Seismic vulnerability mapping of Urubamba city using H/V method

Springer Nature 2021 L
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Zoning of seismic vulnerability in the city of
Urubamba - Peru using the H/V spectral
quotient method
Manuel Abarca1*
1*Section of Seismology, Imag-e, Los Pinos, Urubamba, 08661,
Cusco, Perú.
Corresponding author(s). E-mail(s): manuel.z.abarca@outlook.es;
Abstract
I decided to carry out a seismicity and seismic vulnerability study in
the city of Urubamba with the H/V spectral ratio method, because
the region shows a high degree of seismic activity, with some large-
magnitude earthquakes; to which is added the geological vulnerability
historically recorded in this city (glacial fall, avalanches from hills,
floods). The theoretical foundations of the H/V method (also called
Nakamura’s) are discussed in depth, in order to clarify some con-
fusing concepts regarding the sources of microseismic activity and
the type of waves that constitute the seismic noise wavefield. Said
microtremor field was recorded with a short period seismometer. The
seismic data were then subjected to a geophysical inversion process
aimed at obtaining a seismic model of the soil. The results of the
fundamental frequency of the terrain, the seismic amplification and
the acceleration were used to elaborate a seismic vulnerability map.
Keywords: Seismology, seismicity, seismic hazard, seismic vulnerability
1 Introduction
The H/V spectral ratio method, or Nakamura’s method, is being widely used to
seismically zonation of urban areas (Akkaya, 2020) (Zaslavsky, 2009) (Parolai
et al, 2001) (Mendecki et al, 2014) (Bignardi et al, 2016) (Gosar, 2017) ,
airports (Courboulex, Mercerat, Deschamps, Migeon, Baques, Larroque, Rivet,
1

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2 Seismic vulnerability in Urubamba - Peru
and Hello, 2020) and even in archaeological studies (Zeid, Corradini, Bignardi,
Morandi, Nizzo, and Santarato, 2016), due to the effectiveness that has been
proven in the determination of some seismic variables, such as the frequency
of fundamental resonance of the ground (f0), the amplification factor (A0) of
the acceleration (or of the speed of the seismic waves), the thickness of the
superficial sedimentary layer and others.
This is a technology that evaluates the dynamic seismic response of the soil
at the present moment; unlike other seismic hazard studies that are based on
the analysis of historical seismic information. Its main assumption is that the
soil has the same dynamic response to large-magnitude earthquakes as it does
to very small-amplitude background seismic activity.
It is methodologically simple, since it only requires a seismic station in
three components, recording for a short period of time, which can vary from 30
minutes to 24 hours. The ratio of the horizontal (H) to the vertical (V) com-
ponents in the frequency domain directly reveals two important parameters:
the fundamental frequency and the amplification. The theoretical principles
underlying the method are presented in section 3.
2 Seismicity of Urubamba
Perhaps the first thing I should point out is why study the seismic charac-
teristics of the land on which the city of Urubamba sits?. The answer to this
question unfolds into two aspects, one is the purely scientific and seismologi-
cal aspect, the other is pragmatic and has to do with the social and economic
reality in which scientific research is carried out. From the purely seismological
point of view, it would be enough to see on a map the number of earthquakes
and seisms of lesser magnitude that have historically occurred in the surround-
ing region and neighboring Urubamba (Fig. 1). From the year 1590 to the
present, 68 earthquakes have occurred with magnitudes ranging from 4.1 mw
to 7.4 mw, in a range of depths that do not exceed 100 km, which means that
all these hypocenters are located within the lithosphere and that they do not
It originates from the subduction mechanism of the Nasca lithospheric plate
under the South American lithospheric plate.
However, and looking at the seismicity map, it can be seen that the city
of Cusco is closer to high-magnitude earthquakes, therefore that would be the
logical target for a study of seismic hazard and vulnerability. Actually this
study began in the city of Cusco, but after having surveyed some measurement
points with the H/V spectral method, I realized that I would need to measure
many points (1000 or more) to cover the area occupied by the city. This became
an unattainable study objective, because I had no sources of financing to cover
the costs of the survey. That is why I decided to move the studio target to
the city of Urubamba, where I could carry out all the surveying by myself and
cover the expenses with my own money.
This is the second reason, and a pragmatic one, for which the study of
seismic vulnerability is carried out in the city of Urubamba.

