Suggested directions in earthquake shaking microzonation research


Tinsley, J.C.; Rogers, A.M.

Workshop on future directions in evaluating earthquake hazards of Southern California, November 12-13, 1985, Los Angeles, California: 345-354

1986


Rogers, Tinsley, and Borcherdt (1985) described an empirical technique for predicting relative site response by comparing ground motion spectra in three period bands (total period band is from 0.2 to 10 seconds) relative to the thickness and the physical properties of the earth materials which lie beneath the instrument sites. A set of three-component recordings of Nevada Test Site nuclear tests and a compilation of geologic attributes at each site comprise the set of basic data employed in the analysis. A suite of site types (clusters) is defined statistically in terms of common geologic attributes. The attributes defining each cluster are those attributes that most strongly correlate with, or influence, site response in a given period band. Maps showing the distribution of these geologic attributes are prepared as overlays and are used to construct derivative maps which, in turn, depict relative site response for part of the Los Angeles area. Future research is desirable, both to explore further the methodology and to test the predictions of the model compared to patterns of damage caused by historical earthquakes, as well as applying the technique to basins other than the Los Angeles region. The principal goal of these and related studies is to develop microzonation technology so that sites which are especially at risk can be identified and appropriate measures can be adopted to reduce significantly losses of life and property.

SUGGESTED
DIRECTIONS
IN
EARTHQUAKE
SHAKING
MICROZONATION
RESEARCH
John
C.
Tinsley
and
Albert
M.
Rogers
United
States
Geological
Survey
INTRODUCTION
Rogers,
Tinsley,
and
Borcherdt
(1985)
described
an
empirical
technique
for
predicting
relative
site
response
by
comparing
ground
motion
spectra
in
three
period
bands
(total
period
band
is
from
0.2
to
10
seconds)
relative
to
the
thickness
and
the
physical
properties
of
the
earth
materials
which
lie
beneath
the
instrument
sites.
A
set
of
three-component
recordings
of
Nevada
Test
Site
nuclear
tests
and
a
compilation
of
geologic
attributes
at
each
site
comprise
the
set
of
basic
data
employed
in
the
analysis.
A
suite
of
site
types
(clusters)
is
defined
statistically
in
terms
of
common
geologic
attributes.
The
attributes
defining
each
cluster
are
those
attributes
that
most
strongly
correlate
with,
or
influence,
site
response
in
a
given
period
band.
Maps
showing
the
distribution
of
these
geologic
attributes
are
prepared
as
overlays
and
are
used
to
construct
derivative
maps
which,
in
turn,
depict
relative
site
response
for
part
of
the
Los
Angeles
area.
Future
research
is
desirable,
both
to
explore
further
the
methodology
and
to
test
the
predictions
of
the
model
compared
to
patterns
of
damage
caused
by
historical
earthquakes,
as
well
as
applying
the
technique
to
basins
other
than
the
Los
Angeles
region.
The
principal
goal
of
these
and
related
studies
is
to
develop
microzonation
technology
so
that
sites
which
are
especially
at
risk
can
be
identified
and
appropriate
measures
can
be
adopted
to
reduce
significantly
losses
of
life
and
property.
VARIABLE
GROUND
RESPONSE
IN
THE
LOS
ANGELES
REGION
Local
geologic
conditions
long
have
been
recognized
as
a
significant
factor
influencing
ground
shaking
(Kanai,
1952;
Gutenberg,
1957;
Medvedev,
1962),
although
the
quantitative
prediction
of
site
effects
using
either
empirical
or
theoretical
models
is
still
developmental.
We
have
extended
to
the
Los
Angeles
area
the
technique
developed
by
Borcherdt
and
Gibbs
(1976),
recasting
the
technique
to
include
the
effects
of
near-surface
site
properties
and
geologic
structure.
To
determine
relations
among
local
geologic
factors
and
site
response,
19
nuclear
explosions
were
recorded
at
98
sites
throughout
the
Los
Angeles
region
(Rogers
and
others,
1980).
Sites
were
selected
to
obtain
as
complete
a
sample
of
underlying
geologic
conditions
and
as
broad
a
geographic
coverage
as
possible.
The
seismic
source
(Nevada
Test
Site)
lies
some
400
to
450
km
from
the
recording
sites;
effects
of
azimuthal
variations
in
the
radiated
energy
are
similar
for
all
sites.
