Monitoring Structural Deformation at Pacoima Dam, California Using
Continuous GPS

Jeffrey A. Behr, *Southern California Earthquake Center, SCIGN-USGS*

Kenneth W. Hudnut and Nancy E. King, *United States Geological Survey*

## BIOGRAPHY

Jeffrey A. Behr is Systems Specialist for the Southern California
Integrated GPS Network (SCIGN). His present responsibilities include the
development of software and systems for network communications,
processing and analysis for the developing 250-station array, with
emphasis on SCIGN's near-real-time earthquake response capability. He
received his M. Sc. degree in Geological Sciences from the University of
Colorado, Boulder, in 1992 and has been working in continuous GPS since
1993.

Kenneth W. Hudnut is a Geophysicist with the United States Geological
Survey in Pasadena. He is a member of the SCIGN executive committee,
vice chair of the SCIGN coordinating board and chairs the crustal
deformation working group of the Southern California Earthquake Center.
He received his Ph.D. in Geology from Columbia University in 1989.

Nancy King is a Geophysicist with the United States Geological Survey at
USGS-Pasadena and is a member of the SCIGN Coordinating Board. She
received her Ph.D. in Geophysics from the Scripps Institution of
Oceanography in 1990.

**ABSTRACT**

Agencies responsible for dam safety have long used conventional
surveying methods to measure the displacements of benchmarks as part of
dam monitoring programs. Such surveys have provided infrequent though
precise estimates of a dam's motions. With the development of high
precision GPS methods to monitor plate tectonic motions and crustal
deformation rates, an alternative method for monitoring such structural
motions became available. While high- precision GPS approaches the
horizontal positioning capability of conventional surveying methods, its
great benefit lies in a much higher temporal resolution and nearly
unattended continuous operation.

In September 1995, Pacoima Dam, located in the San Gabriel Mountains
north of Los Angeles, California, was instrumented with a triad of
continuously operating GPS receivers to test the feasibility of applying
these techniques to the field of structural monitoring. Nearly three
years of data have been analyzed from this sub-array to provide
quarter-daily estimates of station-to-station baseline lengths.
Quantitative methods were assessed to allow the identification of a
number of outlying data points that could be misinterpreted as GPS
station motion in a real-time system.

![](media/image1.wmf)

Figure 1. Pacoima Dam. Continuously recording GPS stations DAM1, on the
left abutment, and DAM2 at the center of the arch are identified. View
is to the north.

Examination of the derived baseline time series indicates that Pacoima
Dam is experiencing an annual cycle of upstream-downstream (E-W) motion
at the center of the dam arch of approximately 15-18 mm peak-to-peak
amplitude. Comparison of motion to daily regional temperature records
strongly indicates that the dam responds to annual and shorter-period
ambient temperature variations. Spectral methods are used to model this
relationship to allow a more accurate estimation of the thermoelastic
behavior of the structure.

**INTRODUCTION**

![](media/image2.wmf)In coordination with the application of continuous
GPS to crustal deformation monitoring in the L. A. Basin, the U. S.
Geological Survey and Los Angeles County embarked in 1995 on an
open-ended program to continuously monitor the positions of 2 points on
Pacoima Dam, California (Figure 1). This structure (at 113 m, the
tallest dam in the world at the time of its completion in 1929)
experienced severe shaking (\>1 g) and significant damage during the
1971 San Fernando and 1994 Northridge earthquakes (Swanson and Sharma,
1979; USGS and SCEC Scientists, 1994). On September 1, 1995, two
monuments on the dam and another at the U. S. Forest Service's Fire Camp
9, 2.5 km to the NW (Figure 2), were instrumented with dual-frequency
P-code GPS receivers and incorporated into the Los Angeles Basin's Dense
GPS Geodetic Array. The design of this system, its communications and
operations are based directly on that of the Permanent GPS Geodetic
Array, the forerunner of SCIGN (Bock et al., 1997).

Figure 2. Location Map. In addition to stations DAM1 and DAM2, CMP9
station is less than 3 km away from Pacoima Dam. Data from three other
SCIGN stations (ROCK, LEEP and CHIL) were also used in this study.

