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237
Bulletin of the Seismological Society of America, Vol. 96, No. 1, pp. 237–257, February 2006, doi: 10.1785/0120050052
The Observed Wander of the Natural Frequencies in a Structure
by John F. Clinton, S. Case Bradford, Thomas H. Heaton, and Javier Favela
Abstract
The Southern California Seismic Network (
SCSN
) has recently installed
seismic stations in two buildings on the Caltech campus (Millikan Library and the
Broad Center). Continuous real-time accelerometer data from these structures are
now freely available to the community. This dataset provides a new opportunity to
observe, and better understand, the variances in the primary dynamic property of a
building system, its natural frequencies. Historical data (triggered strong-motion re-
cords, ambient and forced vibration tests) from the well-studied Millikan Library
show dramatic decreases in natural frequencies, attributed mainly to moderately large
local earthquakes. The current forced vibration east–west fundamental frequency is
22% lower than that originally measured in 1968. Analysis of the new continuous
data stream allows the examination of other previously unrecognized sources of
measurable change in the fundamental frequencies, such as weather (wind, rain, and
temperature), as well as nonlinear building vibrations from small local and moderate
regional earthquakes. Understanding these nonlinear shifts is one of the long-term
goals of real-time building instrumentation and is critical if these systems are to be
used as a postearthquake damage assessment tool.
Introduction
The past few years have seen a proliferation of real-time
structural monitoring testbeds. Analysis of the resulting data
is leading toward a better understanding of building re-
sponse. It is well known that natural frequencies of a soil-
structural system have nonlinear variations under different
levels of excitation (Kuroiwa, 1967; Foutch, 1976; Luco
et
al.
, 1986), and current research at the California Institute of
Technology (Caltech) into ambient, forced (Bradford
et al.
,
2004), and earthquake vibration analysis of large concrete
buildings, concrete dams (Alves and Hall, 2003), and wood-
frame buildings (Camelo, 2003) indicates that during small
shaking events, there is a measurable change in recorded
natural frequencies of all these types of structures. In the
case of wood-frame structures, natural frequencies may be
reduced by a factor of two during stronger shaking, even
without identifiable structural damage (Camelo, 2003). This
nonlinear structural softening is not well characterized or
understood and needs to be accounted for if real-time build-
ing monitoring is to be used effectively as a postearthquake
damage assessment tool.
This article attempts to document the amount of fre-
quency shifting in the instrumented large structures at the
Caltech campus, the Robert A. Millikan Library, and the
Broad Center. The current state of instrumentation on cam-
pus is described, and the observed changes in fundamental
frequencies are correlated with weather, earthquake history,
and building usage.
The temporal wandering of the natural frequencies of the
Millikan Library has been documented previously (Kuroiwa,
1967; Trifunac, 1972; Udwadia and Trifunac, 1974; Foutch,
1976; Luco
et al.
, 1987; Chopra, 1995). Since its construction
in 1967, a decrease in these resonant frequencies may be ob-
served from yearly forced vibration experiments and from
strong-motion records. This frequency drop has been inter-
preted to be due to a corresponding softening in system stiff-
ness. Recent ambient and forced vibration tests indicate that
the fundamental natural frequency of the structure is now ap-
proximately 22% lower in the east–west direction and 12%
lower in the north–south direction than was determined
shortly after construction (Kuroiwa, 1967). Strong-motion re-
cords indicate that the natural frequencies drop even further
during moderately large events. The
M
6.1 Whittier Narrows
Earthquake, with a epicentral location 19 km from the library,
is one example. By comparing the forced vibration measure-
ments prior to the event (Levine
et al.
, 1988) with the coda
of the strong-motion records, the building’s east–west and
north–south natural frequencies are shown to decrease by
17% and 25%, respectively. The structure recovers stiffness
somewhat after a moderately large shaking event, but because
of the lack of data in the immediate aftermath of these main-
shocks, the recovery time frame cannot be constrained. Fur-
ther, Kuroiwa (1967) and others noted that the resonant fre-
quencies drop measurably when the applied force during
forced vibrations is increased—during construction in 1966
the fundamental east–west frequency dropped 3% when ap-
plied force was increased by a factor of 8.
238
J. F. Clinton, S. C. Bradford, T. H. Heaton, and J. Favela
Recent improvements in the quality and quantity of in-
strumentation in the building and at other sites on the Caltech
campus have led to renewed investigation of the structure.
Analysis of structural response to previously unrecorded am-
bient and small-intensity ground motions is now possible.
Data are presented which indicate that not only do the
natural frequencies change significantly during strong shak-
ing, as evidenced by analog recordings of large earthquakes
in the recent past, but there are also measurable changes in
the resonant frequencies of the buildings due to:
forced vibrations using varying forces
minor earthquake shaking
weather conditions (rain and wind events, extremes in tem-
perature)
These last two factors also affect the recently con-
