of 31
Bulletin
of
the
Seismological
Society
of
America,
Vol
73,
No
6,
pp
1553-1583,
December
1983
INVERSION
OF
STRONG
GROUND
MOTION
AND
TELESEISMIC
WAVEFORM
DATA
FOR
THE
FAULT
RUPTURE
HISTORY
OF
THE
1979
IMPERIAL
VALLEY,
CALIFORNIA,
EARTHQUAKE
BY
STEPHEN
H.
HARTZELL
AND
THOMAS
H.
HEATON
ABSTRACT
A
least-squares
point-by-point
inversion
of
strong
ground
motion
and
tele-
seismic
body
waves
is
used
to
infer
the
fault
rupture
history
of
the
1979
Imperial
Valley,
California,
earthquake.
The
Imperial
fault
is
represented
by
a
plane
embedded
in
a
half-space
where
the
elastic
properties
vary
with
depth.
The
inversion
yields
both
the
spatial
and
temporal
variations
in
dislocation
on
the
fault
plane
for
both
right-lateral
strike-slip
and
normal
dip-slip
components
of
motion.
Inversions
are
run
for
different
fault
dips
and
for
both
constant
and
variable
rupture
velocity
models.
Effects
of
different
data
sets
are
also
investi-
gated.
Inversions
are
compared
which
use
the
strong
ground
motions
alone,
the
teleseismic
body
waves
alone,
and
simultaneously
the
strong
ground
motion
and
teleseismic
records.
The
inversions
are
stabilized
by
adding
both
smoothing
and
positivity
constraints.
The
moment
is
estimated
to
be
5.0
x
102s
dyne-cm
and
the
fault
dip
90
°
+
5
°.
Dislocation
in
the
hypocentral
region
south
of
the
United
States-Mexican
border
is
relatively
small
and
almost
dies
out
near
the
border,
Dislocation
then
increases
sharply
north
of
the
border
to
a
maximum
of
about
2
m
under
Interstate
8.
Dip-
slip
motion
is
minor
compared
to
strike-slip
motion
and
is
concentrated
in
the
sediments.
The
best-fitting
constant
rupture
velocity
is
80
per
cent
of
the
local
shear-wave
velocity.
However,
there
is
a
suggestion
that
the
rupture
front
accel-
erated
from
the
hypocenter
northward.
The
1979
Imperial
Valley
earthquake
can
be
characterized
as
a
magnitude
5
earthquake
at
the
hypocenter
which
then
grew
into
or
triggered
a
magnitude
6
earthquake
north
of
the
border.
INTRODUCTION
The
15
October
1979
(23:16:54)
Imperial
Valley
earthquake
(ML
=
6.6)
provided
a
wealth
of
strong-motion
records.
Twenty-two
records
were
obtained
from
the
U.S.
Geological
Survey
network
in
the
Imperial
Valley
within
an
epicentral
distance
of
60
km
(Brady
et
al.,
1980)
and
seven
records
were
obtained
from
the
northern
Baja
California
strong-motion
array
(Brune
et
al.,
1982).
The
strong-motion
records,
together
with
the
teleseismic
recordings,
make
the
1979
Imperial
Valley
earthquake
the
best-instrumented,
moderate-sized
event
to
date,
with
the
possible
exception
of
the
1971
San
Fernando
earthquake.
The
complicated
topographic
and
geologic
setting
of
the
San
Fernando
earthquake
makes
it
difficult
to
study.
In
comparison,
the
structure
of
the
Imperial
Valley
is
relatively
simple,
consisting
of
a
deep
sedimentary
basin
with
relatively
fiat-lying
layers.
Furthermore,
a
recent
seismic
refraction
study
of
the
area
(Fuis
et
al.,
1982)
yielded
fairly
detailed
information
on
the
P-wave
velocity
structure.
Thus,
recordings
of
the
1979
Imperial
Valley
earth-
quake
provide
us
with
a
unique
opportunity
to
construct
detailed
and
physically
realistic
models
of
the
rupture
history
and
wave
propagation
for
this
earthquake.