Pacoima Dam trends a few degrees west of north (abutment to abutment) in
an east-west running section of steep-walled Pacoima Canyon. Station
DAM1 was installed on the roof of a single-story, concrete operations
building on the south (left) thrust block of the dam. Station DAM2 was
installed near the center of the concrete arch atop a \~2 m tall
steel-tube monument (Figure 3). These stations form a 103.7-m baseline
differing in height by only 0.66 m. Station CMP9 sits atop a ridge
approximately 2.5 km distant, more than 550 m above the dam's crest
(Figure 2).

Hudnut and Behr (1998) describe the initial 2 years of operation and
observations for this system. The highlight of that analysis was the
identification of an oscillatory displacement of the DAM2 station of
approximately 17-mm peak-to-peak amplitude with respect to DAM1 with an
approximately annual period. The analysis showed that this displacement
was strongly related to air temperature records from Burbank, CA.,
approximately 20 km to the south. It also suggested that the dam might
be responding to higher frequency temperature variations. However,
because the record available for that study was only two-years in
length, we were only able to roughly estimate a transfer function
between input temperature and output annual displacement. This paper
reexamines this issue with the benefit of an added year of data. In
addition, we reanalyzed the data in 6-hour sessions in order to assess
the trade-off between decreasing latency and probable decrease in
precision using higher-frequency GPS solutions.

![](media/image3.wmf)

Figure 3. Station DAM2. The Dorne-Margolin choke ring antenna is mounted
on a steel pier, and GPS receiver, modem and power supply are in the
NEMA-type enclosure mounted to the fencing.

A goal of earthquake response efforts is to obtain and provide rapid,
accurate measurements of the locations and amplitudes of significant
tilts, strains and displacements following moderate to large
earthquakes. At those same times and in much the same way, owners and
operators of buildings and engineered structures need prompt, reliable
estimates of structural displacements for safety and hazard analysis.
But beyond this, continuously operating GPS, if implemented properly,
can provide frequent, precise estimates of structural motions during
periods unaffected by seismic motions.

GPS currently offers more than one method for structural monitoring
applications. Two end-members of these methods might be described as
static post-processing of GPS data (Hudnut & Behr, 1998) and Real-Time
Kinematic (RTK) positioning (Celebi et al., 1998). While this paper
summarizes our investigation of the first method, RTK methods are being
tested at USGS-Pasadena for incorporation into the SCIGN as a
supplemental tool for near-real-time earthquake displacement
measurement. We have proposed and hope to implement real-time telemetry
of RTK data from Pacoima Dam back to the USGS offices to aid the
development of robust RTK systems for both structural monitoring and
earthquake response.

## GPS ANALYSIS

We performed quarter-day solutions for the Pacoima Dam network plus
three additional SCIGN stations (ROCK, LEEP and CHIL) for 1059 days from
September 1, 1995 to July 26, 1998. These solutions used phase and
pseudorange data collected by Ashtech Z-12 dual-frequency, P-code
receivers and choke-ring antennae. Precise ephemerides generated by the
International GPS Service (IGS) (Beutler and Neilan, 1997) and UT1/polar
motion estimates provided by the U.S. Naval Observatory (USNO) were used
in the solutions.

We performed the initial processing of the GPS data using the GAMIT
software (King and Bock, 1998). This package prepares the station
observation data and IGS ephemeris, then computes the residual
observations and partial derivatives from a geometric model. The package
then marks and attempts to repair cycle-slips and outliers in the data
using various combinations of phase and pseudorange data. Finally,
station coordinates, orbital parameters and phase ambiguities are
estimated in a least-squares adjustment.

Ambiguity resolution in GAMIT is an iterative process, involving the use
of alternating estimations of geodetic parameters, real-valued, and
integer biases using several combinations of phase and range data (Feigl
et al., 1993). In short, geodetic parameters and real-valued biases are
first estimated for all independent double differences using the
ionosphere-free linear combination phase observable (LC). This is
followed by estimation of wide-lane biases using independent L1 and L2
data while fixing the LC-derived geodetic parameters and applying
appropriate constraints on the ionosphere. GAMIT next forces wide-lane
biases to integer values using the decision-function (Dong and Bock,
1989) and the addition of P-code pseudo-range data. With wide-lanes now
held fixed, geodetic parameters and L1 biases are estimated using the LC
observations. After the narrow-lane (L1) biases are forced to integer
values, again via the decision function, the LC observations are used
once more for the final geodetic parameter estimation.

