8CUEE CONFERENCE PROCEEDINGS
8th International Conference on Urban Earthquake Engineering
March 7-8, 2011, Tokyo Institute of Technology, Tokyo, JapanDYNAMIC CHARACTERISTICS OF THE SURFACE SOILS IN LIMA, PERU
Diana Calderon1), Toru Sekiguchi2), Zenon Aguilar3), Fernando Lazares4), and Shoichi Nakai5)1) Doctoral Student, Chiba University, Japan
2) Assistant Professor, Dept. of Urban Environment System, Chiba University, Japan
3) Professor, Fac. of Civil Engineering, National University of Engineering, Peru
4) Researcher, CISMID, National University of Engineering, Peru
5) Professor, Dept. of Urban Environment System, Chiba University, Japandiana_c@graduate.chiba-u.jp, tsekiguc@faculty.chiba-u.jp, zaguilar@uni.edu.pe, f_lazares@uni.edu.pe, nakai@faculty.chiba-u.jp

Abstract: We have obtained dynamic characteristics of the surface soils at eight places in Lima, Peru; specifically weestimated the shear-wave velocity profile. The method we used was the inversion of dispersion curves calculated fromarray measurements. Small and large arrays of microtremors were carried out, and a new type of sensor was introduced
for the large array measurement. Important results are the relative shallow stiff soil layer in the area classified as alluvial
gravel deposit, that covers most of the area of Lima city; and the apparently deep soft soil layer in places identified as
VSV and CMA. In these last places, it is recommended to complete the analysis with large array measurements.

1.

INTRODUCTION

This study is part of the project “Enhancement ofEarthquake and Tsunami Disaster Mitigation Technology inPeru”, in which Japanese Government represented by Chiba
University and the Peruvian government represented by theNational University of Engineering (UNI) are working
together with the objective to estimate seismic risks, hazards
and vulnerabilities in Lima, the capital of Peru, and twoother cities of the country. In particular, the results of thisstudy will focus on Lima city only.
Lima is situated in the central coast of Peru, borderedby the Pacific Ocean, in a zone of high seismic activity
known as, the Ring of Fire.
Due to the high seismicity of this area and to the rapidly
growing urbanization, a study of the soil conditions thatcharacterize areas of low or high probability to be affectedby earthquakes is of great importance, specially in places
like Lima that have scarce information of deep soilstructures.
In this context, this study aims to obtain a primary ideaof the Lima’s soil structure to the depth extending to thebedrock, which will make possible the analysis of thedynamic characteristics of the surface soils of Lima
To accomplish this objective, microtremor arraymeasurement campaigns were carried out at 8 places of thecity; new long-period sensors of microtremor wereintroduced as part of the technology enhancement politics.

shows a list of these points with details of their exact
location.
Figure 1 shows a map of the Lima’s surface soil
distribution (estimated in 2005) and the distribution of themicrotremor array measurement points.
Table 1. Symbols and location of the measured points in thisstudy
ID

District

Institution

LatitudeLongitude

CMD

Rimac

12.013995°

77.050580°

PQR

12.071319°

77.033171°

DHN

Lima
cercadoCallao12.064413°

77.155016°

CMA

Callao12.060734°

77.123570°

VSV

Villa El
Salvador
PuentePiedra
LaMolina
LaMolina

UNI CISMID
Central Parkof Lima
Direction ofHydrograph
School“Maristas”
School“6066”
PrivateHouse
University
La Molina

12.213421°

76.938803°

11.852260°

77.074035°

12.082051°

76.938943°

Municipality

12.077994°

76.917278°

PPIEMO
MOL

3.
2.

SOIL CONDITION AND BORING DATAAREA OF STUDY

The study was developed over the Lima metropolitan
area; where 8 points of measurements were located. Table 1

As it can be seen from Figure 1, most of Lima area iscovered by alluvial gravels that are found at few meter
depth,; however, there are concentrated eolian, clays and- 537 -Two measurement campaigns were carried out, the firstconsists of 8 sets of small arrays (Figure 1); each set is madeof linear arrays of 0.5 and 2m sensor distance, and circulararrays of 10, 20 and 45m radius.
The second campaign consists of 2 sets of large arrays,
each set made of circular arrays of 100, 200, 400 and 800m
radius.
4.1

Implementation of microtremor sensors
Two types of sensors of microtremors were introduced
to Peru through this project. One was the well-known
GEODAS sensor (with natural period of 1 second), and theother was a sensor produced by Tokyo Sokushin company
with a natural period of 5 seconds.
5.

