of 16
Bulletin
of
the
Seismological
Society
of
America.
Vol.
67,
No.
2,
pp.
315-330.
April1977
A
STUDY
OF
THE
STRONG
GROUND
MOTION
OF
THE
BORREGO
MOUNTAIN,
CALIFORNIA,
EARTHQUAKE
BY
THOMAS
H.
HEATON
AND
DoNALD
V.
HELMBERGER
ABSTRACT
Several
synthetic
models
are
constructed
to
fit
the
first
40
sec
of
the
transversely
polarized
displacement,
as
recorded
at
El
Centro,
of
the
April
9,
1968
Borrego
Mountain
earthquake.
The
modeling
is
done
in
the
time
domain
using
the
response
computed
for
a distributed
set
of
point
shear
dislocations
embedded
in
a
layered
half-space.
The
beginning
1
0
sec
of
the
observed
record
is
used
to
model
the
spatial
and
temporal
distribution
of
faulting
whereas
the
remaining
portion
is
used
to
determine
the
upper
crustal
structure
based
on
surface-wave
periodicity.
A
natural
depth
criterion
was
provided
by
comparing
the
amplitude
of
the
direct
arrival
with
the
surface-wave
excitations.
Trade-offs
are
found
to
exist
between
source
models
and
velocity
structure
models.
Within
the
framework
of
a
layer
over
a half-space
model,
faulting
of
finite
vertical
extent
is
required,
whereas
the
horizontal
dimensions
of
faulting
are
not
resolvable.
A
model
which
is
also
con-
sistent
with
the
teleseismic
results
of
Burdick
and
Mellman
indicates
massive
faulting
near
a
depth
of
9
km
with
a fast
rise
time
producing
a 1
0-cm
displacement
pulse
of
1 sec
duration
at
El
Centro.
The
faulting
appears
to
slow
down
approaching
the
surface.
The
moment
is
calculated
to
be
approximately 7 X 1
0
25
dyne-em
which
is
somewhat
smaller
than
the
moment
found
by
Burdick
and
Mellman
(1976).
INTRODUCTION
Understanding
the
nature
of
strong
ground
motion
is
a problem
of
importance
to
both
seismologists
and
earthquake
engineers.
Generally,
the
engineering
community
has
been
particularly
interested
in
the
shorter
periods
whereas
the
former
investi-
gators
usually
study
the
more
coherent
longer-period
motions.
However,
in
recent
times
their
domains
of
interest
appear
to
overlap
in
the
frequency
band
from
0.1
to
10
Hz
because
man-made
structures
have
become
larger
and
because
seismologists
have
become
increasingly
interested
in
the
details
of
faulting
that
can
only
be
obtained
from
a combination
of
teleseismic
and
local
observations.
In
many
situations,
the
seismic
waves
recorded
in
the
local
field
travel
more
nearly
horizontal
paths
than
waves
which are
recorded
at
teleseismic
distances.
This
allows
us
to
sample
waves
from
earth-
quakes
·,;;hich
leave
the
source
area
in
directions
which
are
inaccessible
to
researchers
studying
the
wave
forms
of
teleseismic
records.
Unfortunately,
the
fact
that
energy
in
the
Lt
:1l
field
travels
nearly
horizontal
paths
implies
that
reflections
from
hori-
zontal
crustal
layers
are
both
large
and
complicated.
In
the
local
field,
a clear
distinc-
tion
between
body
waves
and
surface
waves
is
not
possible.
Thus,
in
many
respects,
interpreting
the
relative
effects
of
source
and
earth
structure
is
a more
tractable
prob-
lem
for
teleseismic
modeling
than
for
local
field
modeling.
Yet,
as
we
will
show
in
this
paper,
it
is
possible
to
model
local
observations
of
earthquakes
with
realistic
source
and
crustal
structure
models.
Obviously,
it
is
important
to
construct
earthquake
source
models
which
are
compatible
with
both
local
and
teleseismic
wave
forms.
This
test
of
compatibility
is
especially
important
with
respect
to
the
assumed
Q
structure
of
the
Earth
which
must
be
used
when
correcting
teleseismic
observations.
Thus,
the
315
316
THOMAS
H.
HEATON
AND
DONALD
V.