Each
site's
response
characteristics
over
the
period
band
0.2
to
10
seconds
was
345
estimated
by
computing
Fourier
spectra
and
alluvium-to-crystalline
rock
spectral
ratios
(Rogers
and
others,
1980).
The
site
CIT,
underlain
by
crystalline
rock,
was
instrumented
for
every
nuclear
explosion
and
was
the
rock
site
against
which
recordings
measured
at
all
other
sites
were
compared
(see
figure
I
A).
Distant
nuclear
explosions
generate
ground
motion
records
in
which
the
effects
of
site
conditions
are
readily
apparent.
Figure
I
A
shows
time
histories
recorded
simultaneously
at
eight
sites
from
a
single
Nevada
Test
Site
nuclear
explosion.
This
example
illustrates
several
effects
of
local
site
conditions
that
are
observed
commonly
in
recorded
time
histories
when
the
source
of
shaking
is
distant.
Maximum
amplitudes
of
motion
recorded
on
the
alluvial
sites
are
several
times
larger
than
those
recorded
on
the
sedimentary
and
crystalline
rock
sites.
The
degree
of
amplification
occurring
in
the
long-period
peak
amplitudes
visible
in
these
records
is
greatest
at
sites
underlain
by
the
thickest
sediments
(HOI:
300
m;
MIL:
370
m;
ATH:
370
m;
GMB:120
m;
FS4:
15
m).
The
amplitude
spectral
ratios
computed
for
the
simultaneous
recordings
shown
in
figure
1
A
are
presented
in
figure
IB.
These
ratios
show
that
the
effects
of
site
conditions
relative
to
those
at
CIT
are
strongly
frequency
dependent,
and
amplification
occurs
for
many
of
the
sites
over
most
of
the
frequency
band
for
which
the
signal-to-noise
ratio
is
favorable
(Rogers
and
others,
1980).
Amplification
factors
of
the
horizontal
component
of
ground
motions
range
from
2
to
7
at
frequencies
less
than
I
Hz
for
those
sites
on
thick
sections
of
alluvium;
lower
amplification
factors
are
found
at
these
frequencies
for
the
site
FS4
underlain
by
a
thin
alluvial
section.
Considerable
amplification
at
intermediate
frequencies
(1-2
Hz)
and
at
higher
frequencies
(2-5
Hz)
occurs
at
several
sites,
notably
FS4,
where
a
prominent
ground
resonant
frequency
is
observed.
Resonance
is
not
apparent
for
thick
alluvial
sites
(spectra
are
relatively
flat
across
the
entire
observed
frequency
range).
Spectral
ratios
at
site
GOC
suggest
that
the
response
of
the
two
crystalline
rock
sites
(GOC,
CIT)
is
similar
at
lower
frequencies,
but
at
intermediate
and
high
frequencies,
ground
motions
at
GOC
are
higher
than
at
CIT.
Relative
to
CIT,
site
3838,
located
on
sedimentary
rock,
shows
a
uniformly
greater
response
than
GOC,
but
a
lesser
response
than
the
sites
underlain
by
thick
alluvial
sections.
COMPARISON
OF
GEOLOGIC
FACTORS
AND
GROUND
RESPONSE
Geologic
parameters
were
chosen
to
characterize
the
recording
sites
because
either
the
parameters
have
some
direct
application
in
a
theoretical
model
of
site
response
or,
in
past
studies,
the
parameters
have
been
reported
to
have
some
influence
on
ground
shaking.
Parameters
such
as
percent
(silt+clay)
and
depth
to
water
table
have
been
reported
to
influence
site
response,
whereas
shear-wave
velocity
(or
void
ratio,
which
strongly
influences
the
shear
modulus),
thickness
of
Holocene
deposits,
thickness
of
Quaternary
deposits,
and
depth
to
crystalline
basement
rocks
are
parameters
that
might
be
used
directly
to
model
site
response.
Most
of
these
data
are
available
in
the
literature
or
are
obtainable
from
published
geologic
maps,
records
of
water
wells,
and
geotechnical
studies
conducted
for
engineering
purposes;
these
data
are
of
especially
great
value
if
they
can
also
be
used
to
estimate
site
response
in
some
quantitative
manner.
346
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rl
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v1.
4.0
5.0
0.0
1.0
2.0
3.0
10
5.0
MIL
ATH
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1.0
2.0
3.0
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10
SEDIMENTARY
ROCK/CRYSTALLINE
ROCK
-
8.