Failure
to
adequately
model
records
from
this
earthquake
would
seriously
undermine
our
confidence
in
the
validity
of
previous
modeling
studies
of
earthquakes
for
which
less
data
is
available.
To
date,
the
strong-motion
data
set
has
formed
the
basis
of
a
number
of
studies.
1553
1554
STEPHEN
H.
HARTZELL
AND
THOMAS
H.
HEATON
Niazi
(1982)
determined
acceleration
directions
using
the
horizontal
ground
motions
across
a
differential
array
at
E1
Centro
(station
locations
indicated
by
DIF
in
Figure
7).
This
array
consists
of
five
digital
accelerometers
positioned
on
a
north-south
line
210
m
long.
From
these
data,
Niazi
inferred
that
the
rupture
propagated
northwestward
from
the
epicenter
in
Mexico.
Niazi
further
estimated
an
average
rupture
velocity
of
2.7
km/sec
during
the
first
6
sec
of
faulting.
Spudich
and
Cranswick
(1982)
have
also
analyzed
the
E1
Centro
differential
array
data.
They
calculated
apparent
velocities
of
particular
phases
by
cross-correlating
records.
Their
work
implies
an
average
rupture
velocity
of
2.5
km/sec
at
depth,
but
also
suggests
that
the
rupture
velocity
was
lower
during
the
first
few
seconds
of
faulting
and
that
the
rupture
accelerated
as
it
moved
to
the
north.
Their
analysis
also
suggests
that
large
high-frequency
vertical
accelerations
(0.6
to
1.74
g)
recorded
on
several
strong-motion
records
near
E1
Centro
are
due
to
P
waves
originating
from
the
vicinity
of
the
Imperial
fault
where
it
crosses
Interstate
8
and
at
a
depth
of
approximately
8
km.
Archuleta
(1982)
proposed
the
alternative
interpretation
that
the
large
vertical
accelerations
are
a
surface-reflected
PP
phase
originating
further
to
the
south
near
Bonds
Corner
at
a
depth
of
about
4
km.
By
examining
polarization
diagrams
of
particle
velocity
for
stations
near
the
trace
of
the
fault,
Archuleta
(1982)
estimated
an
average
rupture
velocity
of
2.5
to
2.6
km/sec.
Three
previous
studies
have
used
the
strong-motion
data
to
estimate
the
distri-
bution
of
slip
for
the
1979
earthquake:
Hartzell
and
Helmberger
(1982),
Olson
and
Apsel
(1982),
and
Le
Bras
(1983).
Hartzell
and
Helmberger
(1982)
used
forward
modeling
to
deduce
the
slip
distribution.
Their
model
is
characterized
by
an
average
rupture
velocity
of
2.5
to
2.7
km/sec
(0.8
to
0.9
times
the
basement
shear-wave
velocity).
The
slip
is
predominantly
below
a
depth
of
5
km,
north
of
the
hypocenter
and
south
of
the
E1
Centro
area.
Two
regions
of
noticeably
larger
slip
were
suggested,
particularly
one
located
under
Interstate
8,
which
is
held
to
be
responsible
for
the
large
vertical
accelerations
recorded
near
E1
Centro.
They
estimated
the
moment
from
strong-motion
records
to
be
5.0
×
1025
dyne-cm,
which
was
shown
to
be
consistent
with
the
amplitudes
of
teleseismic
shear
waves.
Olson
and
Apsel
(1982)
used
a
least-squares
inversion.
They
parameterized
the
problem
by
dividing
the
Imperial
fault
plane
into
sections,
2
with
depth
and
10
along
the
strike
of
the
fault.
Each
section,
or
subfault,
is
allowed
to
rupture
during
five
separate
time
intervals,
each
separated
by
0.75
sec.
Their
slip
distribution
is
significantly
smoother
than
the
model
of
Hartzell
and
Helmberger
(1982).
The
major
differences
in
the
two
models
may
be
due
to
the
different
parameterizations
of
the
problem.
Hartzell
and
Helmberger
(1982)
used
a
constant
rupture
velocity,
with
fixed
timing,
requiring
that
the
waveforms
be
explained
by
spatial
variations
in
slip.
