Ruido en Colima.pdf

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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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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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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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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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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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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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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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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


11/14


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


12/14


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-


13/14


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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