Applicability of the H/V spectral ratio of microtremors in assessing site effects on seismic motion

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2002; 31:261–279 (DOI: 10.1002/eqe.108)

Applicability of the H=V spectral ratio of microtremorsin assessing site e4ects on seismic motion

Victor H. S. Rodriguez∗;† and Saburoh Midorikawa

Department of Built Environment; Interdisciplinary Graduate School of Science and Engineering; TokyoInstitute of Technology; 4259 Nagatsuta; Midoriku; Yokohama 226; Japan

SUMMARY

The authors examine the reliability of site response estimations obtained by the horizontal to vertical(H=V) spectral ratios of microtremors by means of cross-validation with the ratio of the horizontalspectra of earthquake motion with respect to reference sites. The data comprise microtremor and groundmotion records recorded at 150 sites of Yokohama strong motion array. The use of non-supervisedpattern recognition techniques aims to group the sites with more objectivity. Attributes de?ning theoverall shape of the ampli?cation spectra serve as input in the computation of Euclidean distancesimilarity coe@cients amongst sites. The implementation of the Ward clustering scheme leads to theattainment of a meaningful tree diagram. Its analysis shows the possibility of summarizing the resultsinto six general patterns. A good coincidence of site e4ects estimates at 80 per cent of the sites becomesapparent. However, this coincidence appears poor for sites characterized by H=V ampli?cation ratiosaround 2 or smaller and predominant periods longer than 0:5 s. In such cases, the presence of sti4,sandy sediments in the soil pro?le proves common. To proscribe H=V estimations, relying solely onthe small spectral ratios criterion seems inadequate. Copyright ? 2001 John Wiley & Sons, Ltd.

KEY WORDS: H=V spectral ratio; microtremors; seismic motion

1. INTRODUCTION

Damage to structures settled on soft ground appears as a recurring phenomenon accompanyingthe occurrence of earthquakes. Di4erent authors have identi?ed signi?cant ampli?cations ofearthquake ground motion, known as site e4ects, as one of the main factors responsible for thisdamage. They also attribute their great variability to a strong dependence on geological andtopographical conditions [1–3]. Methods based on the analysis of strong motion data prevailwhen estimating these site e4ects, for they emerge as a straightforward representation of the

∗ Correspondence to: Victor H. S. Rodriguez, Department of Built Environment, Interdisciplinary Graduate School ofScience and Engineering, Tokyo Institute of Technology, 4259 Nagatsuta, Midoriku, Yokohama 226, Japan.

† E-mail: victor@enveng.titech.ac.jp

Received 15 November 2000Revised 7 May 2001

Copyright ? 2001 John Wiley & Sons, Ltd. Accepted 7 May 2001

262 V. H. S. RODRIGUEZ AND S. MIDORIKAWA

origin of the damage. However, the availability of ground motion records seems like a privi-lege shared by only a few territories among a large number of regions threatened by earthquakedisasters.This problem moved researchers to look for new alternatives. At present, the use of mi-

crotremors, an idea pioneered by Kanai et al. [4], remains as one of the most appealing ap-proaches in site e4ects studies. Researchers in Japan continued improving microtremor-relatedtechniques for decades. However, in other countries some researchers distrusted microtremortechniques, on the basis of ?ndings pointing to di@culties in distinguishing source and sitee4ects in microtremor recordings [5]. Meanwhile, Nogoshi and Igarashi [6–8] suggested thatmicrotremors are predominantly composed of Rayleigh waves, basing their assumption onthe similitude of the horizontal to vertical spectral ratio of microtremors (H=V) with that ofRayleigh waves. The overall situation in the use of microtremors for site e4ect estimationsstarted changing, drastically, after the 1985 Mexico earthquake. In Mexico city, which su4eredconsiderable damage [9], information attained from strong motion records clearly coincidedwith that provided by microtremor studies [10–12].The H=V technique gained renewed attention from the engineering community, due to

