Bulletin
of
the
Seismological
Society
of
America.
Vol.
68,
No.
I,
pp.
31-48.
February
1978
PREDICTABILITY
OF
STRONG
GROUND
MOTION
IN
THE
IMPERIAL
VALLEY:
MODELING
THE
M4.9,
NOVEMBER
4,
1976
BRAWLEY
EARTHQUAKE
BY
THOMAS
H.
HEATON
AND
DoNALD
V.
HELMBERGER
ABSTRACT
·
Strong-motion
displacements,
recorded
at
33
km
(IVC)
and
36
km
(ELC)
from
the
November
4,
197
6
Brawley
earthquake,
are
modeled
using
the
Cagniard-
deHoop
technique.
The
IVC
record
consists
almost
entirely
of
transversely
polarized
motion,
whereas
the
ELC
record
contains
an
approximately
equal
proportion
of
transversely
and
radially
polarized
motion.
A
simplified
shear-wave
velocity
model
was
determined
from
the
compressional
wave
refraction
studies
of
Biehler,
Kovach,
and
Allen
(1964).
The
epicentral
location
and
focal
mechanism
computed
from
P-wave
first-arrival
studies
were
used
to
locate
and
orient
a
double-couple
point
source
within
the
layered
half-space.
The
far-field
time
function
and
source
depth
were
the
only
parameters
without
good
independent
constraints.
A
triangular
far-field
time
function
with
a duration
of
1.5
sec
and
a source
depth
of
7
km
were
sufficient
to
model
the
first
25
sec
of
tangential
ground
motion.
It
appears
that
the
effects
of
velocity
structure
on
the
propag"ation
of
long-period
SH
waves
are
predictable
in
the
Imperial
Valley.
A
study
of
the
synthetic
Fourier
amplitude
spectra
indicates
that
wave
propagation
effects
should
be
included
in
studies
of
source
spectra
and
seismic
wave
attenuation.
INTRODUCTION
The
Imperial
Valley
of
Southern
California
is unusual
in
that
it
has
the
rare
com-
bination
of
flat
lying
sediments
and
earthquakes.
Furthermore,
the
upper
crustal
velocity
structure
has
been
studied
extensively
by
Biehler
(1964).
The
Imperial
Valley
is thus
particularly
well
suited
for
wave-form
modeling
studies
of
strong
ground
motion
from
local
earthquakes.
In
this
paper,
we
will
examine
the
tangentially
polarized
ground
motion
from
a
ML
4.9
earthquake
which
occurred
on
November
4,
1976.
Our
approach
will
be
to
use
a velocity
structure
model
which
is
based
on
Biehler's
work,
along
with
the
calculated
hypocentral
location
and
fault-plane
solution,
to
predict
the
tangentially
polarized
ground
motion
observed
for
this
earthquake.
Pre-
vious
modeling
of
local
SH
wave
forms
(Heimberger
and
Malone,
1975;
Heaton
and
Heimberger,
1977)
has
been
somewhat
unsatisfying
because
velocity
structure
as
well
as
source
model
parameters
have
been
constrained
primarily
by
the
condition
that
synthetic
and
observed
wave
forms
match
each
other.
Obviously,
any
successful
model
must
satisfy
this
constraint,
but
due
to
questions
of
uniqueness
and
the
appli-
cability
of
plane
layered
structure
models
to
complexly
faulted
regions,
one
cannot
help
but
feel
that
the
choice
of
model
parameters
seemed
somewhat
ad
hoc.
In
view
of
this
objection,
we
pose
the
following
question:
Is
it
possible
to
predict
the
motion
from
an
earthquake
using
a model
whose
velocity
structure
parameters
are
deter-
mined
independently
of
the
wave-form
modeling?
We
will
show
that
the
answer
in
this
particular
case
is
yes!
Thus
we
will
demonstrate
a model
which
is
consistent
with
both
the
observed
wave
forms
and
the
independent
constraints
on
velocity
structure
and
epicentrallocation.
We
will
also
investigate
the
effect
of
changes
in
the
model
parameters
on
the
syn-
31
32
THOMAS
H.
HEATON
AND
DONALD
V.
HELMBERGER
thetic
wave
forms.
Since
we
used
generalized
ray
theory
to
generate
the
synthetics,
it
is
possible
to
associate
arrivals
on
the
record
with
specific
travel
paths.
Although
we
prefer
to
view
our
models
in
the
time
domain,
we
will
also
present
Fourier
ampli-
tude
spectra
of
our
synthetics.
We
will
show
that
synthetic
amplitude
spectra
for
layered
half-spaces
are
significantly
different
than
spectra
calculated
for
a homogeneous
half-space.
The
effects
of
structure
must
be
included
when
making
estimates
of
source
parameters
or
seismic
wave
attenuation.
THE
NOVEMBER
4
BRAWLEY
EARTHQUAKE
During
the
period
from
November
3 through
November
8,
1976,
a swarm
of
more
than
400
earthquakes
was
recorded
by
the
U.S.
