Joint-inversion of Soil Profile with Receiver Function and Dispersion Curve using
Arrays of Seismometers
D.Calderon1, T.Sekiguchi1, S.Nakai1, Z.Aguilar2, F.Lazares2
Department of Urban Environment System, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, Chiba, Japan
2
CISMID, National University of Engineering, Rimac, Lima, Peru
email: diana_c@graduate.chiba-u.jp, tsekiguc@faculty.chiba-u.jp, nakai@faculty.chiba-u.jp
zaguilar@uni.edu.pe, f_lazares@uni.edu.pe

1

ABSTRACT: The soil profile estimation of Lima, the capital of Peru, is of great importance to adequately design buildings towithstand seismic activity. Particularly, the La Molina district, known for being a rapidly developing urban area, as well as
having reported notable damage during past seismic events, has been studied largely. However, these studies have not explored
depths greater than 50m. In this study, we intend to estimate soil profiles with depths reaching to the basement rock in La
Molina. For this purpose we will apply the joint-inversion technique of dispersion curve and receiver function. The inversion ofdispersion curve alone and receiver function alone is initially performed separately. The resulting inverted profiles will be used
as a reference for the boundary matrix of the joint-inversion method. Our results have shown that the H/V spectrum obtainedwith the inverted profile is in good agreement with the observed H/V spectrum obtained with microtremor measurements.
Moreover, it is in good agreement with available boring data and Ps logging profile.
KEY WORDS: Phase velocity dispersion curve; Receiver function; Joint-inversion; Shear-wave velocity profile

1INTRODUCTION

In March 2010, the project “Enhancement in the Earthquake
and Tsunami Disaster Mitigation Technology in Peru”(SATREPS) started with support of the Japan International
Cooperation Agency (JICA) and the Japan Science andTechnology Agency (JST).
The objective of the first stage of this project is themicrozonation of Lima, the capital of Peru, which is situatedon the central coast of Peru, bordered by the Pacific Ocean, ina zone of high seismic activity known as the Ring of Fire.
In this study, the soil profile estimation extending down tothe seismic bedrock is carried out using the joint-inversion
technique of dispersion curve and receiver functions. The
target area is the La Molina district, located in a valley to theeast of Lima (Figure 1).
According to Repetto et al. (1980) the La Molina district
was formed by alluvial materials deposited by the ancient
tributaries of the Rimac River (Quebrada Pampa Grande andPampa Arenal). He also stated that the low area at La Molina
may have been a lake in the past, and that the soils deposits inthe area contain higher levels of silt and clay to depths of atleast 16 m below the existing ground surface.
Historically, La Molina has reported excessive earthquake
damage during the most significant earthquakes in Lima,
showing a higher intensity than in central Lima; wheredamage tended to be lower (Stephenson et al., 2009), hence
the importance of the soil profile estimation in this district.
The joint-inversion method of receiver function anddispersion curve has been often used during recent decades..
The merit of this method is the improvement in the estimationof soil profiles using the joint-inversion method whencompared with stand-alone inversions.

Julia et al. (1998) mentioned that surface waves provide
constraints on averages of the absolute shear velocities atdifferent depth ranges. Ammon et al. (1990) discussed that thereceiver function constrains shear velocity contrasts ofinterfaces located in the medium and the relative travel timeof the converted waves reverberated between those interfaces.
Julia et al.(2000) mentioned that the joint-interpretation of
surface wave dispersion and teleseismic P-wave receiver
function seems intuitively to provide tighter constraints on theshear velocity structure than any technique individually.
2APPLICATION OF THE JOINT INVERSIONWe used data recorded in the seismic station named MOL thatbelongs to the CISMID accelerometer network. This stationceased operation in 2008.
2.1

Observed Receiver Function

The observed receiver function was calculated using records
from four earthquakes with epicenters located about 150 km
south-west of the seismic station MOL.
Figure 1 (a) shows the location of station MOL, the array
EMO and the earthquakes epicenters on the soil distributionmap (Cismid, 2005); while Figure 1 (b) additionally shows thelocation of the measurement for the MASW method
conducted by Cismid (2010). Table 1 contains the informationof the events used for the calculation.
These earthquakes were chosen because they have a similar
incident angle, focal distance and azimuth.
The average of the receiver functions of the four earthquakes
is the observed receiver function shown in Figure 2.