revision and improvements made by Nakamura and Ueno [13] and Nakamura [14], whoproposed a quasi-transfer function calculation model, which basically states that the horizontalto vertical motion ratio at the base layer (H=VB) approximates one, and accordingly, the H=Vratio at the surface turns into an estimation of site response. Several researchers have later ontheoretically supported the H=V technique through numerical simulations, including Field et al.[15], and Bard and Lachet [16], who modelled the microtremors’ source as random impulsesdistributed on the surface; and Lermo and ChavNes-GarcNOa [17], Tokimatsu [18], and Konnoand Ohmachi [19], who relied on results attained from the numerical simulation of Rayleighwaves. The simulations carried out by these authors have supported earlier ?ndings by Nogoshiand Igarashi [5–7], in spite of other theoretical interpretations claiming that microtremors mayinclude both body and surface waves in non-clari?ed proportions. The same authors have alsosuggested that the possibility of estimating site e4ects from the H=V ratio of microtremorsseems the result of a near disappearance of the vertical motion of Rayleigh waves at theresonance frequencies of the sites, which causes the H=V ratio to become asymptoticallyin?nite. Therefore, the ability of the H=V ratio to reveal the resonance frequencies becomesa function of the velocity contrast between the soil pro?le layers.In addition to the afore-mentioned studies, several researchers have provided numerous

examples of good results derived from the practical application of the H=V technique indiverse geological environments, such as Field et al. [20–22], Field and Jacob [23], Zhao etal. [24; 25], Kanno et al. [26], Horike et al. [27], and Toshinawa et al. [28]. Most of theseauthors coincide in ascertaining the robustness of the H=V technique in the estimation of theresonance periods, and its relative suitability to determine ampli?cation ratios. Accordingly,the recent trend in the use of microtremors to estimate site conditions relies on the H=Vtechnique appropriateness to determine the resonance periods and relative ampli?cation ratiosof the sites, at a relatively low economic cost.However, until today researchers have not arrived at a conclusive agreement on the applica-

bility of these estimates, as pointed out by Bard [11], who considered as urgent the followingissues: (1) To improve the understanding of the wave?eld of short-period microtremors, and(2) To assess the reliability of H=V-based transfer functions through empirical comparisonswith better-understood instrumental estimates. In this paper, the assessment of the reliability

Copyright ? 2001 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2002; 31:261–279

ASSESSING SITE EFFECTS ON SEISMIC MOTION 263

Figure 1. Location of the area under study and epicentres of the events employed in the analysis.

of site e4ects estimations based on the H=V spectral ratios relies on cross-validation withestimates of site e4ects from earthquake motion data based on the reference site method(RSM) proposed by Borcherdt [29].

2. DATA USED AND ANALYSIS PROCEDURE

Figure 1 illustrates the location of Yokohama city within the Kanto plain, a region situated inthe East-central part of Honshu, the main island of the Japanese archipelago. The city coversan area of 434 km2, with a population of 3:3 millions. At present, Yokohama counts with astrong motion network composed of 150 recording sites (Figure 2), whose installation startedwith 18 sites in 1996, and complemented with the instalment of other 132 observation sitesin 1997. The strong motion data consist of accelerograms for three events, with epicentresshown in Figure 1. The microtremor data comprise three measurements made at all sites witha three-component velocity meter. The response of the instrument remains nearly constantfrom 0.2 to 10 Hz, as illustrated in Figure 3.These sites display a broad range of geological conditions, bounded between ?ll and soft

rock (see Figure 2). The prevailing landscape features include the presence of hills or plateauscovered by Pleistocene loam deposits composed of volcanic ash; and lowlands, composed ofHolocene sediments deposited along the sea and aggrading rivers. The availability of the S-wave velocity pro?les down to soft rock [30] permits to analyse their relation with the transferfunctions.

Figure 2. Yokohama city strong motion array and geomorphological features: (1) Fill and reclaimedland, (2) Holocene, (3) Pleistocene, (4) Loam plateau and (5) Soft rock.

Figure 3. Frequency–magni?cation characteristics of the velocimeter employedin microtremor measurements.

Figure 4. Flowchart of methodology.

