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Bulletin of the Seismological Society of America, Vol. 97, No. 2, pp. 591604, April 2007, doi: 10.1785/0120060095
Site Effects in a Volcanic Environment: A Comparison between HVSR
and Array Techniques at Colima, Mexico
by F. J. Chavez-Garca, T. Domnguez, M. Rodrguez, and F. Perez
Abstract Colima city is the capital of the Mexican federal state of the same name.It is located close to the Pacific coast and is subjected to a large seismic risk. We
present a microzonation study in this city, based on microtremors using single-station
and array measurements. We applied horizontal-to-vertical spectral ratios (HVSR)
analysis to single-station measurements at 310 sites within the city, concentrating
measurements in zones that were damaged by the January 2003 (M7.4) earthquake.
The results show that a seismic zonation based exclusively on single-station micro-
tremor measurements is not a reliable alternative when the local geology is complex
and site effects are not the result of a single-impedance contrast. For this reason, we
applied two independent analysis techniques to array measurements of microtremors:
the spatial autocorrelation (SPAC) method and the refraction microtremor (ReMi)
method. We used linear arrays to record 25-sec microtremor windows at eight siteswithin the city, which were analyzed with those two techniques. The result of both
techniques of analysis is a phase-velocity dispersion curve, which can be inverted to
obtain a shallow S-wave velocity profile. Two of the sites were the location of shallow
(50 m) boreholes, where P- and S-wave velocity profiles were measured using a P-S
suspension log. The phase-velocity dispersion curves obtained from the ReMi and
SPAC analyses of the microtremor records showed very good agreement. The velocity
profiles inverted from the phase-velocity dispersion curves showed good agreement
with the suspension logging measurements at one of the two sites where they were
available and poor agreement at the other site. The transfer functions computed from
the inverted soil profiles are in good agreement with previous estimates of local am-
plification from spectral ratios analysis of earthquake records. Our results are com-
patible with previous indications of site effects and explain the failure of single-stationmicrotremor measurements when the concept of dominant frequency loses its meaning.
Finally, we propose an estimate of local site amplification at the city of Colima, which
will be useful for future predictions of ground motion at this city.
Introduction
Damage distribution during large earthquakes is fre-
quently controlled by site effects. Subsoil impedance con-
trasts can significantly amplify the shaking level, as well as
increase the duration of strong ground motion. The larger
cities around the world have already been the subject of mi-
crozonation studies, where the different levels of ground-
motion amplification are measured throughout the city.
However, especially in developing countries, a very signifi-
cant effort has yet to be made.
Seismic microzonation has been based on observational
studies, where ground-motion amplification is measured
by using spectral ratios of small events (Borcherdt, 1970;
Chavez-Garca et al., 1990). In recent years, though, a
wealth of studies have been based on ambient vibration
(microtremor) records, given the ease and low cost with
which these data can be obtained in regions of moderate to
low seismicity. In early studies, the site resonant frequency
was deduced from spectral ratios of microtremor records
(used in the same way as earthquake records, e.g., Kagami
et al., 1986; Seo, 1992), or it was taken to be the frequency
of the peak of the Fourier amplitude spectrum of horizontal
components (e.g., Kobayashi et al., 1986; Gutierrez and
Singh, 1992). Later, the use of spectral ratios computed be-
tween horizontal components relative to the vertical com-
ponent recorded simultaneously (HVSR) became very pop-
ular (e.g., Nakamura, 1989; Lermo and Chavez-Garca,
1994; Field and Jacob, 1995, among many others. See, for
example, the review article by Bard, 1999.). It is now gen-
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592 F. J. Chavez-Garca, T. Domnguez, M. Rodrguez, and F. Perez
Figure 1. Location of Colima city, Mexico, and its regional geology.
erally recognized that the HVSR technique provides a reliable
estimate of the resonant frequency. Some authors have also
shown that, in some cases, the amplitude of that ratio is a
good estimate of the site maximum-amplification value rela-
tive to bedrock motion. A consensus regarding the use of
HVSR to estimate maximum amplification does not yet exist.
Microzonation efforts require inexpensive techniques,
such as HVSR. It is important, however, to understand thelimitations ofHVSR, and establish some guidelines to know
when the results from this technique can be considered re-
liable. Recent articles have shown many examples where this
technique was used with profit (e.g., Toshinawa et al., 1997),
but it is clear that it is not a cure-all. A few reports show
examples where HVSR was not useful (e.g., Volant et al.,
1998), or where the dominant frequency was correctly de-
termined but the associated amplitude was ineffective to es-
timate the relative local amplification (Malagnini et al.,
1996). It seems clear that when we observe amplification
due to a single, large impedance contrast between a soft soil
layer and its basement, HVSR is reliable. It is when ampli-
fication is caused by more complex local geology that theusefulness of HVSR becomes problematic and the question
of its reliability is posed more acutely.