2.2

Observed Dispersion Curve

2.3

In the calculation of the observed dispersion curve, linear
arrays and circular arrays of sensors (Figure 3) were measured.
The method of analysis and characteristics of the arrays andsensors are discussed more in Calderon et al. (2011).

2.4(a)

Inversion of Dispersion Curve alone

In this study, as in Calderon et al. (2011), the complete curve
shown in Figure 3 was used as the target for the stand-alone
dispersion curve inversion process. The inversion results areshown in Figure 4.
Inversion of Receiver Function alone

For this inversion a boundary matrix is defined after a trialand error process. The calculated dispersion curve is shown inFigure 5 and the inverted profile is shown in Figure
2.5

Joint-Inversion

Based on the profiles obtained in the individual inversion
process carried out in the previous section, we created aboundary matrix for the joint-inversion (Table 2).

(b)

Figure 3. Observed dispersion curve

(a)
(b)

Figure 1 (a) Location of seismic station MOL, earthquakes
epicenters and array EMO; (b) soil distribution map (Cismid,2010) showing additionally MASW, down-hole, and waterwell location.
Table 1. Characteristics of the seismic events used for thecalculation of the observed receiver function
Inc angle
DepthMLDateTime(km)(°)
2006/10/20 05:49:07
43
6.2
75.5
2006/10/26 17:54:40
42
5.8
74.7
2007/08/15 19:02:5530
4.978.6
2007/08/15 20:02:38
34
5.5
77.1

Figure 2. Averaged observed receiver function(c)Figure 4. Inversion of dispersion curve stand-alone.(a)observed and calculated dispersion curve. (b) inverted profile(c) observed and calculated H/V spectrum

Table 2. Boundary matrix for the Joint-inversion
Vs (m/s)[150-300][300-500][500-1000][500-1000][700-1200][1500-1800][2000-2300][3000-3300]

Figure 5. Calculated receiver function after the inversion

3H(m)[1-10][1-10][5-20][5-20][10-30][20-40][20-40]-AVAILABLE BORING DATA AND DOWN-HOLE

A very deep water-well logging down to the bedrock wasconducted by the Water and Sewerage Company of Lima.
This data was collected by Cismid (2010) and identified as
P29. The soil column is shown in Figure 9. In this profile therock is found at 130m.
The only down-hole data available in this area was from ameasurement carried out after the October, 1974 Lima’s
earthquake, the exact location of this logging is unknown but
it is about 100m from the old location of station MOL(Repetto,1980). A boring data from this place is also available. Boththe down-hole profile and the soil column are identified as
DH and are shown in Figure 10(a) and 10(b) respectively.
Figure 6. Inverted profile after using the inversion of receiver
function alone.
4
For the upper layers, the boundaries were chosen based on
the profile obtained by the dispersion curve inversion; and forthe deep layers the boundaries were chosen based on theprofile obtained by the receiver function inversion.
For the evaluation function we have followed Kurose andYamanaka (2006).

⎛ 1 ⎞ ⎡ Robs (t i ) − Rcal (t i ) ⎤⎟⎟∑ ⎢ϕ RF = ⎜⎜⎥σ RF (t i )⎝ N RF ⎠ ⎣⎦2⎛ 1 ⎞ ⎡ C obs (Ti ) − C cal (Ti ) ⎤⎟∑ ⎢ϕ ph = ⎜⎜⎥⎟ ⎢Nσ ph (t i )
⎥⎦ph⎝
⎠ ⎣

ϕ = 0.5(ϕ ph + ϕ RF )

(1)

2(2)

(3)

where:
NRF and Nph are the number of data;σRF(ti) and σph(ti) are the standard deviations of the receiver
function Robs(ti) at time ti
Cobs(Tj) is the observed phase velocity at period Tj
ϕ is the objective function of the joint-inversion
Results of calculated receiver function, dispersion curve, andthe inverted profiles are shown in Figure 7.
Finally the profile data is used to calculate the H/V spectrum(Figure 8).