Figure 5. Spectral analysis Qowchart.

A combination of spectral analysis and pattern recognition techniques becomes the cor-nerstone of this study. As shown in Figure 4, the whole process involved three main steps:(1) Spectral analysis: Selection of an appropriate smoothing function that provides a goodcorrelation between seismic motion and microtremor ampli?cation spectra; (2) Pattern recog-nition: To reveal hidden trends in the form of spectral patterns (clusters). The training sampleconsists of spectral parameters attained in Step 1; and (3) Interpretation: Examination of thecorrelation amongst spectral patterns, surface geology, and borehole data.

3. SPECTRAL ANALYSIS

The ground motion data include accelerograms of three events with magnitudes Mj=4:6; 4:8,and 5.7 (Figure 1). However, the analysis only deals with portions of 10:24 s, starting fromthe onset of the S-wave arrival. In case of microtremors, the spectral analysis involves threeportions of 20:48s for each site. Figure 5 illustrates in detail the whole process. In both cases,Fast Fourier transforming the orthogonal NS and EW components as a complex vector yields

the horizontal motion Fourier spectrum at each site. After this, the application of two methodsleads to the attainment of the transfer functions: (1) The horizontal to vertical spectral ratioof microtremors (H=V) and (2) The ratio of the horizontal spectra of seismic motion withrespect to reference sites (RSM). The H=V spectral ratio of microtremors technique consistsin the division of the horizontal motion spectra by the vertical component spectrum at eachparticular site. All ?nal ampli?cation spectra attained by the application of the H=V or RSMmethod turn into an average of di4erent transfer functions, resulting from the analysis of threemicrotremor or ground motion records, respectively.

3.1. Horizontal spectral ratio of ground motion with respect to reference sites (RSM)

Borcherdt [29] introduced this method, whose strongest assumption suggests that the Fourierspectrum of the site taken as reference matches the Fourier spectrum of the source. The methodconsists in dividing the earthquake spectra of the site of interest by a nearby reference sitespectrum. In frequency domain (f), the amplitude spectrum of ground motion due to thejth event recorded at the ith site (Aij(f)) appears as the product of a source (Oj(f)), path(Pij(f)) and site e4ect (Si(f)) terms as

Aij(f)=Oj(f)Pij(f)Si(f) (1)

To apply this method, the reference site r(i= r) must bear a negligible site response:Sr(f)=0, and path e4ects Pij(f) must operate in a similar way for all sites. This lastcondition applies only when the interstation spacing appears small compared to the epicentraldistance. Under these two conditions, the estimation of site e4ects at each site (Sri ) takes theform of the following expression:

Sri =1J

J∑j= 1Aij(f)=Arj(f) (2)

The ideal seismic bedrock appears as the perfect reference site: an outcrop with an S-wave velocity of about 3 km=s. Notwithstanding, this condition becomes too restrictive forengineering purposes. Hence, the de?nition of reference site categorizes as such a place owninggood site conditions, expressed by negligible ampli?cation of seismic waves. In structuralmodels, researchers usually adopt as the engineering bedrock a layer characterized by anS-wave velocity between 400 and 600 m=s. Obviously, the selection of the reference site(s)seems the most acute di@culty in this method. To ?nd an ideal reference within the area ofYokohama, completely covered by ?ll and reclaimed land, becomes quite di@cult. However,it appears possible to ?nd engineering bedrock sites with an S-wave velocity between 400and 600 m=s. In this study, the ?ve reference sites appear on soft rock, at locations indicatedin Figure 2.The underground structure below the engineering bedrock seems likely to vary, which stands

as another factor justifying the use of ?ve reference sites instead of only one. Such variationsraise concerns regarding the trustworthiness of transfer functions if the same spectrum remainsas reference. In such a case, we may divide certain horizontal motion Fourier spectra by areference spectrum characteristic of a site having a completely di4erent underground struc-ture. This implies di4erent path e4ects, and Equation (2) becomes invalid. To minimize thisproblem, we calculated the reference spectra for each particular site j(RSj(f)) as a weighed

Figure 6. EW component accelerograms registered for the 16 May 1998 earthquake: (a)–(e) Recordsat the ?ve reference sites; (f)–(j) records at another ?ve sites with evidences of sites e4ects.