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Seismic vulnerability in Urubamba - Peru 3
Urubamba province seismicity
72°30'W 72°00'W 71°30'W
14°00'S
13°30'S
13°00'S
1000
2000
3000
4000
5000
altitude
m
0
0
Fig. 1 Seismicity of the Urubamba region from the 1590 to 2018 years.(source:Centro
Regional de Sismologia - CERESIS)
I also have some geological reasons to pay special attention to the city
of Urubamba. It has experienced some disastrous events such as glacier
avalanches, mountain collapses and river floods. The soils on which the city
is based are of the alluvionic type, so it is important to know the dynamic
response of these soils to seismic events. On the other hand, an earthquake
could act as a trigger for geological disasters like those that have already
occurred in the past.
2.1 Seismic intensities
Another way to analyze susceptibility to earthquakes is through seismic inten-
sities. This information will tell us how the earthquakes were perceived by
the population of the place, as well as what were the physical effects on the
anthropogenic structures and buildings.
There is very little registered information about intensities in the city of
Urubamba (Tavera, Agüero, and Fernández, 2016). This is because chroniclers
and historians have focused their main attention on the nearby city of Cusco,
due to its historical and cultural relevance. Therefore, I will use an empirical
relationship that provides seismic intensities from the seismic magnitudes, the
formula I use is,
I0 = 1.68mw − 2.1 − 0.0206∆ (1)

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(modified from (Bakun and Wentworth, 1997)); where I0 is the MKS intensity,
mw is the seismic moment magnitude and ∆ is the epicentral distance in km.
Table 1 Seismic Intensitites as function of magnitude and
epicentral distance
Data ∆ mw I0
1650-03-31 33.8 7.4 X
1744-11-14 24.9 6.5 VIII
1941-09-18 61.9 6.4 VII
1950-05-21 24.9 6.3 VIII
1991-07-06 23.2 7.0 IX
The maximum seismic intensity felt in the city of Urubamba is X (MKS),
which is certified by historical records (Tavera, Agüero, and Fernández, 2016).
This intensity involves serious damage to the city’s infrastructure. Our for-
mula predicts that other earthquakes could also have caused high intensities;
however, we do not find agreement with these in the recorded testimonies. It
probably has to do with the depths of the hypocenters, because although the
epicentral distances (∆) are of the order of 20-30 km, the depths are greater,
so it would be necessary to take into account the attenuations suffered by the
seismic waves on their journey towards the surface.
Be that as it may, the high seismicity of the area near Urubamba (number
of intracrustal earthquakes), the small epicentral distances (they imply high
seismic intensities), the existing potential of other geological hazards that could
be triggered by seismic events and the urban growth that would occupy soils
of poor quality (in terms of elasticity) recommend carrying out a study of the
seismic dynamic response and seismic vulnerability in the ground occupied by
the city of Urubamba.
3 The H/V spectral quotient method
The H/V spectral quotient method, also known as the Nakamura method
(Nakamura, 2008), is widely used to study the dynamic response of soils to
seismic events. It is based on the principle that the elastic behavior of rocks
before the arrival of large amplitude seismic waves (high magnitude earth-
quakes) will be the same as when faced with small amplitude seismic waves
(microseismicity).
Then the field procedure consists of setting up a three-component seis-
mograph (or accelerograph), preferably a broadband one, and recording the
microseismicity over a period of time (about an hour). To fully understand the
meaning of what the spectral ratio H/V indicates, it is necessary to know the
seismic components of microseismicity, that is, what types of seismic waves

