar
to
those
of
the
Pasadena
station.
On-scale
records
are
available
for
almost
every
large,
shallow
subduction
zone
earthquake
that
has
occurred
since
1938.
One
notable
exception
is
the
1964
Alaska
earthquake.
For
completeness,
we
have
substituted
the
Pasadena
Wood-
Anderson
torsion
seismometer
record
for
the
1964
Alaska
earthquake.
Besides
the
1964
Alaska
event,
the
only
other
gap
in
the
data
set
is
for
e~thquakes
in
Mexico.
These
events
are
less
than
30
°
from
Pasadena
and
have
been
omitted
to
avoid
upper
mantle
triplications.
The
locations
of
the
earthquakes
studied
are
given
in
Figure
1
and
Table
1.
In
total,
63
events
are
analyzed.
In
Figure
1
and
Table
1
a
numbering
scheme
is
adopted
for
identification
of
the
events
and
is
used
throughout
this
paper.
The
data
968
STEPHEN
H.
HARTZELL
AND
THOMAS
H.
HEATON
have
been
processed
as
follows.
The
vertical
component
of
the
Benioff
1-90
instrument
is
first
digitized
and
bandpass-filtered
from
1
to
60
sec
using
a
double-
pass
zero
phase
Butterworth
filter
(Oppenheim
and
Schafer,
1975).
The
filtering
is
done
to
remove
long-
and
short-period
noise,
primarily
from
digitizing.
The
records
are
then
interpolated
to
a
uniform
time
step
of
0.2
sec.
This
time
spacing
gives
a
Nyquist
frequency
of
2.5
Hz,
which
is
more
than
sufficient
for
the
following
analysis.
The
effects
of
the
earth's
structure,
attenuation,
and
the
instrument
response
are
removed
in
the
inversion
process
described
below.
+60
+40
+20
--20
--40
--60
/64
-
/
+90
+120
+
150
+180
-150
-120
-90
-60
-50
FIG.
1.
Locations
of
the
large
shallow
subduction
zone
earthquakes
studied
and
the
event
numbers
which
they
have
been
assigned.
Light
lines
mark
major
crustal
plate
boundaries.
INVERSION
METHOD
We
now
describe
what
we
mean
by
the
teleseismic
P-wave
time
function
and
how
we
can
calculate
it
from
the
observed
P-wave
train.
Consider
the
fault
shown
in
Figure
2,
where
the
x
coordinate
runs
along
the
fault
strike,
z
is
depth,
and
6
is
the
fault
dip.
If
the
dislocation
rake
angle
is
constant
everywhere
on
the
fault
surface,
then
a
single
component
of
the
teleseismically
observed
ground
motion
can
be
written
as
~zzl
zl
fOO
L
U(t)
=
f)(x,
z,
t)*G(x,
z,
t)
1
dx
dz,
sin
(i)
where
zl
and
zt
are
the
top
and
bottom
depths
of
the
fault,
L
is
the
fault
length,
G(x,
z,
t)
is
the
earth's
impulse
response
:for
each
point
on
the
fault,
and
•
and
•
denote
time
differentiation
and
convolution
operators,
respectively.
D
(x,
z,
t)
is
the
TELESEISMIC
TIME
FUNCTIONS
FOR
LARGE
EARTHQUAKES
TABLE
1
EARTHQUAKE
PARAMETERS
969
Event
No.