Array set CMD was chosen in this study to be therepresentative array set; in consequence we will show andcomment the detailed procedure to come up with its shear
wave velocity profile.
We used two methods to construct the dispersion curve;
the high resolution F-k method proposed by Capon in 1979,
and the Centerless Circular Array (CCA) proposed by Cho
et al in 2006.

Figure 1. Soil distribution map (CISMID, 2005) andlocation of microtremor arrays.
silts deposits, of which depths to the base rock are in somecases unknown .
A typical soil profile of the alluvial gravel deposit isshown in Figure 2. The profile corresponds to a soil pit near
the array set named CMD. In Lima, soil pits are more
popular than SPT explorations because the stiffness of thesoils in many areas does not allow the conduction of SPT
explorations.
The majority of boring data available in Peru has asimilar pattern of profile at CMD, it means the gravel isshallow and the depth of exploration is about 3m.
4.

MICROTREMOR ARRAY MEASUREMENTS

One of the reasons to conduct array measurements wasthe limited depth in the available boring data and thepractical way to perform it.

Depth (m)01
2Soil Column
CMD

Silty Clay
Silty Sand
Sand

Gravel3

ANALYSIS OF RESULTS

5.1 F-k spectrum
The F-k method uses the cross-spectrum between eachpair of sensors as a factor to compute the F-k power
spectrum. This can be seen with the formula of the F-kspectrum
 KP′(k x , k y , f ) =  ∑ qmn ( f ) ⋅ exp{− i 2π k x ( xn − xm ) + k y ( yn − ym ) }
 n ,m =1


[]

−1

where K is the number of channels, kx is the wave-number inthe x-direction, and ky is the wave-number in the y-direction,and f is the frequency.
qmn(f) is the inverse of a Hermitian matrix whose
elements are formed by the cross spectrum between
channels m and n. (xn,yn) are the coordinates of the sensor n,and (xm,ym ) are the coordinates of sensor m.
Since the cross spectrum is an important factor in thecomputation of the F-k spectrum, it is necessary to verify thecross-spectra to see if there is a good correlation between thesignals. In general a well correlated cross-spectrum curve isa smooth descending or ascending curve from 0 to 360
degrees or vice verse. If the curve follows this trend the F-kspectrum is verified. Sometimes more than one smooth
curve appears, in this case, in the period domain, the curve toverify should be the first at the right side. For example, inFigure 3(a) there are two curves but the one to verify is thecurve from 0.025 to 0.07 s, and in Figure 3(b) the curve isfrom 0.2 to 0.4 s. We will expect that in the dispersion curvefor the period ranges mentioned, the curve shows continuity
for the array of 10 and 200m respectively.

Figure 2. Soil Column CMD (collected data E13 ofRimac district in the study of CISMID, 2005) located at
the National University of Engineering.

- 538 -5.2 Dispersion curve
Tokimatsu (1995) mentioned that to obtain reliable
results of phase velocities, the effective wavelength range isrelated with the sensor distance as follows
Dmax > λmax/3
Dmin < λmin/2
which can be written as:

Figure 3. Cross spectra of CMD , (a) For the array of
10m, (b) for the array of 200m.
Figure 4 shows F-k spectra for different array sizes anddifferent periods. It is well-known that a sharp peak develops
for ideally noise-free data; from this statement we canconclude that the ratio of noise to signal is low for theperiods shown in each F-k spectrum, because in almost all
the cases the peak is sharp. This can be used as another way
to verify the dispersion curve.
It is also known that the sharp of the peak vary with thecoherence value, usually the coherence is high for sharp
peak spectra. Another factor that affects the coherence is thenumber of peaks in the F-k spectrum, when more than one
peak appears the coherence decreases. The presence of morethan one peak may be due to external noise, in our case we
can see that more than one peak occurs specially for thelarge arrays, which can tend to receive more noise.