R
FS4
ALLUVIUM
HO
I
ALLUVIUM/CRYSTALLINE
ROCK
cn
0.03
Id
U
-0.031
0
3838
SEDIMENTARY
ROCK
GOC
CRYSTALLINE
ROCK
CIT
0
100
260
300
SECONDS
0.0
1.0
2.0
3.0
4.0
S.0
CRYSTALLINE
ROCK/CRYSTALLINE
ROCK
3
R
0
d
0.0
1.0
10
10
4.0
s.o
FREQUENCY
(HZ)
Figure
1A.
Radial
component
time
histories
recorded
simultaneously
at
8
sites,
grouped
according
to
the
type
of
geologic
materials
immediately
beneath
each
recording
station.
Figure
113.
Spectral
ratios
of
the
radial
components
of
ground
motion
shown
in
figure
1A,
relative
to
station
CIT,
a
crystalline
rock
site.
We
examined
the
relation
between
site
response
and
the
geologic
parameters
by
grouping
the
sites
according
to
variations
in
one
of
the
geologic
factors
and
then
computing
mean
response
for
each
group.
The
following
ground
response
characteristics
emerged:
o
Sites
underlain
by
Holocene
and
Pleistocene
sediments
undergo
levels
of
shaking
2.6
to
3.4
times
greater
than
those
sites
underlain
by
crystalline
rocks,
for
all
period
bands,
o
The
void
ratio
of
near-surface
deposits
has
a
strong
influence
on
short-period
response,
with
void
ratios
in
the
0.8-0.9
range
indicating
a
mean
response
on
soil
six
times
greater
than
on
crystalline
rock
and
three
times
greater
than
on
low-void-ratio
soils,
and
o
Amplitudes
in
the
long-period
band
(3-10
seconds)
generally
increase
with
increasing
thickness
of
Quaternary
deposits
and/or
depth
to
crystalline
base-
ment
rocks.
Additional
detailed
studies
of
the
influence
of
all
geologic
parameters
were
conducted
using
data
analysis
and
regression
techniques
(Mosteller
and
Tukey,
1977).
These
studies
indicate
,that
the
most
pronounced
changes
in
site
response
were
correlated
with
changes
in
void
ratio,
thickness
of
Holocene
deposits,
depth
to
crystalline
basement
rocks,
and
thickness
of
Quaternary
deposits.
CLUSTERING
OF
SITES
BY
GEOLOGIC
ATTRIBUTES
TO
REFLECT
VARIABILITY
IN
SHAKING
RESPONSE
Sites
that
have
similar
response
characteristics
can
be
clustered
(grouped)
by
computing
an
analytical
measure
of
similarity
among
a
list
of
items
based
on
their
attributes.
In
our
analysis,
the
items
are
the
recording
sites
and
the
attributes
are
the
geologic
properties
of
each
site.
We
cannot
use
the
response
factor
(amplification
factor)
as
an
attribute,
because
we
are
attempting
to
predict
response
as
a
function
of
the
geologic
properties
of
the
site.
The
clustering
algorithm
(IMSL,
1
982)
is
used
to
establish
a
hierarchy
showing
which
items
are
most
nearly
alike,
and
also
show
the
level
within
the
hierarchy
at
which
clusters
of
similar
items
are
most
alike.
Once
this
procedure
is
used
to
form
clusters
based
on
any
chosen
set
of
factors,
discriminate
analysis
(Nie
and
others,
1975)
is
used
to
determine
the
degree
to
which
these
factors
define
unique
clusters;
the
significance
of
each
factor's
discriminating
power
is
computed
based
on
the
statistical
relations
among
factors
within
and
between
the
respective
clusters.
One
can
calculate
the
probability
that
any
single
member
of
a
cluster
belongs
to
that
cluster
or
to
any
other
cluster;
based
on
these
probabilities,
the
percentage
of
sites
that
have
been
correctly
classified
can
be
calculated.
In
our
study,
the
cluster
sets
that
were
selected
were
those
having
the
lowest
dispersion
in
the
defining
variables
while
incorporating
only
those
factors
having
the
most
pronounced
effect
in
a
given
348
period
band.
The
final
sets
of
clusters
are
a
compromise
between
the
many
clusters
required
to
preserve
the
complexity
in
site
response
as
a
function
of
geology,
and
the
requirement
that
each
cluster
contain
enough
cases
to
impart
statistical
validity
to
the
estimate
of
the
average
response
for
the
cluster.