Plots arranged in increasing epicentral distance.

linear combination of the reference sites horizontal spectra (HSi(f)), with weights given bythe inverse of the separation distances (dij) between the reference site i and the particular sitej. The analytical form appears given by Equation (3), which provides the means to spatially‘decluster’ the reference spectra in terms of distance:

RSj(f)=5∑i= 1

HSi(f)dij

/5∑i= 1

Accelerograms for the 16 May 1998 earthquake recorded at the ?ve reference sites, plusrecords at another ?ve sites appear in Figure 6(a)–(e) and (f)–(j), respectively. Two obser-vations arise concerning the ?ve reference sites: (1) Their records appear relatively shorter;(2) The recorded peak ground accelerations seem also relatively smaller. Reference spectracalculated for the ?ve non-reference points (Figure 6(f)–(j)) appear in Figure 7(a)–(e). Theweights given to the reference site horizontal spectra at each point appear to the bottom left.For instance, the weights assigned in case of sites TTT and TTK look similar, because oftheir relatively close location (Figure 2). However, the weights used in case of sites TRJand TDW appear quite di4erent, for they rest relatively far from one another. After attaining

Figure 7. Reference horizontal spectra and RSM ?nal ampli?cation spectra for the ?venon-reference points. (a)–(e) Reference spectra; (f)–(j) RSM ampli?cation spectra. The

circles indicate maximum spectral values.

these reference spectra, the computation of the RSM-based ampli?cation spectra relies on theimplementation of Equation (2), thus dividing the horizontal spectra at each particular site bythe corresponding reference spectra (Figure 7(a)–(e)). Figure 7(f)–(j) illustrates the resultingampli?cation spectra for the ?ve points (TTT, TTK, TRJ, KHS, and TDW).

3.2. Selection of the best smoothing window in terms of correlation

The application of di4erent variants of two ?lters, both derived from a rectangular pulsefunction in frequency domain, provides the means to smooth the spectra: (1) the Parzenwindow (WP), and (2) a logarithmic window (WL). The authors compared the Parzen windowwith other ?lters currently employed in seismic engineering studies, such as the Hanning,Hamming, and Bartlett windows, but found no signi?cant di4erences in the resulting spectra.The Parzen window stands as a well-known digital ?lter. The analytical expression appears

as Equation (4), where f stands for frequency, and u sets a constant:

WP(f)=34u[sin(�uf2

)/�uf2

Konno and Ohmachi [19] pointed out the inQuence of the smoothing function in the H=Vspectra of microtremors. They proposed the use of a logarithmic equation to smooth themicrotremor spectra, thereby reducing the distortion of peak amplitudes. The mathematicalexpression appears as Equation (5) below, where f stands for frequency, fc for centre fre-quency, and b sets a bandwidth coe@cient:

WL(f; fc)=

(log(ffc

)b)/log(ffc

)b]4(5)

Figure 8. Plots of the smoothing functions employed in this study centred at 1, 2, and 5Hz frequencies.(a) Logarithmic window in log scale, (b) Logarithmic window in linear scale, (c) Parzen window in

logarithmic scale and (d) Parzen window in linear scale.

Both log and linear scale plots of these smoothing functions come into view in Figure 8.As shown in Figure 8(a), when plotted using log scale the logarithmic window behavesas a symmetric function that maintains a constant width regardless of frequency, while theParzen window (Figure 8(c)) looks like a non-symmetric function increasing its width atlower frequencies (long periods). On the contrary, as shown in Figure 8(b), when plottedwith linear scale, the logarithmic window appears as a non-symmetric function that increasesits width at higher frequencies (short periods), but the Parzen window seems now a symmetricfunction that has a constant width at any centre frequency (Figure 8(d)).In actual practice, the preceding explanation means that the WP smoothing appears uniform