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permanently reach any point on the Earth’s surface (what is considered seismic
noise in Seismology).
3.1 Sources of seismic noise on the Earth
Those waves of very small amplitude and with a random frequency charac-
ter that appear in the seismograms as a background, are seen more clearly
between seismic events, have been known since the beginning of Seismology.
Seismologists called it seismic noise. In recent years, more attention has been
paid to them, since it was known that they could contain relevant information
about the sources and terrestrial structures that they cross.
In the early days of instrumental seismology, a random characteristic con-
tinued to be attributed to seismic noise, but its origins were intuitively assumed
to be in the oceans and their interactions with shorelines, seabeds and the
atmosphere. The possible origin in meteorological events was already proposed
as early as the 19th century (Bertelli, 1872). Some other sources of seismic noise
would be volcanic activity, low magnitude earthquakes, and human industrial
activity.
Considering that the frequencies of these seismic waves were not completely
random, the name of microseismicity began to be used. Typical frequency
ranges for microseismicity are 0.02 to 0.1 Hz, called primary microseisms,
and 0.1 to 0.5 Hz, called secondary microseisms. (Nishida, 2017). Above 1 Hz
ambient seismic wavefields are linked to human activities. Sometimes called
microtremors, to denote their anthropogenic origin.
As a resume of previous studies about sources of microseimicity we can
say that at low frequency (below 1 Hz) this are natural (oceans, large scale
meteorological storms); at intermediate frequency (1 to 5 Hz) the sources are
either natural (local meteorological conditions) or of anthropogenic kind; and
at higher frequencies the sources are essentially from human activities (indus-
tries, mining, traffic on large cities) (Bonnefoy-Claudet, Cotton, and Bard,
2006).
Trying to locate the sources of microseimicity over the Earth globe, studies
found that the main sources are on the southern Pacific and Indian oceans
during summer months and in northern Pacific and Atlantic Ocean during
winter months (seasons referred to northern hemisphere) (Landes, Hubans,
Shapiro, Paul, and Campillo, 2010) .
As in our research the characteristic resonance frequencies found are in the
range of 1-20 Hz, we will see in greater depth what are the sources of these
microtremors and their types of waves. The interaction of sea waves with the
coast is an important source of microtremors at frequencies above 1 Hz (Hilmo
and Wilcock, 2020). At these frequencies, the microtremors detected at seismic
stations clearly show variations with daily and weekly periods. This confirms
the cultural origin of some part of microtremors (Bonnefoy-Claudet, Cotton,
and Bard, 2006).
Regarding the type of waves found in microtremors, these are basically sur-
face waves (Rayleigh and Love) and body P waves. The ratio between the two

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will depend on some physical factors of the medium in which they propagate.
Theoretical models show that the relative proportion between Rayleigh waves
and P waves is linked to the spatial distribution of the source and the distance
between source and receiver. If the source is within the bedrock, below the
surface sedimentary layer, the P waves will be the only ones present. In the
event that the acoustic impedance contrast between both layers is very large,
the noise wavefield is dominated by surface waves, while for smaller impedance
contrast, the wavefield also includes P waves generated by close surface sources
(Bonnefoy-Claudet, Cotton, and Bard, 2006). The seismic microtremors at
about 0.6 – 2 Hz consist of a significant amount of body P waves originating
offshore, and the power of the P wave is highly correlated with the offshore
wind speed, demonstrating that these high-frequency P waves are excited by
distant ocean winds (Zhang, Gerstoft, and Shearer, 2009).
3.2 The physical meaning of the quotient of the spectra
of H and V
”The spectrum quotient of the horizontal components and the vertical com-
ponent of microtremors bear resemblance to transfer function for horizontal
motion of surface layer” (Nakamura, 1989).
The transfer function refers to a system that acts as a filter. Analytically
and in the frequency domain (taking the Laplace transform of the input func-
tion) it is defined as the ratio between the output system and the input system
(Buttkus, 2000). If we make the input function a Dirac delta, the output
function will be the transfer function (T(s)) of the filter.
T(s) =
O(s)
I(s)
; (2)
where I(s) is the Laplace transform of the input function i(t),
I(s) = L{i(t)}; (3)
and O(s) is the Laplace transform of the output function o(t),
O(s) = L{o(t)}. (4)
In seismology, it is sometimes useful to consider the Earth as a filter. If we
have as input function a very impulsive P-seismic wave (as might be produced
by an explosion), this can be assimilated with a Dirac delta; then the transfer
function (also known as impulse response) of the ground would have the form,
O(s) = T(s) · L{δ(t)}
T(s) = O(s)
(5)