Two
clusters
for
rock
sites
and
eight
clusters
for
alluvial
sites
were
derived
for
the
short-period
band
(0.2-0.5
sec)
and
the
respective
attributes
of
each
cluster
are
shown
in
figure
2.
To
understand
figure
2,
an
example
may
be
helpful.
Cluster
4A
includes
sites
that
have
a
depth
to
crystalline
basement
rocks
of
greater
than
0.5
km,
a
thickness
of
Holocene
deposits
that
is
greater
than
20
m,
void
ratios
in
the
range
of
0.6-0.7,
and
a
geometric
mean
response
of
about
3.6,
relative
to
crystalline
rock
sites.
Moreover,
if
an
attribute
such
as
Holocene
thickness
is
held
fixed,
response
increases
as
void
ratio
increases
(compare
clusters
I
A,
3A,
and
6A).
Response
also
increases,
for
a
constant
void
ratio,
as
the
thickness
of
Holocene
deposits
increases
and
passes
through
a
critical
range
(compare
clusters
6A,
7A,
and
8A).
Not
surprisingly,
rock
sites
IR
and
2R
indicate
a
geometric
mean
response
that
typically
is
less
than
that
of
the
clusters
of
alluvial
sites.
A
comparison
of
clusters
I
A
and
2A
shows
that
sites
underlain
by
shallow
alluvium
over
crystalline
rock
(2A)
have
a
response
two
times
higher
than
does
the
same
type
of
site
overlying
a
deep
sedimentary
basin,
a
relation
that
emphasized
the
importance
of
a
high
impedance
contrast
at
shallow
depths
as
a
factor
in
ground
response.
Although
we
have
identified
10
clusters,
with
a
moderate
range
in
the
geologic
and
response
factors
in
each
cluster,
it
is
useful
to
compare
average
spectral
level
with
shaking
intensity.
From
Borcherdt
and
others
(1975),
if
we
adopt
the
reasonable
assumption
that
a
factor
of
two
in
mean
spectral
level
corresponds
to
a
change
of
one
Modified
Mercalli
Intensity
unit,
then
from
the
data
in
figure
2,
we
can
infer
that
the
10
clusters
predict
the
true
site-response
more
closely
than
one
intensity
unit
increment
for
90
percent
of
the
cases
(the
geometric
90
percent
confidence
interval
(1.45)
is
less
than
a
factor
of
two).
Clusters
also
were
derived
for
intermediate-
and
long-period
bands
on
the
basis
of
Quaternary
thickness
and
depth
to
crystalline
basement
rock
(Rogers
and
others,
1985),
but
these
clusters
will
not
be
discussed
here.
Map
Showing
Predicted
Site
Response
for
a
Portion
of
the
Los
Angeles
Region
The
response
maps
for
the
intermediate-
and
short-period
bands
for
a
small
area
centered
in
the
Los
Angeles
Civic
Center
are
shown
in
figures
3A
and
3B.
These
figures
are
based
on
the
clusters
just
discussed
and
on
a
set
of
maps
delineating
the
geographic
distribution
of
the
important
geotechnical
attributes
of
each
cluster.
The
intermediate-period
map
(figure
3A),
of
significance
to
structures
between
five
and
30
stories
high,
predicts
that
low
response
will
characterize
areas
underlain
by
rock
and
thickness
of
alluvium
of
less
than
about
150
m;
intermediate
levels
of
response
will
occur
in
areas
where
the
thickness
of
alluvium
is
greater
than
150
m
and/or
where
the
depth
to
crystalline
basement
rock
ranges
between
0.15
and
4
km;
highest
levels
of
response
will
be
observed
in
areas
where
depth
to
basement
rocks
ranges
from
4
to
6
km.
Slightly
lower
levels
of
response
are
predicted
in
the
deepest
parts
of
the
Los
Angeles
basin.
Lowest
levels
of
response
349
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ALLUVIUM
SITE
RESPONSE
CLUSTER
NUMBERS
Figure
2.
Site
clusters
for
short-period
ground
motions
in
the
Los
Angeles
region.
Solid
dots
indicate
the
mean
of
the
short-period
spectral
ratios
for
a
given
cluster,
mean
void
ratio,
Holocene
deposit
thickness,
and
depth
to
crystalline
basement
rock
groups,
as
appropriate.