This set of geodetic parameters and corresponding variance-covariance
matrices are next processed by the GLOBK Kalman filter adjustment
software (Herring, 1998) to provide final quarter-daily estimates for
the Pacoima Dam network. At this stage, we defined the reference frame
for our analysis by applying *a priori* constraints of 5 ppb to the IGS
orbits and 20 and 40 mm, respectively, to the horizontal and vertical
coordinates of the two outermost stations of the network (CHIL and
ROCK). These constraints are roughly twice the expected errors in these
parameters (2-3 ppb for the orbits and 10-20 mm for the coordinates)
(Table 1). Nonetheless, they are sufficiently tight that uncertainties
in the orbits and the geocentric position of the network contribute less
than 1 mm to the uncertainties of the unconstrained baselines in the
analysis.

**TABLE 1. *A priori* constraints applied in GLOBK.**

  ----------------- -----------------------------------------------------
  Parameters        Constraints

  Stations          20 mm NE, 40 mm Up - CHIL & ROCK

  Satellites        0.10 m XYZ, 0.01 mm/s V~x~V~y~V~z~

  Pole              0.25 mas in XY, 0.1 mas/day

  UT1               0.25 mas, 0.1 mas/day
  ----------------- -----------------------------------------------------

GLOBK was developed to combine multiple loosely- constrained
'solutions' - estimates of geodetic parameters and their corresponding
covariance matrices - in a single adjustment with uniform application of
constraints. It is typically used to process global GPS data for the
determination of satellite ephemerides, and regional data for the
estimation of station velocities over multi-year spans. We use GLOBK
primarily to perform a quality check on each independent solution.
Poor-quality solutions are automatically rejected in the final
adjustment. It also affords a computationally efficient method for
testing various combinations of weights and constraints on the geodetic
parameters derived from the GAMIT analysis. For example, once biases had
been fixed in GAMIT, we were then able to process the data with varied
constraints on the station coordinates to obtain an overall assessment
of the quality of the bias-fixing.

## 

## PACOIMA DAM DATA

Following the GLOBK processing, we extracted baseline time series for
stations CMP9, DAM1 and DAM2. The time series were then demeaned and
examined for jumps in the data due to site disturbances or equipment
failures. Such jumps can strongly bias estimates of crustal velocities
and are the subject of focused research in the SCIGN project. One such
failure occurred at DAM2 when the original choke-ring antenna failed and
was replaced on October 23, 1996 (662 days after January 1, 1995). The
magnitude of this offset was estimated by linear least-squares fits to
several multi-day spans of pre- and post-jump data from the CMP9-DAM2
and DAM1-DAM2 time series. The final adjustments and one-sigma
uncertainties are summarized in Table 2. (Note that these are presented
as baseline changes, not as absolute station positions.) Estimated
uncertainties may be inflated due to a) a gap in the DAM1 time series
shortly after the antenna was replaced, and b) our application of a
linear fit to a time series with a significant oscillatory signal.
Although there are more rigorous methods available to calculate these
offsets, we did not consider them necessary for this analysis. It is
apparent, however, that this adjustment provides some indication of the
short-period detection threshold of the system in that we are able to
observe horizontal displacements on the order of 4 mm on the 107-m
baseline from DAM1-DAM2.

Table 2. DAM2 antenna change offsets in mm.

  ------------------- ------------ ------------ ------------ ------------
  Baseline to:        North        East         Up           Length

  CMP9 offset         -3.1         1.4          0.8          -1.6

  CMP9 sigma          1.5          1.8          5.8          1.5

  DAM1 offset         4.3          1.0          -1.8         4.3

  DAM1 sigma          0.5          1.0          1.3          0.3
  ------------------- ------------ ------------ ------------ ------------

## OUTLIER REJECTION

Not unexpectedly, the use of quarter-day solutions resulted in higher
standard errors in the baseline estimates than daily processing, as well
as several significant outliers in the time series. If the data were
being examined as part of a real-time or near-real-time GPS system,
these outliers might be interpreted as significant motion of the DAM2
station. For this reason, we attempt to identify parameters generated by
the GAMIT/GLOBK processing that might be used to flag poor solutions.

