July 2011, Volume 5, No. 7 (Serial No. 44), pp. 618-627
Journal of Civil Engineering and Architecture, ISSN 1934-7359, USA

Estimation of Deep Soil Profiles in Lima Peru
Diana Calderon1, Fernando Lazares2, Zenon Aguilar2, Toru Sekiguchi1 and Shoichi Nakai1
1. Department of Urban Environment System, Faculty of Engineering, Chiba University, Chiba, Japan
2. CISMID, Faculty of Civil Engineering, National University of Engineering, Lima, Peru
Abstract: Deep shear-wave velocity profiles at eight places in Lima Peru were estimated based on the inversion of dispersion curves.
The dispersion curves were calculated from small and large microtremor arrays using two methods: the F-k proposed by Capon(1969) and the CCA proposed by Cho et al. (2004). For the purpose of large array measurement we introduced a new type of sensor.
Important results are the relative shallow depths to the basement rock in the area classified as alluvial gravel that covers most of thearea of Lima city; and the relative large depth to the bedrock in places identified as VSV and CMA. It is recommended that this study
be complemented with PS loggings in order to verify the estimated profiles.
Key words: Microtremor array, dispersion curve, inversion, soil profile, H/V spectrum.

1. Introduction
This study is a part of the project “Enhancement ofEarthquake and Tsunami Disaster Mitigation
Technology in Peru”, in which Japanese Government,
represented by Chiba University, and the Peruvian
government, represented by the National University ofEngineering (UNI), are working together with theobjective to estimate seismic risks, hazards andvulnerabilities in Lima, the capital of Peru, and twoother cities of the country. In particular, the results ofthis study will focus on Lima city only.
Lima is situated in the central coast of Peru,bordered by the Pacific Ocean, in a zone of highseismic activity known as the Ring of Fire.
Lima has a long history of being hit by strong
earthquakes, the latest big event occurred in 1974. At
that time, severe damage in a few small scattered areas
was reported [1], which suggests a soil effect may
have occurred in these areas.
Due to the high seismicity of this area and to therapidly growing urbanization, a study of the soil
Corresponding author: Diana Calderon, PhD Candidate,research fields: microtremor array measurements, seismometer
array measurements, estimation of dispersion curves, inversionof dispersion curve alone and joint-inversion of receiver
functionanddispersion
curve.
E-mail:diana_c@graduate.chiba-u.jp.

conditions that characterize areas of low or highprobability to be affected by earthquakes is of great
importance, especially in places like Lima that havescarce information as to deep soil structures.
In this context, the study aims to obtain a primaryidea of the Lima’s soil structure down to depths
extending to the bedrock, which will make possible
future analysis of the dynamic characteristics of thesurface soils of Lima
To accomplish this objective, small and large
microtremor array measurement campaigns werecarried out at eight places in the city that are the mostrepresentative of the soil dynamic behavior anddemographic aspects; for the large arraymeasurements
newlong-period
sensorsofmicrotremor were introduced.

2. Area of Study
We have carried out microtremor arraymeasurements at eight places distributed in the Lima
Metropolitan area. Fig. 1 shows a map of the Lima’s
surface soil distribution estimated in 2005 [9], and theplaces where the microtremor arrays were measured.
Table 1 shows a list of the measured places withdetails of their exact location.

619

Estimation of Deep Soil Profiles in Lima Peru

arrays, each set made of circular arrays of 100, 200,
500 and 1000 m radius.
In almost all the arrays six sensors were used except
in CMA and in VSV where four sensors were used.
The objective of these arrays measurements was toestimate the soil profile characteristics, such as theshear-wave velocities and the thicknesses of eachlayer constituting the soil profile.
3.1 Implementation of Microtremor Sensors

Fig. 1 Location of microtremor arrays over the soil
distribution map [9].
Table 1 Symbols and location of the measured points inthis study.
ID