Vertical
bars
indicate
the
range
in
the
variable
for
a
given
cluster,
and
side
ticks
indicate
the
90%
confidence
intervals.
350
118
°
15'
118
°
15'
OUSOANN
1.1
2.1
3.6
LI
3.6
I
11
""..
0
2.1
2.1
45
LT
2.
.1
4.4
1.8
2.
14
1
8
a
3.6
ALT
2.1
4.5
1.3
2.1
tog
VIC
woo
0
1.03
ANGELES
CIVIC
CENTER
2
0
3.6
2
.
4
1
3.
1.8
2.1
t.
3.8
3
3
.
8
S.
S
34
°
8
.5
1
5.1
3.6
3.6
4.
8
55
0
2
3A
'
KM
j
i
s
WS
ANGELES
RIVER
118
°
15'
118
°
15'
Figures
3A
and
3B.
Maps
showing
prediCted
relative
shaking
response
for
part
of
the
Los
Angeles
Basin.
Numbers
are
mean
amplification
factors,
com-
paring
levels
of
shaking
to
sites
on
crystalline
basement
rock.
Fig.
3A
is
a
map
for
intermediate
periods
(0.5-3.3
sec).
Stippling
outlines
area
of
Figure
3B.
Fig.
3B
is
the
map
for
short-periods
(0.2-0.5
seconds).
are
predicted
in
the
areas
where
crystalline
basement
is
at
or
near
the
surface
in
the
Santa
Monica
Mountains
and
the
Verdugo
Mountains.
The
short-period
map,
which
is
most
relevant
for
buildings
in
the
two-
to
five-story
class,
has
been
prepared
for
the
central
third
of
the
area
shown
in
the
long-period
map.
The
lowest
response
is
predicted
for
areas
underlain
by
crystalline
and
sedimentary
rock,
and
the
highest
response
will
be
observed
in
regions
where
thickness
of
near-surface
alluvium
(range
I I
to
20
m)
and
high
void
ratio
(exceeding
0.7)
produces
significant
resonant
response
in
this
period
band.
This
map
rather
closely
approximates
a
surficial
geologic
map:
details
of
alluvial
valleys,
including
that
of
the
Los
Angeles
River,
are
delineated.
The
southwest
part
of
the
map
depicts
an
area
where
silty
deposits
(characterized
by
high
void
ratios)
comprising
parts
of
the
recent
floodplain
of
the
Los
Angeles
River
are
widespread
in
the
section
and
wedge
out
against
the
east
flank
of
the
Newport-
Inglewood
zone
of
deformation.
There,
Pleistocene
deposits
characterized
by
low
void
ratios
are
exposed.
We
note
that
high
levels
of
short-period
response
may
occur
at
rock
sites
if
these
sites
are
located
near
the
crest
of
a
ridge
or
other
pronounced
topographic
convexity,
as
shown
by
the
range
of
high
response
for
clusters
I
R
and
2R
(figure
3).
AVENUES
FOR
FUTURE
RESEARCH
.We
anticipate
that
several
avenues
of
inquiry
seem
to
be
especially
important
in
analyzing
the
overall
significance
of
the
empirical
approach
used
in
our
analysis
of
ground
response
in
the
Los
Angeles
region.
In
particular,
testing
of
the
methodology
is
essential,
and
an
experiment
that
will
be
conducted
in
the
near
future
will
use
data
obtained
following
the
March,
1985
Chilean
earthquake.
Digital
recordings
of
aftershocks
were
made
there
at
a
suite
of
sites
that
are
underlain
by
a
wide
variety
of
earth
materials
and
geologic
site
conditions,
in
zones
of
high,
intermediate,
and
low
main-shock
intensities,
and
at
strong-motion
main
shock
recording
sites.
The
testing
could
proceed
along
several
lines:
o
What
is
the
correlation
between
the
change
in
Modified
Mercalli
Intensity
level
and
aftershock
(low
strain)
alluvium-to-rock
mean
spectral
ratios?
Preliminary
results
indicate
a
strong
correlation
exists
between
intensity
change
and
the
short-period
(0.2-0.5
second)
mean
spectral
ratios
in
the
Santiago,
Chile,
area
(Algermissen,
1985).
o
How
well
do
the
short-period
site
clusters
derived
for
the
Los
Angeles
region
(Rogers
and
others,
1985)
predict
geographic
changes
in
intensity
observed
in
Santiago,
Chile?