Olson
and
Apsel
(1982)
set
the
problem
up
with
more
capacity
for
temporal
variation
and
less
spatial
variation
in
slip.
They
obtained
a
trend
in
dynamic
slip
which
implied
a
horizontal
rupture
velocity
between
4.0
and
5.0
km/sec,
which
is
greater
than
the
local
shear-
wave
velocity.
This
slip,
although
more
smoothly
distributed
than
the
patch
of
large
dislocation
in
the
Hartzell
and
Helmberger
(1982)
model,
is
located
in
the
same
place
and
may
be
a
manifestation
of
the
same
phenomenon.
The
present
study
has
a
more
balanced
trade-off
between
spatial
and
temporal
model
parameters
than
these
previous
two
studies.
Olson
and
Apsel
(1982)
obtained
a
moment
of
9.1
×
1025
dyne-cm.
Le
Bras
(1983)
used
an
inversion
scheme
which
minimizes
a
cross-correlation
error
function
between
the
synthetic
waveform
and
the
data.
A
constant
rupture
velocity
is
used,
but
the
mechanism
(strike,
dip,
and
rake)
of
each
subfault
is
allowed
FAULT
RUPTURE
HISTORY
OF
THE
IMPERIAL
VALLEY
EARTHQUAKE
1555
to
vary
somewhat
about
a
pure
right-lateral,
strike-slip,
90°-dipping
fault.
He
found
that
the
fits
to
the
strong-motion
records
are
improved
by
allowing
the
strike,
dip,
and
rake
to
vary
by
_+10".
As
in
the
previous
studies,
the
Le
Bras
(1983)
model
is
characterized
by
an
average
rupture
velocity
of
about
2.5
km/sec,
with
most
of
the
slip
below
5
km
and
north
of
the
hypocenter
but
south
of
the
E1
Centro
area.
He
estimated
the
moment
to
be
5.0
×
1025
dyne-cm.
In
this
paper,
unlike
the
previous
studies,
we
model
both
the
teleseismic
body
waves
and
the
local
strong-motion
records.
The
teleseismic
data
are
included
in
an
attempt
to
add
additional
constraints
on
the
rupture
process.
We
also
wish
to
address
a
basic
question:
What
details
of
the
rupture
history
can
be
deduced
from
(1)
teleseismic
data
alone,
(2)
near-source
data
alone,
and
(3)
the
combined
tele-
seismic
and
near-source
data
sets?
This
is
an
important
question,
since
good
local
instrument
coverage
is
rare
and
most
earthquake
source
studies
must
depend
on
teleseismic
data
alone.
Heaton
(1982)
recently
demonstrated
the
difficulties
involved
in
modeling
teleseismic
body
waves
and
strong
ground
motions
simultaneously
with
a
forward
modeling
approach
and
showed
the
inconsistencies
which
can
develop
between
models
obtained
by
forward
modeling
of
limited
data
sets.
Thus,
one
of
the
objectives
of
this
paper
is
to
explore
the
similarities
and
differences
of
inversion
models
based
on
different
data
sets.
The
data
are
modeled
by
using
a
constrained,
stabilized,
least-squares
inversion
technique.
The
problem
is
parameterized
to
yield
the
best-fitting
(in
a
least-squares
sense)
dislocation
on
a
spatially
and
temporally
discretized
fault.
FORWARD
PROBLEM
Before
pursuing
the
inverse
problem,
several
forward
models
of
the
teleseismic
body
waves
were
run.
These
calculations
are
done
to
investigate
the
dip
of
the
Imperial
fault
and
to
see
what
contributions
individual
phases
make
to
the
tele-
seismic
waveforms.
Hartzell
and
Helmberger
(1982)
obtained
a
model
of
the
distri-
bution
of
dislocation
for
the
1979
earthquake
by
forward
modeling
of
just
the
strong-
motion
data.
It
is
also
of
interest
to
see
how
well
this
model
predicts
the
teleseismic
body
waves.
Figure
I
shows
the
seismic
velocity
structures
used
throughout
this
study
to
compute
strong
ground
motion
(dashed
curves)
and
teleseismic
synthetics
(solid
curves).