District

Institution
Latitude
UNICMD Rimac-12.013995°
CISMID
Lima
Central Park
PQR
-12.071319°
Cercado of Lima
Direction of
DHN Callao-12.064413°
Hydrograph
School
CMA Callao-12.060734°“Maristas”
Villa El School
VSV-12.213421°
Salvador “6066”
PuentePrivatePPI-11.852260°
PiedraHouse
La
University La
EMO-12.082051°
MolinaMolinaLa
MOL
Municipality -12.077994°
MolinaTwo types of sensor of microtremors wereintroduced to Peru through this project. One was thewell-known GEODAS sensor (with natural period of 1
second), which we used to measure small size arrays,
with radius less than 50 m; in these arrays the sensors
were connected with cables to the data acquisition
hardware.
The other was a sensor produced by Tokyo
Sokushin Company with a natural period of 5 seconds.
These sensors were used for large array measurements
because no cable is needed to make the measurements;
the sensors are synchronized by a GPS device.

Longitude-77.050580°

4. Method of Analysis-77.033171°

4.1 Phase-Velocity Dispersion Curve-77.155016°

We used two methods to construct the dispersion
curve; the high resolution F-k method [2], and theCenterless Circular Array (CCA) method [3].
4.1.1 The high Resolution F-k Method
The calculation of the dispersion curve through the
F-k method is based on the calculation ofwave-numbers of predominant waves for different
frequencies; these wave-numbers are obtained fromthe signal power spectrum that is the representation of
the signal power in a wave-number space. From Ref.
[2] the formulation of the power spectrum is given by:-77.123570°-76.938803°-77.074035°-76.938943°-76.917278°

3. Microtremor Array Measurements
Two measurement campaigns were carried out, thefirst consists of eight sets of small arrays (Fig. 1); each
set is made of linear arrays of 0.5 and 2 m sensor
distance, and circular arrays of 10, 20 and 45 m radius.
The second campaign consists of four sets of large⎡ K⎤P′(k x , k y , f ) = ⎢ ∑ qmn ( f ) ⋅ exp{− i 2π k x ( xn − xm ) + k y ( yn − ym ) }⎥⎣n ,m =1
⎦

[

]

−1

(1)
where Pَ is the F-k power spectrum, K is the numberof channels, kx is the wave-number in the x-direction,

620

Estimation of Deep Soil Profiles in Lima Peru

and ky is the wave-number in the y-direction, and f is
the frequency. (xn, yn) are the coordinates of thesensor n, and (xm, ym ) are the coordinates of sensor m.
qmn(f) is the inverse of a Hermitian matrix whose
elements are formed by the cross spectrum between
channels m and n. This cross-spectrum or cross-power
spectrum is calculated using the direct segment
method. According to this method, the value of data
point L in each channel is divided into M
mono-overlapping blocks of N data points. That is,
L=M·N. If the Fourier transform of the data in the lth
segment, mth channel and frequency f is Sml(f),S ml ( f ) = (N )−1 / 2∑a Nr

m , r − (l −1) N eπ

Z 0 (t , r ) = ∫ z (t , r , θ )dθπ

Z 1 (t , r ) = ∫ z (t , r , θ ) exp(iθ )dθ(2)where ar are weights which are used to control the
shape if the frequency window used in estimating thecross-power spectral density, and for simplicity it is−π

Their power spectral densities are denoted by
Gz0z0(r,r; ω ) and Gz1z1(r,r; ω ) respectively (whereω is the angular frequency), and are represented as:M

G z 0 z 0 (r , r ; ω ) = 4π 2 ∑ f i (ω ) J 02 (rk i (ω )) (7)G z1z1 (r , r ; ω ) = 4π 2 ∑ f i (ω ) J 12 (rk i (ω ))Then the estimate of the cross-power spectrum is(3)m, n =1,…,K*: conjugate
Another important parameter is the coherence of thenoise between seismometers m and n, cohmn(f), given
bywhere M is the number of Rayleigh wave modes
present, fi(ω) is the intensity of the ith mode, J0() andJ1() are the zeroth-and first-order Bessel functions of
the first kind respectively, and ki(ω) stands for thewave number of the ith mode. The spectral ratio is
given byM