In this context, the city of Colima is an interesting case
study. Colima is located near the Pacific coast of Mexico
(see Fig. 1). This city is the capital of the federal state of the
same name. Because its current population is only about one-
half million, Colima has not received much attention from
the seismological community. However, this city is located
close to an active subduction zone and has been affected
repeatedly by destructive earthquakes. For example, Colima
state was affected by the Tecoman earthquake of 21 January
2003, which caused 21 casualties and about 90 million U.S.
dollars in damage (Cenapred, 2003), most of which occurred
in the capital city. Unfortunately, it was not possible to cor-
relate observed damage with ground motion, as no strong-
motion station was in operation at the time of that earth-
quake, and the collapsed structures showed blatant designerrors, making it impossible to use them to estimate the dif-
ferences in ground-motion intensity throughout the city.
Colima is located on a thick (about 800 m) sequence of
volcanic deposits, consisting of a mixture of avalanches, la-
har deposits, and reworked volcanic sediments. Previous
seismic experiments have measured amplification due to site
effects as large as a factor 6 between 1 and 3.5 Hz (Gutierrez
et al., 1996). Even if large earthquakes do occur in this re-
gion, the seismicity rate is much lower than that observed
further south along the subduction zone. This makes it dif-
ficult to base microzonation efforts on earthquake records
obtained with temporary networks. Moreover, the two pre-
vious attempts at microzonation of Colima (Lermo et al.,1991; Gutierrez et al., 1996) produced contradictory results.
In this article we analyze ground motion within Colima
city and its relation with subsoil ground conditions. We re-
appraise the results of previous experiments and have made
additional measurements. We measured microtremorrecords
using single-station measurements at 310 points within the
urban area. Given the small size of the city, this means a
large density of measurements throughout. In addition, we
used microtremor measurements recorded using an array of
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Site Effects in a Volcanic Environment: A Comparison between HVSR and Array Techniques at Colima, Mexico 593
Figure 2. Surface geology within Colima city.The main streets and rivers are shown with solid linesas reference. The urban zone is delimited by the ringsformed by the main streets.
geophones. These data were analyzed by using two different
techniques: the SPatial AutoCorrelation (SPAC) method
(Aki, 1957) adapted to measurements using single-station
pairs (Chavez-Garc a et al., 2005, 2006), and the refraction
microtremor method (ReMi) introduced by Louie (2001).
Our purpose is to assess the usefulness of HVSR in the vol-
canic geology of Colima city, both as standalone method
and when complemented by microtremor array measure-ments. We compare our results with those from the previous
studies. Our results confirm that in a volcanic environment
the usefulness of HVSR decreases. In our case study, HVSR
suggests that some site effects are present, but it is unable
to constrain their spatial distribution. The use of the two
array techniques is more fruitful. We obtain phase-velocity
dispersion curves from which shear-wave velocity profiles
are inverted. These profiles are consistent with results from
suspension logging at two sites. Our results agree with pre-
vious site-amplification estimates and allow us to propose a
family of 1D soil profiles throughout the city. We do not
observe a close relation between surface geology and site
response. This probably means that the differences betweenthe outcropping geological formations make sense in terms
of the emplacement process but do not reflect significant
variations in the mechanical properties of the volcanic de-
posits. For this reason, we are unable to separate zones
within the city with homogeneous expected shaking, but our
results allows us to explain the observed effects with a model
that can be used to predict ground motion for future large
earthquakes.
Background
GeologyColima state is located 32 km to the south of the Colima
Volcanic Complex (CVC), which itself is in the western
Trans-Mexican Volcanic Belt (TVB). The CVC consists of
three andesitic stratovolcanoes (Cantaro, Nevado, and Fuego
de Colima), which define a volcanic chain with a north
south orientation as the result of the migration of volcanic
activity due to the subduction of the oceanic plate beneath
the American continent. The Fuego de Colima is one of the
most active volcanoes in Mexico. The city of Colima is built
over the volcanic sequences produced by the CVC, which
overlay a late cretacic limestone basement outcropping east
and west of the city. These volcanic sequences include ma-
terials of different ages and from different depositional pro-cesses. Geologists have identified and dated four avalanche
deposits aged 1800 to 2500 years, and many more fluvio-
laharic and debris flow deposits in between. Three types of
deposits can be mapped within the city (Fig. 2).
Volcanic Debris Avalanche. These are massive deposits
that consist of andesitic rubble, mainly between 5 and 20 cm
diameter, but with some boulders as large as 1 m. These
deposits have great thickness and cover large areas. They are
produced by the total or partial collapse of volcanic edifices
of the CVC. The blocks are cemented by small quantities of
a clay and sand matrix, and present characteristic irregular
cracks. Within Colima, avalanche deposits crop out in its
northern half. Their total thickness is about 600 m.
Volcanic Debris Flows. These are massive deposits (on
the order of several meters) consisting of andesitic, rounded
blocks within a compact sandy matrix. They are the result
of the transportation of the avalanche deposits by subsequent
water flows. The thickness of these deposits around Colima
is between 20 and 30 m, and they crop out to the south of
the city.
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594 F. J. Chavez-Garca, T. Domnguez, M. Rodrguez, and F. Perez
Figure 3. (a) Dominant-period values in secondsmeasured at Colima city by Lermo et al. (1991) frommicrotremor measurements. These authors did notdraw contours from their measured values. (b) Con-tour map of the dominant period in seconds measuredat Colima city by Gutierrez et al. (1996) from micro-tremor measurements.