The
local
P-wave
velocity
structure
(Table
1)
is
based
closely
on
the
refraction
results
of
Fuis
et
al.
(1982)
and
is
an
average
velocity
structure
for
profile
6NNW-13SSE
of
that
study,
which
runs
approximately
down
the
axis
of
the
Imperial
Valley.
The
S-wave
velocities
are
obtained
by
assuming
(1)
a
Poisson
solid
(a
=
~f3
~)
below
a
depth
of
5
km
and
(2)
linearly
increasing
Poisson's
ratio
for
depths
less
than
5
km
such
that
a
=
2.37/~
at
the
free
surface.
TiLe
structure
used
to
compute
the
teleseismic
waveforms
(Table
l)
consists
of
three
layers
over
a
half-
space
and
approximates
the
gradient
structure
used
in
the
near-source
region.
This
simplified
structure
greatly
reduces
the
computational
effort
required
to
model
teleseismic
body
waves
from
a
finite
fault.
Use
of
the
layered
structure
to
compute
the
teleseismic
body
waves
is
justified
by
their
longer
period
and
the
steep
teleseismic
take-off
angles.
The
computation
of
teleseismic
body-wave
synthetics
for
a
three-
dimensional
finite
fault
is
done
by
a
Green's
function
summation
technique.
Heaton
(1982)
gives
a
full
explanation
of
the
method.
The
teleseismic
synthetics
in
this
paper
include
the
responses
of
all
rays
with
up
to
two
internal
reflections
in
the
layered
stack.
All
conversions
between
phases
occurring
at
the
free
surface
are
included
as
well
as
the
more
important
internal
conversions.
The
amplitudes
of
1556
STEPHEN
H.
HARTZELL
AND
THOMAS
H.
HEATON
rays
having
a
greater
number
of
internal
reflections
are
much
smaller
and
can
be
omitted.
Point
source
responses
for
sources
embedded
within
the
gradient
structure
(approximated
by
many
layers)
were
computed
using
a
Haskell
propagator
matrix
technique
and
compared
favorably
with
responses
computed
using
the
generalized
ray
technique
and
assuming
the
simplified
velocity
model.
The
Haskell
matrix
method
is
not
used
in
the
rest
of
this
study
because
the
analysis
requires
the
separation
of
the
responses
of
down-going
(P,
S)
and
up-going
(pP,
sP)
phases,
a
modification
not
yet
implemented
in
the
Haskell
method.
The
teleseismic,
long-period
P
and
SH
waves
predicted
by
the
Hartzell
and
Helmberger
(1982)
model
9WM
are
shown
in
Figures
2
and
3,
respectively.
All
WWSSN
P
and
SH
waveforms
of
acceptable
quality
between
30
°
and
90
°
are
shown.
In
both
figures
the
synthetic
is
the
second,
lighter
trace.
The
amplitude
in
microns
is
given
for
each
synthetic
assuming
a
moment
of
5.0
×
1025
dyne-cm.
This
moment
was
obtained
by
Hartzell
and
Helmberger
in
their
study
of
the
strong-motion
records.
The
waveforms
and
amplitudes
of
the
P
waves
are
fairly
well-matched.
The
Velocity,
km/sec
0
0
2
4
6
N
"-.i'
'
I
,
S
P
16-
---
Near
Field
-
Far
Field
20
I
I
I
I
I
~
I
E
8
P
.E:
FIG.
1.
Near-field
velocity
structure
used
to
compute
strong-mohon
synthetics
and
far-field
velocity
structure
used
to
compute
telese~smxc
body-wave
synthetms.
SH
waveforms
are
well
modeled
except
for
the
two
nodal
stations
MAL
and
SJG,
which
appear
to
be
contaminated
by
noise.
Perhaps
the
most
obvious
difference
is
the
much
longer,
complicated
waveforms
of
the
observed
P
waves,
lasting
for
over
1
min.
The
waveform
complexities
arrive
much
too
late
to
be
explained
by
source
effects,
and
may
be
due
to
structural
complexities
in
the
source
and
receiver
regions.
