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Crustal structure of the peninsular shield beneath Hyderabad (India) from the spectral characteristics of long-period P-waves
Teetonophysics, 51 (1978) 127-137 0 Elsevier Scientific Publishing Company,
127 Amsterdam
-
Printed
in The Netherlands
CRUSTAL STRUCTURE OF THE PENINSULAR SHIELD BENEATH HYDERABAD (INDIA) FROM THE SPECTRAL CHARACTERISTICS OF LONG-PERIOD P-WAVES
D.D. SINGH National
and B.K.
Geophysical
(Submitted
July
RASTOGI Research
18. 1977;
Institute,
revised version
Hyderabad accepted
500007 January
(India) 25, 1978)
ABSTRACT Singh, D.D. and Rastogi, B.K., 1978. Crustal structure Hyderabad (India) from the spectral characteristics physics, 51: 127-137.
of the peninsular shield beneath of long-period P-waves. Tectono-
The crustal transfer functions have been obtained from long period P-waves of thirteen teleseismic events recorded at Hyderabad (HYB), India, The crustal structure beneath this seismograph station has been obtained after comparing these functions with the theoretical crustal transfer functions which were computed using the Thomson-Haskell matrix formulation. The method is suitable and economical for determining the fine crustal structure. The crust beneath Hyderabad is found to consist of three layers with total thickness of 36 km. The thicknesses of top, middle and bottom layers are 21 km, 8 km and 7 km, respectively.
INTRODUCTION
The local crustal structure in the Hyderabad area is not known, though, the regional structure of the peninsular shield of India has been determined by regional gravity data (Subrahmanyam et al., 1969). The knowledge of the local crustal structure is of considerable scientific value. In view of this we attempted to obtain the local crustal structure beneath Hyderabad. A first order seismograph station, equipped with seismographs conforming to WWSSN standards is operating at Hyderabad since 1968. As there are not enough local earthquakes, short-distance travel-time study is not possible to determine the local crustal structure around Hyderabad. Phinney (1964) has given a method of determining the crustal layering beneath a seismograph station using the teleseismic earthquakes. The method utilizes frequency dependent polarization properties of teleseismic P-waves. Phinney has defined the ratio of the vertical spectrum to the horizontal spectrum of longperiod P-wave as crustal transfer ratio - a function which depends on structure beneath the station. The spectral ratio response is due to the narrow
128
cone of structure beneath the receiving station as body waves traverse at a small angle of incidence under the station for the teleseismic events. Therefore, as pointed out by Fernandez and Careaga (1968), it is possible to determine the crustai layering with great horizontal resolution using this method. This property is specially significant as gravity study gives the average picture over the entire structure and surface wave dispersion study gives the average structure over hundreds or thousands of kilometers. Moreover, the spectral ratio method does not require the knowledge of earthquake origin time. The seismic travel time method is very sensitive to the accuracy of origin time determination. However, body wave spectral ratios appear to be most critical with respect to structure in the lower half of the crust considering the period range of 5-50 sec. This method has been applied by Phinney (1964) and afterwards by several workers (Fernandez and Careaga, 1968; Bonjer et al., 2970; Kurita, 1970; Hasegawa, 1971; Rogers and Kisslinger, 1972; Leong, 1975). We have applied this method to determine the crustal structure beneath Hyderabad. THEORETICAL
BACKGROUND
The frequency response of the layers of the crust and upper mantle to the seismic waves is a function of some of the physical parameters of the layered system. The response of layered media to body waves has been studied as early as in 1932 by Sezawa and Kanai (1932, 1937). The use of matrix algebra provided a significant simplification in the numerical calculations involved in the problem (Haskell, 1953). Haskell (1962) considered the effect of the layers on the incident P-waves as a transfer function affecting either the vertical or the horizontal component of motion and gave the following expressions for the vertical and horizontal components of motion at the free surface (1) w,(w) = A(w)Wp(o~, ~1 where A(w) is the spectrum of the incident wave and Ur and Wp are spectral transfer functions. Haskell gave a method of computing the transfer functions if the model is composed of homogeneous parallel layers; in that case Up and Wp depend only on the frequency and apparent velocity of the wave. From eq. 1 division yields: ?!!?= $= UO
Tp(0, c)
(2)