∑ α (ω ) J (rk (ω ))G Z 0 Z 0 (r , r ; ω ) i =1
= M
G Z 1Z 1 ( r , r , ω )E[ p mn ]E[ S m2 ]E[ S n2 ]

(8)

i =1

M

∑

(6)

i =1
M

assumed that ar =1, r =1,….,N.
1*
S ml ( f ) S nl(f)
M l =1

(5)

−π

irf

m = 1,…..,K
l = 1,……,M

cohmn ( f ) =whose vertical component is z(t,r,θ), expressing theirtime histories in Fourier series with respect to θ

N

r =1

pmn ( f ) =developed is formulated in such a way that the
microtremor records, obtained with sensors placedaround the circumference of a circle, are first
integrated into intermediary quantities called “spectral
ratios” before information on the phase velocities is
extracted from them.
This can be explain by considering a circularseismic array of radius r in a field of microtremors,

spectral components of the noise, at frequency f,observed on the mth and nth are uncorrelated. In
addition, if cohmn(f)=1 then the spectral components of
the noise, at frequency f, observed on the mth and nth
sensors are linearly related to each other.
4.1.2 The Centerless Circular Array Method
Cho et al. [6, 7] pointed out that the theory they

2
0

i

(9)

∑ α (ω ) J (rk (ω ))(4)where E is the ensemble average and 0 <|cohmn(f)| ≤ 1.
The physical significance of cohmn(f) = 0 is that the

i

i =1

i

2
1

i

where

α i (ω ) = f i (ω ) / f (ω ),Mf (ω ) = ∑ f i (ω )i =1is the power partition for the ith mode.
Once the spectral ratio on the left-hand side is
known from measurements records, it is possible toestimate rk by inverting the above equation for eachfrequency ω. Since r is known, one can obtain the
wave number k, and finally the phase velocity c = ω/k.

Estimation of Deep Soil Profiles in Lima Peru

4.2 Array Dimension
Tokimatsu in Ref. [5] stated that to obtain reliable
results of phase velocities, the effective wavelength
range is related with the sensor distance as follows
Dmax > λmax/3
Dmin < λmin/2
which can be written as:
2Dmin < λ < 3 Dmax
where Dmax and Dmin is the maximum and theminimum sensor distance respectively, and λ is the
wavelength.
4.3 Inversion Analysis
Several methods of inversion are available, from theconventional least square methods to the genetic
algorithm method. We used the genetic algorithm(GA) approach [8] because it has become very
popular; this method in comparison with the typicalleast square method has the advantage in which asearch can be done for an optimal solution in the local
and global space.
As input data the GA approach requires the numberof layers and an initial model which consists of arange of shear wave velocities and thicknesses foreach layer. In this study the number of layers adopted
was from four to six, and the initial models werechosen in some cases based on available boring dataand shear-wave velocity profiles that were estimatedby surface wave methods, such as the Multichannel
Analysis of Surface waves (MASW) and theMicrotremor Array Measurement (MAM).
The number of generations and number of populations
for the inversion process was from twenty to fifty.

5. Inverted Profiles
Applying the methodology explained above we havecalculated the phase velocity dispersion curves for theeight microtremor arrays measured in Lima city (Fig.
2). Following Tokimatsu [14] we have considered theeffect of higher modes in the inversion process since
the dispersion curves showed an inversely dispersive