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This equality is because the Laplace transform of a Dirac delta is equal to
unity, L{δ(t)} = 1.
This is a simplified way of seeing that a seismogram represents a seis-
mic signal generated in the hypocenter, or in the case of microseismicity or
microtremors in any of the sources seen above, filtered by the geological struc-
tures inside the Earth. A seismogram is a time series that has influences other
than the impulse response of the ground, g(t). It also contains the impulse
response of the recording instrument (seismometer) n(t) and the seismic source
function s(t). In the time domain we will say that the seismogram is the con-
volution of the impulse response of the instrument with the function of the
source and with the impulse response of the ground (Owens, Zandt, and Tay-
lor, 1984), thus the horizontal (h(t)) and vertical (v(t)) components of the
seismic record can be represented by,
h(t) = n(t) ∗ s(t) ∗ gh(t)
v(t) = n(t) ∗ s(t) ∗ gv(t)
(6)
If we convert the functions to the frequency domain by means of the
Fourier transform (which for this case has the same properties as the Laplace
transform) we will have,
H(ω) = N(ω) · S(ω) · Gh(ω)
V (ω) = N(ω) · S(ω) · Gv(ω)
(7)
The transfer function, or quotient of spectras, or deconvolution of the
horizontal component with respect to the vertical component, gives as a result,
H(ω)
V (ω)
=
N(ω) · S(ω) · Gh(ω)
N(ω) · S(ω) · Gv(ω)
(8)
But, since the function of the source and the impulse response of the seis-
mometer are the same in both components, they cancel each other out in the
quotient, leaving only the impulse responses of the ground in the volume of
earth closest to the seismic station (Ammon, Randall, and Zandt, 1990).
H(ω)
V (ω)
=
Gh(ω)
Gv(ω)
(9)
Now, if we take into account that the vertical displacements of the
ground under the seismometer are mainly caused by P waves (Nishida, 2017),
(Bonnefoy-Claudet, Cotton, and Bard, 2006), (Landes, Hubans, Shapiro, Paul,
and Campillo, 2010), we can approximate these to a Dirac delta function.
Since the transform of a Dirac delta is unity, the denominator of our quotient
becomes 1, then
T(ω) =
H(ω)
V (ω)
=
Gh(ω)
1
. (10)

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We see that the transfer function is nothing more than a scaled version
of the horizontal component of displacement with the removal of the vertical
displacements (Ammon, 1991).
An equivalent way to obtain the spectral quotient is performing the decon-
volution by cross-correlation (Jimenez, Vazquez, and Navarro, 2015) (Park and
Levin, 2000) ,
T(ω) =
H(ω) · V c
(ω)
V (ω) · V c(ω)
; (11)
where superscript c indicates complex conjugate.
One of the advantages of using this formulation is that in its development
the cancellation of the source signature is clearly understood; on the other
hand, it is also used to obtain the Green’s function of the elastic medium. If we
assume Nakamura’s assumption that the vertical displacement of the seismic
wave is the same at the basement-sediment interface and at the earth’s surface
(Nakamura, 2008), then deconvolution by means of cross-correlation is giving
us the Green’s function (or impulse response) of the sedimentary layer.
The fundamental frequency of the sedimentary layer and the amplification
factor are inferred from the results still in the frequency domain. But if we
apply an inverse Fourier transform to the transfer function, we would have a
pseudo-seismogram in which all the seismic signals that maintain their charac-
teristics both at the basement-layer interface and at the earth’s surface (such
as P waves and Sv that pass through the sedimentary layer like P and SV)
are grouped into a zero phase pulse called the coherence pulse. We see that
the only waves that differ from the coherence pulse are those that have had
a conversion to another type of wave at the interface; exactly as indicated by
the theory of the Receiver Function (RF). Formula 11 allows us to infer that
all waves that have a coherent vertical displacement between their passage
through the interface and their arrival at the surface are canceled when per-
forming the deconvolution. Then the H/V quotient of the layer is its response
to shear waves.
3.3 Fundamental ground resonance frequency and
amplification factor of seismic acceleration
The ratio of H and V espectrum it is effective to identify the fundamental reso-
nant frequency of a superficial layer of sediments, as it has been demonstrated
by studies that compare the results of H/V with determinations by seismo-
logical techniques based on analysis of seismograms of earthquakes and using
reference sites (Field and Jacob, 1995).
The determination of the amplification factor of the accelerations of the
horizontal body waves Sh in the passage from the bedrock to the superficial
sedimentary layer, directly from the peak amplitude of the spectral ratio H/V
was a proposal resulting from an empirical verification (Nakamura, 2000). Sub-
sequently, Nakamura makes a theoretical development that better explains the
fundamentals of the methodology that allows inferring the amplification factor
from the H/V spectral quotient (Nakamura, 2019).