This implies that by dividing the observed spectrums we obtain a function which is independent of the spectrum of the incident pulse. Therefore Phinney (1964) proposed to employ Tp for the determination of crustal
129
structure beneath a recording station. Observed values of T, can be obtained by Fourier analysis of long-period P-waves from teleseismic earthquakes, the practical details for which are given in the next section. Theoretical curves of Tp(o) can be calculated for a broad class of earth models for various values of c. Instead of c we can take the angle of incidence i, as the two quantities are uniquely related to each other. By variation of the parameters, a theoretical curve can be found which matches the observed one. This theoretical model will represent the crustal structure beneath the station. Hereafter, in this paper we will refer IR(f) lo as observed crustal transfer function ratio and [R(f) IT as theoretical transfer ratio. Referring to Haskell (1962), the expression for the latter quantity can be written as: (3) The right-hand side of this expression consists of the elements of the matrix J which is the (4 X 4) matrix product obtained in solving the boundary value problem of the layered system. More specifically the matrix J is given by Haskell’s (1953) relation (2.19) as: J = E,‘a,_,a,_,
. . . a,
(4)
where each submatrix a, depends on the transmission coefficients ness, density, rigidity, velocity) of the corresponding mth layer. DATA
(thick-
ANALYSIS
We have determined the observed crustal transfer function ratios of thirteen teleseismic events recorded by the three matched component, longperiod, WWSSN type seismographs at Hyderabad. The details of the seismograph station are given in Table I. Details of the earthquakes are given in TABLE Station
I and instrument
characteristics
Station Code Name Latitude Longitude Height above M.S.L. Bedrock Seismographs
Hyderabad HYB 17’25’02”N 78’33’11”E 510 mts Granite Long-period
Seismometer period Galvanometer period Maximum dynamic magnification Mode of recording Damping ratio Run and maintained by
Z, N, B 15 set 100 set 1500 Photographic paper Critical National Geophysical
Press-Ewing
Research
Institute
II
20:47:17.4
Mar. 23,197l
Apr. 12, 1971
Apr. 17, 1972
Sept. 05,1972
Sept. 07,1972
Sept. 24, 1972
Jan. 31, 1973
Feb. 06,1973
Jun. 26,1973
Sept. II,1973
Dec. 19,1973
Jul. 04, 1974
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
19:30;42.1
04:43:01.5
23:18:50.8
22~32100.2
10:37:10.1
20:55:53.1
20:09:35.6
02:55:00.1
17:18:29.5
10:49:42.7
19:03:25.9
17:13:15.1
May 15,197O
1.
28.3 55.6 24.2 122.5 1.9 128.2 1.9 68.1 6.3 131.2 28.2 139.2 31.4 100.6 43.2 146.6 25.6 124.5 9.4 119.5 45.1 94.0
N; E N; E N; E s; E S; E N; E N; E N; E N; E s; E N; E
41.5 N; 79.3 E
50.2 N; 91.3 E
Epicenter
used in the study
Origin time G.M.T.
of earthquakes
Date
Event
Parameters
TABLE
Is.
Mongolia
Sumba
Taiwan Is.
Szechwan Province Kuril Is.
Bonin
Carlsberg Ridge Tanimbar
Halmahera
Taiwan
USSRMongolia Br. KirgizSinkiang Br. S. Iran
Region
Is.
N
58
141
50
N
498
N
47
132
35
44
N
-
6.1
6.0
5.8
5.8
6.1
6.0
6.1
5.6
7.0
5.8
6.0
6.0
5.9
(mb)
(km)
N
Magnitude
Focal depth
30.4
48.4
43.4
62.3
24.4
56.5
56.7
22.0
51.1
41.4
23.0
24.0
34.0
(deg)
Epicentral distance
-
36.5
34.2
37.0
27.3
39.0
40.3
28.3
47.6
33.7
33.4
45.2
39.6
21.7 Average
123.4
70.9
49.8
50.9
67.3
109.8
209.1
110.9
72.9
301.4
01.4
14.5
(deg)
(ded 35.6
Back azimuth (stationepicenter)
Angle of incidence
33 36
38
34
34
36
37
30
34
38
38
37
38
36
(km)
Crustal thickness
131
,J”c l@USSR-MONGOLIA
0
2E
KIRGIZ
10
- SINKIANG ,
to
.o IO
0
HALMAHERA
r %
IO S
CARLSBERG
70
80
RIDGE
90
IO0
110
120
130
I40
E
Fig. 1. Location of the station (closed circle) and earthquakes (open circle). Table
II. The locations of these earthquakes and the recording station are shown in Fig. 1. The first 3-4 min of P-wave long-period trace is reproduced in Fig. 2 for two earthquakes. The long-period P-waves were digitized at the time interval of 0.40 set starting from the onset to a sample length of 45-55 sec. We have digitized our records with the help of WILD-A8 Autograph. This instrument is used for photogrammetric work at Survey of India (C.S.T. and M.P.), Hyderabad, and can be used for digitizing the records with good accuracy. It has a resolution of 10 microns and has a drawing table of large surface area on which the seismograms can be directly placed and digitized. The x- and y-coordinates are printed on a paper and the same figures are displayed on the WILD-EKS system. The discrete amplitude values are then transferred to computer cards. From this digitized data Fourier spectrum was obtained after the application of a hamming window (Blackman and Tukey, 1958). Following considerations have to be kept in mind while obtaining spectra of P-wave.