structed Broad Center on the Caltech campus (the Broad
Center has not yet been shaken or subjected to strong earth-
quake motions).
The lowering of the natural frequencies during transient
events in the Millikan Library is likely due to a combination
of two mechanisms, a nonlinear softening of the superstruc-
ture itself and an interaction of the structure with the
surrounding soil. Changes in occupancy usage are also re-
sponsible for natural frequency changes. Note that the con-
struction of partition walls for office space in three entire
levels during the spring of 2003 coincides with a significant
and permanent raising of the natural frequencies (though the
magnitude of the change in frequency is difficult to explain
considering the relatively small increase in stiffness ex-
pected by the addition of the partition walls).
The natural frequency of a structure, as measured by
accelerometers on the structure, is a combination of the fun-
damental fixed-base period of the structure, as well as the
rocking and horizontal translation frequencies of the same
structure if it moved as a rigid body on the flexible soil
(Trifunac, 1999; Trifunac and Ivanovic, 2003). Throughout
this article, all references to the natural frequencies of the
structure refer to these combined-system frequencies. Note
also that, in addition to the differences in amplitude, forced
vibration tests differ from ambient and earthquake motions
in how energy is imparted to the system. For forced vibration
tests, the energy source located on the roof (the shaker) emits
a continuous single frequency, and energy flows down the
building and out into the half-space. In ambient and earth-
quake vibrations, scattered energy with highly variable fre-
quency content enters the building from the bottom, travels
to the roof, reflects back down, and eventually dissipates into
the half-space.
Historical Evidence for Natural Frequency
Wandering—Millikan Library
The Robert A. Millikan Library is located at the center
of campus at the California Institute of Technology (see Fig.
1a). It is a nine-story reinforced concrete building with a
basement and an enclosed roof (housing air-conditioning
equipment), which was completed in 1967. The library is
21.0 m by 22.9 m in plan, and it extends 43.9 m above grade
and 48.2 m above basement level. Interstory heights are all
4.27 m, except for the height between the first and second
floors, which is 4.88 m. The roof wall is also 4.88 m. The
structural system consists of a moment frame combined with
large stiff reinforced concrete shear walls (30.5 cm thick) on
the east and west sides of the building. These shear walls
provide the predominant resistance to lateral forces in the
north–south direction. A 30.5-cm-thick reinforced concrete
inner core adds stiffness to the building, which along with
the concrete moment frame and the bolted precast concrete
window/wall panels, provides the lateral stiffness in the
east–west direction. The foundation system is composed of
a central pad 9.75 m wide by 1.2 m deep, which extends
across the building to the shear walls on the east and west
sides. Two foundation beams (2.74 m wide by 0.61 m deep)
run parallel to the central pad under the north and south wall,
respectively. A series of stepped beams transfer loads from
these foundation beams to the central pad. More detailed
descriptions of the structural system may be found in Ku-
roiwa (1967), Foutch
et al.
(1975), Foutch (1976), and Luco
et al.
(1986). The alluvium under the foundation consists of
medium to dense sands mixed with gravels, and bedrock lies
at a depth of about 275 m. The water table appears to be at
about 11 m depth (Kuroiwa, 1967; Luco
et al.
, 1987). Fig-
ures 1b and 1c show a north–south cross section and a typical
floor plan.
After the 1971 San Fernando Earthquake, cracking and
spalling of the concrete slabs located on the ground floor
entry plaza were noted (Foutch and Jennings, 1978). Further,
horizontal cracks along the pour line in the core shear walls
between both the basement and first floor, and first and sec-
ond floors, have been observed in the emergency staircase
in the north–south direction. Access to the east–west sides
of the core shear wall is not possible. The steam tunnels that
connect various buildings on campus also suffered some mi-
nor cracking close to the Library. No further structural dam-
age has been observed in the building.
In 1968, the building was instrumented with two per-
manent triaxial Teledyne-Geotech RFT-250 accelerometers,
located on the roof and basement. A 10-channel Kinemetrics
CR-1 strong-motion array was also installed in 1979, with
channels on the basement, sixth floor, and roof. These sys-
tems have since been superseded by a 24-bit continuously
recorded digital triaxial accelerometer, the
SCSN
station
MIK
(installed in 2001), on the ninth floor, and a 36-channel 19-
bit triggered-accelerometer array run by the U.S. Geological
Survey (
USGS
) (installed in 1998), with a minimum of three
channels on each floor. A synchronized shaker was perma-
nently installed on the roof of the building in the early 1970s
and is still used for forced vibration testing (Hudson, 1962).
Yearly modal analysis of the structure (using temporary
deployments of Kinemetrics Ranger SS-1 seismometers)
The Observed Wander of the Natural Frequencies in a Structure
239
Table 1
Natural Frequencies and Peak Roof Accelerations from Selected Strong-Motion Data and Forced Vibration Experiments*
East–West
North–South
Event/Test
Nat. Freq.
(Hz)
%diff1
%diff2
mx accn
(cm/sec
2
)
Nat. Freq.
(Hz)
%diff1
%diff2
mx accn
(cm/sec
2
)
Forced vibrations, 1967
1.45
1.90
Lytle Creek, 1970, M 6.3,
D