in linear scale (constant bandwidth), while the WL smoothing appears uniform in logarithmicscale (proportional bandwidth). In the case of WL the smoothing becomes stronger towardsthe high-frequency portion of the spectrum (short periods). This smoothing level operatesinversely proportional to the width coe@cient (b), which means that relatively small b valuesprovide the strongest smoothing. Smoothing of the spectra at each site takes place by settingbandwidths B=0:1; 0:2; 0:3; 0:4, and 0:5Hz for the Parzen window; and bandwidth coe@cientsb=10; 15; 20; 25, and 30 for the logarithmic window. The application of 10 smoothing levelsproduces 10 RSM and H=V spectral data distributions. The appropriateness of Parzen (WP)or logarithmic (WL) windows in this study relied on the calculation of correlation coe@cientsbetween the RSM- and H=V-based predominant periods, maximum spectral ratios, as well asspectral ratios at 15 ?xed frequency values. Taking into consideration the correlation coef-?cient between predominant periods and maximum spectral ratios distributions, the best WL

appears to be the b=15 variant (Figure 9(a) and (b)), while the best WP appears to be theB=0:3 Hz one (Figure 9(c) and (d)). Even though the coincidence of predominant periodslooks similar for both ?lters (r=0:69vs. r=0:70), the logarithmic smoothing provides the bestoverall correlation of estimates in terms of maximum spectral ratios (r=0:65vs. r=0:51). Thecomparison of the general trend of spectral correlation curves obtained for the ?ve variants of

Figure 9. Scatterplots showing the relation among predominant periods and maximum spectral ra-tios attained from the RSM and the H=V methods. (a), (b): When the spectra are smoothed us-ing a logarithmic window (width coe@cient b=15). (c), (d): When the spectra are smoothed

with a Parzen window (bandwidth B=0:3 Hz).

the WL and WP under consideration reinforces the previous statement, as illustrated in Figure10(a) and (b) respectively. Any point on these two plots represents a correlation coe@cientcalculated from 145 pairs of spectral ratios (RSM vs. H=V) at a certain frequency value. Itappears apparent that the logarithmic function smoothing (Equation (5)) provides a better jointstability and correlation in terms of spectral ratios and predominant periods. Hence, spectralparameters attained with the logarithmic window smoothing (bandwidth coe@cient b=15)become the best choice as input in the pattern recognition process.

4. PATTERN RECOGNITION

An amount of 290 ?nal ampli?cation spectra makes quite arduous the analysis of the relationbetween results attained from both methods and the logging data. This appears especially truewhen, as in this case, the logarithmic scale of the spectra makes personal judgment evenmore prone to error and bias. The application of pattern recognition aims to increase theobjectivity of the analyses, as well as to improve the accuracy of the results. As one possiblesolution, the authors decided to organize the soil pro?les taking into account, simultaneously,the following factors: (1) The shape of the whole ampli?cation spectra within the frequency

Figure 10. Pearson correlation coe@cients (r) between the RSM- and H=V-based spectral ratios at 15?xed frequency values: (a) for all logarithmic windows and (b) for all Parzen windows.

range of interest; (2) The coincidence between predominant periods and maximum spectralratios; and (3) The general agreement level between ground motion- (RSM) and microtremor-based (H=V) estimations. This seems unachievable except through the employment of variablesdescribing the whole shape of the ampli?cation spectra. Unfortunately, traditional statisticaltools now become ine4ective, for they all share a common drawback: they seem limitedto the analysis of up to two variables at unison, i.e. to bivariate analysis. However, theuse of pattern recognition techniques (PR) known as cluster analysis turns into a plausiblealternative. In this study, the application of such techniques aims to organize the sites, so asto unveil relatively homogeneous groups or clusters of ampli?cation spectra. The process isschematically illustrated in Figure 11.If by considering at unison (1), (2), and (3) above the clustering of the sites takes place,