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However, other studies in which the amplification factor derived from the
ratio of the H/V spectra is compared with factors taken from the analysis of
strong motion seismic signals with reference to bedrock outcrop sites, point
out that there are certain discrepancies between both factors (Molnar, Sirohey,
Assaf, Bard, Castellaro, Cornou, Cox, Guillier, Hassan, Kawase, Matsushima,
Sánchez-Sesma, and Yong, 2022). The amplification factor, for a given fre-
quency, is related to the acoustic impedance ratio, giving us an amplification
factor defined by the S-wave velocities in the basement and in the sedimentary
layer (Nakamura, 2008), which is the formula we prefer to use in our analysis,
A0 =
V sb
V sl
(12)
4 Data collection in the field
I have had carried out the seismological data collection in the city of Urubamba
between July 1 and December 31 of the year 2022. I had installed a total of
53 temporary seismological stations, in which the average acquisition time was
3600 seconds, using a molecular-electronic type seismometer, brand R-sensors
(LLC Nordlab) that has the following technical specifications: Model CME-
3211; bandwidth 1-50Hz; sensitivity 2000 V/(m/sec); three components. The
data-logger used is a Dataq brand, model DI-710-ELS, 16-bit analog-to-digital
conversion, better than 2 micro-volts resolution, unity gain (programmable).
The 53 measurement points are indicated on the urban map of the city
(Fig. 2),
All the streets of the city are covered with asphalt or cement, while the
sidewalks are all of the concrete type with stone foundations, in such a way
that the seismometer has always been sitting on a very solid foundation.
The city is small (21,000 inhabitants) and does not have large industries
installed in it or in the vicinity. The only human activity that could create rel-
evant seismic noise is the traffic of motor vehicles. However, the vast majority
of vehicles are of the three-wheeled motorcycle type. So we estimate that the
seismic noise that comes from human activity is of small magnitude and transi-
tory, so it would not have an effect capable of altering the shape of the dynamic
seismic response curves of the soil (Guillier, Chatelain, and Bonnefoy-Claudet,
2007) (Parolai and Galiana-Merino, 2006).
5 Data preparation, processing and inversion
The data-logger that I use creates a data file in its own binary format, it is
necessary to pass it through a program (from the manufacturer) to convert
it into an ascii format readable by any computer. At this point it is already
possible to separate the waveform from the three components, to then apply
my own program that passes the information to the SAC format. With the
seismograms of three components in the SAC format I can use a software like

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Fig. 2 Location of the measurement points, in blue dots, of the seismic spectrum in the
city of Urubamba.The orange polygon determines the limits of the old downtown of the city.
Geopsy with which I obtain the curve of the spectral ratio H/V (example in
Fig. 3).
5.1 Inversion of H/V curves
The H/V spectral ratio curve contains information about the seismic character-
istics of the sedimentary layer closest to the earth’s surface. One such feature is
the fundamental frequency (f0) which is taken directly from the highest ampli-
tude peak on the curve. I although the amplitude of said peak is proposed as
the amplification factor (A0), due to the instabilities that other authors have
detected in this amplification factor, I prefer to use another amplification factor
(formula 12) based on the acoustic impedance ratio between the basement and
the superfical sedimentary layer. It is noteworthy that I am talking about the
seismic basement, that is, that rock that presents seismic velocities and elas-
tic constants high enough to be considered a consolidated rock and that also
shows a high contrast of acoustic impedance with the most superficial layer.
In order to obtain the necessary information that allows me to calculate such
A0 I must know the speeds of the S wave in the basement and in the super-
ficial layer, which is provided by an inversion program of the H/V curve. For
this study I use the Nakamura software (Fig. 4) from the manufacturer Zond.