2Dmin < λ < 3 Dmax
where Dmax and Dmin is the maximum and the minimum
sensor distance respectively, and λ is the wavelength.
This criterion, together with the cross spectrum and theF-k spectrum verification were used to select the points ofthe dispersion curve when using the F-k method (Figure 5).
However, in the case of the CCA method; Cho et al(2004) found phase velocities at very long wavelength
ranges, up to 30 meters the array radius. They stated that it ispossible to calculate phase velocities at very longwavelengths when the signal to noise ratio is high, which
occurs normally in few meter radius arrays.
In Figure 5 we can observed the continuity between thedispersion curves from array L0.5 (linear array of 0.5m
sensor distance) to array C45 (circular array of 45m radius).
Nevertheless, arrays C95, C200 and C400 follow anothercurve. The cause of this difference could be the fact thatthese large arrays were measured at a place separated about
800m from the place where the small arrays were measured,that is, the surface soil may be different in both places. Small
array measurements in the second place are necessary toverify the dispersion curve of the large arrays.
5.3 Inversion of dispersion curves
Several methods of inversion are available, from theconventional least square methods to the genetic algorithm
method. The genetic algorithm approach developed byGoldberg (1989) is recently very popular; this method incomparison with the typical least square method has theadvantage in which a search can be done for an optimal
solution in the local and global space.
In this study we applied the genetic algorithm (GA). To
apply this method we input an observed dispersion curve,
such as the one in dots in Figure 6(a). Previously we had
determined this curve base on the dispersion curve of Figure
5.

Figure 4. F-k Spectra for CMD arrays

Figure 5. Dispersion curve- 539 -

Figure 6. (a) Comparison between the observed and calculated dispersion curve, (b) Comparison
between the profiles estimated by inversion of dispersion curves calculated by microtremor arrays
and by MASW, (c) Comparison of H/V spectra

Figure 7. Dispersion curves- 540 -

Figure 8. H/V Spectra

Figure 9. Comparison of Observed and Calculated H/V spectra- 541 -

This observed curve or target curve, is used to compare all
calculation curves obtained in the process of the inversion.
The final calculated curve is the one that satisfy the ending
criterion, which can be either a limit number of iteration(number of generation) or a minimum fitness value. In thisstudy the first criterion was used, and the value of this limit
was up to 100.
Figure 6(b) shows two profiles, one corresponds to theinversion of the dispersion curve calculated frommicrotremor arrays and the other corresponds to theinversion of the dispersion curve calculated with the MASW
method. It is observable that both profiles are in good
agreement until the depth of 15m more or less.
Finally to verify the profile obtained with themicrotremor array, the H/V spectrum of this profile iscalculated and compared with an observed spectrum. Figure6(c) shows that there is an agreement between both spectra.
5.4 Additional Results
The same procedure taken for the calculation ofdispersion curves and estimation of shear-wave velocity
profile of study point CMD was used at the other study
points.
Figure 7 shows the dispersion curves for the rest of thepoints of study, Figure 8 shows the the H/V spectra, andFigure 9 shows the shear-wave velocity profiles;

6.

DISCUSSION

Looking at the dispersion curves we can see that theCMD place has the most rigid shallow surface soil, it can be
explained from the rock formation proximity.
The places with apparent soft deep deposits are DHN,
CMA, and VSV.
In the case of CMA, the dispersion curve at long period(array of 45m) does not show a clear curve, and it seems that
there is a dip in this part of the curve; it could mean that
there is a layer of high velocity overlying one of lowervelocity, which is what we found in the inverted profile(Figure 9(c)). Indeed, the H/V spectrum of this place has
three clear peaks (Figure 8(c)), one with a period of about 1s,
this peak could belong to soft layer mentioned before. To
verify this peak we need phase velocities at long period,
which can be obtained with large array measurements.
For VSV, the inverted profile (Figure 9 (f)) apparently
points out that there is an important contrast down to 100m.
The H/V spectrum of the calculated and observed datashows an agreement. However to verify this statement, alarge array measurement is necessary.

7.

CONCLUSIONS

The results of this study brought the following
conclusions:
1.
2.

3.

Places located in the area of alluvial gravel of Lima,
showed high shear-wave velocities at shallow depths.
In the majority of the places studied, theimplementation of large array measurements isnecessary to estimate the depth to the base-rock.
In order to verify the results of array inversion,
additional studies, preferably direct exploration test,
such as PS logging is of great importance.

Acknowledgements:
The authors acknowledge support from JICA and JST, forproviding the tools and facilities that made possible this study.
Furthermore, we are grateful to the researches and research
assistants at CISMID who helped in the realization of the tests andin the completion of this study.
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