Bulletin
of
the
Seismological
Society
of
America
Vol.
69
October
1979
No.
5
GENERALIZED
RAY
MODELS
OF
THE
SAN
FERNANDO
EARTHQUAKE
BY
THOMAS
H.
HEATON*
AND
DONALD
V.
HELMBERGER
ABSTRACT
The
exact
Cagniard-de
Hoop
solutions
for
a
point
dislocation
in
half-space
are
used
to
construct
models
of
the
strong
ground
motion
observed
during
the
February
9,
1971
San
Fernando
earthquake
(PC,
=
6.4).
By
summing
point
dislocations
distributed
over
the
fault
plane,
three-dimensional
models
of
a
finite
fault
located
in
a
half-space
are
constructed
to
study
the
ground
motions
observed
at
JPL
(Pasadena),
Palmdale,
Lake
Hughes,
and
Pacoima
Dam.
Since
the
duration
of
faulting
is
comparable
to
the
travel
times
for
various
wave
types,
very
complex
interference
of
these
arrivals
makes
a
detailed
interpretation
of
these
wave
forms
difficult.
By
investigating
the
motion
due
to
small
sections
of
the
fault,
it
is
possible
to
understand
how
various
wave
types
interfere
to
produce
the
motion
due
to
the
total
fault.
Rayleigh
waves
as
well
as
S
to
P
head
waves
are
shown
to
be
important
effects
of
the
free
surface.
Near-field
source
effects
are
also
quite
dramatic.
Strong
directivity
is
required
to
explain
the
difference
in
amplitudes
seen
between
stations
to
the
north
and
stations
to
the
south.
Faulting
appears
to
have
begun
north
of
Pacoima
at
a
depth
of
13
km.
The
rupture
velocity,
which
is
near
2.8
km/sec
in
the
hypocentral
region,
appears
to
slow
to
1.8
km/sec
at
a
depth
of
5
km.
Displacements
on
the
deeper
sections
of
the
fault
are
about
2.5
m.
Fault
offsets
become
very
small
at
depths
near
4
km
and
then
grow
again
to
5m
near
the
surface
rupture.
The
large
velocity
pulse
seen
at
Pacoima
is
a
far-field
shear
wave
which
is
enhanced
by
directivity.
Peak
accelerations
at
Pacoima
are
probably
associated
with
the
large
shallow
faulting.
The
total
moment
is
1.4
x
102s
ergs.
INTRODUCTION
In
this
paper
we
present
some
preliminary
results
derived
from
strong
motion
modeling
of
some
of
the
more
diagnostic
observations
obtained
from
the
San
Fernando
data
set.
In
two
related
studies
(Heaton
and
Helmberger,
1977,
1978),
strong
ground
motions
for
several
earthquakes
located
in
the
Imperial
Valley
were
examined.
The
records
in
these
situations
were
taken
at
distances
several
times
larger
than
the
source
dimensions
and
only
transversely
polarized
motions
were
modeled.
Ground
motions
for
these
events
were
shown
to
be
profoundly
affected
by
seismic
velocity
structure.
Although
source
characteristics
were
important,
relatively
simple
source
models
were
all
that
were
necessary
to
produce
adequate
synthetic
records.
This
study
attempts
to
understand
recordings
of
the
1971
San
Fernando
earthquake.
Since
this
earthquake
was
well
recorded
by
many
close
stations,
a
more
detailed
inspection
of
source
processes
is
required.
Present
address:
Dames
&
Moore,
Suite
1000,
1100
Glendon
Avenue,
Los
Angeles,
California
90024.
1311
1312
THOMAS
H.
HEATON
AND
DONALD
V.
HELMBERGER
Several
new
complications
are
introduced
by
the
small
source-to-receiver
dis-
tances.
Near-field
terms
can
no
longer
be
neglected
as
in
the
previous
studies.
Furthermore,
fault
finiteness
requires
that
waves
from
differing
parts
of
the
fault
must
approach
the
receiver
from
differing
directions.
This
means
that
the
observed
ground
motion
cannot
be
rotated
into
radial
and
transverse
directions.
Thus
we
cannot
isolate
SHwave
forms
and
we
are
forced
to
consider
P
waves,
SVwaves,
and
Rayleigh
waves.
For
many
reasons,
life
becomes
more
complicated
as
we
move
closer
to
the
earthquake
source.
Fortunately,
as
the
source-to-receiver
distance
becomes
small,
the
effects
of
plane-layered
structure
become
less
dramatic.
In
an
attempt
to
understand
the
most
basic
features
of
the
interplay
between
source
and
structural
effects,
we
chose
first
to
model
the
San
Fernando
earthquake
as
a
three-
dimensional
fault
located
in
an
elastic
half-space.
The
purpose
of
this
study
is
two-fold.
We
would
first
like
to
understand
the
types
of
phenomena
which
should
be
expected
from
a
three-dimensional
fault
which
is
located
in
a
half-space.