Lahars, Lacustrine Sand, and Gravel Deposits. These are
stratified deposits a few centimeters to a few meters thick,
consisting of andesitic blocks within a sandy matrix. They
are about 50 m thick within the city, where they crop out
mainly in the western half.
Previous Microzonation Studies
The importance of the city of Colima and the past oc-
currence of large earthquakes have spurred previous at-
tempts at microzonation of the city. The first one was carried
out by Lermo et al. (1991). They estimated amplification at
four sites from standard spectral ratios (Borcherdt, 1970)
using data from a single, small earthquake. They found a
dominant period of 0.22 sec with an amplification factor of
2 on the avalanche deposits (downtown), and a dominant
period of 0.15 sec with an amplification of 4 on the fluvial
deposits. However, their reference station was located north
of the city, on volcanic deposits similar to those that crop
out at Colima city, making their amplification values un-
trustworthy. In addition, Lermo et al. (1991) measured mi-crotremors at 36 sites, along two perpendicular lines across
the city and estimated the dominant period as that for which
Fourier spectra of the microtremor measurements had their
maximum. They found values between 0.25 and 0.33 sec on
the volcanic avalanche, and above 2 sec on the fluvial de-
posits. Figure 3a reproduces the dominant period map pre-
sented by Lermo et al. (1991).
A few years later, and in part because of the occurrence
of a large (M 7.9) event in 1995, Gutierrez et al. (1996)
carried out a second attempt at the microzonation of Colima.
These authors installed a temporary seismic network of dig-
ital PRS-4 seismographs by Lennartz, coupled to three-
component 1-Hz sensors. They successfully recorded a fewsmall events (M4.5). They used a seismic station on lime-
stone as reference (10 km to the east of the city) to evaluate
relative amplification using spectral ratios. Their empirical
transfer functions show significant amplification on the av-
alanche deposits (up to a factor of 6), distributed about a
wide-frequency band, without well-marked peaks. Sites on
fluvial deposits showed smaller amplification (between a
factor of 2 and 5) and dominant periods between 0.3 and
0.8 sec. In addition, Gutierrez et al. (1996) measured micro-
tremors at 57 sites, and estimated the dominant period from
peak Fourier amplitude spectra. They observed dominant pe-
riods of about 0.3 sec, similar to those of Lermo et al. (1991)
and proposed a second dominant period map, where con-
tours were drawn (Fig. 3b). Finally, Gutierrez et al. (1996)
measured P- and S-wave velocities at two shallow (50 m)
boreholes by using suspension logging. The measurements
for the first 20 m were unreliable, however.
Analysis Techniques, Data Used, and Results
In the next paragraphs, we describe in brief the three
techniques we use to analyze microtremor records. They are
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Site Effects in a Volcanic Environment: A Comparison between HVSR and Array Techniques at Colima, Mexico 595
Figure 4. Location of the points where single-station microtremor measurements were carried out.A total of 310 points are shown (open circles), fromwhich only 125 were retained for the determination
of dominant period and local amplification (filled cir-cles). Stars indicate the location of SPAC/ReMi mea-surements. The location of the two shallow boreholesis indicated with open squares.
the HVSRs, an innovative approach to the SPAC method, and
the ReMi method. In addition, we present the experiments
and the results obtained in each case.
HVSR
Spectral ratios of horizontal components relative to the
vertical recorded simultaneously have been widely used to
determine site response from ambient-vibration records. The
two previous microtremor studies in Colima interpreted
dominant period from Fourier amplitude spectra maxima. In
addition the number of measurements made was small. For
those reasons, we recorded single-station microtremors at
310 sites within the Colima urban zone (open and filled cir-
cles in Fig. 4). A Kinemetrics K2 recorder with triaxial ac-
celerometers was used. At each site 3 to 5 min of ambient
vibration was recorded. From each record, we selected a
1-min window in which the records showed the smallest
number of transitory signals and the noise appeared most
stationary. We computed the spectral ratio between horizon-
tal and vertical motion from the selected window. The hor-
izontal components were combined by using a simple mean.
Despite the careful window selection, most of the records
did not produce a useful HVSR; the resulting ratios showed
no clear peak. From the 310 measured sites, only 125 (filled
circles in Fig. 4) produced HVSR where a peak could be
identified, and from which a value of dominant period and
maximum amplification were determined. Figure 5 shows
an example of an HVSR with a clear peak and another that
was rejected because no clear peak could be identified.
The 125 retained values of dominant period and maxi-
mum relative amplification, as measured from the HVSR,
were used to draw the contours shown in Figure 6. The max-
imum amplification values vary between 2 and 5, althoughthe vast majority are smaller than a factor of 2. These values
are consistent with the maximum amplification estimates by
Gutierrez et al. (1996), given that HVSR of microtremor re-
cords usually underestimates amplification (Bard, 1999), but
are clearly not very significant. Moreover, the contours of
dominant period values are not correlated with surficial ge-
ology and do not coincide with either the map of Lermo
et al. (1991) or that of Gutierrez et al. (1996) shown in
Figure 3. We have used this standard technique with as many
sites as possible within Colima, and are convinced that
Figure 6 reflects limitations in the HVSR method. These lim-
itations must result from the absence of a clear-cut impe-
dance contrast as the origin of the local amplification, some-thing also apparent in the transfer functions determined by
Gutierrez et al. (1996).