57 km
1.30
10.3
10.3
49
1.88
1.1
1.1
34
San Fernando, 1971, M 6.6,
D

31 km
1.0
31.0
31.0
306
1.64
13.7
13.7
341
Forced vibrations, 1974
1.21
16.6
16.6
1.77
6.8
6.8
Whittier Narrows, 1987, M 6.1,
D

19 km
1.00
31.0
17.4
262
1.33
30.0
24.9
534
Forced vibrations, 1988
1.18
18.6
2.5
1.70
10.5
4.0
Sierra Madre, 1991, M 5.8,
D

18 km
0.92
36.6
22.0
246
1.39
26.8
18.2
351
Forced vibrations, 1993
1.17
19.3
0.8
1.69
11.1
0.6
Northridge, 1994, M 6.7,
D

34 km
0.94
35.2
19.7
143
1.33
30.0
21.3
512
Forced vibrations, 1994
1.15
20.6
1.7
1.67
12.1
1.2
Forced vibrations, 1995
1.15
20.6
0.0
1.68
11.6

0.6
Beverly Hills, 2001, M 4.2,
D

26 km
1.16
20.0

0.9
9.3
1.68
11.6
0.0
11.8
Forced vibrations, 2002, full weights
1.11
23.4
3.5
3.6
1.64
13.7
2.4
8.0
Forced vibrations, 2002, half weights
1.14
21.4
0.9
1.9
1.67
12.1
0.6
4.1
Big Bear, 2003, M 5.4,
D

119 km
1.07
26.2
6.1
14.2
1.61
15.3
3.6
22.6
Continuous data average, May 2001–Nov. 2003
1.19
1.72
San Simeon, 2003, M 6.5,
D