4.1

DISCUSSION
Observed Dispersion Curve

The observed phase velocity dispersion curve (Figure 3)
shows a shoulder for periods from 0.1 to 0.3 s. This behavior
generally is caused when a layer of higher velocity isoverlying a layer of lower shear velocity. In our case, after
the inversion, the calculated dispersion curve does not fit theobserved one in the period range where the shoulder appears.
Therefore, the real values of velocities in this range of periods
may be underestimated.
Another special characteristic of the observed dispersion
curve is the steep slope for the period range from 0.25 to 0.45
s. The velocities in this range are more scattered than for
shorter periods. According to Kurose and Yamanaka (2006),
this is a result of the small amplitudes of long-period
microtremors.
Yamanaka et al. (1995) pointed out the lower resolution in
deep structure after inverting phase velocities for periods up to5 seconds in Tokyo, Japan. In the case of Lima, the soils are
more rigid than in Japan; thus the limit period is expected tobe shorter; for La Molina the limit could be considered 0.3 s.
However, in order to verify the resolution of the deep
structure obtained by inverting the dispersion curve alone,observed phase velocities up to 0.3 s were taken. The resulting
velocity profile is shown in Figure 4(b). Here the basementrock is found at 60 m depth. Later we compare the profiles
with the joint-inversion and verify the resolution.
4.2

Observed Receiver Function

Although the quantity of seismic records used for thecalculation of the averaged observed receiver function is small,the similarity of the characteristics of the earthquakes led us toan acceptable receiver function.
When performing the inversion of the receiver function
alone, we can see in Figure 5 the correlation in the first andthird peaks, but not in the second peak. This is likely due tothe problems inherent in using the inversion receiver function
alone, that is, that low resolution fails to accurately estimatethe shallow layers.
4.3

Joint-inverted Profile

For the joint-inversion the observed dispersion curve waslimited to 0.3s; this is because it is expected that the deep
structure is constrained by the receiver function. Despite thecalculated dispersion curve not fitting well with the observed
curve for periods up to 0.1 s (which can cause a high or low
estimation of the shear velocity in shallow layers); the H/Vspectrum of the inverted profile shows a good agreement withthe observed H/V spectrum calculated from one point
microtremor measurements. These spectra show more than
one peak, which accounts for the diverse soil layers as seen in
the profile.
4.4(b)

Comparison with available boring data and down-hole

When comparing the down-hole data with the inverted
profile (Figure 7(c) and (d)) we can see a good agreement for
the upper layers.
The other data we have to compare is the water-well logging,which indicates that the rock is at 130m. When looking at thisdepth in the inverted profile estimated with the joint-inversion(Figure 7(d)); we found that the bedrock is at about 110m;
verifying this the resolution of the inverted profile.
4.5(a)(c)Influence on the Distance between the Seismometer
Station and the Array Location.

The array EMO was carried out on the campus of La Molina
University, which is about 1 km distance from the MOL
station (Figure 1(b)).
La Molina district is in a valley where the depth to thebedrock is variable over short distances, and that is the reason
why we want to verify the influence of the separation distance
between EMO and MOL when applying the joint-inversion
method.
In Stephenson et al. (2009) it is mentioned that the MOL
station is over a coarse gravel substrate, and the bedrock is 2030m depth. The EMO array, on the contrary, is located on theUniversity campus, in the middle of a valley.
The difference in the shallow soils for these two places could
account for the misfit of the first phase in the calculated
receiver function (Figure 7(a)). However, since the receiver
function places constraints on deep structure, which ishomogeneous in both places, for a depth of more than 100m,
and the dispersion curve controls the shallow structure, thefinal inverted profile can be considered valid for the locationof the seismometer array EMO. The agreement in the H/Vspectra, boring data, and down-hole logging verifies thisstatement.

(d)Figure 7(a) Observed and calculated receiver function. (b)Observed and calculated dispersion curve. (c); and (d)Comparison of soil profiles obtained by stand alone methods,
joint-inversion method and MASW for the first 50m and150m respectively.

4.

CONCLUSIONS

The application of the joint-inversion method of receiver
function and dispersion curve led us to the next conclusions:---Figure 8. Observed and calculated H/V spectrum from thejoint-inverted profile

For the array in La Molina (EMO), the largest period in
the phase velocity curve where we can expect acceptable
results, is about 0.3s.
The inverted profile estimate with the joint-inversion
method can be considered representative for the locationof the EMO array.
Future plans for the SATREPS project include installing aseismometer near the area where the EMO array wasconducted. Using the seismic records from this station, averification of the profile presented in this study isrecommended as a future goal.

ACKNOWLEDGMENTS
We would like to express our thanks to the people at CISMID,
especially to Eng. Selene Quispe, for her assistance inproviding the data; and to the research assistants for their help
in performing the measurements.
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Figure 9. Water-well logging (data collected by Cismid,
2010 from the Water and Sewerage Company of Lima)

(a)

(b)

Figure 10(a) and (b). Boring data and down-hole profile
respectively (Repetto, 1980)

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