During our initial analysis of two years' daily solutions (Hudnut &
Behr, 1998) we suspected that the lack of data from one or more
'regional' GPS stations (ROCK, CHIL or LEEP) might weaken the quality of
the network solution. We were concerned that the small aperture dam
network would require distant sites to strengthen the network geometry.
In that analysis all stations except DAM1 and DAM2 had coordinates
constrained to 1-1-5 cm (NEU), while orbits and earth orientation
parameters were loosely constrained. In essence, we were relying more on
our regional station coordinates to define the reference frame. However,
we found no relationship between missing regional data and outliers in
the 24-hour solutions. Instead, we observed a relationship between low
numbers of double difference observations and outlier occurrence.

![](media/image4.png){width="3.2in" height="3.3986111111111112in"}

Figure 4. Outlier rejection results for the DAM1-DAM2 E-W baseline. Data
extracted from the GAMIT/GLOBK solutions (top frame) have several
extreme outliers removed via the double difference technique (middle).
Little or no improvement was made in the application of the chi-square
test so the remaining outliers were removed in a first-difference cut
(bottom).

In the present treatment, our solutions have 75% fewer double
differences because of the switch to quarter-day sessions while still
processing at a 120-s sampling interval. Nevertheless, the low
double-difference technique was again applied. We compiled 3-year time
series of the number of double difference observations for each station
for each 6-hour session and calculated mean values for each series. If
either one of the baseline end-points provided less than 75% of mean
values, we delete that session from all baseline time series involving
that station. This succeeded in removing several outliers (Figure 4,
Table 3) though it was less successful than its application to the
24-hour solutions.

We investigated a second rejection test by examining the values of the
GLOBK chi-square per degree of freedom for each independent solution. As
stated above, we use GLOBK to analyze each solution independently and to
identify and reject sessions that exceed a configurable chi-square
cutoff parameter, here set to 10.0. This cutoff may have been too high.
Chi-square per degree of freedom should fall around 1.0 if the data have
been weighted properly. We reexamined the GLOBK estimates and flagged
solutions that had chi-square per degree of freedom \> 3. Although 25
solutions were tagged and removed, the Pacoima Dam time series cleaned
by this method did not show significant decrease in the number of
outliers. One probable failure with this technique is that the
chi-square value is determined for all data in a solution and is not a
site-specific parameter. This may lead to the rejection of high-quality
data from the Pacoima Dam network when the problem data may have been
from a regional station. At this point, we do not favor secondary
removal of data based on high chi-square per degree of freedom.

Table 3. Baseline estimates after each cleaning stage.

+--------------------+----------+--------+---------+---------+-----+
| Baseline           | GAMIT/   | Low DD | High    | First   | \%  |
|                    |          |        | Chi2    | Diff.   |     |
|                    | GLOBK    |        |         |         |     |
+--------------------+----------+--------+---------+---------+-----+
| CMP9-DAM1          | 3911     | 3869   | 3847    | 3790    | 89  |
+--------------------+----------+--------+---------+---------+-----+
| CMP9-DAM2          | 3893     | 3886   | 3862    | 3810    | 90  |
+--------------------+----------+--------+---------+---------+-----+
| DAM1-DAM2          | 3831     | 3789   | 3767    | 3731    | 88  |
+--------------------+----------+--------+---------+---------+-----+

\% is the total sessions out of a possible 4236 (1059 days, 4
sessions/day)

We have not yet found a satisfactory method for rigorous identification
and removal of all outliers in the Pacoima Dam time series. Although the
identification of low numbers of double differences holds promise for
application in a near-real-time continuous GPS monitoring system, other
methods for flagging poor quasi-observations need to be determined.

While systematic techniques for complete outlier removal have not been
identified, in order to continue with the analysis of DAM2 motion we
forced the removal of the remaining bad data. A first-difference
(rate-of-change) time series was calculated for each component of the
three baselines. The mean and standard deviation were then calculated
for each component and all data points greater than 3-standard
deviations from the mean were removed. Gaps in the time series were then
filled using a linear interpolant (cubic and Akima splines were tested
but introduced significant structure into the time series and were
deemed inaccurate). This data set was used for the analysis of the
deformation at Pacoima Dam.

The final, cleaned and adjusted DAM1-DAM2 time series are displayed in
Figure 5. Although there is evidence that station DAM1 experiences
annual displacement of a few mm opposite in trend to the motion of DAM2,
we restrict our analysis to the dominant motion of the center of the dam
arch. This is justifiable because of the lower uncertainties associated
with the short DAM1-DAM2 baseline, and because of the existence of
higher than average systematic noise in the data recorded at CMP9. This
baseline focuses the deformation analysis along a segment of the dam
that experienced troubling damage during the Northridge earthquake,
extension and fracturing of the downstream façade at the left
abutment/thrust block contact. Before analyzing recent deformation on
this baseline, we examine the nature and the quality of the quarter-day
baseline estimates.