621

trend.
Using the dispersion curves we have estimated theshear-wave velocity profiles shown in Fig. 3. The
inversion process was carried out several times due tothe non-uniqueness solution related to this process;and a total of five cases of results are plotted in the
figure.
In order to verify the profiles we have calculated
the H/V spectra of the Rayleigh waves for thefundamental mode and compared it to the observed
H/V spectra measured at each place (Fig. 4).
A discussion to the estimated profile at each placeis presented below. For depth to the bedrock weunderstand the depth at which the shear velocity is
about 3000 m/s.
5.1 Estimated Profile at PPI (Puente Piedra District)
This district is located in the northern part of Lima
city; according to the microzonation study [9] atshallow depths the sediments are from loose to densefine sands, silty clays and landfills. In other parts there
is a gravelly material composed of medium dense
poorly-graded gravels with clays and silts. Underlying
these materials there are poorly-graded sands of
medium to loose compactness. According to thezonation map most of the urban area of the district isin the most competent zone from the seismic andgeothecnical point of view. It is important to point out
that the previous microzonation study at this place
was made based on shallow soil exploration data.
The estimated shear-wave velocity profile foundfrom the inversion analysis is shown in Fig. 3a. The
maximum size of the arrays was a circle of 28 m
radius. Based on the shear-wave velocity profile andthe boring data near PPI a description of the soils is
attempted. There is a shallow layer of about 5 m withsoils of low velocity that can be regarded as loose
sands, underlying this soil until about 60 m the soil
velocity increases to values that may account for
dense sand, down to 60m the soil velocity may
correspond to a dense gravel deposit.

622

Estimation of Deep Soil Profiles in Lima Peru

Fig. 2

Observed and calculated dispersion curves.

Fig. 3

Estimated shear-wave velocity profiles.

5.2 Estimated Profile at DHN (The El Callao District)
This place is located in the border between the El
Callao district and the La Punta district.

The geological formation at this place is particular
because the shallow materials have been taken by thesea from the cliffs located at the southern districts of
Miraflores and Chorrillos [13].

Estimation of Deep Soil Profiles in Lima Peru

Fig. 4623

Observed and calculated H/V spectra.

The soil profile here consists of a poorly-gradedgravel layer overlying a dense sand deposit until about
15 m. Under this layer there is a fine sand deposit withsilts and clays, organic clayey silt, and stiff highplasticity clays with about 20 m thickness. Finally,
there is a dense sandy gravel deposit [9].
According to the micozonation study of 2005 [9]DHN is located at zone 4, which is characterized as
the less competent soils that show high amplificationand large period of vibration.
The estimated shear-wave velocity profile is shownin Fig. 3b. Based on this profile and boring data near
DHN, we have observe that at few meters depth there
is a change of velocities from large to low values that
may be caused for the heterogeneous conformation of
the deposit, underlying there is a layer with velocities
that may account for stiff clays or silts until 35 m
depth, the last layer estimated with the arrays shows avelocity value that is coherent with the dense gravel
mentioned in Ref. [9].
5.3 Estimated Profile at PQR (Lima District)
Lima district is at the center of the Lima

Metropolitan area. Stratigraphically the alluvial deposit
covers most of the city soils and it is expected that the
thickness to the base rock here be about 200 m [9].
The soil profile consists of a very shallow layer(about 1 m) of silts that overlay the conglomerate of
the Rimac River. This conglomerate is medium denseat shallow depths and increases its compactness withthe depth.
Based on the shear-wave velocity profile shown in
Fig. 3c, there is a shallow layer of less than 5 m that
may correspond to silt deposits, after this the soil
velocity increases gradually until 100 m, that is the
maximum depth of the estimated profile, the velocity
values until this depth may account for theconglomerate.
5.4 Estimated Profile at MOL (The La Molina District)
MOL is one of the two places measured in the La
624
Molinadistrict. It is located in front of the district

Municipality.
The land surface of the district is heterogeneous,varying from outcrops in the slope of the hills tocolluvial soils in the lowlands near to the hills; and624