SPAC
Aki (1957) proposed the SPAC method almost 50 years
ago. As presented in that publication, the method requires
ambient-noise records obtained in a circular array of stations,
with one station at the center. This geometry allows the com-
putation of the cross-correlation between many station pairs
at the same interstation distance, r, and sampling many dif-
ferent azimuths at the recording site. The correlation coef-
ficients, q(r, x), as a function of frequency x, are computed
as the normalized cross-correlation between all station pairs
separated a distance rand averaged over all azimuths, h. Aki
(1957) showed that
2p
1q(r,x) (r,h,x) dh2p(r 0,x) 0 (1)rx
J0 c(x)where (r 0, x) is the average autocorrelation function
at the center of the array, (r, h, x) is the cross-correlation
function between the records obtained at coordinates (r, h)
and the record obtained at the center of the circle, c(x) is
the phase velocity at frequency x at the site, and J0() is the
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596 F. J. Chavez-Garca, T. Domnguez, M. Rodrguez, and F. Perez
Figure 5. Examples of the results obtained using HVSR with single-station micro-tremor measurements. (a) The result for a site where a clear peak can be observed at aperiod slightly greater than 0.2 sec. (b) The result for a site where no significant peakcan be observed.
Figure 6. Contour maps of dominant period in seconds (a) and relativeamplificationderived from 125 single-station microtremor measurements, analyzed using HVSR (b).
Bessel function of first kind and order zero. In this equation,
the only unknown is the phase velocity, c(x), which can be
obtained from the inversion of the correlation coefficients.
The subsoil structure can be deduced from the inversion of
the phase-velocity dispersion curve following standard pro-
cedures (e.g., Herrmann, 1987). The details of the method
have been presented in several publications (e.g., Asten,
1976; Chouet et al., 1998).
Chavez-Garc a et al. (2005) presented an extension of
SPAC, in which phase-velocity dispersion curves were ob-
tained from data recorded using a temporary seismic array
with a very irregular geometry. The basic difference with
respect to Akis (1957) approach was to substitute the
temporal averaging for the azimuthal averaging required by
the method. Chavez-Garca et al. (2005) showed a compar-
ison between correlation coefficients computed for a single-
station pair with those computed using an azimuthal average
at approximately the same interstation distance. The results
indicated that the substitution of temporal averaging for the
aziuthal average required by the SPAC method is valid. The
good results obtained led the same authors to apply SPAC
with an array of stations as different as possible from a circle,
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Site Effects in a Volcanic Environment: A Comparison between HVSR and Array Techniques at Colima, Mexico 597
a line of stations (Chavez-Garca et al., 2006). The results
were again very good, further supporting the use of the SPAC
temporal averaging method.
We carried out measurements at eight locations through-
out the city (shown as stars in Fig. 4, coinciding with single-
station measurements sites), sampling the different surficial
formations. We used an Oyo Geospace DAS-1 exploration
seismograph with a 24-bit dynamic range and a line of 12,vertical-component, 4.5-Hz natural frequency geophones.
The sampling rate was 2 msec. This system had a flat re-
sponse for velocity between 4.5 and 250 Hz. At each loca-
tion, the geophones were installed with a 6-m distance be-
tween them, giving a total length of 66 m, and five time
windows of about 25 sec of ambient vibration were recorded.
We verified in the field that the power spectral density for
all 12 traces was comparable, thus ruling out the possibility
of including signals in the analysis that were not common
to the whole geophone spread. Following Chavez-Garca
et al. (2006), we considered all possible station pairs to com-
pute correlation coefficients. The recorded data were base-
line corrected and tapered over 10% of their duration. They
were then filtered using a set of 38 Butterworth bandpass
filters, 1 Hz wide, between 3 and 40 Hz. The correlation
coefficient for each frequency was computed by using the
filtered traces as the average of the normalized, zero-lag
cross-correlation for eight 3-sec windows extracted from the
filtered records. These computations were repeated for all
possible station pairs for each site, and the results at the same
interstation distance were averaged for all five 25-sec mi-
crotremor windows recorded. An analysis of the range of
validity of the measurements (Rodrguez and Chavez-
Garca, 2006) indicated that our results are reliable in the
range from 5 to 20 Hz.Figure 7 shows an example of the results. The mean and
standard deviation correlation coefficients are given as a
function of frequency for all station pairs analyzed from the
records at location Parque (see Fig. 4). In the SPAC method,
each interstation distance is useful to constrain phase veloc-
ities for a different wavelength. As we treat each station pair
independently, data from a single linear array give us results
for the 11 different interstation distances shown in Figure 7.
We observe that, in all cases, the coefficients follow the
shape of a zero order, first kind Bessel function, as they
should according to equation (1). This suggests that it is
correct to assume the equivalence between the azimuthal
averaging included in the initial proposal of SPAC (Aki,1957) and the temporal averaging proposed in Chavez-
Garca et al. (2005, 2006), where a more detailed validation
has been presented. A similar result was presented by Ohori
et al. (2002) using microtremor measurements obtained us-
ing T-shaped arrays, although these authors do not explain
how they circumvented the requirement of the azimuthal
average.
