Synopses of Master Papers

Bulletin of IISEE, 47, 37-42, 2013

RECEIVER FUNCTION ANALYSIS FOR
CRUSTAL VELOCITY STRUCTURE BENEATH
SALT RANGE, PAKISTAN
Shahid Mahmood ∗MEE11607

Supervisor: Tatsuhiko HARA ∗∗ABSTRACT
We applied a receiver function technique to investigate the crustal structure beneath the KTAS seismic
station in the Salt Range area of Pakistan. The station was installed in 2010 and is a constituent stationof the Pak-China Seismic Network of Pakistan Meteorological Department. The teleseismic broadband
waveform data recorded by this seismic station were used for this research. We calculated receiver
functions using the source equalization technique to obtain good receiver functions for three events.
Then, we compared the observed receiver functions to synthetic receiver functions computed for thefour crust models taken from the global crust model CRUST 2.0 to find significant differences.
Since in the study area, the Salt Range, there exist salt reservoirs (halite i.e. rock salt), andsince such a halite layer is not included in these four models, we modified one of the four models sothat the modified models have the shallowest layer with physical properties (density, and shear wave
velocity etc.) with halite beds. Then, we calculated synthetic receiver functions for these modified
models. Comparison between the synthetic and observed receiver functions suggested the existence ofa possible halite layer.
We carried out inversion of the observed receiver functions for crust structure using genetic
algorithm including a parameter range of a halite layer. Two selected teleseismic events were stacked
for inversion. The obtained model contains a top layer whose physical property is consistent withhalite, and the synthetic receiver function computed for this model explained the earlier part of thereceiver functions. This result suggested the existence of halite in the study region. The depth of Moho
was estimated to be about 55 km, which is consistent with previous studies.
Keywords: Receiver function, crust model, Salt Range, Genetic Algorithm.

1. INTRODUCTION
The Salt Range, with a latitude of 32.67 (32° 40' 0 N) and a longitude of 72.58 (72°34' E), is a
hypsographic (mountains) located in the area / state of Punjab in Pakistan (Figure 1). The Salt Range isthe surface expression of the leading edge of decollement thrusts over northward offsets of thecrystalline basement (Crawford, 1974; Seeber and Armbruster, 1979; Yeats and Lawrence, 1984).
Seismic drill-hole data indicate total southward displacement of the Salt Range and Potwar Plateau of
at least 20 km (Farah et al., 1977; Baker et al., 1988). The western part of the Salt Range ischaracterized by a major strike-slip fault that extend along the western Salt Range and Indus River(Baker et al., 1988; McDougall and Khan, 1990)∗∗∗

Pakistan Meteorological Department (PMD).
International Institute of Seismology and Earthquake Engineering (IISEE), Tsukuba, Japan.

2. DATAIn this study we used teleseismic broadband data for three events which was recorded by the
Pak-China seismic network of the PMD. The broadband seismic station KTAS of this network issituated in the Salt Range which is our study area as shown in Figure 1. The list of the events is shownin Table 1.

Table 1. The list of the events used in this study.
No.

Lat

Long

Mag

Depth
(km)

07/31/2011
23:39:02-3.64

144.536.8

10

03/21/2012
22:15:06-6.21

146.146.9

11003/14/2012
09:08:40

41.01

145.01

7.7

30.7

Date &
time(GMT)

1

2

3

Figure 1. Regional map and study
area (within the rectangle).

3. THEORY AND METHODOLOGY
Body waves in the course of propagation pass through different structural features and discontinuities
in the crust or upper mantle of the earth. During this P-wave energies are partially converted to
S-waves which appear within the P-wave coda after the P-wave. These converted S-waves (Ps) havegreater amplitudes on horizontal components than on vertical components. Converted phase
generation indicates the existence of discontinuities between homogeneous layers of crust and upper
mantle through which the primary P waves pass. In order to model the converted phases fromteleseismic waveforms we attempt to recover them by removing source and deep mantle effects fromteleseismograms. We require three components of the data to equalize the source in order to remove
the effects of the distant structures and the source from the seismogram, to study structure beneath theseismic station. For this purpose we follow the procedure given by Langston (1979), who assumed thatthree displacement components at a station are expressed by;
𝐷𝑅 (𝑡) = 𝐼(𝑡) ∗ 𝑆(𝑡) ∗ 𝐸𝑅 (𝑡)𝐷𝑇 (𝑡) = 𝐼(𝑡) ∗ 𝑆(𝑡) ∗ 𝐸𝑇 (𝑡)𝐷𝑉 (𝑡) = 𝐼(𝑡) ∗ 𝑆(𝑡) ∗ 𝐸𝑣 (𝑡)(1)where V, R and T stand for vertical, radial and tangential components, respectively, 𝐼(𝑡) is the impulse
response of the recording instrument 𝑆(𝑡) is the seismic source function, 𝐸 is the impulse response of
the structure and an asterisk indicates convolution operation. In Langston’s (1979) method, it isassumed that 𝐸𝑣 ∼ 𝛿(𝑡) where 𝛿(𝑡) is Dirac delta function. Then by dividing the Fourier transformof the horizontal component by that of vertical component radial receiver function is calculated and isexpressed by;𝐸𝑅 (𝜔) =𝐷𝑅 (𝜔)𝐷𝑣 (𝜔)
𝐺(𝜔)
𝜑(𝜔)