Estimation of Deep Soil Profiles in Lima Peru

large fluvial-alluvial deposits in the plains of thevalley at large distances from the hills. There are also
areas covered by eluvial materials, specifically eolian
sands deposited in large amounts in the depressions
and on the hillsides. These heterogeneous materials
make the stratigraphy of the area to be very variable[11].
According to the microzonation study [11] MOL isin the zone II that corresponds to colluvial gravel soils
and poorly-graded sand layers of moderate thickness.
The estimated shear-wave velocity profile is shownin Fig. 3d. We can observe that the velocities increase
gradually until about 30 m depth; from this depth toabout 60 m (maximum estimated depth) there issignificant change in the velocity value, which can be
due to the presence of a very dense gravel deposit.
5.5 Estimated Profile at EMO (National Agrarian
University Campus)
EMO is the second place of measurement in the La
Molina district. It is located inside the campus of the
National Agrarian University.
The shear-wave velocity profile estimated is shownin Fig. 3e, we can observe the gradual increase of thevelocity until approximately 100 m depth. From thisdepth there is a thick deposit with a relatively large
value of velocity of very dense gravels until it reaches
the bedrock at the depth of about 200 m.
From the microzonation study of this district [11]four seismic zones are identified in the Campus; itmeans that there is high variability on the soils;
therefore, an averaged estimated profile may fail tocharacterize a unique point of the array at large depths.
The effect of this soil variability can be observed in
the mismatch of the second peaks of the H/V spectra(Fig. 4e).
5.6 Estimated Profile at VSV (Villa El Salvador
District)
This district is located in the south of Lima, andconsists of a coastal border composed by eolian sea

deposits; plain areas covered by gravel and eolian
sands transported from the Lurin River and from thebeaches nearby; and a hill called Lomo de Corvina
composed of eolian sands, transported during the
Pleistocene epoch by winds from the adjacent beach[10].
Lithostratigraphic units that outcrop in the hill
Lomo de Corvina and surroundings consists of
sedimentary rocks of the early cretaceous epoch
represented by the Pamplona formation, sea deposits
and eolian deposits of the quaternary period [10].
According to the microzonation study in Ref. [10],the area of study belongs to zone III, and consists ofloose eolian sand deposits of large depths and sea
deposits. The shallow layer consists of landfill until 2
m depth, underlying this material there is a very thickpoorly-graded medium to fine sand of loose
compactness that increases with the depth.
Fig. 3f is the shear-wave velocity profile, fromwhich we observe that there is a low velocity for thevery few meters, this velocity accounts for a shallow
soft sand deposit. From 10 m to 200 m depth thevelocity increases gradually, with values that arecharacteristics of a very dense sand. Finally just above
the bedrock, there is a layer with a thickness of 400 m
with a uniform velocity layer of a very stiff soil orrock. The total depth to the bedrock is about 600 m.
5.7 Estimated Profile at CMA (“Marianistas” School)
This place is located in the Bellavista district thatbelongs to the Callao Province.
It is on the alluvial deposits that covers most of thecentral area of Lima city. Contrary to the soils incentral Lima, the soils forming this deposit are fine.
These are clays of 15 m thickness that were
deposited by the Rimac River during the Holocene
epoch when the river sedimentation power had
decreased [13].
According to Ref. [9] the soil conformation around
CMA consists of soft and stiff organic clays of highplasticity, high humidity of about 10 m depth.

Estimation of Deep Soil Profiles in Lima Peru

Underlying these materials there are fine soils of large
depths such as clays of low and high plasticity,
organic clays, and semi-dense silts until the alluvial
gravel characteristic of Central Lima is found.
The estimated shear-wave velocity profile presented
in Fig. 3g, shows a soft soil layer that is very shallow
and may account for the organic soils described above.
The next layer is of about 150 m, with a velocity
characteristic of very stiff soils. It is noticeable thatfrom 200 m down the layers show an increasing
velocity and the thickness of these layers is very
random. However, the depth to the bedrock can be
regarded as about 800 m.
5.8 Estimated Profile at CMD (CISMID–Center for
Seismic Research and Disaster Mitigation, UNI)CISMID is a Research Center that belongs to the
National University of Engineering. It is located in the
alluvial deposit that covers most of the area of Lima
city, and near the formation Puente Inga, which consistof igneous rocks. Due to the short distance to the hills
the soils found here are stiff gravels at few meters depth.
The estimated shear-wave velocity profile is625