HELMBERGER
inclusion
of
local
observations
into
the
data
set
in
earthquake
studies
is
becoming
increasingly
important.
In
most
previous
wave-form
modeling
of
strong
ground
motion,
researchers
have
circumvented
the
complications
of
horizontal
layering
by
considering
only
records
which
are
taken
very
close
to
the
causative
fault.
Most
studies
of
this
nature
approxi-
mate
the
earth
response
by
the
response
of
a homogeneous
whole
space
with
an
ampli-
tude
correction
of
two
in
order
to
approximate
the
free
surface.
Since
only
direct
waves
can
be
generated
by
such
a model,
simple
source
models
will
result
in
relatively
simple
pulse-like
wave
forms.
Unfortunately,
strong
ground
motion
records
displaying
simple
pulse-like
wave
forms
are
relatively
rare.
Some
of
the
better
examples
are:
(1)
the
Pacoima
Dam
recording
of
the
1971
San
Fernando
earthquake
which
has
been
modeled
by
Trifunac
(1974),
(2)
the
Cholame
no.
2
recording
of
the
1966
Park-
field
earthquake
modeled
by
Aki
(1968),
Trifunac
and
Udwadia
(1974),
Kawasaki
(1974),
and
Anderson
(1974).
Anderson
and
Richards
(1975)
have
reviewed
several
of
the
different
source
models
which
have
been
used
in
modeling
such
records
and
they
give
some
insight
into
the
ambiguities
which
are
present
in
modeling
ground
motion
very
close
to
an
earthquake.
They
demonstrate
that
a variety
of
source
models
with
quite
different
rupture
motions,
rupture
geometries,
rupture
velocities,
and
rise
times
can
produce
very
similar
near-field
motions
in
a homogeneous
whole
space.
Things
change
considerably
when
horizontal layering
is introduced
into
the
problem.
If
the
structure
is
not
known,
even
greater
ambiguity
in
source
modeling
exists
due
to
the
introduction
of
more
variables.
Things
may
not
be
as
hopeless
as
they
first
appear
though,
since
if
the
structure
is
known
its
effects
can
be
used
to
advantage.
That
is,
the
response
of
a layered
medium
is unlike
that
of
a homogeneous
medium
in
that
the
response
of
the
layered
medium
is
a sensitive
function
of
the
position
of
the
source
within
the
layers.
Thus
if the
structure
is
known,
the
complications
due
to
that
structure
can
help
clear
up
ambiguities
concerning
the
source.
Consider
the
dilemma
presented
by
any
single
displacement
record
taken
in
a homogeneous
whole
space.
It
is
practically
impossible
to
distinguish
a source
composed
of
several
point
disloca-
tions
from
another
source
which
consists
of
only
one
point
dislocation.
This
am-
biguity
is
not
as
severe
in
a layered
space
since
each
of
the
several
point
sources
will
interact
with
the
structure
in
a predictable
fashion.
A
case
will
be
made
that
the
El
Centro
record
of
the
Borrego
Mountain
earthquake
cannot
be
adequately
modeled
with
just
one
point
dislocation.
This
distinction
could
not
be
made
for
homogeneous
whole-space
models.
THE
BoRREGo
MouNTAIN
EARTHQUAKE
The
Borrego
Mountain
earthquake
occurred
at
2:29
GMT
on
April
9,
1968
and
has
been
assigned
a magnitude
of
6.4
(Allen
and
Nordquist,
1972).
A
surface
rupture
which
extended
nearly
31
km
was
recognized
along
three
well-defined
zones
of
frac-
ture
(north,
central,
and
south
segments)
which
comprise
the
Coyote
Creek
fault
which
is
itself
a segment
of
the
San
Jacinto
fault
zone
of
southern
California.
A
maxi-
mum
right-lateral
offset
of
38
em
was
measured
along
the
north
segment
and
right-
lateral
offsets
of
25
to
30
em
and
8 to
14
em
were
measured
on
the
central
and
south
segments,
respectively
(Clark,
1972).
The
central
and
south
segments
are
distinguished
from
the
north
segment
in
that
approximately
half
the
displacements
measured
were
recognized
to
be
due
to
post
earthquake
creep
(Burford,
1972).