We
will
mention
the
long
P-wave
durations
again
when
we
discuss
the
record
section
length
to
be
used
in
the
inversion.
In
general,
the
Hartzell
and
Helmberger
(1982)
near-source
model
does
a
good
job
of
predicting
the
teleseismic
body-wave
ampli-
tudes,
and
a
fair
job
of
modeling
the
waveforms.
Hartzell
and
Helmberger
(1982)
and
Olson
and
Apsel
(1982)
both
assumed
a
vertical
dip
for
the
Imperial
fault.
However,
Archuleta
(1982)
used
epicentral
distributions
and
results
of
seismic
refraction
studies
(Fuis
et
al.,
1982)
to
argue
in
favor
of
a
75°NE
dip.
Well-located
epicenters
(horizontal
error
less
than
2.5
km)
along
the
Imperial
fault
tend
to
cluster
on
the
east
side
of
the
fault
(Johnson,
1979).
Upon
first
inspection,
this
pattern
suggests
that
the
Imperial
fault
dips
to
the
east
FAULT
RUPTURE
HISTORY
OF
THE
IMPERIAL
VALLEY
EARTHQUAKE
1557
at
about
75
°
.
However,
Johnson
(1979)
argued
convincingly
that
many
of
these
earthquakes
are
not
actually
occurring
on
the
Imperial
fault
plane.
It
appears
that
the
seismicity
is
actually
occurring
along
a
collection
of
north-south-trending
planes
aligned
along
the
northwest-southeast-trending
Imperial
fault.
The
resulting
pat-
tern
is
one
in
which
seismicity
is
distributed
to
the
northeast
of
the
observed
fault
trace,
thus
creating
the
illusion
of
a
dipping
fault.
The
dip
of
the
Imperial
fault
is
explored
further
in
Figures
4
and
5.
These
two
figures
compare
long-period
P
and
SH
synthetics,
respectively,
for
different
dips
at
four
stations
widely
spaced
in
TABLE
1
CRUSTAL
STRUCTURES
Depth
(km)
a
(km/sec)
fl
(km/sec)
p
(gm/cm
3)
Near-Source
Crustal
Structure*
0.0
1.9
08
1.80
5.0
5.5
3.0
2.55
110
5.6
314
2.70
11.5
7.2
4.16
2.80
Teleselsmic
Crustal
Structuret
0.0
2.75
1
25
2
0
2.5
4.25
2.25
2
25
5
0
5.55
3.1
2.65
11.0
7
2
4.2
2.8
*
Elastic
parameters
vary
hnearly
between
the
horizons.
¢
Elastm
parameters
constant
between
the
borlzons.
Imperial
Valley
Verhcal
P
waveforms
9WM
Str~ke
=
143
°
Dip
=
90
°
Rake
=
180
°
Mo=
5xlO
25
dyne-cm
Peak
amphtudes
gwen
~n
microns
0
20
40
60
sec
BOG
4.9
LPS
~
4.4
FIG
2.
Comparison
of
observed
(top
trace)
and
computed
(bottom
trace)
teleseismic,
long-period,
vertical
P
waves
for
model
9WM
of
Hartzell
and
Helmberger
(1982).
Amplitudes
of
synthetms
are
for
a
moment
of
5.0
×
102~
dyne-cm.
1558
STEPHEN
H.
HARTZELL
AND
THOMAS
H.
HEATON
azimuth.
The
9WM
model
of
Hartzell
and
Helmberger
(1982)
is
used.
Synthetics
are
shown
for
dips
of
80
°
west
to
75
°
east
in
5
°
increments.
From
the
amplitudes
and
waveforms
in
Figures
4
and
5,
it
is
difficult
to
pick
one
dip
which
explains
the
data
better
than
any
other.
The
P
waves
are
somewhat
more
diagnostic
than
the
SH
waves.
Station
ANT
is
near
nodal
for
P
as
are
other
stations
to
the
south.
These
stations
rule
out
dips
of
75
°
east
and
shallower.
We
conclude
that
any
dip
in
the
range
of
90
°
plus
or
minus
5
°
does
an
equally
good
job
of
fitting
the
data.
