micro tremor h and v spectral radio comp a ration using surface wave scheme_scf_3_jerez

8/3/2019 Micro Tremor h and v Spectral Radio Comp a Ration Using Surface Wave Scheme_scf_3_jerez

1/9

COMPARISON BETWEEN MICROTREMOR H / V SPECTRAL RATIO AND THEORETICALRESULTS BY USING A SURFACE WAVE SCHEME

A. G. Jerez 1, 2, M. Navarro 1, 2 and F. Luzn 1, 2

1Dpto. Fsica Aplicada, Universidad de Almera, Caada de San Urbano s/n, 04120-Almera, Spain, e-mail: [email protected]

2Instituto Andaluz de Geofsica, Universidad de Almera, Caada de San Urbano s/n,04120-Almera, Spain.

SUMMARY

In this work we study the shape of the H/Vspectral ratio for ambient seismicnoise in a known layered structure. An analytical approach is used to computethe theoretical ratio due to a distribution of an infinite number of point sources onthe ground surface for the real model (supposed as layered medium).Onlyeffects of Rayleigh and Love waves are considered. The results confirm that ageneral agreement can be obtained from simulations based on surface wavesthough the precise shape of the predominant peak is not reproduced. Thesurface sources, which generated the surface waves, can be characterized

using horizontal (LH) and vertical forces (LV). When the ratio among these forces(LH / LV) was between 0.75 and 1.50 the comparison of real and synthetic datahad a reasonable good agreement. The shape of the Nakamuras ratio appearsmainly determined by the fundamental and higher Rayleigh modes exceptaround the predominant peak where Love and body waves have the highestweight. On the other hand, the observed predominant period agrees with thefundamental period computed for vertically incident Swaves in a model of onelayer with averaged properties of the real layered structure.

INTRODUCTION

The existence of non-consolidated sedimentary deposits in the shallow part of a geologicalstructure may be the cause of increase in the seismic hazard. The reason is the possibility ofamplifications of seismic waves for certain frequency bands due to the velocity contrast betweensoft and stiff materials (see Snchez-Sesma and Luzn, 1995). An especially dangerous situationoccurs when the resonant frequency coincides with the natural periods of the buildings andadditional effects of resonance appear on the edifices.

Soil conditions are often variable even inside of a relatively small area as a town so it isnecessary to find a low-cost method to obtain a detailed dynamic characterization of soil.Evaluation of soil behavior from the spectral ratio between horizontal and vertical spectralcomponents of microtremors was introduced by Nogoshi and Igarashi (1971) and used later byNakamura (1989).The applicability of this method and its theoretical basis has been discussed bymany authors (e. g. Lachet and Bard, 1994; Konno and Ohmachi, 1998; Nakamura, 2000; AlYuncha and Luzn, 2000; Luzn et al., 2001; Enomoto et al., 2002)


2/9

An important question refers to the composition of the elastic waves which make up ambientseismic noise. In the original Nakamuras explanation, horizontal component of microtremorsconsists of multi-reflected S waves whereas the vertical component is mainly dominated by Pwaves which not suffer amplification in a thin sedimentary layer because of its higher wavelength.Amplification of vertical motion is due, under these hypothesis, to the effects of Rayleigh waves.Considering that H/V ratio is 1 at bedrock, Nakamura (1989) concludes that spectral ratio atsurface is a reliable estimation for transfer function of surface layers corrected of the effects ofRayleigh waves.