where 𝜑(𝜔) = max[𝐷𝑣 (𝜔)𝐷𝑣 (𝜔), 𝑐 max{𝐷𝑣 (𝜔)𝐷𝑣 (𝜔), ] and 𝐺(𝜔) = 𝑒
water level.

(2)
−𝜔2
4𝑎2

, where 𝑐 stands for4. FORWARD MODELING AND INVERSION
We used a set of programs developed by Dr. C.J. Ammon to calculate observed and synthetic receiver
functions (http://eqseis.geosc.psu.edu/~cammon/HTML/RftnDocs/rftn01.html). We calculated theobserved receiver function for event 1 (Table 1) by setting ‘c’ as 0.01 and ‘a’ as 5 and compared it to
the synthetic receiver functions of four crust models IK, I2, R0, and PD taken from CRUST 2.0 model
package from REM website (http://igppweb.ucsd.edu/~gabi/crust2.html), which lie beneath and in thevicinity of KTAS seismic station (Figure 2a). We observed the significant differences between themand then we modified the crust model PD taking into account the presence of salt (halite) beds in theSalt Range area. However, Vs is set as 2.8 and 2.1 km/s and density is set to 2.2 and 2.4 g/cc for the
first and second layer, respectively (Table 2). Their thicknesses are varied to make five different
modified models. Comparison of synthetic receiver functions for these models and observed receiver
function (Figure 2b) suggested significant effect of halite layer for receiver function and earlier parts(0 to 2 sec) were somewhat similar. This result suggests possible existence of halite beneath KTAS.

(a)Table 2. Comparison of original PD crust
type model and its modified versions
including halite property in the first layer(Bourbie et al., 1987).

(b)

Figure 2. Comparison of observed RF with
Synthetic RF’s for PD, R0, IK, I2 crust types (a)and Synthetic RF’s for five modified models (b).

ModifiedPD
Modelsh1(km)[Vs=2.8(km/s),
rho=2.2(g/cc)]

h 2(km)[(Vs=2.1)km/s),
rho=2.4(g/cc)]

Model 10.3

1.0Model 20.15

1.0Model 30.3

0.3

Model 40.3

2.0Model 50.6

4.0h1(km)[Vs=1.2(km/s),
rho=2.1(g/cc) ]h2(km)[Vs=2.1(km/s),
rho=2.4(g/cc]

1.0

1.0

Original
PD
Model

5. RECEIVER FUNCTION INVERSION BY GENETIC ALGORITHM
We used Genetic Algorithm inversion program developed by Shibutani et al. (1996), who adopted‘tournament selection scheme’ (e.g., Sambridge and Gallagher, 1993). The model parameters arethickness of layers, shear wave velocity, Vp/Vs ratio and density of each of six layers, which are asediment layer, hard sediment, upper crust, middle crust, lower crust and mantle (Table 3). The rangeof these parameters for the shallowest ‘sediment’ layer is set for halite following Bourbie et al. (1987).
For other layers the parameter ranges are set referring to Shibutani et al. (1996) and CRUST 2.0 model
package. For each model parameter, upper and lower bounds and 2n possible values are specified. In
our case the total number of bits is 41. These model parameters are coded into a binary string in the
inversion process.The model space to be searched is 241 . Events no.1 and 2 were stacked, and used asdata for inversion .The final model is shown in Figure 3 and Table 4.
Table 3. Model parameters in genetic algorithm receiver function inversion.

