SYNTHESIS
OF
SAN
FERNANDO
STRONG-MOTION
RECORDS
Thomas
H.
Heaton
and
Donald
V.
Helmberger
Seismological
Laboratory
California
Institute
of
Technology
Three-dimensional
models
of
a
finite
fault
located
in
a
half-space
are
constructed
to
study
the
ground
motions
from
the
9
February
1971
earthquake
as
observed
at
JPL,
Palmdale,
and
Lake
Hughes
(Array
Station
#4).
The
Cagniard-De
Hoop
Technique
is_used
to
compute
the
ground
motions
due
to
infinitesimal
point
sources
which
are
evenly
distributed
(0.5
km
spacing)
on
the
fault
plane.
The
responses
are
summed
with
time
lags
determined
by
the
assumed
hypocentral
solution
and
rupture
velocity.
Nonuniform
fault
displacement
is
modeled
by
varying
the
weights
of
individual
point
sources.
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.
Recent
modeling
of
teleseismic
body
waves
by
Langston
has
indicated
that
the
fault
changes
dip
from
50°
to
30°
at
a
depth
of
approximately
5
km.
This
feature
has
been
incorporated
into
our
models.
The
assumed
fault
geometry
and
station
locations
are
shown
in
Figure
1.
In
Figure
2,
we
display
assumed
fault
displacements
for
a
preliminary
model
which
is
used
to
explain
the
motions
at
JPL,
PLM,
and
LKH.
The
overall
moment
for
this
model
is
1.5
x
10
26
ergs.
The
hypo-
center
is
assumed
to
lie
in
the
region
of
maximum
displacement
and
a
rupture
velocity
of
1.8
km/sec
(as
suggested
by
Langston)
is
also
assumed.
Although
stations
LKH
and
JPL
are
situated
at
roughly
equal
epicentral
distances,
there
appears
to
be
a
dramatic
difference
in
the
character
and
amplitudes
of
ground
motion
seen
for
these
stations.
This
can
be
seen
in
Figures
3
and
4.
In
these
figures,
the
synthetic
ground
motions
for
the
fault
model
described
above
are
compared
with
the
integrated
accelerograms
for
these
stations.
Because
the
integrated
accelerograms
have
been
filtered
with
an
8
sec.
Ormsby
filter,
the
synthetics
are
displayed
both
with
and
without
the
inclusion
of
this
filter.
Although
it
appears
that
the
particular
fault
model
used
for
Figures
3
and
4
is
not,
in
detail,
correct,
it
does
well
at
explaining
the
differences
in
character
and
amplitude
of
ground
motions
as
seen
between
JPL
and
LKH.
An
examination
of
Figure
5
helps
one
to
appreciate
the
complex
interplay
between
source
and
wave
propagational
effects.
In
this
figure
the
fault
is
subdivided
into
5
strips
each
of
which
has
a
width
of
4
km.
Also
shown
are
synthetic
motions
(JPL,
North)
for
a
single
point
source
located
in
the
middle
of
each
subfault.
Although
these
point
sources
produce
easily
interpreted
specific
arrivals,
it
is
clear
that
the
JPL
record
results
from
complex
and
not
easily
interpreted
interaction
of
both
source
and
propagation
effects.
These
synthetics
also
demonstrate
the
dramatic
effect
of
the
free-surface.
Rayleigh
wave
and
sP
head
wave
contributions
are
of
great
importance.
52
The
effects
of
even
more
complicated
earth
structure
in
these
records
is
yet
to
be
studied,
but
detailed
synthesis
of
records
for
simpler
aftershocks
should
add
some
insight
to
this
problem.
•LKH
Lake
Hughes
Circular
Rupture
'-....
Front
2km
Assumed
'------~·
•PLM
Palmdale
Assumed
Fault
Shape
....,._Hinge
Line
.........._
Approx.
Surface
Rupture
0
5
10
km
~
0
2
4
km
Fig.
1:
Assumed
geometry
for
the
San
Fernando
Fig,
2:
Contour
map
of
assumed
fault
dis-
fault
and
receivers.
Model
consists
of
a
placements
for
the
preliminary
San
Fernando
three
dimensional
finite
fault
in
a
half-space.
model
displayed
in
Figures
3,
4,
and
5.
A
Green's
function
technique
is
used
to
inte-
grate
the
exact
solution
for
a
point
disloca-
tion
over
the
rectangular
grid
shown.
A
cir-
cular
rupture
front
propagates
from
an
assumed
hypocenter
and
displacement
magnitudes
are
pre-
scribed
on
the
fault
surface,
53
Lake
Hughes
#
4
s~G.-M~---·---,\
(LKH)
f
N21oE
'•,,,,\
'
...
__
.,.,-
..
_-
...
_
.....
,
...
,---
0
6
12
sec
18
24
Fig.
3
and
4:
Preliminary
model
of
JPL
and
LKH
displacement
records,
Massive
faulting
at
depth
of
13
km
and
a
rupture
velocity
of
1,8
km/sec,
are
assumed,
The
top
trace
is
the
synthetic
ground
motion;
the
middle
trace
is
the
synthetic
ground
motion
filtered
with
an
8
sec
Ormsby
filter;
and
the
bottom
trace
is
the
observed
displacement
which
has
also
been
filtered
at
8
sec.
Notice
the
contrast
between
the
records
at
JPL
and
LKH
which
lie
at
approximately
equal
epicentral
ranges.
54
Depth,
km
A
§
13.0
JPL
(North)
e1
8
9.8
•2
c
6.7
•
3
D
4.0
~
•4
_A_
E
2.1
•
5
SR
s
''
'
~
~
2
c
~
-A)\
3
~
~
D
p
•'
'
4
~
E
'
..
p
SP
S R
p
•'
NP
5
'
P-
P
Wave
SP-
S
To
P
Head
Wave
NP-
Near
Field
P
Wave
S-
Shear
Wave
R-
Rayleigh
Wave
0
6
12
18
24
sec
Fig.
5:
Decomposition
of
the
N
component
of
synthetic
ground
motion
for
JPL.
The
finite
fault
is
broken
into
5
strips
whose
individual
contributions
are
shown
on
the
left.
Re-
sponses
of
point
sources
which
lie
in
the
middle
of
these
strips
have
been
convolved
with
both
3
sec.
and
0.8
sec.
triangular
far-field
time
functions
and
are
displayed
in
the
middle
and
on
the
right,
respectively.
By
studying
the
point
source
responses,
contribu-
tions
of
individual
phases
can
be
recogni2ed
in
the
synthetic
for
the
finite
fault.
Notice
the
complex
interplay
of
source
and
wave
propagational
effects.
55