Current researches show that Nakamuras explanation, based on body waves, does not reallydemonstrate that spectral ratio is the soil response for horizontal oscillations neither aroundpredominant frequency (Bard, 1999). Better results have been obtained supposing thatmicrotremors are composed by a high ratio of surface waves. This assumption is supported onthe presence of dispersion in seismic noise which is a typical characteristic of Rayleigh and Lovewaves. That evidence has been obtained from multiple experiments using arrays of sensors. (e.g.Flores et al., 2003; Enomoto et al., 2000)

In many papers (Nogoshi and Igarashi, 1971; Lachet and Bard, 1994; Konno and Ohmachi, 1998)the general agreement between ellipticity curves of Rayleigh waves and microtremor spectralratio is established. Ellipticity curves represent the horizontal to vertical ratio for the motion of aparticle due to a plane Rayleigh wave. In case of a soft layer over a stiff half space, existingenough impedance contrast (upper than 2.5 - 3) these theoretical functions show a well definedpeak which position is in fairly good accord with the fundamental resonant frequency of verticallyincident S waves f0 Although the real contribution of surface and body waves is still discussed(see for example Nakamura, 2000 and Konno and Ohmachi, 1998 or Arai and Tokimatsu, 2000),all them recognize that Nakamuras method provides a reliable estimation of the fundamentalfrequency for this kind of geological structure. Lachet and Bard (1994) show from simulationsusing surface sources that this agreement appears again for many layered profiles.

Other interesting matter is the possibility that information about the level of amplification for thecase of earthquake could be obtained from microtremor spectral ratio. In the case of high contrastof impedance between sedimentary layer and basement the ellipticity curve of fundamentalRayleigh mode suffer a divergence for a frequency near to f0 so the identification of amplificationfactors seems difficult for this approach. Though, Konno and Ohmachi (1998) developed asmoothing function in order to deal with these infinite peaks and found reasonable correlationswith the theoretical maximum amplification for vertically incident S waves. On the other handLachet and Bard (1994) found, taking simulations of body and surface waves into account, worsecorrelation, and a high influence of Poissons ratio for the upper layer on the peak amplitude.

Several recent works try to obtain more information than the fundamental frequency from thewhole shape of the spectral ratio and not only from the region around f0. In Konno and Ohmachi

(1998) is already noticed that this function shows a trough for a frequency about 2 f0 which can beused to obtain the resonant frequency. The possibility of a good characterization for thesedimentary structure is analyzed by Fh et al. (2003) by using genetic algorithms in order toinvert the soil profile from a fitting of the measured H/V. In that paper only the fundamentalRayleigh mode is used in the forward calculation and the method fails for some particularstructures in which higher modes of surface waves and body waves should be considered.Arai and Tokimatsu (2000, 2004) improve that method taking all modes for surface waves and therelative contribution of Rayleigh and Love waves as 40% and 60% respectively for the entireconsidered frequency band.

In this paper we use the scheme developed by Arai and Tokimatsu in order to check the reliabilityof this technique for a known soil profile which characteristics were obtained form downhole andfrom S-wave refraction surveys.


3/9

WAVEFIELD DUE TO A RANDOM DISTRIBUTION OF SURFACE SOURCES

It is currently accepted that the ambient noise wavefield is mainly made up of Rayleigh and Lovewaves in the interest band (Tamura, 1996). The lower geometrical attenuation for this kind ofwaves in relation to body waves and the shallow location of the responsible sources contribute tothis situation. The solutions for the surface wave wavefield created by several kinds of sourceswere solved by David G. Harkrider (1964).

The motion due to a point source located on the free surface of an homogeneous layered solidcan be computed by using a cylindrical coordinate system ),,( zr (where zgrows with depth). In

this system, a solution of the Naviers equation can be expressed for the displacement as:

zwurqS ++= r

(1)

where the dependence tie is here and subsequently omitted.