It may be surprising that we get good results from the
linear SPAC method using only five 25-sec window mea-
surements. Chavez-Garca et al. (2005) used several days of
continuous microtremor measurements, whereas Chavez-
Garca et al. (2006) analyzed 30-min windows of ambient
noise. The length of the records necessary to be able to sub-
stitute temporal averaging for the azimuthal average required
by the SPAC method has not been established and most likely
it is site dependent. Relative to our previous articles, we note
that the frequencies analyzed in this article are higher, im-plying many cycles even in short time windows. In addition,
we have averaged the results of all station pairs at the same
interstation distance. This means that, for each window re-
corded by one of our arrays, the result for 6 m interstation
distance, for example, was obtained as the average of 11
correlation coefficients between different station pairs. We
must mention, however, that the good results obtained with
such short time windows here may be not representative of
other geologic or geographic settings.
ReMi
The ReMi method, introduced by Louie (2001), is basedon the p-f (ray parameter-frequency) transformation de-
scribed by McMechan and Yedlin (1981), applied by Mokh-
tar et al. (1988), and programmed in Herrmann (1987). This
transformation permits the separation of the different waves
composing the records obtained in an array of stations, ac-
cording to their different apparent velocity through the array.
The Louies innovation was in the application of this trans-
formation to ambient vibration records obtained using a stan-
dard exploration seismograph, without any seismic source.
The p-f transformation allows stacking all the recorded
waves according to their apparent wavelength. If a large
component of the recorded wave field consists of Rayleigh
waves (for vertical-component geophones) it is possible toidentify their phase-velocity dispersion as a function of fre-
quency from the image produced in the p-f plane.
The interpretation of the images obtained from the
ReMi method, however, is not straightforward. The maxi-
mum values in the image would correspond to the Rayleigh
phase-velocity dispersion curve if the microtremor wave
field were traveling in the direction of the linear array of
geophones. The recorded wave field, however, includes Ray-
leigh waves propagating with similar power in many differ-
ent directions. If this were not the case, we would not have
obtained good results from the SPAC method, where a req-
uisite is the presence of similar energy propagating in dif-
ferent directions. Thus, the condition that brings about the
success ofSPAC makes the interpretation of the results from
ReMi more problematic. Stephenson et al. (2005) proposed
to choose, for each frequency, the average value between the
slowness where the power density is maximum and the slow-
ness value for which the power density basically becomes
zero. This point corresponds to the slowness value for which
the spatial coherence between the records becomes insignif-
icant (Rodrguez and Chavez-Garc a, 2006). Another pos-
sibility is choosing the peak of the derivative with respect
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598 F. J. Chavez-Garca, T. Domnguez, M. Rodrguez, and F. Perez
Figure 7. Example of the correlation coefficients as a function of frequency com-puted for the records obtained at site Parque (Fig. 4). Each diagram shows the average(symbols) and standard deviation (error bars) of the correlation coefficients computedfor station pairs at the indicated distance. The value of dx is the distance betweengeophones, equal to 6 m.
to slowness of the ReMi image on the large slowness flankof the peak.
The data used for ReMi were the same records em-
ployed for the SPAC analysis; five 25-sec ambient vibration
records (with a 2-msec sampling) recorded using the explo-
ration seismograph at eight sites within the city (see Fig. 4).
The ReMi images obtained from each 25-sec window were
stacked to improve the signal-to-noise ratio. To facilitate the
picking of the dispersion curve, we smoothed the stacked
image on the p-fplane with two successive rectangular win-
dows, the first was 11 points long in the frequency direction,
and the second was 5 points long in the slowness direction.
Figure 8 shows, for example, the resulting ReMi images ob-
tained at the two borehole sites in Colima. The open squaresindicate the manual pick of the slowness-frequency curve
following the suggestion by Stephenson et al. (2005). The
filled squares show the machine picks at the maximum, for
each frequency, of the derivative of the image with respect
to slowness. We observe good agreement between the two
picks, which were made independently. A similar agreement
was obtained for all eight sites in the frequency range where
the results can be considered reliable. Figure 8 shows clearly
the limits of the method; we obtain useful phase-velocity
dispersion only in the frequency range from 4 to 18 Hz, inagreement with Louie (2001).