The
second
goal
is
to
achieve
a
better
understanding
of
the
particular
source
processes
of
the
San
Fernando
earthquake.
The
second
goal
is
the
more
important
and
difficult
to
achieve.
The
San
Fernando
earthquake
created
a
wealth
of
teleseismic
body-wave
and
surface-wave
data
and
also
local
static
offset
data.
It
thus
provides
a
unique
cross-check
of
several
different
techniques
of
studying
the
slip
on
the
fault
plane.
Ultimately,
we
would
like
to
find
a
single
model
which
explains
all
of
these
observations.
However,
in
this
study
we
will
not
attempt
to
model
these
different
data
sets
simultaneously.
We
will
comment
on
the
compati-
bility
of
our
strong-motion
models
which
have
been
derived
by
other
authors.
A
large
number
of
papers
have
been
written
about
the
San
Fernando
earthquake
and
we
will
not
attempt
to
summarize
the
results
of
all
previous
studies.
However,
these
are
several
papers
which
we
found
very
useful
in
constructing
our
models.
The
study
of
teleseismic
body
waves
by
Langston
(1978),
Alewine's
(1974)
inversion
of
static
offset
data
and
teleseismic
surface-wave
data,
Hanks'
study
of
observed
strong
ground
motion
(1975),
and
the
inversion
of
strong-motion
data
by
Trifunac
(1974)
all
proved
very
useful
in
our
construction
of
San
Fernando
models.
Although
Trifunac's
models
were
for
a
finite
fault
in
a
whole
space,
we
learned
from
his
synthetic
Pacoima
Dam
ground
motion.
Thus,
there
are
several
similarities
between
our
preferred
fault
model
and
Trifunac's
final
fault
model.
The
numerical
calculations
involved
in
our
synthetics
consist
of
several
relatively
laborious
and
expensive
steps.
Once
a
particular
fault
to
station
geometry
is
chosen,
it
is
time
and
money
consuming
to
change
that
geometry.
We
have
chosen
to
model
four
stations
and
no
attempt
was
made
to
find
alternate
stations
or
source-to-station
geometries
which
might
produce
better
synthetics.
In
retrospect,
we
would
have
ignored
the
station
at
Palmdale
since
a
half-space
seems
to
be
a
very
poor
approx-
imation
of
earth
structure
near
this
station.
Also,
it
appears
that
a
different
fault
dip
versus
depth
relationship
might
have
improved
the
comparison
between
synthetic
and
real
data.
However,
it
is
not
our
purpose
to
discover
the
best
half-space
model.
We
would
like
to
discover
the
gross
features
of
the
model
which
are
required
by
the
data.
Because
of
the
large
number
of
parameters
involved,
a
thorough
search
of
the
model
space
can
result
in
an
endless
groping
process.
Until
we
learned
the
signifi-
cance
of
different
parameters,
we
were
victims
of
this
grope.
The
merits
of
this
process
are
that
much
can
be
learned
about
what
will
not
work.
We
are
now
faced
with
the
problem
of
showing
the
reader
what
we
have
learned
from
this
process
and
why
we
have
chosen
the
model
presented
in
this
paper.
It
would
be
impractical
and
tedious
to
present
all
of
our
unsuccessful
models.
Thus
GENERALIZED
RAY
MODELS
OF
THE
SAN
FERNANDO
EARTHQUAKE
1313
our
plan
is
to
preseat
several
simple
models
and
to
then
try
and
understand
why
they
do
not
work
and
how
they
could
be
improved.
THE
DATA
The
1971
San
Fernando
earthquake
produced
by
far
the
largest
single
strong-
motion
data
set
yet
available.
Shown
in
Figure
1
are
the
locations
of
most
of
the
eE071
eF
104
eGII0
ACCELEROGRAPH
SITES
MAJOR
FAULTS
EXPOSED
BASEMENT
ROCK
....
IO
~---
BASEMENT
ELEVATION
IN
THOUSANDS
OF
FEET
SEA
LEVEL
DATUM.
0
tO
20
30
km
VICTORVI
LLE
SANTA
SUSANNA
MTS
D
OXNARO
SAN
SANTA
MONICA
MTS
(DAREA
I
(~)AREA
2
(])AREA
3
E
075
C
054
O
059
E
083
F
089
R
249
O
065
F
098
I
134
P217
0
112
I
I:tl
$265
K
157
N
188
K
159
J
148
R
253
$ANTATALII
J
c..,~
IS,
SAN
GABRIEL
r
LLJ
t
062'
F'~
2-'v-ALF
y~
'
"~
;
l'
•
~
BASIN
~
~\
~,
-20
'
~
'Nl~O
~,._
eF
087
P220
SAN
CLEMI
O
FIG.
1.
The
site
locations
of
accelerometer
recordings
of
the
San
Fernando
earthquake
are
superim-
posed
on
the
gross
geological
and
structural
features
of
the
area.
The
encircled
cross
is
the
Allen
et
al.