There
may
also
be
small-scale
variations
in
the
strike,
dip,
and
rake
along
the
fault
as
suggested
by
Le
Bras
(1983).
To
determine
the
contributions
of
individual
teleseismic
phases
to
the
total
waveform,
the
long-
and
short-period
P-wave
synthetics
for
model
9WM
are
decomposed
in
Figure
6.
Each
record
is
shown
broken
down
into
the
contributions
of
P,
pP,
sP,
and
the
combined
response
of
the
remaining
phases.
One
interesting
feature
of
the
ray
decomposition
is
the
fact
that
the
P,
pP,
and
sP
phases
are
each
smaller
than
the
combined
response
of
all
other
phases,
particularly
at
longer
Peak
amplitudes
given
~n
microns
Imperial
Valley
Tangential
SH-waveforrns
9WM
S~rlke
=145
°
Dip=
90
°
Rake
=
180
°
Mo=5xlO
25
dyne-crr
GEO
15.4
MAL
2.9
SJG
8.8
~E
ESK
~
"~
TU
o
Fro.
3.
Comparison
of
observed
(top
trace)
and
computed
(bottom
trace)
teleselsmic,
long-period
tangential
SH
waves
for
model
9WM
of
Hartzell
and
Helmberger
(1982).
Amplitudes
of
synthetics
are
for
a
moment
of
5.0
x
1025
dyne-cm
periods.
This
result
is
explained
when
one
considers
the
gradient-like
nature
of
the
earth
structure
assumed.
Since
there
is
such
a
large
velocity
variation
within
the
sediments,
the
ray
which
reflects
off
the
free
surface
should
not
be
expected
to
be
significantly
larger
than
rays
reflecting
internally
in
the
sediments.
Thus,
the
P,
pP,
and
sP
phases
are
each
similar
in
amplitude
or
smaller
than
the
collective
response
of
all
the
reflected
and
converted
phases
within
the
sediments.
Waves
reflected
from
a
velocity
gradient
are
smoothly
distributed
in
time.
Thus,
reflection
off
of
a
gradient
is
analogous
to
low-pass
filtering.
Therefore,
the
energy
reflected
from
a
gradient
has
a
long-period
spectrum.
This
explains
why
the
combined
response
of
all
other
phases
is
more
prominent
in
the
long-period
records,
compared
to
the
phases
P,
pP,
and
sP,
than
in
the
short-period
records.
DATA
SET
AND
PREPROCESSING
Strong-motion
data.
The
surface
trace
of
the
Imperial
fault
and
the
strong-motion
stations
of
interest
to
this
study
are
shown
in
Figure
7.
The
epicenters
of
both
the
FAULT
RUPTURE
HISTORY
OF
THE
IMPERIAL
VALLEY
EARTHQUAKE
1559
Imperial
Valley
Vertical
P
waveforms
9WM
Strike
=
14:5
°
Dips
from
80°W
to
75°E
Rake
=
180
°
Mo
=
5xlO
25
dyne-cm
Peak
amplitudes
given
in
microns
0
I0
20
.30
I
i
I
I
sec
JG
~0
obs
8ow~
85w~
85E
__/~
7.,
~o~-,J',-_~
SJG
_
4.5
ANT
,.
Ix9
_%~ow~
-~~4.44"1
85W
"~
--
Y
0.5
A
v
5.9
80E
A-
2.0
FIG.
4.
Variation
in
long-period
P
waveforms
with
fault
dip
for
model
9WM
of
Hartzell
and
Helmberger
0982).
Amplitudes
of
synthetics
are
for
a
moment
of
5.0
×
10
~5
dyne-cm.
Imperial
Valley
Tengenhal
SH-waveforms
9WM
Strike
=
143
°
Dips
from
80°W
to
75°E
Rake
~
180
°
M
o=
5
x
1025
dyne-cm
Peek
amphtudes
given
in
microns
0
I0
20
30
I
[
I
I
sec
~
ARE
COL
f',,
17.5
KEV
2.4
~/-~_~
9o
-~W~
-~'~
22
4~
~
STU
8.4
ARE
A
6.8
~8ow~
~~5~
--~/-~8OF
~./~
FIG.