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Fig. 3 H/V curve of spectral quotient at the point ssv-0.1.
Fig. 4 H/V curve fitted by inversion; red line is observed curve, blue line is inverted curve.)
6 Results
The first parameter that we can have as a characterization of the sedimen-
tary layer close to the surface is the fundamental frequency f0 (Fig. 5), taken
directly from the spectral quotient curve.
The geophysical inversion gives us as results the best fit variables, velocities
of the S waves, velocities of the P waves and the thickness of each one of
the layers. Since the H/V operation is equivalent to determining the Green’s
function of the superficial sedimentary layer, the relevant and most reliable
parameters are V s of the first layer and of the seismic basement (Fig. 6),
and thickness of the sedimentary layer (Fig. 7). With these we evaluate the
amplification factor (Fig. 8), which is a very important element of analysis in
seismic hazard and vulnerability studies.
Another important factor to consider in the present research is the acceler-
ation (Fig. 9) of the S wave at the basement-sedimentary layer interface. For
its calculation we have used the formula given by Nakamura (2008), taking as

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Fig. 5 Map of fundamental frequency f0 distribution in Urubamba city. The orange line
delimits the historical downtown of the city.
design earthquake one of magnitude 7.4, like the one that occurred in the year
1650.
6.1 Seismic vulnerability
Earthquake damage over buildings structures can occur when exceeding the
strain limit of the constructive material. It is possible to develop strain indices
for various components of the structure as well as for the ground because the
transmission of seismic energy from the ground to the structure of a building
depends on a number of variables, including the coupling between the ground
and foundation and the fundamental frequency of the ground. Then the vul-
nerability index focused on the strain was defined for the ground (Nakamura,
1997)) as,
Kg
∼
=
A2
0
f0
; (13)
if the efficiency of applied seismic force is assumed to be 60% of static force.
Thus, Kg can be considered an index to indicate the ease of deformation of
measured points, which is expected to be useful to detect weak points of the
ground.
The Kg value (Fig. 10) is an index depending on the dynamic properties
of soil. With this parameter, it is possible to evaluate the vulnerability of a
point-based site under a large earthquake occurrence.
Even though Nakamura (2008) places the value kg >= 1000 as the limit
between the areas of liquefaction and less damage, in the San Francisco area

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2.1
2.2
2.3
2.3
2
.
3
2.4
2
.4
2
.
5
2
.
5
2
.5
2.5
2
.
6
2.6
2.6
2
.
6
2
.6
2.6
2
.7
2.7
2.7
2.7
2.7
2.7
2.7
2.7
2.
8
2.8
2.8
2
.8
2
.
8
2.8
2.8
2.8
2.9
2.9
2.9
2.9
2.9
2.9
2.9
3
3
3
3
3
3
3.1
3.1
3
.
1
3.1 3.1
3
.1
3.2
3
.2
3.2
3.3
3.3
3.4
3.5
3.6 3.7
−13.310
−13.305
−13.300
−72.120 −72.115 −72.110
S-wave velocity in Basement
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
km/s
Fig. 6 Map of S wave velocity in the seismic basement. )
(USA), this is a locality-dependent parameter. The values of the elastic con-
stants of the rocks in each place of the world will condition the dynamic
response of the soils before a great magnitude earthquake; in such a way that
the limit of Kg between the zones of high vulnerability and of low vulnera-
bility will be given in different values of said index. In the case of the city
of Urubamba, macroseismicity data (damage to buildings) are almost non-
existent. Although I have tried to carry out a macroseismic survey in the city,
consulting former residents who lived through the 1986 earthquake (the last
major earthquake felt in the area), the information is uncertain, since all those
who lived through it directly were in a house different from the one they cur-
rently occupy. In any case, based on these data and on direct observation of the
visible damage in old buildings, a limit of high vulnerability can be estimated
in the range of Kg greater than 3000X10−6
.
Viewing the existing geological and geotechnical hazard maps for the city
of Urubamba, I do not find any correlation with the seismic vulnerability map
shown here. This is mainly explained because the geological and geotechnical
maps were based on surface sampling and on the evaluation of the dangers
coming from the streams and rivers that cross the city.
7 Conclusions
The city of Urubamba has been hit by several large earthquakes, the most
powerful being that of 1650, which was felt with an intensity of X. This, added