Surface
ruptures
of
1 to
2~
em
were
also
reported
by
Allen
et
al.
(1972)
for
segments
of
the
Superstition
Hills,
Imperial,
and
San
Andreas
faults.
These
displacements
are
presumed
to
be
due
STRONG
GROUND
MOTION
OF
BORREGO
MT.,
CALIFORNIA
EARTHQUAKE
317
to
fault
creep
which
was
triggered
by
the
Borrego
Mountain
earthquake.
Figure
1
shows
the
spatial
relationship
of
these
various
faults.
Rupture
appears
to
have
initi-
ated
on
the
north
segment.
Aftershocks
define
a diffuse
zone
which
is
about
50
km
in
length
(Allen
and
Nordquist,
1972).
No
conspicuous
increase
in
seismicity
could
be
found
for
the
Superstition
Hills,
Imperial
and
San
Andreas
faults.
-----
•·
.,,
....
~
Surface
rupture
after
earthquake
...
:··
••
t,\_';\11\~
.
C:'?'i\\'i.."l::l
~
I
~<:1\.<:l'i'.b.l)l)
"'''~"-"'
l:>'i_\."\1>.
------
.....
.
Fw.
1.
Oblique
map
of
the
Salton
Trough.
Jagged
lines
indicate
segments
of
faults
that
moved
in
association
with
the
1968
Borrego
Mountain
earthquake.
The
distance
between
meridians
shown
is
93.5
km
along
the
33°N
parallel
(Figure
modified
from
U.S.
Geol.
Survey
Profess.
Paper
787).
Faulting
on
the
north
segment
of
the
Coyote
Creek
fault
displays
several
features
which
clearly
distinguish
it
from
other
fault
segments
which
had
rupture
associated
with
the
earthquake.
Both
the
initiation
of
rupturing
and
the
largest
offsets
occurred
on
the
north
segment.
As
compared
with
the
central
and
south
segment,
the
north
segment
had
fewer
aftershocks
and
very
little
postseismic
creep.
Burdick
and
Mellman
(1976)
argue
pursuasively
that
these
variations
in
the
behavior
of
the
fault
segments
reflect
different
behaviors
deep
in
the
Earth.
Their
modeling
of
teleseismic
wave
forms
seems
to
require
a short
duration
source
time
function
and
hence
a small
source
318
THOMAS
H.
HEATON
AND
DONALD
V.
HELMBERGER
dimension.
They
suggest
a circular
fault
of
radius
8 km.
If
indeed
such
a small source
area
is required,
then
clearly
the
north
segment
is
the
likely
candidate.
THE
EL
CENTRO
STRONG
GROUND-MOTION
RECORD
The
Borrego
Mountain
Earthquake
triggered
114
strong-motion
seismographs
in
southern
California
and
southeastern
Nevada
(U.S.
Coast
and
Geodetic
Survey
et
al.,
1968).
Most
of
the
instruments
were
located
in
the
Los
Angeles
area
which
is
approximately
200
km
from
the
epicentral
region.
The
closest
strong-motion
stations
were
located
at
El
Centro,
San
Diego,
and
Perris
Dam
which
are
at
epicentral
dis-
tances
of
60,
100,
and
120
km,
respectively.
We
chose
to
model
only
the
El
Centro
recording
because
it
was
the
closest
station
and
was
the
only
station
located
in
the
same
geologic
province
(the
Salton
Trough)
as
the
earthquake.
Moreover,
Carder
displacement
meters
were
located
at
El
Centro,
providing
reliable
information
at
periods
beyond
8 sec.
(x)
Sensitivity
in
cm/g;
(*)
Static
magnification.
Fw.
2.
El
Centro
accelerograph
and
Carder
displacement-meter
record
from
the
Borrego
Mountain
earthquake
(U.S.
Coast
and
Geodetic
Survey
et
al.,
1968).
Figure
2 shows
both
displacement
records
as
well
as
accelerograph
records
from
El
Centro.
The
accelerograph
records
have
been
integrated
to
obtain
both
ground
ve-
locity
and
displacement
(Hudson
et
al.,
1971).