Geological
Survey
Imperial
Valley
short-period
seismic
array.
This
swarm
occurred
approximately
15
km
northwest
of
a
well-studied
swarm
which
occurred
along
the
Brawley
fault
in
February
of
1975
(Johnson
and
Hadley,
1976).
Unlike
the
February
1975
swarm,
which
produced
sig-
nificant
surface
deformation
(Sharp,
1976),
no
surface
deformation
has
yet
been
as-
sociated
with
the
November
1976
swarm.
The
largest
event
in
the
November
1976
swarm
occurred
at
10i41
GMT
on
November
4 and
was
assigned
a magnitude
of
4.9.
By
using
P-wave
arrival
times
from
the
Imperial
Valley
seismic
array,
the
epicentral
location
(shown
in
Figure
1)
was
determined
by
the
U.S.
Geological
Survey
to
be
33°05'
North
latitude
and
115°36'
West
longitude
(Madeline
Schnapp
and
Gary
Fuis,
personal
communication).
The
USGS
hypocentral
depth
was
4!
km
with
low
P
residuals.
However,
we
prefer
a depth
of
7
km
based
on
our
modeling
of
strong-
motion
wave
forms.
Since
the
hypocenter
is
only
loosely
constrained
by
P
for
these
solutions,
this
difference
does
not
appear
significant.
Assuming
a hypocentral
depth
of
7 km,
we
computed
a focal
mechanism
using
P-wave
first-motion
data
from
68
stations
in
the
joint
Caltech-USGS
Southern
California
seismic
array.
The
focal
mechanism,
which
is shown
in
Figure
2,
indicates
predominantly
right-lateral
faulting
along
a steeply
dipping
fault
which
trends
N-NW.
Because
the
motion
is mostly
strike-
slip
along
a vertical
plane,
this
solution
is relatively
insensitive
to
changes
in
the
as-
sumed
hypocentral
depth.
Two
long-period
strong-motion
seismic
stations
were
triggered
during
the
swarm
sequence.
A
three-component
4X
torsion
seismometer
with
a free
period
of
10
sec
was
located
at
Imperial
Valley
College
(IVC)
at
a distance
of
33
km
from
the
epicenter
(see
Figure
1).
This
instrument
records
on
photographic
paper
on
a revolving
drum
for
a full
24
hours
after
being
triggered.
The
instrument
triggered
6 hours
before
the
M4.9
earthquake
being
studied
in
this
paper
and
thus
the
entire
wave
train
of
the
earthquake
was
well
recorded.
Shown
in
Figure
3 are
the
records
from
IVC.
The
instrument
response
has
been
deconvolved
and
the
resulting
ground
motion
has
been
heavily
filtered
at
periods
longer
than
20
sec
with
an
Ormsby
filter
(Hudson
et
al.,
1971).
Unfortunately,
the
vertical
torsion
recording
shows
a long-period
drift
near
the
onset
of
motion
which
seems
to
have
a positive
net
area.
This
indicates
some
non-
linearity
in
the
instrument
response
which
made
deconvolution
impossible.
Despite
this,
it
seems
clear
from
the
original
records
that
horizontal
ground
motion
was
much
larger
than
vertical
ground
motion.
Also
shown
in
Figure
3 are
the
displacements
rotated
into
radial
and
tangential
directions.
An
inspection
of
these
rotated motions
clearly
shows
that
the
ground
motion
at
IVC
was
dominated
by
transversely
polarized
shear
waves,
as
would
be
expected,
since
IVC
lies
near
a
P-SV
node
(Figure
2).
A
second
recording
of
ground
motion
was
made
by
the
horizontal
Carder
displace-
ment
meters
located
in
El
Centro
at
a distance
of
36
km.
No
long-period
vertical
in-
STRONG-MOTION
DISPLACEMENTS,
BRAWLEY
EARTHQUAKE:
NOVEMBER
1976
33
strument
is present
at
this
station.
The
horizontal
instruments
have
a static
magni-
fication
of
1.0
with
free
periods
near
6
sec.
These
instruments
appear
to
have
triggered
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San
Fel1pe
FIG.
1.
Index
map
of
Salton
trough
showing
locations
of
seismic
refraction
profiles
and
cross-
section
lines
A-B
(Fig.
5a)
and
C-D
(Fig.
5b).
Also
shown
are
the
long-period
strong-motion
stations,
IVC
and
ELC,
and
the
epicenter
of
the
M4.9,
November
4,
1976
earthquake.
Stippling
indicates
generalized
outline
of
pre-Tertiary
crystalline
rocks
bordering
the
Salton
trough.
This
figure
has
been
modified
from
Biehler,
Kovach,
and
Allen
(1964).
near
the
start
of
the
S
wave
and
thus
the
beginning
of
the
record
is lost.
The
records
from
ELC
are
shown
in
Figure
4.
Also
shown
is
the
ground
motion
obtained
by
de-
convolution
of
the
instrument
response
and
Ormsby
filtering
of
periods
beyond
15
sec.