323 km
1.14
21.4
0.0
20.4
1.54
18.9
7.8
14.3
*% diff1 is the difference between the recorded frequency and that obtained in the first forced vibration tests (Kuroiwa, 1967); % diff2 is the differen
ce
between the recorded frequency and that obtained in the most recent forced vibration test prior to the event; Nat. Freq. is natural frequency; mx accn i
s
maximum acceleration. A complete history is presented in Clinton (2004). Note the 1967 entry is representative of the results from all tests from 1967
up
to the 1970 Lytle Creek Earthquake; the building was already fully loaded with books.
Figure
1.
Millikan Library. (a) View from the northeast. The two dark walls in the
foreground comprise the 30.5-cm-thick east shear wall, which is somewhat narrower
on the ground floor because of walkway openings. The wall panels and concrete mo-
ment frame are visible on the north face. (b) North–south section. Walkway openings
on the ground floor, which cut through the shear walls, are represented by crosses.
(c) Typical plan view. The dark circle is the approximate position of
SCSN
Station
MIK
on the ninth floor, the arrows are the approximate positions and orientations of the
three
USGS
channels on each floor (from first floor to roof).
during civil engineering classes at Caltech, as well as the
triggered event data from the RFT-250 and CR-1 arrays,
have provided us with a relatively detailed history of the
evolution of the dynamic properties of the building. A sum-
mary of the fundamental natural frequencies observed dur-
ing strong shaking and selected forced vibration tests is pre-
sented in Table 1 (a more complete list is in Clinton, 2004).
Figures 2 and 3 present graphical interpretations of Table 1.
In Figure 2, the natural frequencies are plotted against the
date of the observation. There is a clear trend toward lower
natural frequencies as time increases, with major steps oc-
curring during large earthquakes. Figure 3 plots frequency
versus the coincident roof acceleration amplitude, on loga-
rithmic axes. There is a clear pattern of frequency dropping
240
J. F. Clinton, S. C. Bradford, T. H. Heaton, and J. Favela
Figure
2.
Graphical interpretation of Table
1. Dashed lines are east–west natural frequen-
cies, dashed-dotted lines are north–south-
natural frequencies, all from forced vibration
testing. Shaded area is the likely region of nat-
ural frequencies taking into consideration er-
rors in measurement, caused by unknown
shaker weight configuration and weather con-
ditions for each test, and experimental error.
Crosses indicate the actual time of a forced vi-
bration measurement. Circles indicate the nat-
ural frequency estimated from the strong-
motion recording of the event, with the number
in italics giving the peak acceleration recorded
for the event (cm/sec
2
).
Figure
3.
Graphical interpretation of Table
1—peak rooftop acceleration (accn) amplitude
versus frequency, log scaling. For both east–
west and north–south, the best-fitting least-
squares solution for all the data is plotted in
dashed lines. Outlying data from tests and
earthquakes prior to main permanent natural
frequency shift (pre-Whittier Narrows for
north–south; pre-San Fernando for east–west)
are removed from dataset for the solid-line re-
gressions, with labeled functional form.
with increasing excitation amplitude. The best-fitting line is
a good fit to the data, though a very large variance still exists.
Kuroiwa (1967) first observed variation in the natural
frequencies, measuring a decrease in natural frequencies
proportional to the applied force imparted by the shaker.
This has been consistently observed since then. For example,
in the tests carried out in July 2002 by Bradford
et al.
(2004),
during shaking with full weights, an east–west natural fre-
quency of 1.11 Hz was measured, and during shaking with
only four side weights, the natural frequency was 1.14 Hz—
a difference of 0.03 Hz or 2.5%. This change in weights
corresponds to a factor of nearly 2 difference in the ampli-
tude of the rooftop sinusoidal acceleration, and a factor of
2.23 change in the applied force. Similar changes were ob-
served in the north–south fundamental frequency. Thus, with
weight configurations variable in some of the forced tests
(and unknown in some cases), this level of variability in
reporting of results should be noted. It is assumed that the
forced vibration test results in Table 1 are taken with the
shaker loaded with half-full weights. The shaded area in Fig-
ure2isa

0.03 Hz error band for the natural frequencies,
which reflects both this loading uncertainty and temporal
The Observed Wander of the Natural Frequencies in a Structure
241
fluctuations caused by the changing weather conditions, as
discussed in this article.
The natural frequencies from strong shaking are deter-
mined from the resonance of the structure (measured at the
roof channels) in the immediate aftermath of a large event.
This is illustrated in Figure 4, which shows the response of
the east–west channels of the CR-1 array at Millikan to the
1987
M
6.1 Whittier Narrows Mainshock (Levine
et al.
,
1988).
Table 1 shows the initial natural frequencies of the
building at 1.45 Hz in the east–west direction and at 1.90 Hz
in the north–south direction. For this initial test, and many
subsequent tests, the higher order modes, including the first
torsional frequency, are not clearly and unambiguously iden-
tified because of the poor signal-to-noise ratio for the re-
cording systems of the time. (SMA-1s, CR-1s, and Ranger
SS-1s all have a dynamic range in the order of 3 orders of
magnitude (60 dB), compared with the 144-dB resolution of
the 24-bit instruments.)
The recorded history includes four moderately large
shaking events, all with roof accelerations of at least 340
cm/sec
2
(over 34%
g
). Several smaller events, including the
1970 Lytle Creek Earthquake, and some more recent events
recorded on the digital instruments, with accelerations below
50 cm/sec
2
, are also included on Table 1 for comparison.
During strong motion, the natural frequencies temporarily
fall by about 20%. Surprisingly, after each strong-motion
event, the structural system stiffens and natural frequencies
return to near pre-earthquake levels, usually with a perma-
nent drop in frequency of less than 2.5%. Some events have
led to a larger permanent decrease of all subsequent forced
vibration resonant frequencies. In the most extreme case, the
east–west fundamental frequency dropped permanently by
16.6% in tests subsequent to the 1971 San Fernando event.
East–West Fundamental Frequency
In the east–west direction, the lateral forces are primar-
ily resisted by the elevator core and the concrete moment
frame (the architectural facade of stiff window frames pro-
vide additional stiffness). Table 1 shows that the very first
significant earthquake motion (from the 1970
M
5.3 Lytle
Creek earthquake,
D