In order to obtain an analytical solution for the motion equation we employ the Hankel integraltransform. The problem is reduced to a contour integration in the complex wavenumber plane.The effects of surface waves appears as poles of the resulting integrand and the motion due tobody waves is related to the branch line integration along the real and imaginary axes (Tamura,1996). Taking only the effects of surface waves into account it is possible to obtain thedisplacement on the free surface due to an harmonic point force with horizontal component LVand vertical LV applied at the coordinates origin as a summation of normal modes (m index) of

Rayleigh and Love waves:

+=m

VR

HRS mm

www +=m

VR

HRS mm

qqq =m

HLS m

uu (2)

The superscript (H or V) refers to the source component which is related to each term. Thesubscript (R or L) alludes to Rayleigh or Love waves. S means surface waves. The value foreach contribution was computed by Harkrider (1964) as:

)()()(2

)2(0 rkHAL

iw RmRmV

VRm

= (3)

)(Im)()(2

)2(1

2

rkHwuALiq Rm

m

mRmV

VRm

=

&& (4)

cos)(Im)()(2

)2(1 rkH

w

uAL

iw Rm

m

mRmH

HRm

=

&

& (5)

cos)(Im)()(2

)2(0

2

rkHw

uAL

iq Rm

m

mRmH

HRm

=

&

&(6)

sin)()()(2

)2(0 rkHAL

iu LmLmH

HLm

= (7)

In these expressions,ARm() andALm() are the medium response factors for Rayleigh and Lovewaves, respectively, defined by Harkrider (1964) which depend on the layer parameters. )2(nH is


4/9

the Hankel function of second kind and order n, ( )mm wu && / is the ellipticity of the m Rayleighmode, defined in Haskell (1953) which controls the behavior of this kind of waves at large

distance and is referred to the direction of the horizontal force.

In order to obtain an approximation to the surface wavefield, the procedure described by Arai and

Tokimatsu (2000, 2004) was followed. We assume a random dense distribution of point sourcesand consider that they work independently (multiplied by random phases). It is also supposedindependence between different modes of surface waves. If kr is large enough (kr>>1) we cantake an approximated expression for Hankel functions (Abramowitz and Stegun, 1972):

krkrHn /2)(2

)2( (8)

Then, adding the power spectrum of each mode and integrating for the entire distribution ofsources, we find the vertical and horizontal powers as:

(9)

(10)

respectively, in which VH LL /= and is a common constant for both expressions. Now, the

theoretical spectral ratio is computed as:

V

H

P

PVH =/ (11)

This quantity should be equivalent to microtremor spectral ratio if the mentioned assumptionswere satisfied. Note that sources should be placed not too close to the observation device. Theminimum distance must be about one wavelength or higher for some soil structures (see Tamura,1996).

SOIL STRUCTURE FOR THE INVESTIGATION SITE

The site under study is situated inside of Almeria University Campus, located in the southern partof Almeria province (southern Spain). Geologically, this region has sedimentary materialscomposed of Neogene and Quaternary elements, posterior to the main tectonic stage and they

were deposited after a period of intense erosion. The main landform is formed by Holocenealluvial deposits created by the Andarax River, which runs through the region from North toSouth, composed by silt, sand and gravel uppermost Pleistocene gravel. Between the surfacedeposits and the basal gravel, the layer containing a lot of fine materials distributes.A physical model of the soil structure, composed of six homogeneous layers over a half-space,was obtained from borehole data carry out by CEMALSA Geotechnical Company on the

investigation place. A first approach to the characteristic of the materials has been obtained onthe basis of the empiric calculation of the NSPT -value, following the approaches of Yoshida and

Motonori (1988). These authors relate the value ofwith the NSPT value on the basis of the typeof sedimentary formation.

The shear velocity values obtained (Figure1) have been contrasted with other values assigned to

each geologic material according to several classification (Navarro et al., 2001). The values of theP-wave velocity and density were calculated from by using a linear fitting of previous data

+

+

m mL

mLV

m mmmR

mRVH

k

AL

w

u

w

u

k

ALP

22

2

2222

2

221

&

&

&

&

+

m mmR

mR

VV w

u

k

A

LP

222

2

21 &

&


5/9

determined for similar materials in the region (Alcala et al., 2002). For depth higher than 21meters a stiffer basement appears. We take a value of 600 m/s for its shear velocity. This resulthas been obtained as an average from several refraction surveys in the area.