Latitude
Longitude
Depths
(kin)
Strike
Dip
Rake
Distance
Azimuth
Reference
1
2
5
6
9
10
13
17
18
19
22
23
24
25
26
27
28
29
30
31
33
34
36
37
38
39
41
42
43
45
47
49
56
61
62
63
64
65
66
68
69
72
73
74
75
76
8O
81
84
85
86
88
89
9O
91
92
5.5S
153.9E
27/34/41/48
345
45
4.9S
153.2E
22/29/36/43
240
40
6.6S
155.1E
17/24/31/38
306
36
7.1S
155.2E
15/22/29/36
303
40
33.7N
136.05E
17/24/31/38
216
10
33.13N
135.84E
17/24/31/38
220
10
34.1N
141.6E
35/42/49/56
135
70
36.58
N
141.34E
27/34/41/48
210
(200)
15
(10)
36.97N
141.71E
17/24/31/38
200
15
(10)
37.24N
141.75E
33/40/47/54
200
15
(10)
40.8N
143.2E
9/16/23/30
156
20
32.54N
132.3E
17/24/3i/38
207
17
39.47N
142.9E
5/12/19/26
151
30
38.15N
142.2E
15/22/29/36
190
20
42.5N
143E
9/16/23/30
220
20
43.05N
145.8E
35/42/49/56
230
27
44.38N
148.58E
22/29/36/43
225
30
44.8N
149.5E
40/47/54/61
223
22
44.7N
150.7E
45/22/29/36
225
10
43.5N
147.4E
17/24/31/38
220
16
44.2N
148.8E
22/29/36/43
213
20
44.1N
148.6E
26
52.6N
159.5E
30
53.2N
159.8E
10
57.8N
163.6E
16
56.0N
163.3E
10
(18)
54.0N
163.0W
70
51.6N
175.4W
18
51.3N
178.6E
18
55.5N
158.4W
10
61.0N
147.5W
20
60.5N
141.5W
12
14.5N
92.6W
20
0.01S
80.1W
20
1.2N
79.4W
20
1.9N
79.3W
20
10.5S
77.0W
15
14.5s
74.8w
i5
10.7S
78.7W
22/29/36/43
335
(330)
12
12.26S
77.8w
5/12/19/26
340
17
39.5S
74.5W
22/29/36/43
10
10
32.5S
71.1W
27/34/41/48
15
24
15.5S
166.9E
15/22/29/36
330
45
15.8S
167.2E
15/22/29/36
334
35
16S
166.8E
17/24/31/38
334
10
22.3S
170.4E
5/12/19/26
322
25
14N
91W
17/24/31/38
296
15
14.5N
91.5W
17/24/31/38
296
15
8.67N
83.16W
17/24/31/38
308
20
44/51/58/65
195
15/22/29/36
214
54/61/68/75
225
17/24/31/38
225
17/24/31/38
225
17/24/31/38
287
17/24/31/38
260
27/34/41/48
289
27/34/4!/48
260
9/16/23/30
246
5/12/19/26
250
15/22/29/36
296
17/24/31/38
31
17/24/31/38
31
17/24/3!/38
31
15/22/29]~6
~40
10.3N
85.2W
17/24/31/38
308
20
li.7N
86.5W
17/24/31/38
308
20
21.5N
145.5E
17/24/31/38
160
20
16.0N
148.0E
17/24/31/38
160
20
24.0N
143.0E
17/24/31/38
160
20
30.7S
72.0W
17/24/31/38
20
25
31.2S
68.7W
17/24/31/38
20
25
90
91.4
56.0
1
55
91.6
56.0
1
90
91.0
55.9
1
90
91.2
55.9
1
90
83.1
53.5
2
90
83.6
53.3
2
-135
79.1
56.2
3
92
77.9
56.5
4
91
77.5
56.7
4
93
77.3
56.8
4
37
74.4
58.3
5
90
86.3
51.5
6
29
75.3
57.9
7
76
76.5
57.2
8
90
73.6
58.6
9
112
71.6
60.3
10
90
69.1
62.4
11
90
68.4
63.0
12
90
67.7
63.7
13
90
70.3
61.4
14
88
69.1
62.4
15
51
69.3
62.3
15
1!0
59.3
72.8
16
90
59.0
73.4
17"
92
55.8
79.1
18
90
56.3
77.6
18
-90
37.0
103.9
19
90
44.2
90.2
20*
137.7
48.0
85.3
21
90
34.9
110.7
22*
90
32.8
131.4
23
90
30.4
139.5
24
90
30.3
-45.2
25
126
49.2
-42.4
26*
!26
48.8
-43.6
26*
126
48.4
-44.1
26
90
59:i
-39.a
27*
90
63.6
-39.5
27*
90
58.2
-38.3
27
90
60.0
-38.3
28
90
83.6
-35.1
29
93
79.7
-38.1
30
100
86.6
53.3
31
90
86.5
53.2
31
90
87.0
53.3
31
90
88.1
51.8
32
80
31.7
-46.0
33*
80
31.0
-46.2
33*
90
40.9
-46.5
34*
90
38.3
-46.6
34*
90
36.5
-47.0
34*
90
83.2
56.1
35*
90
84.3
56.2
35*
90
83.7
55.5
35*
110
77.8
-37.7
36*
110
80.0
-39.8
36*