57 km), with comparatively small
rooftop accelerations of 49 cm/sec
2
, resulted in a decrease
of 10.3% in the natural frequency as measured in the strong-
motion record. A further softening occurred during the larger
magnitude, closer 1971
M
6.6 San Fernando event (
D

31
km, peak roof accelerations

306 cm/sec
2
, with the fun-
damental frequency measured at about 1.0 Hz during the
strong shaking. Subsequent forced vibration tests indicate
the frequency dropped permanently by 16.6%, to 1.21 Hz,
from these two events. No earthquake recorded since has
generated east–west motions that exceeded the velocities and
accelerations of the San Fernando event. Correspondingly,
subsequent natural frequencies from strong-motion and
forced vibration do not show any significant loss of stiffness
of the structural system. The most recent east–west natural
frequency recorded from forced vibrations is 1.14 Hz (Brad-
ford
et al.
, 2004). The general mode shape has remained
constant throughout the history (Foutch, 1976; Bradford
et
al.
, 2004), though the component of rocking in the east–west
mode is not well characterized by recent studies, e.g., Brad-
ford
et al.
(2004), which do not account for rocking at the
base of the elevator core, because sensors are located only
at the edges of the building. Foutch
et al.
(1975), using a
dense temporary deployment of sensors, shows that the rock-
ing contribution at the base is significant.
North–South Fundamental Frequency
For the north–south direction, with the lateral resistance
provided by the massive shear walls, a different pattern
emerges. Very little frequency loss occurs during the Lytle
Creek event—even the strong-motion record shows a de-
crease of only 1.1%. Instead, it is the San Fernando event,
with rooftop accelerations of 341 cm/sec
2
, that causes the
first major frequency drop; natural frequencies from forced
vibrations fell from 1.9 Hz to 1.77 Hz after the event. Mode
shapes before and after the San Fernando event show major
differences. This can be illustrated by considering the rela-
tive contributions to the displacements at the roof; before the
earthquake, less than 3% of the peak roof displacement is
attributed to basement rocking, yet after, and in subsequent
tests, approximately 30% of the roof motion is due to base-
ment rocking (Jennings and Kuroiwa, 1968; Foutch, 1976;
Bradford
et al.
, 2004). Another major decrease occurs during
the 1987
M
6.1 Whittier Narrows event (
D

19 km), where
the highest rooftop accelerations (534 cm/sec
2
) were re-
corded during the shaking. Figure 2 shows that this event
caused the largest intraevent frequency drop (nearly 25%),
with a 4% permanent decrease in forced frequencies. Sub-
sequent natural frequency measurements from forced vibra-
tion tests are relatively constant, and no further softening
beyond the 1.33 Hz recorded in Whittier Narrows occurs
during strong motions (including the Northridge Earth-
quake). The most recent forced north–south natural fre-
quency is 1.67 Hz (Bradford
et al.
, 2004).
East–West Second Mode Frequency
At construction, the second east–west mode frequency
was determined as 6.2 Hz (Kuroiwa, 1967) (though it is not
clear whether the building had been fully completed at this
time; the heavy cladding may not have been added). During
the San Fernando event, the frequency dropped to

4.95 Hz
(McVerry, 1980; Beck and Chan, 1995). Investigations sub-
sequent to this earthquake have indicated the second mode
varies from 4.17 Hz (Beck and Chan, 1995) to 5.35 Hz
(Teledyne-Geotech-West, 1972). The most recent measured
forced east–west second modal frequency is 4.93 Hz (Brad-
ford
et al.
, 2004).
242
J. F. Clinton, S. C. Bradford, T. H. Heaton, and J. Favela
Figure
4.
East–west components of CR-1
array in Millikan Library, recorded during the
M
6.1 Whittier Narrows earthquake
D