MICROTREMOR OBSERVATIONS

In order to determine the predominant period of soil two short-period microtremor measurementwere recorded on the investigation place. The data acquisition was a SPC 35, composed of athere-components high sensitive seismometer with a natural period of 1 second, and a digital

recorder. Each observation time was 180 sec and the signal was sampled every 0.01 seconds.We took special care to avoid disturbances caused by machinery, traffic or other human activitiesnear the instrument during microtremor measurements. At each observation, six parts of therecords of 20.48 sec. were selected in order to conduct a Fourier analysis. The signal was Fouriertransformed and smoothed using a 0.3 Hz Parzens window. On the other hand, a singlehorizontal spectrum was generated using geometrical average of two horizontal spectra (Figure2), and H/Vwas computed obtaining the response of soil (Figure 3). The results show that H/Vspectra ratio is very stable and the predominant period value obtained is around 0.35 sec.

An averaged Swave velocity can be estimated from:

1=

==

n

i i

i

n

1i

i

h

h

(12)

where i and hi are the Swave velocity and the thickness for the layer irespectively and n is thenumber of layers. In our model n = 6 (see figure 1). This formula provides a shear velocity valueof 223 m/s for a sedimentary layer of H= 21 meters. By using an approach based on vertically

incident Swaves a value of 0.37 sec. is obtained for the fundamental resonant period T0= 4 H /This value shows good agreement with the predominant period obtained from microtremormeasurement.

Figure 1. Soil profile of the site under study, located in the AlmeraUniversity. Values for the half-space are not displayed here.


6/9

COMPARISON WITH RESULTS OBTAINED FOR SURFACE WAVES

In order to study the reliability of an interpretation forH/Vspectral ratio by using a method basedon surface waves we applied the previously explained methodology and carried out a simulationfor the soil profile obtained from borehole data. We take the equations (9) to (11) which providean approach to the shape of the spectral ratio due to a random distribution of sources andconsider that the layered structure shown in figure 1 is over a half-space defined above.

Two interesting magnitudes to study are the medium responses ARm() and ALm() for eachRayleigh and Love mode (see figure 4). These functions control the relative weight of the modesof surface waves. We can notice from figure 4a that the fundamental Rayleigh mode is thepredominant one in the considered band of frequencies except for a narrow gap around 0.25 sec.in which the first higher mode dominates. For a period of 0.087 sec. this higher mode presentsagain an important influence. Second higher Rayleigh mode reaches its maximum level for 0.06s.We can also notice that, in this case of high impedance contrast, the contribution of thefundamental mode vanishes at 0.28 sec. The particle motion around this period is almosthorizontal and a divergence in H/Vappears forT= 0.28 sec. For this band, the contribution ofsurface waves is due to Love modes only (figure 4b).

The finite height for the real predominant peak (see Fig. 3) can be only explained for this profiletaking body waves into account (Nakamura, 2000; Tamura, 1996) Contributions of Love waves(Figure 4b) show a simpler dependence on frequency. The fundamental mode carries the higheramount of energy for the entire range of periods. First and second higher modes give maximumcontributions forT=0.073 and T= 0.116 sec. respectively.

Considering all these modes, the theoretical shape for H / Vratio was calculated from equation(11). Since source characteristics are unknown, and in order to study its effect, several values forthe source ratio LH / LV were considered. These results are displayed in figure 5 for LH / LVvarying from 0 (vertical force) to 2 ( predominance of horizontal force) Similar characteristicsappears for all these cases: a) Infinite value forT= 0.28 sec.; b) a clear trough in about 0.15 sec.and c) secondary peaks forT= 0.07 and T= 0.12 sec. In accord with Arai and Tokimatsu (2000)we find that all the Rayleigh wave modes determine the shape ofH/Vwhile Love waves establishthe level of the spectral ratio (note that no Love wave results forLH/ LV = 0)

0,1 1 100,1

1

10

SPECTRALRATIO

H/V

PERIOD (SEC)

Figure 3. Microtremor averaged spectral ratio

(thick line) computed from 12 windows of20.48 sec. each one.