![](media/image5.png){width="3.2506944444444446in"
height="4.30625in"}Figure 5. Final DAM1-DAM2 baseline time series, Sept.
1, 1995 through July 26, 1998. Time series have had outliers removed via
double-difference, chi-square and first-difference techniques.

## SUB-DAILY SOLUTIONS

During our analysis of the baseline time series power spectral density,
we observed a surprising amount of power at the Nyquist frequency (2
cycles per day). It was an immediate concern that we were aliasing a
high-frequency signal in the quarter-day solutions that had been
averaged out in the daily solutions (Figure 6, frame 1). We observed in
the E-W component of the DAM1-DAM2 quarter-day time series a repetitive
displacement pattern in which the quarter-daily estimates varied by 2-3
mm from the daily position estimates. Aware of the thermoelastic
response of the dam, we first looked for a correlation using sub-hourly
temperature records from meteorological instruments located at SCIGN
stations CHIL and CLAR (Chilao Flat in the San Gabriel Mts. and
Claremont College in Claremont, CA.). However, no relationship could be
found between sub-daily temperature and displacement because amplitude
variations in the two signals did not correlate. We next examined
baselines from the other sites in the network to determine if this was a
site-specific effect and found that it was not.

The time series exhibit significant sub-daily scatter in the baseline
lengths that appears to be systematic. In Figure 6 we display the E-W
component of two baselines measured in the dam processing, DAM1-DAM2 and
CHIL-LEEP, for a 20-day period from July 1997. This component is
representative of the scatter in the north and length components, but
approximately 25% of the amplitude in the vertical. The amplitude of the
scatter in the CHIL-LEEP baseline is approximately twice that of
DAM1-DAM2 while DAM1-DAM2 appears to be more repetitive in structure.
These baselines differ in length by 2 orders-of-magnitude.

The structure in the baseline series reflects the scatter in the number
of double differences available for each solution. Initial examination
of short segments of double difference and position time series relate
low number of double differences to the more extreme outliers. However,
it is not yet clear if the low double differences reflect reduced
satellite availability for these sessions or data cleaning, which might
indicate a period of higher multipath for a particular session. It is
clear that the dam stations have a myriad of multipath sources, but
examination of phase residuals over several weeks and modeling of
probable reflectors needs to be performed to assess a multipath source.

![](media/image6.png){width="3.247916666666667in"
height="3.5347222222222223in"}

Figure 6. East component baseline length estimates for the DAM1-DAM2 and
CHIL-LEEP baselines. DAM1-DAM2 quarter-day (o) vs. full-day (\*)
(frame 1) and CHIL-LEEP (\*) (frame 2).

We have not yet begun to analyze the source of these signals, but have a
number of possibilities to consider. They may be due to incorrectly
resolved biases or a consequence of the fact that we do not use phase
center models in our processing. They may be due to thermal effects on
the receiver electronics, antenna LNA or antenna cable. It could
possibly be azimuth and elevation dependent interactions with antenna
radomes that would appear as phase noise similar to multipath. And it
may be a combination of effects. In any case, now that this signal has
been identified we can work to identify its source and methods to
alleviate it, thereby improving the quality of sub-daily analyses and
their applications.

## THERMOELASTIC DEFORMATION AT DAM2

It was observed relatively early in the lifetime of the Pacoima Dam
network that the dam was experiencing eastward displacement at the
center of the concrete arch as regional temperatures increased, and
westward displacement as temperatures cooled. Hudnut and Behr (1998)
estimated a rough transfer function of 0.5 mm per degree F for the
annual signals in these series, with a lag between nodes in temperature
and displacement of about 40 days. We were not able to perform a
rigorous analysis of the data using spectral methods because of the
limited duration of the time series. In this analysis, however, we have
available an additional year's data from Pacoima Dam and from the
Burbank temperature sensor used in the previous study.