132
USSR-MONGOLIA
BORDER
PP I J
NS
EW
l$IRGIF
-S INKI fNG
FORDER I
NS
EW
v..
Fig. 2. The first few minutes of long-period P-waves recorded at Hyderabad by PressEwing Seismographs.
The selection of the sample length of the record to be used is very critical. The length should be sufficient to include important reverberations of the crust, since these reverberations are the physical reason of the transfer functions, The length should not be too long so as to avoid the later phases such as PP or PcP. If these later phases with different angles of incidence are included the resultant spectrum will be the superposition of several elementary spectra. Considering these factors a sample length of about 50 set is optimum. The superposition of the later phases can be avoided by the selection of epicentral distances at which these phases arrive at a considerable time after the initial P-wave. For the events we have studied, the later phases arrive only after a minute. Phases such as pP and sP may be considered as part of the P package with
133
the same angle of incidence and transfer function. The inherent transient character of the seismic signal is another limitation which allows only a statistical estimation of the true spectrum of the phase. The short length of the available record limits the frequency resolution of the spectrum. This resolution is a function of the sample length TL of the seismogram used and is given by Blackman and Tukey (1958). Resolution in cps = l/TL. For a sample length of 50 set, the resolution is 0.02 cps. This means that a statistically independent observation is obtained for every increment of the frequency of 0.02 cps. This increment is sufficient to observe the fine details of the theoretical curves. CALCULATION
OF OBSERVED
The observed IE(f)l,
CRUSTAL
crustal transfer
TRANSFER
function
FUNCTION
RATIO
ratio is given by:
= IV(f)lllMf)l
(5)
where I V(f) I and lH(fi I are the Fourier amplitudes of vertical and horizontal components of P-wave trace motion, respectively. This ratio is nothing but the tangent of the frequency-dependent apparent angle of emergence of the P-wave. If u( tK ), v(tK) and r(tK) are discrete P-wave trace motion amplitudes of vertical, NS and EW components, respectively, at certain time tK = KAt (K = 0,1,2, . . . . N - l), the vertical and horizontal P-wave amplitude spectra are given by: N-l
lV(f)l=
N-l
K 1 cos 27rfKAt]* + [ c
I[K~04t
u(tK) sin 2nfKAt]*]“*
K=O N-l
Wf)l = 1 c p. ii
(6)
N--l cos
4k)
2~fKAt] * + [KGo w( tK) sin BnfHAt] *) I’*
(7)
in the range 0 < f < fN where fN = :At is the Nyquist frequency. The horizontal trace amplitude tu(tK) at any instant tK can be determined as the horizontal component of the total vector field from the relations: 6K
= a=t~[r(tK)/v(tK)l
W(tK)
= v(tK)/cos
@K
Equations 6 and 7 yield the amplitude response spectra of two truncated data sequences. A hamming window was applied to the digitized data which was then used to obtain smoothed spectra. Dividing the smooth spectra of the vertical and horizontal components of the motion, we obtain the observed crustal transfer-function ratio of the crust beneath the receiving station as in eq. 5. The summation in eq. 6 and 7 was done by the Simpson’s method. The methodical procedure described so far consists of the following steps.