19
km, velocity time series. The top trace is from
the basement, the second is from the sixth
floor, and the last two are from the roof. The
last trace includes a sample of how the funda-
mental frequency of the building is estimated,
after the main energy (seen from the basement
trace) has passed.
Response to Small Earthquakes
Table 1 also contains fundamental frequencies deter-
mined from shaking due to the small
M
4.2 Beverly Hills
event (
D

26 km) in September 2001. Even though mea-
sured accelerations from the event are about double the ac-
celerations from the sinusoidally excited forced vibration
tests, the measured fundamental frequencies are higher than
those from forced testing. This may be attributed to changes
in the ambient pre-earthquake natural frequency due to cli-
matic changes, and will be discussed in detail later.
The February 2003
M
5.4 Big Bear event (
D

119
km) produced accelerations almost double those from the
M
4.2 Beverly Hills event, and yet it had a more significant
effect on the fundamental frequencies—the drop in fre-
quency from Big Bear is much greater than double the drop
observed in Beverly Hills. This suggests that the relationship
between fundamental frequency and acceleration is nonlin-
ear. Further, it is observed that the fundamental frequency
during the Big Bear event drops by 6.1% in the east–west
direction, and only 3.6% in the north–south direction, even
though the north–south accelerations are larger. This indi-
cates that the east–west direction is more susceptible to soft-
ening under small excitations and that larger motions are
required to start significant softening in the north–south di-
rection (the ambient data will corroborate this observation).
The response of the library to this earthquake will be studied
in more detail.
Figure 3 indicates there is, in general, a linear relation-
ship between the logarithm of the acceleration amplitude and
logarithm of the frequency, though the scatter of the data is
large, and, at least for the small amplitudes, may be due to
the ambient variations in natural frequencies.
The Current System of Instrumentation at Caltech
Currently, five buildings on the Caltech campus have
the real-time telemetry of high-dynamic-range digital instru-
mentation. These are the Millikan Library, the Broad Center
for the Biological Sciences, the
USGS
Building at 525 S.
Wilson Avenue, the Robinson Building, and the Athenaeum.
A dense array at Millikan Library is comprised of triggered
digital accelerometers with dial-up data retrieval.
The Caltech Civil Engineering Department operated an
older network of analog film-recording SMA-1s at a number
of sites on and around the campus, as well as a 12-channel
CR-1 at Millikan Library, which had been operational on
campus since the 1970s. However, this network has not been
maintained since the mid-1990s and is currently not opera-
tional.
Millikan Library (
MIK
,
USGS
-Caltech Array)
In January 1998 the
USGS
and Caltech Civil Engineer-
ing Department installed a 36-channel dense network of
FBA-11 accelerometers recording triggered event data on
two 19-bit Mt. Whitney dataloggers with dial-up data re-
trieval. A triaxial EpiSensor accelerometer was also installed
on the ninth floor of the structure and has been continuously
transmitting 24-bit data since February 2001, to the Southern
California Earthquake Data Center (
SCEDC
), as station
MIK
in the California Integrated Seismic Network (
SCSN
).
This improved sensor configuration prompted a detailed
forced dynamic analysis (using the existing shaker located
on the roof), which was performed in the summer of 2002
(Bradford
et al.
, 2004). The results of this study are sum-
marized in Table 2. At the time of the tests, the approximate
first mode frequencies during forced vibration (1/2 weights)
are 1.14 Hz for the east–west direction, 1.67 Hz for the
north–south direction, and 2.38 Hz for the torsional mode.
Broad Center (CBC)
This is a three story structure with an irregular floor plan
and two deep basements (see Fig. 5). It was completed in
The Observed Wander of the Natural Frequencies in a Structure
243
Table 2
Natural Frequencies for the Millikan Library
and the Broad Center
Millikan Library (Hz)
Broad Center (Hz)
Orientation
First
Mode
Second
Mode
Third
Mode
First
Mode
Second
Mode
East–West
1.14 [1.19]
4.93
7.83
2.67
3.01
North–South
1.67 [1.72]
7.22
?
2.43
2.81
Torsional
2.38 [2.46]
6.57
?
3.65
?
Millikan Library frequencies are from forced vibration tests, summer
2002 (Bradford
et al.