then the corresponding S-wave velocity pro?les may also look similar. Such an assumptionemerges on the grounds of previous studies indicating that spectral ratios calculated for di4er-ent frequencies of the spectrum reQect the characteristics of the soil pro?le at di4erent depths[18]. Thus seen, each soil layer operates as one of the components of a multilayer ?lter actingon the upcoming waves; and accordingly, the overall shape of the ampli?cation spectra be-comes an indirect representation of the underground structure. Two di4erent soil pro?les cancertainly appear characterized by similar predominant periods and maximum spectral ratios.Nevertheless, the overall shape of their corresponding ampli?cation spectra may still appearquite contrasting. To reduce the problem only to peak periods and spectral ratios seems equiv-alent to restricting the analysis to a very small portion of the whole spectrum, which makesit di@cult to disentangle the relation between spectral characteristics and logging data.The calculation of Euclidean distances amongst sites provides a measure of their mutual

similarities; and therefore, the shorter the distances the stronger the resemblance among sites,and vice versa. The Euclidean similarity coe@cient establishes similarities as the distance (dij)between two sites i and j within a space Ek , with dimensions de?ned by the number of kattributes (Ak) employed in the analysis, as expressed by Equation (6) [31; 32].

√34∑k = 1

(Aki − Akj)2 (6)

Figure 11. Pattern recognition process.

The predominant periods and maximum spectral ratios attained from both methods(Figure 9), and 15 spectral ratios representing the contribution at di4erent frequencies from0.5 to 10 Hz (Figure 10(a)) suit the parameters k in Equation (6). Taking these 34 variablesin raw form may result in misleading results, for they would carry deceptive weights in thesimilarity coe@cient calculations, due to the following:

(a) Parameters measured in di4erent scales: For instance, 0.1 does not carry the same weightas 10 in the calculations (Equation (6)). This turns into a disadvantage, because predominantperiods would weigh less than most of the spectral ratio values. However, the standardizationof the data set guarantees unit free measures by converting all the variables to the sameunit system, in this case to values between 0 and 1, while keeping their relative relation.This procedure takes the form of the following expression, where x stands for the variableto be standardized, and xmin and xmax represent the minimum and maximum values of the xdistribution, respectively:

xs =x − xmin

xmax − xmin(7)

(b) Considering the correlation amongst spectral ratios and the standard deviation of theirdistributions, it seems apparent that spectral ratios at certain frequencies become more mean-ingful than others (Figure 10); thus, they must not carry the same weight. Weighing the34 variables with respect to their standard deviation ensures that the weight given to thembecomes proportional to the spread of their values.The computation and arrangement of all possible Euclidean distances among sites according

to Equation (6) takes the form of a similarity or dissimilarity matrix. Later on, the applicationof the Ward clustering algorithm leads to the attainment of the clusters or groups. Themathematical and computational features of both procedures do not fall within the scope of

Figure 12. Grouping attained from the application of pattern recognition. (a) Dendrogram showing therelative similarity amongst sites, (b) Grouping scheme showing the division into 20 groups of sites

sharing very similar characteristics.

this study, so we will not treat them further. The representation of the results of this clusteringprocess in graphical form leads to the attainment of a plot called tree diagram or dendrogram[31], as illustrated in Figure 12(a). This graph illustrates at which similarity levels the 145sites appear to gradually group into increasingly similar subclusters, until reaching the bottomlevel, where all sites stand alone and similarity equals 1.

5. INTERPRETATION

The interpretation of the tree diagram stands as a di@cult task, because we attempt to identifypreviously unknown groups. The clustering scheme depicted in Figure 12(a) reveals hiddentrends in the correlation between the RSM and H=V site response estimations. For example, atdendrogram cut 2 the clusters composed of 11 and 20 sites (Patterns 1 and 6) appear robustin terms of both coincidence and shape of ampli?cation spectra (Figure 12(b)). However, forthe rest of the clusters this similarity of spectra does not appear meaningful until we group theremaining 53, 38, and 23 sites into smaller subclusters, as shown at dendrogram cut 2. Finally,the authors merged the dendrogram analysis results with their own academic judgement toregroup the resulting 20 clusters into the generalized patterns illustrated in Figure 13.Typical S-wave velocity pro?les for each of these general patterns appear in Figure 14,

while Figure 15 illustrates their location on top of a simpli?ed geomorphological map. The

Figure 13. Generalization of results into six patterns. Thick line: RSM ampli?cation spectra; Thin line:H=V ampli?cation spectra; Shaded area: H=V spectra ±1 standard deviation; Tm ; Am: Predominantperiods and maximum spectral ratios for the H=V-based spectra; Ts; As: Predominant periods and

maximum spectral ratios for the RSM-based spectra.