Figure
3 shows
that
the
ground
motion
obtained
by
double
integration
compares
favorably
with
the
ground
motion
obtained
by
deconvolution
of
the
instrument
response
from
the
Carder
displacement
meter
records.
The
Carder
instruments
have
free
periods
of
6.4
sec
on
the
E-
W
component
and
6.8
sec
on
the
N-S
component.
The
deconvolved
Carder
records
have
been
heavily
filtered
at
periods
beyond
14
sec
with
an
Ormsby
type
filter
to
avoid
the
inherent
instability
present
in
the
deconvolution
process.
We
believe
that
the
deconvolved
Carder
record
gives
a very
reliable
representation
of
the
ground
motion
at
El
Centro.
The
agreement
between
the
integrated
accelerogram
and
the
deconvolved
Carder
record
is
remarkable
when
one
realizes
that
the
free
periods
of
the
accelerographs
are
about
0.067
sec.
However,
there
does
appear
to
be
significant
disagreement
in
the
absolute
amplitude
scales.
This
discrepancy
raises
questions
about
the
reliability
of
the
gains
reported
for
these
instruments.
El
Centro
is
only
from
being
directly
along
the
strike
of
the
earthquake
fault
plane.
Since
the
earthquake
was
strike-slip
along
a vertical
fault,
we
expect
to
be
very
close
to
an
SH
radiation
maximum
and
SV
and
P
radiation
nodes.
The
tangen-
tially
polarized,
radially
polarized,
and
vertical
components
of
ground
motion
are
also
shown
in
Figure
3.
The
vertical
component
is
a
doubly
integrated
accelerogram
(Hudson
et
al.,
1971).
The
horizontal
components
were
rotated
such
that
the
azimuth
of
the
tangential
and
radial
axes
were
S37°W
and
S53°E,
respectively.
The
first
40
sec
of
displacement
are
dominated
by
transversely
polarized
motion
as
indicated
in
STRONG
GROUND
MOTION
OF
BORREGO
MT.,
CALIFORNIA
EARTHQUAKE
319
Figure
3c.
Considerable
radially
polarized
motion
is
present
in
the
next
40
sec
of
ground
motion.
One
possibility
is
that
this
departure
from
transverse
polarization
is
due
to
lateral
reflections
of
surface
waves
in
the
Salton
Trough.
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-
Deconvolved
Corder
d1spl.
Integrated
occelerogrom
D.
C.
displ.
lntegr
occel.
Vertical
Rod1ol
Tangential
40
sec
60
so
FIG.
3.
Summary
of
observed
ground
motion.
(a)
Comparison
of
deconvolved
Carder
displace-
ment
meter
record
and
integrated
accelerogram
for
N-S
component.
(b)
Comparison
of
decon-
volved
Carder
displacement
meter
record
and
integrated
accelerogram
for
E-W
component.
(c)
Ground
motion
rotated
into
vertical,
radial,
and
tangential
components.
thermal
reserves.
The
Borrego
Mountain
earthquake
occurred
along
the
western
side
of
the
trough
whereas
El
Centro
lies
close
to
the
axis
of
the
depression.
The
work
of
Biehler
(1964)
and
Hamilton
(1970)
indicates
that
considerable
variation
in
upper
crustal
velocity
structure
exists
along
the
path
from
Borrego
to
El
Centro.
A
summary
of
the
crustal
structure
found
by
Hamilton
(1970)
for
the
Borrego
vicinity
is
given
in
Table
1.
Also
in
Table
1 is
the
uppermost
crustal
structure
reported
by
Biehler
(1964)
for
his
closest
refraction
line
to
El
Centro.
Clearly,
the
thick
layer
of
sediments
under-
lying
El
Centro
is
not
present
in
the
epicentral
region.
In
fact,
basement
rocks
are
exposed
in
the
Superstition
Hills
which
lie
20
km
from
El
Centro
and
along
the
line
between
the
epicenter
and
El
Centro.
Fortunately,
the
basin
structure
near
El
Centro
consists
of
relatively
flat,
laterally
homogeneous
sediments.
Experience
has
shown
us
that
the
major
effect
of
sediments
is
to
allow
postcritical
angle
multiple
reflections
to
occur
in
the
section.
Furthermore,
for
a source
beneath
the
sediments,
reflection