The Burbank temperature record is the nearest continuous data that we
have for this analysis. Dam core temperature sensors were removed from
the structure shortly after the Northridge earthquake and there are no
continuous observations taken on the dam itself. Although we have now
taken steps to alleviate this problem by installing a three-sensor
meteorological package with the support of our colleagues in the SCIGN
project, that sensor did not become operational until mid-August 1998.
In the future we hope to be able to use the data from these on-site
meteorological sensors to better estimate the thermal cycles in Pacoima
Canyon. Additionally, although we processed the data in quarter-day
solutions, we chose to analyze the coherence between the two signals
using the daily temperature data and a displacement time series
decimated to 1 sample per day using an anti-aliasing low-pass filter. As
discussed in the previous section, we were unable to model short term
variations in temperature and displacement due to the incoherence of the
two signals recorded 10's of kilometers apart.

We present in Figure 7 the 3-year time series of Burbank temperature and
DAM1-DAM2 E-W displacement. Our first step in the analysis of this data
set was to detrend both time series by a sinusoidal signal of annual
period to minimize the likelihood of low-frequency leakage into
neighboring frequency bins. Although these series are not precisely fit
by a sinusoid (note the advanced onset in spring 1997 and the retarded
onset in spring 1998 of temperature increase and eastward displacement),
this approach was successful in removing much of the annual signal.
Initial results using an impulse response function derived from input
temperature and output displacement with annual signals present provided
very poor results. Our results with the annual signal removed were much
better. In removing the annual signal it was found that the best-fit
sinusoids for displacement and temperature could be related by a gain of
1 mm per degree C with a lag of 35 days.

![](media/image7.png){width="3.2527777777777778in"
height="4.0152777777777775in"}

Figure 7. Three-year records of Burbank temperature and dam displacement
fit by sinusoid function with annual period. The sinusoids are
subtracted from the observed data to produce the residuals used in the
spectral analysis.

We used Welch's method in MATLAB 5.1 to perform the spectral analysis.
This method breaks the time series into shorter sections, estimates
spectra for each section, and averages the results. This method reduces
the variance of the estimated spectra, at the cost of reducing frequency
resolution as well. To reduce bias (leakage) we applied a taper to each
section. We used the Hanning taper and, after experimentation, a section
length of 128 days.

We assume that temperature is the input to a linear time-invariant
system with dam deformation as the output. In the time domain y(t) =
g(t)\*x(t), where x(t) is temperature, y(t) is dam deformation, g(t) is
the impulse response function and \* is the convolution operator. In the
frequency domain Y(ω) = G(ω)X(ω) where ω is frequency and X, Y, and G
are the Fourier transforms of x, y, and g, respectively. G(ω) is the
complex-valued transfer function between the input and output describing
the amplitude and phase changes as a function of frequency. For a linear
system, the transfer function is G(ω)=h~xy~(ω)/h~xx~(ω), where h~xy~(ω)
is the cross-spectrum between input and output and h~xx~(ω) is the power
spectrum of the input. The gain spectrum, \|G(ω)\|, and the phase
spectrum, arg(G(ω)), describe how the system modifies amplitude and
phase, respectively. Coherence \|h~xy~(ω)\|^2^/h~xx~(ω)h~yy~(ω) is in
the range \[0,1\] and describes the correlation between input and output
as a function of frequency. The impulse response function g(t) is the
inverse Fourier transform of the transfer function G(ω). Convolution of
g(t) with input temperature produces predicted output and allows us to
assess the success of the model. See Priestley (1981) for a complete
description of these methods.

The coherence, gain and phase calculated for input residual temperature
and output residual displacement are presented in Figure 8. The series
appear to be coherent up to a frequency of approximately 1 cycle per 14
days. Beyond that frequency our confidence in the estimated transfer
function is limited. We find that the gain falls off at 1/f^2^ and our
phase lag is fairly constant between --35 and -50 degrees.

![](media/image8.png){width="3.3in" height="3.7819444444444446in"}

Figure 8. Coherence, gain and phase between input Burbank temperature
and output dam displacement. Analysis performed with a data section
length of 128 days.