Figure 14. Typical S-wave velocity pro?les for the six patterns illustrated in Figure 13.

extremes are Pattern 1 (Figure 13(a)), with member sites characterized by no matching ofestimates; and Patterns 2 and 6, whose member sites display a remarkable agreement of esti-mates (Figure 13(b) and (f)). The agreement between estimated RSM and H=V ampli?cationspectra seems good also for Patterns 3, 4, and 5, even though no coincidence of predominantperiods comes to light at some sites. The following provides a concise description of thesesix patterns:Pattern 1: No coincidence of RSM and H=V estimates. The H=V maximum ampli?cation

ratios appear around 2, with H=V predominant periods around 0:6 s (Figure 13(a)). Membersites appear located close to or in the border of the river channels, particularly on deluvial

Figure 15. Location of sites pertaining to each of the ?nal six patterns and their relationwith geomorphology. (1) Fill and reclaimed land, (2) Holocene, (3) Pleistocene, (4) Loam

plateau and (5) Soft rock.

and alluvial sediments (Figure 15). This may explain the presence of frequent intercalationsof thick, sandy sediments in the soil pro?le as a consequence of their deposition when therivers Qood adjacent areas. The S-wave velocities of such layers oscillate around 300 m=s(Figure 14(a)).Pattern 2: Very good agreement of estimates. The H=V spectral ampli?cation ratios appear

between 3 and 5, with H=V predominant periods around 0:4 s (Figure 13(b)). The membersites appear located mostly on Loam plateau (see Figure 15). A clear contrast between theengineering bedrock and the upper sedimentary layers becomes apparent (Figure 14(b)).Pattern 3: Good coincidence of estimates. The H=V spectral ampli?cation ratios appear

around 3, and the predominant periods around 0:2 s (see Figure 13(c)). The impedance ratioseems high, but the thickness of the sedimentary layers appears smaller than in Patterns 2and 4 member sites (Figure 14(b) and (d)).Pattern 4: Good coincidence of estimates. The H=V spectral ampli?cation ratios appear

around 3.5, and the predominant periods around 0:3s (see Figure 13(d)). The impedance ratio

Figure 16. Scatterplots showing the relation between RSM- and H=V-based predominant periods andmaximum ampli?cation ratios for each of the six patterns.

seems high, and the thickness of the sedimentary layers tends to increase when comparedwith Pattern 3 member sites (Figure 14(d)).Pattern 5: Although the H=V ampli?cation ratios seem relatively small, a good matching of

estimates becomes apparent (Figure 13(e)). The H=V maximum spectral ampli?cations appeararound 2, with predominant periods around 0:15 s. The impedance ratio between lower andupper layers seems high, but the thickness of the top sedimentary layers displays a cleartendency to have very small values (see Figure 14(e)).Pattern 6: The agreement of estimations at these sites seems very good (Figure 13(f)). H=V

ampli?cation ratios appear around 4, with predominant periods around 0:9 s(Figure 14(f)). As seen in Figure 15, the spatial distribution of these 19 sites seems re-lated to the river channels, ?ll, and reclaimed land. The presence of thick, soft sedimentarydeposits in the soil pro?le arises as one of the main characteristics of Pattern 6 member sites(see Figure 14(f)).The scatterplots in Figure 16 illustrate the relation between predominant periods and max-