Figure 2. Example of amplitude Fourier spectrum

for each component. Single horizontalcomponent spectrum is represented by black lineand the Fourier spectrum of vertical component

0,1 11E-4

1E-3

0,01

0,1

FOURIER

SPECTRUM(M

KINE*SEC)

PERIOD (SEC)


7/9

From figure 5 we can notice that a reasonable agreement between theoretic and measuredfunctions is obtained for a value of the source ratio about 0.75. It means that the proportionamong horizontal to vertical load for the averaged source does not suffer strong variations withfrequency.

Figure 5. H / V ratio computed for the contribution of surface waves due to an uniform

distribution of point sources on grown surface. Thick line symbolizes the averaged spectral ratiofor microtremors. Each thin line is related to a value of the horizontal to vertical load ratio LH/ LVat source position.

B

Figure 4. Soil response for Rayleigh and Love normalmodes divided by the wavenumber. This ratiodetermines the weight of each mode in the total power.

A


8/9

CONCLUSIONS

We have carried out a comparative study between an empirical measurement of the horizontal tovertical spectral ratio for ambient noise and the theoretical results from a surface wave scheme.From this study the following conclusions are obtained:

(1) The predominant period for this sedimentary structure, obtained by using Nakamurasmethod for ambient noise is about 0.35 sec. and coincides with the fundamental mode ofvertically incident Swaves, taking an averaged model with a layer over the consolidatedhalf-space.

(2) A general good agreement is found between measured and simulated shapes of H/Vspectra. Two secondary peaks should be related to first and second higher Rayleighmodes and a clear trough, in about 0.15 sec. is also successfully predicted.

(3) The contribution of Rayleigh waves vanishes about 0.28 sec. For this and slightly largerperiods (the main peak) almost all vertical motion is supplied by body waves in order to

explain the real form of the peak. The largest contribution to horizontal spectra of Lovewaves (forLH / LV > 0 ) is found inside this gap too.

(4) Love waves determine the general level for the simulated ratio. If we consider only verticalloads (LH = 0) basic characteristic of Nakamuras quotient are already obtained.Theoretical ratio can provide a reasonable approach for a fixed value of the source ratioLH / LV. It means that the proportion horizontal load to vertical load for the averagedsource doesnt vary strongly with frequency.

ACKNOWLEDGMENTS

We would like to express sincere thanks to geotechnical company CEMALSA which provided us

with the borehole data. This research was supported by the CICYT grants REN 200308159C0201, REN 200204198C0202/RIES, by the European Community with FEDER, and theresearch team RNM 194 of Junta de Andaluca (Spain)

REFERENCES

Abramowitz, M. and I.A. Stegun (1972). Handbook of mathematical fuctions, Dover, New York.

Alcal-Garca, F. J., Espinosa, J., Navarro, M., and Snchez, F. J. (2002) Propuesta de DivisinGeolgica de la Localidad de Adra (Provincia de Almera). Aplicacin a la Zonacin SsmicaRev. Soc. Geol. Espaa. 15 pp. 55-66

Al Yuncha, Z. and Luzn, F. (2000). On the Horizontal To Vertical Spectral Ratio in SedimentaryBasins. Bull. Seism. Soc. Am.Vol. 90, 4, pp.1101-1106.

Arai, H. and K. Tokimatsu (2000). Effects of Rayleigh and Love Waves on microtremors H/Vspectra. Proc. 12th World Conf. on Earthquake Engineering, paper 2232, CD-ROM

Arai, H. and K. Tokimatsu (2004). S-Wave Velocity Profiling by Inversion of Microtremor H/VSpectrum. Bull. Seism. Soc. Am., 94(1), pp. 53-63.