Discussion
We derived contour maps of dominant period and max-
imum amplification using the results from HVSR. The dom-
inant period values and the maximum-amplification values
are similar to those observed in previous studies (Lermo
et al., 1991; Gutierrez et al., 1996). However, all three
dominant-period maps are different, and none of them shows
a good correlation with surficial geology (compare Fig. 2,
3, and 6a). We observe that the amplification values are
small (90% of the values are smaller than a factor 3); more
than half of the measurements points indicated no amplifi-
cation at all. However, spectral ratios of earthquake records
have shown that local amplification within Colima attains a
factor of 6, although no clear resonant frequency could be
identified. We thus conclude that single-station microtremor
measurements are not useful to evaluate site effects in the
city of Colima. The reason is probably the complexity of the
volcanic geology. Surface geology shows four different
types of volcanic sediments, without obvious spatial rela-
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Site Effects in a Volcanic Environment: A Comparison between HVSR and Array Techniques at Colima, Mexico 599
Figure 8. Examples of images obtained inthe p-f (horizontal slownessfrequency) planeby using the ReMi method. (a) Image corre-sponding to the measurements at UCOL (seeFig. 4). (b) Image corresponding to the mea-surements at STAB (see Fig. 4). The solidsquares show the result of the automatic pick;for each frequency the slowness for which thederivative of the image with respect to slow-ness is a maximum. The open squares indicatethe choice of phase-velocity values for eachfrequency, using the criterion proposed by Ste-phenson et al. (2005).
tions among them. These relations, in addition, may vary
with depth, as it is known that the thickness of the deposits
may change over short distances. Finally, the distinction be-
tween types of volcanic sediments is made in terms of their
depositional mechanism, which may be not closely related
with the average S-wave velocity within the deposits. This
is clearly a situation where HVSR is not useful to evaluate
site effects.
The evaluation of the results of SPAC and ReMi has to
follow a different line. The first check is the comparison
between the phase-velocity dispersion curves obtained from
the two methods. Figure 9 shows, for example, the compar-
ison between the dispersion curves selected from the ReMi
images (those hand picked) and the phase-velocity disper-
sion curves derived from the SPAC method at UCOL and
STAB sites. We observe very good agreement in the fre-
quency range from 5 to 17 Hz. For frequencies smaller than
5 Hz, the results from the SPAC method are not reliable.
Wavelength at this frequency is about 112 m, close to double
the array length, making the measurement of phase differ-
ences unreliable (Chavez-Garca et al., 2005). For frequen-
cies greater than 18 Hz for UCOL or 16 Hz for STAB, phase
velocities from the SPAC method increase with frequency,
which is clearly unphysical. At these high frequencies,
wavelengths become shorter than 16 m and we approach the
limits imposed by the fundamental sampling theorem. How-
ever, contrary to the ReMi results, the mean phase-velocity
dispersion curve derived from the SPAC method suffers no
ambiguity, and an error bar can be estimated through the
inversion process of the correlation coefficients (see the de-
tails in Chavez-Garca et al., 2005). A similar agreement
between ReMi and SPAC was obtained for all eight sites, in
the frequency range where the results can be considered
reliable.
We are interested in site amplification, however, and
phase-velocity dispersion curves cannot be our final result.
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600 F. J. Chavez-Garca, T. Domnguez, M. Rodrguez, and F. Perez
Figure 9. Comparison between phase-velocitydispersion curves at locations UCOL (a) and STAB(b). The gray circles show the phase velocity deter-mined with the manual picking from the ReMi im-ages. Open squares with error bars show the meanvalues and the standard errors determined from theSPAC measurements. The solid line shows the phase-
velocity dispersion curve computed from the S-wavevelocity profile inverted at the corresponding locationusing the open squares as input data.
We have inverted the phase-velocity dispersion curves de-
rived from the SPAC method, first, because the difference
between ReMi and SPAC dispersion curves is smaller than
the error bars. Second, the inversion procedure we use, that
included in Herrmann (1987), takes into account the stan-
dard deviation of the data points. For the inversion of the
phase-velocity dispersion curves we have arbitrarily fixed
the layer thicknesses, small enough to give flexibility to the
inversion, but accepting that our data are not enough to con-
strain the model completely (the inversion results are not
unique, and phase-velocity dispersion has low vertical res-
olution and is more sensitive to vertically averaged elastic
properties than interfaces). Density was set to 1.8 g/cm3, and
the Poissons ratio was fixed to 0.25. We inverted exclu-
sively for S-wave velocity. The frequency range in which
our phase-velocity dispersion values are reliable implies that
we are able to constrain the S-wave velocities in the upper
30 to 40 m depths. The nonlinear inversion procedure is
replaced by a linearized stochastic least-squares problem,
which is iterated until the changes to the model in any one
iteration are small, and the analyst judges the computed dis-
persion curve to be close to the data. An example of this
judgment is shown in Figure 9 for sites UCOL and STAB.
The solid line corresponds to the dispersion curve computed
for the final profile inverted from the data for those two sites.
From the inversion of phase-velocity dispersion curves,
we obtained velocity profiles at the eight sites where linearmeasurements were made. However, it is possible to verify
these profiles only at two locations, UCOL and STAB, where
Gutierrez et al. (1996) measured S-wave velocity using a
suspension log. Their measurements, down to 50 m depth,
are shown by the gray circles in Figure 10. Suspension log
(SL) measurements at UCOL show a very large scatter in the
upper 22 m and no clear layering. At STAB, no measurement
could be made for the upper 10 m because of the very poor
quality of the signals (Gutierrez et al., 1996). The solid lines
in Figure 10 show the final model derived from the inversion
of phase-velocity dispersion at these two sites. We observe
good agreement at UCOL, especially if we ignore the scat-
tered points above 22 m depth. The results for STAB showa much poorer agreement; the S-wave velocities derived
from phase-velocity dispersion are consistently higher than
the SL measurements. It would seem that we need only to
decrease S-wave velocities between 10 and 45 m depth to get
an improved fit. However, when we do that, the phase-
velocity dispersion computed from that profile does not
match the observed dispersion curve at all. We have to ac-
cept that there is no S-wave velocity profile that could si-
multaneously fit the observed dispersion curve at STAB and
the SL measurements. The more likely reason is the different
nature of the measurements. A borehole measurement is a
punctual measurement that may not be representative of
a significant volume of the subsoil (especially if it compriseslarge boulders, where the hitting of a large boulder or hitting
just between boulders can greatly change the results). Phase-
velocity dispersion measurements, on the contrary, allow
the estimation of the average properties for the larger volume
averaged by the surface waves. It is clear that more exten-
sive measurements of S-wave velocity are badly needed at
Colima.