Since
the
beginning
of
the
record
was
lost,
the
deconvolution
of
the
first
pulse
on
the
record
is
questionable.
Rotation
of
the
displacements
indicates·
that
there
34
THOMAS
H.
HEATON
AND
DONALD
V.
HELMBERGER
were
much
larger
radial
displacements
at
ELC
than
there
were
at
IVC.
The
fact
that
the
radial
and
tangential
wave
forms
are
quite
dissimilar
suggests
that
this
change
in
00
•
\&
,~
I
•
•
w
ooQJ
0
cP
0
0
0
co
'b
Strike
N26°W
..
Dip
70°W
•
Rake
180°
S
~:LC
IVC
E
•
•
FIG.
2.
Focal
mechanism
for
the
M4.9,
November
4
earthquake
determined
from
P-wave
first
motions observed
at
68
stations
in
the
joint
Caltech-USGS
Southern
California
seismic
ar-
ray.
The
azimuths
of
the
stations,
IVC
and
ELC,
are
also
shown.
0
2mm
+
0
up
10
sec·
(a)
Torsion
Displacement
10
sec
(b)
Torsion
Displacement
(c)
10
sec
Tors1on
Radial
displacement
(d)
Tangential
displacement
60
sec
FIG.
3.
Summary
of
ground
motion
observed
at
IVC.
(a)
NW
component
of
ground
motion
with
and
without
the
instrument
response.
(b)
NE
component
of
ground
motion
with
and
without
instrument
response.
(c)
Vertical
component
of
gr.ound
motion
with
the
instrument
response.
The
instrument
response
could
not
be
deconvolved
because
of
the
long-period
arrival
which
appears
to
have
a
net
positive
area.
(d)
Ground
motion
rotated
into
radial
and
tangential
components.
amplitude
ratios
is
not
due
to
a poor
rotation
of
predominantly
transverse
motions.
The
difference
in
the
magnitude
of
radial
displacements
between
ELC
and
IVC
is
consistent
with
the
fact
that
the
azimuth
of
ELC
is further
from
the
P
and
SV
node
shown
in
Figure
2.
Notice
that
there
is a remarkable
degree
of
coherence
between
the
STRONG-MOTION
DISPLACEMENTS,
BRAWLEY
EARTHQUAKE:
NOVEMBER
1976
35
tangential
wave
forms
recorded
at
IVC
and
ELC.
This
is
as
it
should
be
since
the
differences
in
range
and
azimuth
between
ELC
and
IVC
are
only
3 km
and
13°,
respectively.
CRUSTAL
STRUCTURE
IN
THE
SALTON
TROUGH
The
Salton
trough
is
a structural
depression
which
is
the
northward
continuation
of
the
Gulf
of
California.
This
depression
is underlain
and
bounded
by
Mesozoic
and
older
crystalline
rocks.
As
much
as
6 km
of
upper
Tertiary
and
Quaternary
marine
and
nonmarine
sediments
fill
this
depression.
Also
present
in
the
Salton
trough
are
several
major
active
right-lateral
fault
zones,
recent
volcanism,
and
potential
geo-
Carder
displacement
(a)
meter
(b)
(c)
Displacement
Carder
displacement
meter
Displacement
Radial
displacement
Tangential
displacement
FIG.
4.
Summary
of
ground
motion
observed
at
ELC.
Since
this
instrument
was
probably
triggered
by
the
directS
wave,
the
beginning
of
the
record
is lost.
(a)
North
component
of
ground
motion
with
and
without
instrument
response.
(b)
West
component
of
ground
motion
with
and
without
instrument
response.
(c)
Ground
motion
rotated
into
radial
and
tangential
components.
No
long-period
vertical
strong-motion
instrument
is
present
at
this
station.
thermal
reserves.
The
November
1976
B:r.awley
swarm
as
well
as
the
stations,
IVC
and
ELC,
lie
near
the
axis
of
this
depression.
The
work
of
Biehler
et
al.
(1964)
on
P-wave
refraction
profiles
indicates
that
there
is very
little
variation
in
upper crustal
velocity
structure
along
the
axis
of
the
Salton
trough.
This
is illustrated
by
the
cross
section
A-B
which
is
shown
in
Figure
5a.
Although
the
total
thickness
of
sediments
varies
considerably
as
one
travels
perpendicular
to
the
axis
of
the
trough,
the
depths
of
individual
layers
within
the
sediments
are
amazingly
consistent
as
one
crosses
the
Salton
trough.
This
can
be
seen
in
the
cross
section
C-D
shown
in
Figure
5b.
Thus
the
overall
impression
of
sedimentary
structures
down
the
axis
of
the
trough
is one
of
relatively
plane
layers.
Unfortunately,
there
are
several
reasons
why
the
velocity
models
calculated
by
Biehler
et
al.
(1964)
cannot
be
used
directly
in
our
modeling.
Most
importantly,
we
need
to
know
shear-wave
velocities
and
the
refraction
studies
were
for
only
com-