Bard, P.Y., (1999) Microtremor Measurements: A Tool for Site Effect Estimation? The Effects ofSurface Geology on Seismic Motion. , Vol. 3, 1251-1279, Balkema.

Enomoto, T., Kuriyama, T., Abeki, N., Iwatate T., Navarro, M. and Nagumo M. (2000) Studi onMicrotremor Characteristics Based on Simultanious Measurements Between Basement and


9/9

Surface Using Borehole. Proc. 12th World Conf. on Earthquake Engineering, paper 918/4/A, CD-ROM

Enomoto, T., Kuriyama, K.; Navarro, M., and Iwatate, T. (2002): Site-Effects Evaluation by H/VSpectra Comparing Microtremor With Strong Motion Records Observed at Ground Surface andBasement Using Borehole, 12th European Conference on Earthquake Engineering, paper 596.Londres.

Fh, D., Kind, F. and Giardini, D., (2003), Inversion of local S-wave velocity structures fromaverage H/Vratios, and their use for the estimation of site-effects Jour. of Seism. , 7, pp. 449-467.

Flores, H., Aguirre E. and Aguirre J. (2003) SPAC: An Alternative Method to EstimateEarthquake Site Effects in Mexico City. Geofs, Int. Vol. 42 (2), pp. 227-236

Harkrider, D. G. (1964), Surface waves in multilayered elastic media. Part 1 Bull. Seism. Soc.Am., 54(2), pp. 627-679.

Haskell, N. A. (1953), The Dispersion of Surface Waves on Multilayered Media Bull. Seism.Soc. Am., 43(1), pp. 17-34.

Konno, K. and Ohmachi, T. (1998), Ground-Motion Characteristics Estimated from Spectral Ratiobetween Horizontal and Vertical Components of Microtremor, Bull. Seism. Soc. Am., Vol. 88, N.1, 228-241.

Lachet, C. and Bard, P.Y. (1994), Numerical and Theoretical Investigations on the Possibilitiesand Limitations of Nakamura`s Technique, J. Phys. Earth, 42, pp. 377-397.

Luzn, F., Z. Al yuncha, F.J. Snchez-Sesma and C. Ortiz-Alemn (2001). A Numerical Experiment

On the Horizontal to Vertical Spectral Ratio in Flat Sedimentary Basins. Pure and AppliedGeophysics, 158, pp 2451-2461.

Nakamura, Y. (1989). A method for dynamic characteristics estimation of subsurface usingmicrotremors on the ground surface, Q. Rept. RTRI Japan 30, 25-33.

Nakamura, Y. (2000) Clear Identification of Fundamental Idea of Nakamuras Technique and ItsApplicationsProc. 12th World Conf. on Earthquake Engineering, paper 2656, CD-ROM

Navarro, M. T. Enomoto, F.J. Snchez, I. Matsuda, T. Iwatate, A. Posadas, F. Luzn, F. Vidal, K.Seo (2001). Surface Soil Effects Study Using Short-period Microtremor Observations in AlmeriaCity, Southern Spain. Pure appl. Geophys, 158, 2481-2497.

Nogoshi, M. and Igarashi, T. (1971) On the Amplitude Characteristics of Microtremor (part 2),Jour. Seism. Soc. Japan, 24, 26-40

Snchez-Sesma, F.J. and F. Luzn (1995). Seismic Response of Three-Dimensional AlluvialValleys for Incident P, Sand Rayleigh Waves. Bull. Seism. Soc. Am. Vol. 85, pp. 269-285.

Tamura S. (1996). Comparison of Body and Rayleigh Wave Displacements Generated by aVertical Force on a Layered Elastic Medium. Proc. 11th World Conf. on Earthquake Engineering,paper 1722, CD-ROM

Yoshida Y. and Motonori I. (1988) Empirical Formulas of SPT Blow-Counts for Gravelly SoilsProc. ISOPT-1, Orlando (USA)

micro tremor h and v spectral radio comp a ration using surface wave scheme_scf_3_jerez

Documents