The application of the impulse response function obtained from this
transfer function provides a reasonable fit to the displacement data
(Figure 9). Input temperature (frame 1) is convolved with the impulse
response function

![](media/image9.png){width="7.05in" height="5.114583333333333in"}

Days after January 1, 1995

Figure 9. Convolution of the derived impulse response function with
temperature from the Burbank Valley pumping station, September 1, 1995
through July 26, 1998. The filter was convolved with temperature data
with the annual signal removed (frame 1) to produce a time series of
predicted deformation (dark/red trace, frame 2) which compares
reasonably well to observed deformation (light/green trace, frame 2).
The predicted deformation is then subtracted from the observed
deformation to produce a time series of residual deformation (frame 3)
with thermoelastic signal removed. Displacements remaining in this
series show clear evidence for a relationship between dam displacement
and periods of increased reservoir depth (frame 4) at Pacoima Dam.

to create a time series of predicted dam displacements (frame 2). When
this predicted series is subtracted from the observed dam deformation we
are left with a residual time series of dam deformation (frame 3) with
thermally- induced displacements removed. The signal remaining in the
residual time series show much less strength for periods of a few to
several days out to a few weeks. One of the strongest signals in the
residual series may be a response to a rapid increase in reservoir
elevation at \~780-790 days after Jan. 1, 1995.

### 

Although the coherence estimate between temperature and displacement was
not significantly strong at periods shorter than 2 weeks, there are some
significant variations in the predicted deformation that correspond with
observed displacements totaling a few mm over periods of a few to
several days. While the largest signals occur over periods of a few
weeks, the impulse response function seems to have predicted some
short-term displacements. The residual deformation record shows an
overall reduction in displacements of more than 1-3 mm over periods of a
few days to a few weeks.

While a simple physical model might easily be developed for this system,
one was not attempted here due to limitations in time. However, the
gain, which appears to fall off as 1/f^2^ from a value of 1mm/°C at
annual period, corresponds well to a coefficient of thermal expansion of
10^-5^/°C, a typical value for steel and concrete. For a structure of
113-m height and approximately 150-m arch length, this would result in a
thermoelastic coefficient of \~10^-3^/°C, essentially what we observe on
this dam. The other factor would be the coefficient of thermal
diffusivity controlling the rate at which the dam absorbs heat into its
core.

## CONCLUSIONS

At this time our evaluation of the dam at daily or sub-daily intervals
is limited due to our discovery of systematic noise in the sub-daily GPS
positions. We will pursue identification and reduction of this noise as
a way of further reducing latency while maintaining accurate, absolute
positions. Our goal is to improve on a current horizontal resolution of
4-6 mm each day, as is done typically for SCIGN near-real-time analysis
at USGS-Pasadena (<http://www-socal.wr.usgs.gov/scign/Analysis)>.

The Pacoima Dam experiment successfully demonstrates the applicability
of continuous GPS to the field of structural monitoring. The 3-year DAM1
to DAM2 baseline time series indicates that the center of the dam arch
undergoes an annual cycle of E-W displacement with peak-to-peak
amplitude of 17±2 mm. Conventional surveying measurements taken after
the 1994 Northridge and the 1971 San Fernando earthquakes indicate that
the arch of the dam moved eastward by approximately 0.5 and 0.6 inches,
respectively (Morrison Knudsen Corp., 1994). These displacements are
within the range of thermoelastic signals reported here. It is unclear
whether or not the earthquake-related measurements accounted for
thermally induced displacement.

Spectral analysis of the residual time series (annual cycle removed)
indicates strong coherence at frequencies as high as 1 cycle per 14 days
between remotely recorded temperature and dam displacement. We were able
to derive and apply an impulse response function between input
temperature and output displacement that enable a resolution of 2-4 mm
displacement over periods of a few days. The residual deformation record
could be used to model the structure's response to changes in reservoir
level and to identify anomalous displacements at Pacoima Dam.

## ACKNOWLEDGEMENTS

This project would not have been possible without the efforts of Bob
Reader, Robert Kroll and Chuck Peer at L.A. County Department of Public
Works. Much the same can be said for our colleagues in SCIGN and the IGS
for the infrastructure they provide. We thank Maryann Vander Vis, also
of L.A. County D.P.W., for compiling geotechnical data from, and
background research on, Pacoima Dam. Repeated thanks are due to John
Galetzka, Aris Aspiotes, Shannon Van Wyk and Daryl Baisley at USGS-SCIGN
Operations Center and to L.A. County dam personnel for the installation
and continued excellent operation of the GPS stations. Special thanks go
to Robert King for his review of a draft of this paper and his continued
guidance in GPS data analysis, and to Hadley Johnson and Duncan Agnew
for their insights and suggestions on time series analysis techniques.
The photographs in Figures 1 and 3 were taken by John Galetzka.

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