A
strong
correlation
would
demon-
strate
a
broader
applicability
of
the
technique.
o
Comparison
of
the
mean
site-response
spectral
values
observed
during
the
main
shock
and
aftershocks
in
the
Chilean
earthquake
wou
d
help
support
the
validity
of
the
numerical
values
of
relative
ground
shaking
predictions
for
strong
motion
conditions.
352
In
our
view,
the
methodology
should
also
be
expanded,
both
in
an
applied
sphere
and
in
a
research
sphere.
We
would
apply
the
technique
to
a
broader
geographic
region
of
the
Los
Angeles
area;
mapping
of
predicted
ground
response
according
to
the
clusters
derived
for
the
Los
Angeles
area
but
involving
parts
of
the
San
Fernando
Valley
is
in
progress.
Depending
on
the
success
of
this
endeavor,
continuation
of
the
work
in
other
basins
of
southern
California
may
be
advisable.
In
the
research
sphere,
we
must
collect
additional
data
to
permit
improved
estimates
of
the
mean
values
and
standard
deviations
for
the
respective
clusters
and
add
new
clusters
and
perhaps
redefine
or
regroup
components
of
the
existing
clusters
as
necessary
using
new
data
from
many
regions.
Further
evaluation
of
the
effects
of
site
response
relative
to
peak
acceleration,
velocity,
and
displacement
parameters
is
needed,
in
order
to
translate
the
results
of
the
study
in
terms
which
are
more
directly
useful
in
engineering
practice.
The
results
could
also
be
cast
in
terms
of
modifications
to
design
spectra.
Microzonation
maps
should
have
potential
applications
for
land-use
planning
purposes,
where
it
may
be
desirable
to
avoid
the
siting
of
critical
facilities
and
lifelines
in
zones
of
predicted
high
levels
of
shaking
and
siting
of
high-rise
structures
in
zones
of
long-period
intense
shaking.
In
the
latter
case,
it
is
particularly
important
to
avoid
the
siting
of
high-rise
structures
having
resonant
period
equal
to
or
nearly
equal
to
that
of
the
predominant
period
of
ground
shaking
of
the
site,
as
demonstrated
by
the
1985
Mexico
earthquake
and
building
damage
to
high-rise
structures
in
Mexico
City.
Where
avoidance
cannot
be
accomplished,
special
consideration
(at
least
for
critical
structures)
should
be
given
to
the
design
of
these
facilities
when
they
are
sited
in
zones
of
predicted
high
shaking
intensity.
For
instance,
it
is
possible
to
use
design
spectra
that
account
for
site
conditions;
or
modify
the
design
of
buildings
in
order
that
the
predominant
period
of
the
building
does
not
coincide
with
the
predominant
period
of
ground
shaking.
Microzonation
maps
have
been
and
will
continue
to
be
important
to
studies
of
earthquake
losses.
Accurate
estimates
of
future
losses
depend
heavily
on
understanding
the
geographic
variation
in
ground
shaking.
In
turn,
such
studies
are
important
elements
of
emergency
preparedness
and
response.
In
summary,
application
of
ground
shaking
microzonation
techniques
to
determine
the
nature
of
any
increased
risk
owing
to
geologic
site
conditions
should,
over
the
long
term,
help
to
significantly
reduce
losses
of
life
and
property
that
stem
from
collapse
of
and
structural
damage
to
buildings.
353
REFERENCES
Algermissen,
S.T.,
1985,
Preliminary
report
of
investigation
of
the
central
Chile
earthquake
of
March
3,
1985:
U.S.
Geological
Survey
Open-File
Report
85-542,
180
p.
Borcherdt,
R.D.,
Joyner,
W.B.,
Warrick,
R.E.,
and
Gibbs,
J.F.,
1975,
Response
of
local
geologic
units
to
ground
shaking,
in
Borcherdt,
R.D.
(ed),
Studies
for
seismic
zonation
of
the
San
Francisco
Bay
region:
U.S.
Geological
Survey
Professional
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941-A,
p.
52-67.
Borcherdt,
R.D.,
and
Gibbs,
J.F.,
1976,
Effects
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geologic
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in
the
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Francisco
Bay
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v.
66,
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1957,
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1982,
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1952,
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of
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v.
30,
pt.
I,
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J.V.,
1962,
Engineering
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1965,
260
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'
Mosteller,
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R.D.,
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Perkins,
D.M.,
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354