To compute local amplification, we have extrapolated
the surficial stratigraphy obtained from the inversion of
phase-velocity dispersion curves. Based on geologic consid-
erations, we assumed a half-space at 800 m depth. The lack
of a clear resonant frequency in our HVSR results, together
with the broadband character of the amplification observed
in the earthquake spectral ratios by Gutierrez et al. (1996)
argue against a significant clear-cut impedance contrast. For
this reason, we extrapolated our results, assuming a very
smooth S-wave velocity gradient between 40 and 800 m
depth. The topmost 140 m of the final shear-wave velocity
profiles for all eight sites are shown in Figure 11. On these
profiles, only the topmost 40 m are constrained and the
deeper structure was extrapolated. We observe surficial ve-
locities between 200 and 400 m/sec, which increase to 600
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Site Effects in a Volcanic Environment: A Comparison between HVSR and Array Techniques at Colima, Mexico 601
Figure 10. Shear-wave velocity profiles for locations UCOL (a) and STAB (b). Thegray circles show the values measured using a suspension log in 50 m depth boreholesby Gutierrez et al. (1996). The solid lines show the velocity profile obtained from theinversion of the phase-velocity dispersion curves observed using SPAC at the corre-sponding location.
to 900 m/sec at 40 m depth. This velocity increase occurs
gradually in several layers. Although the shallow structure
is well constrained on average (the averaging imposed by
the surface waves), the precise location of the shallow in-terfaces cannot be well resolved by dispersion curve inver-
sion. For this reason, we have not tried to classify the sites
based on measures like Vs30. This approach would require
additional S-wave measurements, preferably using methods
with larger resolution at shallow depths.
We do not observe any obvious correlation between the
velocity profiles and surficial geology. A likely explanation
is that a geologist may differentiate between geologic types
based on the different deposition mechanisms. However, it
is far from evident that the mechanical properties of a deposit
would change significantly because the shape of the blocks
in a given matrix goes from angular to more or less round.
Different geologic types may have similar S-wave velocities,
whereas this parameter may vary within a single volcanic
deposit because of its heterogeneity. It is clear that we do
not have the data for a more refined comparison (for ex-
ample, no geologic profiles are available from the shallow
boreholes of Gutierrez et al., 1996). Clearly, a more system-
atic study of S-wave velocity distribution within Colima is
badly needed to better understand the relation between sur-
face geology and site response.
Finally, we computed transfer functions for vertical in-
cidence of shear waves on the profiles shown in Figure 11.
The results are given in Figure 12. Lacking data, we have
neglected anelastic attenuation; therefore, amplification is
overestimated for frequencies larger than 3 Hz. Maximumamplification attains of about a factor 5, in excellent agree-
ment with the amplification factors observed by Gutierrez et
al. (1996) using spectral ratios of small earthquake records.
The frequency of the amplification peaks varies among sites
and, similar to the soil profiles, it is not easy to relate them
to surface geology. Moreover, the transfer functions show
peaks related to the resonance of different layers or that
could result from the contribution of two or more layers. We
cannot ascribe a large significance to the precise frequency
of the resonant peaks in Figure 12 and therefore we do not
claim that those transfer functions faithfully reflect local am-
plification at our eight sites. The layering in the models is
poorly constrained because of the low vertical resolution of
surface-wave dispersion. In addition, the inversion is not
unique. Finally, other observations argue against a clear res-
onant peak: the failure of the HVSR measurements to identify
one, the differences between the dominant period maps pro-
duced by different studies, and the broadband amplification
observed in earthquake spectral ratios. This, plus the impos-
sibility of relating computed amplification to surface geol-
ogy, makes it difficult to propose a microzonation map for
Colima based on our results. We do observe, however, that
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602 F. J. Chavez-Garca, T. Domnguez, M. Rodrguez, and F. Perez
Figure 11. Shear-wave velocity profiles invertedfrom phase-velocity dispersion curves observed usingthe SPAC method for the eight sites indicated withstars in Figure 4. Given the frequencies for whichphase dispersion was observed, these profiles are re-liable only down to 40 m depth. Below that depth,the profiles are an extrapolation.
seismic amplification is fairly homogeneous throughout the
city, and occurs in the same frequency band.