resulting profiles it is recommended to carry out PS
loggings campaigns.
Among all the estimated profiles, the soil profile at
CMD shows the shallowest depth to the bedrock;while the soil profile at CMA shows the largest depth
to the bedrock. For future amplification studies inLima, CMD could be regarded as a reference site.
In the dispersion curves of VSV and CMA (Fig. 2f
and Fig. 2g respectively), there is a large range of
periods where there are scarce or no values ofvelocities. This problem is studied particularly at VSV
in Fig. 5; here we can observe that for the period range
from 0.5 s to 1.5 s the dispersion curve is discontinue;
moreover, when we look at the Fourier spectrum weobserve that for the same range of periods the powerof the wave is the minimum; therefore, the reason of
the lack of points in the dispersion curve in that rangeof periods is the low power of the microtremors. A
solution to complete the dispersion curve may beinstalling seismometers in an array configuration inorder to analyze surface waves from earthquake
records.

presented in Fig. 3h, it consists of a layer with athickness of about 20 m in which the velocities arecharacteristics of a very stiff gravel. At this depth thevelocity shows a sudden increase which may accountfor the presence of weathered rock, this increase invelocities continues until it reaches the bedrock at
approximately 100 m depth.
It is worth pointing out that profile at this place isthe more rigid and shallow among other profiles
estimated in this study; therefore, it can be regarded asa reference site for future amplification analysis.

6. Discussion
We have obtained deep soil velocity profiles ateight points in Lima city; four of them with depths
extending to the bedrock while the other four withdepths reaching approximately 60 m, with velocities
between 1000 to 1500 m/s. In order to validate theFig. 5 Observed phase velocity dispersion curve andFourier Spectrum for the VSV array.

Estimation of Deep Soil Profiles in Lima Peru

626

From the H/V spectra at EMO (Fig. 4e), we could
observe that the second peak of the calculated H/Vspectrum is for a period larger than in the observed
spectrum; to understand this behavior we have studied
the spatial variability of soils at EMO.
Fig. 6 shows the distribution of the six sensors usedin the array of 400 m radius at EMO. As we canobserve the sensors are over three different types ofsoils. To verify the effect of the soil spatial
heterogeneity we calculated the H/V spectra of three
sensors shown in Fig. 7, sensor number six’s H/V
spectrum showed a second peak in a period larger thanin sensor number one and three’s H/V spectra.
For the mentioned above, we can conclude that thedifference between the H/V spectra at EMO (Fig. 4e)is due to the spatial variability of soils inside the array,
which may also cause low accuracy in the estimatedprofile.

7. Conclusions
We have carried out small and large arrays
measurements over Lima city in order to estimate
deep soil profiles; in the process we have found thenext conclusions:a. We have obtained four profiles with depths that
extend to the bedrock. The other four profiles reachvelocities from 1000 to 1500 m/s at about 60 m depth.
b. The shallowest profile with 100 m depth to the
bedrock is CMD. Thus, this place could be regarded
as a reference site for future soil amplification studies.
c. We have identified a range of periods from 0.5 to
1.5 s at VSV where the signal power is low; and wehave found that this is related to the discontinuity ofthe dispersion curve.
d. In order to complete the dispersion curves in therange of periods where the signal is low, it isrecommended to make an array of seismometers,
because seismic records contain surface waves withhigh signal to noise power.
Finally, it is recommended to perform PS logging in
the places where arrays were measured in order toverify the estimated profiles.

Acknowledgement

Fig. 6 Large array of 400m radius at EMO over the soil
distribution map of the La Molina district [11].

We would like to express our gratitude to Eng.
Miguel Diaz for his help in carrying out the surface
wave measurements (MASW); the data of thesemeasurements was very useful for the initial model ofthe inversion analysis.

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[2]
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[4]
Fig. 7

Various H/V spectra of the array of 400m at EMO.

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