imum ampli?cation ratios for the six patterns illustrated in Figure 13. The H=V predominantperiods estimations coincide with the RSM ones at 80 per cent of the sites. In the case ofthis parameter, the largest overestimations appear clearly associated with Pattern 1 membersites. This seems apparent when comparing the correlation coe@cients between the RSM andthe H=V period distributions: including Pattern 1 sites r1 = 0:69 and excluding them r2 = 0:93.However, the H=V technique displays a clear tendency to overestimate both parameters (pointsunder the x=y lines), with only a few underestimations (points over the x=y line). Themaximum ampli?cation ratios show a more complex behaviour, with both under- and over-estimations in all groups. To exclude Pattern 1 sites does not improve the correlation coe@-cient either (r1 = 0:69 vs r1 = 0:66), for as seen on Figure 13(a), the spectra appear basicallyQat, without noticeable peaks. Although predominant periods and maximum spectral ratiosemerge as pairs, the fore-mentioned di4erences suggest that dissimilar factors may inQu-ence their respective distributions. In general, the coincidence of RSM and H=V estimations

appears good at most of the sites (80 per cent), with the exception of some sites pertainingto Pattern 1.In this regard, it appears worth mentioning the following:

(1) The cross-validation process performed in this study stands on the grounds that theRSM method provides better understood spectral estimates, at least from the theoreticalpoint of view. Nevertheless, site and topographical e4ects may also a4ect the referencesites themselves [33]. This inQuence, almost irrelevant in other cases, may turn con-spicuous on sites characterized by a nearly Qat response. Therefore, the coincidence ofestimates in this study provides evidence of the applicability of H=V estimations at 80per cent of the sites under the conditions previously discussed; but the non-coincidenceconstitutes no conclusive proof of its non-applicability at the remaining 20 per cent(Pattern 1). Any conclusions on this particular issue must rely on an exhaustive studyregarding the inQuence of both site and topographical e4ects on the selected referencesites.

(2) In spite of this, the application of hierarchical clustering techniques appears useful tode?ne spectral patterns that proved useful when evaluating the reliability of site re-sponse estimations using microtremors. The lack of instrumental data, mainly groundmotion data, in many seismically active regions of the world limits the applicabilityand reliability of many microzonation techniques currently in use. In this regard, theattainment of spectral ampli?cation patterns, obtained for speci?c geotechnical environ-ments may provide insight to clarifying the reliability issue of site response estimationsin other regions sharing similar characteristics.

6. CONCLUSIONS

Through the application of di4erent spectral analysis and pattern recognition techniques, theauthors cross-validated the reliability of site response studies using the H=V spectral ratio ofmicrotremors with the ratio of ground motion with respect to reference sites (RSM) withinYokohama city, Japan. A good coincidence of H=V of microtremors- and ground motion- basedampli?cation spectra appears clearly at 80 per cent of the sites. However, the coincidenceseems poor when the H=V-based maximum ampli?cation ratios decrease to around 2 forpredominant periods longer than 0:5 s. These sites seem characterized by the presence ofintercalations of thick, sti4 sandy layers in the soil pro?le, with low impedance ratios betweenlower strata and the upper sedimentary layers. In such cases, researchers should treat H=Vestimations with extreme care and avoid relying only on H=V estimates. However, somesites show a clear good coincidence of estimates, even for small spectral ratios pertaining topredominant periods located in the short-period portion of the spectrum. Therefore, to proscribeH=V estimations, relying solely on the small spectral ratios criterion becomes inadequate.

ACKNOWLEDGEMENTS

This study became possible under the auspices of a scholarship granted by the Japanese Ministry ofEducation, Culture, Sports, Science and Technology. Hereby, we express our deepest gratitude to all

working Japanese people who make such opportunities available. Gratitude also goes to the membersof the Western Branch of the National Centre for Seismological Research (CENAIS), and the Insti-tute of Geophysics and Astronomy (IGA) of the Republic of Cuba for their cooperation and support.Suggestions from Professors Takumi Toshinawa, Kazuoh Seo, Hiroaki Yamanaka and Tatsuo Ohmachiremain highly appreciated. Special thanks to Hideaki Nishida, for his incredible work compiling themicrotremor data.

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Applicability of the H/V spectral ratio of microtremors in assessing site effects on seismic motion

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