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10
1
0
10
2
0
2
0
2
0
2
0
20
30
30
3
0
30
30
4
0
4
0
50 50
60
60
70
80
9
0
−13.310
−13.305
−13.300
−72.120 −72.115 −72.110
Basement depth
0
10
20
30
40
50
60
70
80
90
100
m
Fig. 7 Thickness of the superficial sedimentary layer, or depth to the seismic basement. )
to several catastrophic events of the geological type (avalanches, landslides,
floods) that have been recorded historically, which can reappear, triggered by
earthquakes, justify the need to carry out seismic hazard and vulnerability
studies in Urubamba. Traditionally, geologists have not paid attention to the
seismicity of this area, because they always considered that it was due to the
subduction mechanism of the Nasca plate under the South American plate;
but it’s not like that. The seismicity of the entire region around Cusco and
Urubamba has an intraplate origin, in local stress accumulation systems.
The interpretation of the data from the 53 temporary seismological stations
that I measured H/V spectral quotient in the city of Urubamba, was done
through geophysical inversion software. The fundamental resonance frequency
(Fig. 5), of the superficial sedimentary layer, the amplification factor (Fig. 8)
and the acceleration (Fig. 9) maps, seismo-dynamically characterize the soil
under the city sufficiently to make decisions in the design of engineering works.
The seismic vulnerability index Kg that I calculated for the 53 points
evaluated in Urubamba (Fig. 10) indicates areas of high, medium and low vul-
nerability. Empirically, I have set a limit to the value Kg = 3000, to identify
areas of high vulnerability above this value.
However, all the other parameters found in this research have to be taken
into account for the design of engineering works. For example, the depth and
seismic velocity maps of the basement will serve to design the best foundation
for a building. The acceleration map should serve as a guide for the calculation

A
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2.8
3
3
3
3
3.2
3.2
3.2
3.2
3
.
2
3
.4
3.4
3.4
3.4
3
.4
3.6
3
.
6
3.6
3.6
3.6
3.8
3.8
3.8
3.8
3.8
3
.
8
3
.8
4
4
4
4
4
4
4.2
4.2
4.2
4
.2
4.2
4.4
4.4
4.4
4.4
4.6
4.6
4
.
8
4.8
5
5.2
5.4
5.6
5.8
−13.310
−13.305
−13.300
−72.120 −72.115 −72.110
Amplification factor from Cb/Cs
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
5.2
5.4
5.6
5.8
6.0
A
Fig. 8 Amplification factor in the sedimentary layer. Cb and Cs are S wave velocities in
basement and sedimentary layers respectfully.)
of the structures and in which places it would be necessary to build with
anti-seismic structures.
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100
1
0
0
100
1
0
0
100
100
200
2
0
0
2
0
0
200
2
0
0
300
3
0
0
3
0
0
3
0
0
3
0
0
400
400
4
0
0
4
0
0
500
500
5
0
0
500
600
600
600
600
60
0
7
0
0
7
0
0
700
7
0
0
800
8
0
0
800
900
9
0
0
900
1000
1
0
0
0
1000
1100
1
1
0
0
1100
1200
12
00
1200
1300
1
3
0
0
1300
1400
1400
1500
1
5
0
0
1600
1600
1700
1700
1800
1800
1900
1900
2000
20
00
2100
2200
−13.310
−13.305
−13.300
−72.120 −72.115 −72.110
Acceleration of S wave in basement
0
100
200
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400
2500
cm/s
2
Fig. 9 Acceleration of the S wave at the basement-sediment interface.
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4
0
0
6
0
0
600
600
600
6
0
0
800
800
800 8
0
0
800
800
1
0
0
0
1000
1000
1
0
0
0
1000
1000
1000
1200
1200
1200
1
2
0
0
1200
1200
12
00
1
2
0
0
1
4
0
0
1
4
0
0
1
4
0
0
1400 1400
1400
14
00
1
4
0
0
1
6
0
0
1600
1600
1600
1600
16
00
1
6
0
0
1
8
0
0
1800
1800
1800
1
8
0
0
1
8
0
0
2
0
0
0
2
0
0
0
2000
2
0
0
0
2000
2000
2200
2200
2
2
0
0
2200
2200
2
4
0
0
2400
24
00
2400
2600
2
6
0
0
2
6
0
0
2800
2800
3000 3
0
0
0
3200
3
2
0
0
3400
3400
3
6
0
0
3600
3800
3800
4
0
0
0
4000
4
2
0
0
4
4
0
0
4600
4
8
0
0
−13.310
−13.305
−13.300
−72.120 −72.115 −72.110
K factor of seismic vulnerability
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
3000
3200
3400
3600
3800
4000
4200
4400
4600
4800
5000
5200
5400
5600
K
Fig. 10 Index of seismic vulnerability Kg.
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