(1973)
epicenter
and
the
arrows
point
to
stations
which
are
studied
in
this
paper
(modified
from
Hanks,
1975).
accelerometers
which
recorded
this
event.
We
were
faced
with
the
choice
of
which
records
from
this
immense
set
we
would
model.
Because
we
are
using
a
half-space
model,
it
is
important
that
the
stations
be
near
the
fault.
In
order
to
minimize
redundant
information,
stations
from
different
azimuths
were
chosen.
The
stations
1314
THOMAS
H.
HEATON
AND
DONALD
V.
HELMBERGER
for
which
records
were
synthesized
are
Pacoima
Dam
(PAC),
Jet
Propulsion
Laboratory
(JPL),
Lake
Hughes
Array
Station
4
(LKH),
and
Palmdale
Fire
station
(PLM).
These
stations
are
indicated
in
Figure
i
by
the
codes
C041,
Gll0,
J142,
and
Gl14,
respectively.
These
codes
refer
to
the
cataloging
system
used
in
the
series
of
strong-motion
data
reports
published
by
the
Earthquake
Engineering
Research
Laboratory
of
the
California
Institute
of
Technology.
It
is
from
these
reports
that
our
observed
ground
displacement
curves
have
been
taken.
In
Figure
2
through
5
we
show
the
corrected
accelerograms,
integrated
ground
velocity,
and
displacement
curves
for
these
stations
(Trifunac
et
al.,
1973b).
The
processing
of
these
accelero-
grams
involves
base
line
corrections
and
Ormsby
filtering.
The
basis
for
this
processing
can
be
found
in
papers
by
Trifunac
(1971)
and
Trifunac
et
al.
{1973,
a
and
b).
It
is
impossible
for
an
accelerometer
to
recover
static
or
even
very
long-period
ground
displacement
information
and
thus
these
integrated
displacement
curves
are
really
displacements
in
which
periods
longer
than
10
sec
have
been
heavily
filtered.
In
fact,
the
base
line
correction
can
effectively
filter
periods
of
less
than
10
sec.
For
instance,
the
Pacoima
station
probably
experienced
a
large
static
offset
which
cannot
be
easily
seen
when
simply
viewing
the
displacement
curves.
Hanks
(1975)
has
presented
a
relatively
comprehensive
discussion
of
the
sources
of
long-period
errors
for
this
data
set.
In
his
1975
paper,
Hanks
also
investigates
the
coherence
of
displacements
between
stations
which
are
located
near
each
other.
In
general,
he
finds
this
coherence
to
be
very
good.
In
particular,
the
records
from
stations
in
the
Pasadena
area
(i.e.,
JPL)
are
very
similar
to
each
other.
The
same
is
true
of
records
obtained
in
the
Lake
Hughes
area.
Unfortunately,
there
are
only
two
stations
to
the
northeast,
Palmdale
and
Pearblossom.
We
chose
Palmdale
since
it
was
closest.
Hanks
(1975)
points
out
that
both
the
intensity
of
shaking
and
amplitude
of
displacements
were
generally
larger
for
regions
south
of
the
hypocenter.
In
partic-
ular,
this
is
true
of
the
stations
which
we
have
chosen
to
model.
We
will
use
these
observations
to
try
and
pin
down
the
slip
on
the
fault
plane.
THE
MODEL
Our
model
consists
of
a
three-dimensional
finite
fault
located
in
a
half-space.
A
circular
rupture
front
is
assumed
to
propagate
at
a
given
rupture
velocity
from
the
hypocenter.
The
slip
angle
and
dislocation
time
history
are
assumed
to
be
uniform
throughout
the
fault
plane.
The
Cagniard-de
Hoop
technique,
together
with
a
linear
interpolation
scheme,
is
used
to
compute
the
ground
motions
from
point
dislocations
which
are
evenly
distributed
(0.5
km
spacing)
on
the
fault
plane.
These
responses
are
summed
with
time
lags
which
are
determined
by
the
assumed
hypocentral
solution
and
rupture
velocity.
Nonuniform
fault
displacement
is
modeled
by
varying
the
weights
of
individual
point
sources.
We
are
thus
using
a
numerical
Green's
function
technique
to
integrate
over
the
fault
plane.
This
is
very
similar
to
the
finite
fault
models
which
were
constructed
for
the
Borrego
Mountain
earthquake
in
our
1977
paper.
However,
unlike
the
Borrego
study
in
which
we
considered
only
SH
motions,
there
are
many
added
complexities
due
to
the
inclusion
of
P
and
SV
waves,
near-field
terms,
and
a
more
general
fault-to-station
geometry
which
dictates
that
waves
arrive
from
different
azimuths.
This
last
complication
has
two
effects,
both
of
which
are
included,
without
approximation,
in
our
models.
The
first
effect
originates
from
the
fact
that
sources
having
different
locations
on
the
fault
plane
have
different
radiation
patterns
with
respect
to
a
fixed
station.
The
second
effect
is
to
make
the