Conclusions
We have presented a site effect study in the city of Co-
lima based on HVSR, SPAC, and ReMi microtremor meth-
ods. Single-station HVSR measurements were carried out at
310 sites within the Colima urban zone. These data were
analyzed by using horizontal-to-vertical spectral ratios (e.g.,
Lermo and Chavez-Garca, 1994). However, a resonant peak
could be identified at only 125 of the measurement sites.
Moreover, the amplitude of this peak was very small, and
the configured isoperiod map is not correlated with surface
geology because the site effects at Colima are not the result
of fairly homogeneous soft sediments overlaying a fairly ho-
mogeneous bedrock, where amplification would be due to
the impedance contrast across a single interface. Clearly, in
this study, when the geology is complex and seismic-motion
amplification cannot be readily tied to a single resonant fre-
quency, HVSR cannot provide a reliable estimate of site ef-
fects. Thus, the disagreement between previous studies
based on microtremors at Colima city was not the result of
an insufficient number of measurement points.We have shown that the limitations of single-point mea-
surements can be partially overcome with array measure-
ments of microtremors. We obtained good results using the
SPAC method with a linear array, supporting the use of this
method with array geometries different from a circle and
confirming previous studies that have used this method. The
results from the SPAC method were validated by comparison
with results analyzed with the ReMi method. Both methods
provided very similar phase-velocity dispersion curves. We
inverted those curves to obtain shallow shear-wave velocity
profiles throughout the city. The inverted profiles were com-
pared with shear-wave velocity profiles measured with sus-
pension log measurements at two locations, UCOL andSTAB. The agreement is good at one location and poor at
the other; at the STAB site, the dispersion curves observed
either with ReMi or SPAC are incompatible with the S-wave
velocity profile measured using a suspension log. Indeed,
borehole velocity measurements, although more reliable,
may not be representative of the values that may affect
surface-wave propagation, especially if the subsoil volcanic
sediments include large boulders as in Colima city. The pres-
ence of large heterogeneities is suggested by the scatter of
the suspension log measurements for the upper 20 m at
UCOL, and the lack of measurements for the upper 10 m at
STAB.
Our final results are well constrained for the top-most 40 m and show surface velocities between 200 and
400 m/sec, increasing to 600900 m/sec. This large velocity
increase, however, occurs gradually, in several layers, and
not across a single interface. Moreover, the inverted soil pro-
files show a large variability throughout the city, with no
obvious correlation with surficial geology. This could be an-
ticipated given the intrinsic variability common in volcanic
deposits. Colima appears then as a good example of where
surface geology is a poor proxy for site characterization. The
fact that site amplification is due to several layers with grad-
ually increasing velocity explains the failure of HVSR to
identify a resonant peak and is consistent with the failure of
previous studies to identify resonant frequencies either with
microtremor measurements or using spectral ratios of earth-
quake records.
We extrapolated the shallow profiles inverted from the
dispersion curves down to 800 m, based on geologic con-
siderations. We computed transfer functions for vertically
incident shear waves on the complete soil profiles. The com-
puted level of amplification is similar to that observed by
Gutierrez et al. (1996) from spectral ratios of earthquake
records. The presence of different shallow impedance con-
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Site Effects in a Volcanic Environment: A Comparison between HVSR and Array Techniques at Colima, Mexico 603
Figure 12. Transfer functions computed for vertical, plane, and shear-wave inci-dence on the velocity profiles shown in the preceding figure. Attenuation was neglected.
trasts brings about several peaks in the transfer functions
with similar amplitude. Therefore, even if the global ampli-
fication is important, it is distributed in a wide frequency
range, and the frequency of the first resonant peak varies
largely throughout the city.
In conclusion, our results allow us to integrate previous
indications of site effects and explain the failure of single-station microtremor measurements when local geology is
complex, a problem that can be overcome, in part, using
array measurements. Our results indicate that it is not worth-
while to make a microzonation of the city. Seismic ampli-
fication level is similar all over the city, and the concept itself
of resonant frequency loses its meaning in this geologic con-
text. The best approach at the moment is to consider a ho-
mogeneous amplification factor of 6 for the frequency band
between 0.2 and 5 Hz. We are convinced that this is the best
that can be proposed at the moment, and is in agreement
with all the data that have been analyzed to date in Colima.
This estimate will have to be validated when a strong motion
network operates in this city, but for now it can be used to
predict seismic risk.
Acknowledgments
We thank Abel Cortes for the time he spent explaining the volcanic
deposits of Colima valley to us. We also thank Juan Tejeda Jacome for his
continuous support and help throughout the different stages of the field
work. The comments by two anonymous reviewers and the Associate Ed-
itor, A. McGarr, helped us to improve our manuscript. Signal processing
benefited significantly from the availability of SAC (Goldstein et al., 1998).
This research was supported by Conacyt, Mexico, through contract SEP-
2003-C02-43880/A.
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Instituto de IngenieraUNAM, Ciudad UniversitariaCoyoacan, 04510, Mexico D.F., Mexico
(F.J.C.-G., M.R.)
Observatorio VulcanologicoUniversidad de ColimaColima, 28045, Colima, Mexico
(T.D.)
Facultad de Ingeniera CivilUniversidad de ColimaColima, 28045, Colima, Mexico
(F.P.)
Manuscript received 28 April 2006.
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