Lower
Upper
n
Increment
Lower
Upper
n
Increment

0
0.45
2
0.15
2.4
3.10
3
0.1

Hard
Sediment
0
3.5
3
0.5
2.10
2.80
3
0.1

Lower
Upper
n
Increment
Lower
Upper
n
Increment

1..70
2.4
3
0.1
2.00
2.3
2
0.1
300
150

1.70
2.0
2
0.1
2.3
2.6
2
0.1
675
300

“Halite”
Thickness(km)
Vs(km/s)

Vp/Vs

Density(g/cc)

Qa
Qb

Upper
10.00
20.0
4
0.7
3.30
3.6
2
0.1

Crust
Middle
10.00
20.50
4
0.7
3.50
3.80
2
0.1

lower
8.00
18.50
4
0.7
3.70
4.0
2
0.1

0.0
0.0
0.0
0
4.0
4.7
3
0.1

1.73
1.73
0
0.0
2.67
2.67
0
0.0
1450
600

1.73
1.73
0
0.0
2.81
2.81
0
0.0
1450
600

1.73
1.73
0
0.0
3.18
3.18
0
0.0
1450
600

1.73
1.73
0
0.0
3.25
3.25
0
0.0
1450
600

MantleThe shear wave velocity of the shallowest layer is 2.4 km/s, which is a little slower than typical valuesof halite (Bourbie et al., 1987), The estimated thickness is 300 m. A comparison of synthetic RF forthis model and observed RF is given in Figure 4. From 0 to 2 seconds the part of the synthetic receiver
function is consistent with that of the observed receiver function which is consistent with thecomparison shown in Figure 2(b). These results suggest the presence of halite in the region. The
differences in the later part of the receiver functions are likely due to complex deep crustal structures.
In Figure 5 we can see that Moho depth is not well constrained and is varying according todifferent models. Although, there exists a certain uncertainty for Moho depth considering thedifferences among those of these models, it seems that the depth of Moho is larger than 50 km. An
integrated study by Johnson and Vincent (2002) estimated the average regional Moho depth to be 50
km. The studies by Jhonson and Vincent (2002) and Soomro (2009) suggested that the crust becomesthinner in the central and southern part of Pakistan. This seems inconsistent with our study, where the
Moho depth beneath KTAS is about 55 km. However, the deep crust ‘trough’ extends toward ourstudy area in the model by Jhonson and Vincent (2002) (Figure 9 of their paper), and our result is
consistent with their model.

Table 4. The final model obtained byinversion.

Figure 3. Vs, density and
Vp/Vs for the final
model obtained by RF
inversion are shown in
the upper left and right,
and lower left panels,
respectively.

Thickness
Layer (km)

Vs
(km/
s)

Vp/V
s

Density(g/cc)

1

0.3(0.3)

2.40

1.70

2.30

2

3.5(3.8)

2.20

2.00

2.30

3

19.8(23.6)

3.40

1.73

2.65

4

16.3(39.9)

3.70

1.73

2.77

5

15.0(54.9)

3.90

1.73

2.86

6

0.0(54.9)

4.70

1.73

3.30

Figure 4. The synthetic RF for the final model and theobserved RF.

Figure 5. Models whose residuals
between the synthetic and observed
RFs are comparable to that of the
final model. The densities, Vs and
Vp/Vs are shown in the upper left,
upper right, and lower right panels,
respectively.

6. CONCLUSION

We performed receiver function analysis to study the crustal structure beneath the KTAS seismic
station of the Pak-China seismic network, which is located in the Salt Range area of Pakistan. We usedbroadband waveform data recorded at KTAS for three teleseismic events with magnitudes larger than
6.0.We calculated radial receiver functions using the source equalization technique developed byLangston (1979) by the receiver function codes developed by Charles J. Ammon.

Then, we compared the observed receiver functions to synthetic receiver functions
computed for the four crust models, which are designated in the vicinity of KTAS in the global crustmodel CRUST 2.0. We found that the observed and synthetic receiver functions are significantly
different. Considering the possible existence of halite beds in the study area, we modified one of thefour models so that the shear wave velocity and density of the shallowest layer are in the possible
range of halite. The early part of the observed receiver functions are consistent with that of thesynthetic receiver functions computed for some of these modified models, which suggests a possible
existence of halite beds.
We performed inversion of the observed receiver functions for crust structure beneath
KTAS using a genetic algorithm. We set the parameter ranges considering halite property for theshallowest layer. The shear wave velocity of the shallowest layer of the obtained model is 2.4 km/s,
which is consistent with a possible existence of halite considering the estimation uncertainty, although
it is a little slower than typical values of shear wave velocities for halite. The estimated Moho depth isabout 55 km, which is consistent with the model developed by Jhonson and Vincent (2002).

ACKNOWLEDGEMENT
I am thankful to Dr. T. Shibutani for allowing me to use the genetic algorithm codes developed by him.
I am thankful to Dr. C.J. Ammon for making available receiver function codes, which we used in thisstudy. I express my sincere gratitude to Dr. B. Shibazaki and Dr. T. Yokoi for their valuablesuggestion and guidance for improving manuscript of my master report during my study.

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