2004). For the three fundamental frequencies, in pa-
rentheses are the 2-year average frequencies from continuous ambient MIK
data. Broad Center results are from the ambient vibration data from 14 days
of continuous data during February 2003 and are preliminary (in the ab-
sence of a forced vibration modal analysis of the structure).
the summer of 2002 and has been instrumented since Feb-
ruary 2003. The basements are enclosed by stiff shear walls,
and the steel superstructure is braced with stiff unbonded
braces in both the north–south and east–west directions.
The building houses a 24-bit
SCSN
station, recording
eight channels of EpiSensor accelerometer data. Three tri-
axial instruments are installed, all on the plan of the un-
bonded braced frame-line that is the structural core of the
building. Two are located near the northwest intersection of
the frame line, one on the first floor, with the other on the
roof. The final accelerometer, which only has its horizontal
channels logged (the datalogger supports only eight channels
of data), is near the southeast intersection of the frame line.
All eight channels comprise
SCSN
station CBC. The instru-
ment layout is illustrated by the schematic in Figure 5c.
In the absence of a forced vibration modal analysis for
the building, the natural frequencies were investigated by
using the CBC ambient data alone. Clinton (2004) describes
this method in more detail. Table 2 presents the resonant
frequencies determined by this analysis. Because the trans-
lational fundamental and first overtone frequencies are very
close, which is unusual for typical structures, it is possible
some dynamic feature of the building is not appreciated in
this analysis. Ideally, further instrumentation and a forced
vibration test are needed to confirm the dynamic properties
of the Broad Center listed in the table.
Figure
5.
Broad Center. (a) View from the southwest. (b) View from the northwest.
Structural core of the unbonded-brace frame is located below the parapet wall visible
on the roof. (c) Schematic plan view showing placement of strong-motion sensors. 1 is
on the first floor; 2 and 3 are located on the roof.
244
J. F. Clinton, S. C. Bradford, T. H. Heaton, and J. Favela
525 S. Wilson Avenue,
USGS
Office (
GSA
)
GSA
is a 24-bit
SCSN
station with a triaxial EpiSensor
accelerometer located in the basement of the two-story
wood-frame house (used as
USGS
Pasadena offices).
GSA
data are often used as a reference station for data from the
Millikan Library and Broad Center. The station, operating
since July 2000, is approximately 150 m due west of the
Millikan Library, and about 200 m south-southwest of the
Broad Center.
Robinson Building (
CRP
)
CRP
is a 24-bit
SCSN
station, located about 18 m below
grade, in the unused Solar Telescope pit of the Robinson
Building. It houses a high-gain broadband (Guralp CMG-1)
and a strong-motion (Tokyo-Sokushin velocity sensor VSE-
355G3) instrument. It is the only station on campus with a
high-gain digital instrument permanently deployed. It has
been operational since March 2003 and is about 75 m south-
west of Millikan Library.
The Athenaeum (
CAC
)
SCSN
station
CAC
is a 19-bit K-2 datalogger with a
triaxial accelerometer deployed at the Athenaeum. Located
in the basement,
CAC
occupies the same site as the old
analog Athenaeum/Caltech station that has recorded earth-
quakes since the 1960s. Data are continuously telemetered
to the
SCSN
/
SCEDC
, but because the information is only 19-
bit, only events that trigger on the network are permanently
stored in the
SCEDC
.
Continuous and triggered data from these (and all other)
SCSN
stations may be obtained from the
SCEDC
at
www.data.scec.org. Triggered data from some of the events
recorded by the
USGS
-Caltech array on Millikan Library is
available through the National Strong Motion Program at
nsmp.wr.usgs.gov.
Analysis of the Continuous Data Streams
As discussed in the preceding section, two buildings on
the Caltech campus. Millikan Library and the Broad Center,
have continuous data from instruments located on their up-
per floors available through the
SCEDC
. These data streams
can be used to analyze the evolution of each building’s nat-
ural frequencies over the life of these stations, and at other
interesting timescales. The natural frequency changes are
correlated with weather data from the JPL Weather Station.
This is the nearest digital continuously monitored weather
station, and it is located 8.5 km north of the Caltech build-
ings at the Jet Propulsion Lab. Data are available from the