5.
Varmtion
in
long-period
SH
waveforms
with
fault
dip
for
model
9WM
of
Hartzell
and
Helmberger
(1982).
Amplitudes
of
synthetics
are
for
a
moment
of
5.0
×
102~
dyne-cm
1560
STEPHEN
H.
HARTZELL
AND
THOMAS
H.
HEATON
1979
and
1940
Imperial
Valley
earthquakes
are
indicated
by
stars
(Chavez
et
al.,
1982).
The
instruments
forming
the
E1
Centro
strong-motion
array
are
labeled
numbers
1
through
13.
The
two
horizontal
components
from
the
following
12
stations
are
used
in
the
inversion:
from
the
E1
Centro
array
numbers,
3,
4,
5,
7,
8,
10,
and
11,
the
E1
Centro
differential
array
station,
Calexico,
Meloland,
Holtville,
and
Bonds
Corner.
The
vertical
components
of
strong
ground
motion
are
not
used
because
of
incomplete
knowledge
of
the
seismic
velocity
structure.
The
P-wave
velocities
are
fairly
well-known
from
refraction
surveys.
However,
the
S-wave
velocities
have
been
deduced
from
the
P-wave
velocities
assuming
a
particular
distribution
of
Poisson's
ratio.
Poisson's
ratio
controls
the
S-minus-P
time.
Therefore,
if
we
have
misjudged
Poisson's
ratio,
we
cannot
simultaneously
match
the
correct
arrival
time
of
the
P
and
S
waves.
Hartzell
and
Helmberger
(1982)
noted
this
problem
and
Imperial
Valley
P-
Waveforms
9WM
Strike
=
143
°
Dip
=
90
°
Rake
=
180
°
M
o
=
5x
102Sdyne
-
cm
Long-
periods
?
zp
4,0
oo
Short
-periods
RES
SJG
COL
4.3
n
3.0
obs~
obs
-----~
__@5.9
4
4
.
total~
tota,.~./"\._
3.7
P
--"'-k./
'
P~
pP
~
pP
sP
~
....
s
P
.J~
ot
her
s---/'k,,j~other
~
0
I
o
2o
5p
RES
BLA
MAT
sec
0.059,
0.049,
L,
0.074
C
OL
~.~/_~
ES
~
obs
-~~
obs
~
Vl~,/~<
\\
/
.~
"~VV
"w~
-
total
v,~/,w---total--,~
--
.....
~
SJG
~
pP
~..
pP
Wb'-~-
--~b'~'-
....
s
P
~
s
P
-'-'q4/"4V'e~ot
h
e
r
s---,4/VwVc,,'-~ot
h
e
r
s----4k/b-4/--~---------
Fro.
6.
Decomposition
by
phase
(P,
pP,
sP,
and
all
other
phases
combined)
of
selected
long-
and
short-period,
teleselsmm,
vertical
P
waves
for
model
9WM
of
Hartzell
and
Helmberger
(1982).
observed
that
the
vertical
synthetics
match
the
observations
better
if
they
are
shifted
in
time
a
small
amount
relative
to
the
horizontal
components.
To
avoid
this
problem,
we
have
chosen
to
model
only
the
horizontal
components,
which
are
predominantly
shear-wave
energy.
The
Green's
functions
used
to
calculate
the
strong-motion
synthetics
are
com-
puted
with
the
DWFE
(Discrete
Wavenumber/Finite
Element)
code
of
Olson
(1982),
which
is
similar
to
the
finite-difference
method
of
Alekseev
and
Mikhailenko
(1979,
1980).
The
advantage
of
this
code
is
that
it
can
easily
handle
linear
gradients
in
material
properties,
such
as
encountered
in
the
upper
5
km
of
the
Imperial
Valley
(Figure
1).
The
Green's
functions
include
all
theoretical
arrivals
within
the
specified
time
interval
and
are
valid
in
the
frequency
band
from
0.0
to
2.0
Hz.
Since
a
linear,
least-squares
inversion
is
to
be
used,
care
must
be
taken
to
use
only
linear
operations
when
processing
the
data.
We
wish
to
model
the
velocity