start of continuous data storage from
MIK
, up to the end of
November 2003. This includes 2.5 years of data for
MIK
,
and 10 months for CBC, which started recording in mid-
February 2003.
The JPL weather station logs data every second; the
channels used for comparison are rainfall (cumulatively
measured per day, millimeters), wind gusts (meters per sec-
ond), and temperature (degrees Celsius). Subsequent plots
present only total rainfall, maximum wind gusts, and the
maximum and minimum temperatures.
Entire Station Duration,
MIK
and CBC
Figure 6 is a spectrogram plot for the entire history of
the station
MIK
, alongside JPL weather data. The three in-
dividual spectrogram subplots are centered about each of the
east–west, north–south, and torsional fundamental frequen-
cies. Figure 7 is a similar spectrogram for the history of
station CBC. Because the natural frequencies at CBC are not
well determined, individual spectrogram subplots are pre-
sented for each of the east–west and north–south channels,
over a wide range of frequencies that encompass the ob-
served spectral peaks.
Each spectrogram is made by dividing the acceleration
time series into lengths of time (a slice) and taking the fast
Fourier transform (
FFT
) of this time window. The magnitude
of the
FFT
is then represented by a color contour along the
y
axis at the time on the
x
axis to which the
FFT
corresponds
(the midpoint slice time). Plotting this for each slice leads
to the composite spectrogram. In Figures 6 and 7, the
FFT
length is 1 hr long, and there is no time overlap between
slices. Each
FFT
has also been first smoothed over a fre-
quency of 0.002 Hz and then decimated to a sampling fre-
quency of about 0.001 Hz. In these figures, the acceleration
amplitude scaling is linear for both
MIK
and CBC, with up-
per and lower bounds arbitrarily set to prevent unusual highs,
such as the 22 February 2003 Big Bear earthquake, from
swamping the color bar.
Because the three fundamental frequencies of Millikan
Library are well separated and of large magnitude, the hourly
peak in the
FFT
can be traced over time, as seen in Figure
8. Here the average of all the peaks is determined, and the
deviation from this average is plotted. The daily average of
the
FFT
peak is plotted as a thick line, with the hourly
FFT
peak plotted as a thin line. The timing of small earthquake
excitations and forced vibration testing of the structure are
highlighted by vertical bars. These are the source of the ob-
vious large deviations from the mean.
Figure 8 shows considerable variation in natural fre-
quencies over 2 years. In particular, note the sensitivity of
the fundamental east–west and torsional modes to rainfall,
as evidenced by the large shifts during the winter months,
when storms with several days of rainfall are a regular oc-
currence in southern California. These rain events are infre-
quent during the summer months. The north–south mode is
not as sensitive to the rainfall and, in general, has smaller
short-term deviations than the east–west and torsional
modes. There is also a steady and unusual rise in the three
fundamental frequencies during the spring of 2003, from
April to July 2003. This occurs at the same time as a change
in usage of three midlevel floors of the library (third, fourth,
The Observed Wander of the Natural Frequencies in a Structure
245
Figure
6.
Spectrogram of natural frequencies as observed at
MIK
, May 2001 through
November 2003. Spectrogram composed of 1-hr time windows, each scaled so maxi-
mum is 1 and plotted with linear color bar. Weather data are from JPL weather station
(
D

8.5 km). Vertical breaks in data are due to days with data glitches or no recorded
data. Tick marks on
x
axis correspond to first of the month labeled underneath. The
peaks in natural frequencies are observed to wander over the course of the 2.5 years.
No long-term correlation with temperature is observed, though rain causes temporary
lengthening of natural frequency.
246
J. F. Clinton, S. C. Bradford, T. H. Heaton, and J. Favela
Figure
7.
Spectrogram of all six horizontal channels at station CBC, the Broad
Center, February 2003 through November 2003. One-hour spectrogram windows, no
scaling, linear color bar. Sharp red horizontal lines are due to machine noise in the
building. Natural frequencies are represented by the broad peaks, near 2.6 Hz, 3.0 Hz,
and 3.6 Hz, for the east–west channels, and near 2.4 Hz, 2.8 Hz, and 3.6 Hz for the
north–south channels. Notice the 7-day noise cycle with relative quiet on the weekends.