134
(1) Calculation of the observed crustal transfer function ratio /R(f) lo from digitized trace amplitudes of long-period P-waves of 50 set duration from teleseismic events. (2) Computation of the theoretical crustal transfer function ratio I R(f) IT from some assumed model parameters, (3) Determination of the thickness of the crust at the recording station from that theoretical curve which matches the observed one. DISCUSSION
Figure 3 shows the observed crustal transfer function ratio computed with the relations mentioned earlier for six of the events listed in Table II. We tried to find out the crustal model which fits best with the observed curves. This is an arduous process. A large number of crustal models have to be considered for this purpose. Theoretical transfer functions have to be determined for these models and after comparison with the observed ones, the best-fitting model has to be selected, The crust may consist of several layers and the layer parameters which have to be changed are P-velocity (oL), Svelocity (p), density (p) and layer-thickness (h). The theoretical crustal transfer function curve depends upon these parameters as well as the incidenceangle of the P-wave. The angle of incidence of P-waves in our study ranges from 27.3” to 47.6”. As a first-degree approximation, we have assumed that the S-velocity (0) and density (p) are related to P-velocity (LY) and the Poisson’s ratio (a) through the following relations and have varied only the P-velocity, Poisson’s ratio and layer thickness: fl= a (!2_%)
1’2
p = 2.35 + 0.036 (LY- 3.00)2 In the finally selected model, the S-velocity and density of each layer is varied from the values thus determined in the range of +0.3 unit with an increment of 0.1 to get the best-fitting value. The values of Poisson’s ratio (u) are selected in the range of 0.24-0.27. A P-wave velocity of 8.1 km/set has been assumed below the Moho for all the models. For the three-layered model the P-wave velocities were taken in the ranges of 5.6-6.2 for the first layer, 6.3-6.8 in the second layer and 6.57.5 km/see in the third layer. The velocities were varied with an increment of 0.1. The velocities for one-layer, two-layer and four-layer crustal models were taken from the ranges mentioned above. The total crustal thickness was varied in the range of 30-42 km. The thickness of individual layers was suitably varied. The crustal thickness affects the peak position of the crustal transfer function curve. The increase in the crustal thickness shifts the peak position towards the lower-frequency side. This criterion has been much useful in arriving at the correct model. The variations of P velocity, Poisson’s
f:\\ LA
IO
USSR
MONGOLIA BORDER f,
6
’ I
!
4
:
i
I
2
KIRGIZ - SINKIANG
16
I 1
6
_-
.
-.
‘./
4’
0
135
--l-J
0
:
CARLSBERG
RIDGE
4
r
TANIMBAR
-
oex Observed
- - -
Theoretical
IN
in J
4 3 2
I OU
IS.
I
/ i I ’ I I 1
:
,/---‘,_I
0
004
:
I
0 I2
-FREQUENCY
0 20
0
004
0.12
0,20
HZ-
Fig. 3. Observed (continuous line) and theoretical (broken line) crustal transfer functions for six of the earthquakes listed in Table II.
ratio and thickness of layers in the ranges mentioned above would give several hundreds of combinations but we stopped proceeding further in the directions in which we started to get bad fit between theoretical and observed curves. In this way we have calculated theoretical crustal transfer function curves for about 100 models and matched these with the observed ones. A one-layer model, with 6.25 km/set velocity above Moho, showed a reasonably good fit yielding the average crustal thickness of 35 km. The three-layer mod& showed better fit but two and four layer models did not
136 h FREE SURFACE
(Km)
d
A
(KmlSsc)
P
o(m/Sec)
tgm/C.Cf
21
5.81
3.12
2.66
8
6,41
3.62
2.75
7
6.66
3.94
2.91
6.10
4.61
3.34
CONRAD
MOtiO
oc
Fig. 4. The selected three-layered erustai model.
fit with the observed curves. The three-layer model which fitted best is given in Fig, 4, For the individual events the thickness of the top layer was varied till the best match was obtained between observed and theoretical curves. The value of crustal thickness obtained for each event for this three-layer model is given in Table II. The average crustal thickness obtained from all the events is 36 km. From Fig. 4 the average density of the crust is 2.74 g/cm3. For six of the events the theoretical transfer functions are shown by dashed curves in Fig. 3, along with the observed curves which are shown by continuous lines. We observe that the form, amplitude and periodicity of the two curves do not depart significantly. From Table II, we find that the crustal thickness is increasing systematically from about 34 to 38 km with the increase of azimuth from about 15” to 120”. This observation can not be substantiated in absence of other pertinent geophysical data in the vicinity of the NGRI seismic station. The two earthquakes, Tanimbar Island (event number 7) and Taiwan region (event number ll), are showing less crustal thickness values in comparison to other events of the similar azimuth and this may be due to the poor signal to noise ratio. The average crustal thickness in the peninsular shield of India has been inferred from the gravity data to be 34 km (Subrahmanyam et al., 1969). The travel-time study of the earthquake sources at short distances has given a crustal thickness of 35 km near the Gauribidanur array, which is 430 km south of Hyderabad (Arora, 1971). The deep seismic sounding studies 300 km south of Hyderabad have given a crustal thickness of about 35-40 km (Kaila et al., 1976). It can be seen that all these methods have given a crustal thickness of about 34-40 km in this region. Hence the crustal structure found by us beneath Hyderabad is consistent with the average erustal structure of the Peninsular shield found by gravity method and the crustal structure in the southern parts of the Peninsular shield found by seismic methods.
137 CONCLUSION
The fine crustal structure has been obtained beneath Hyderabad, India, using spectral amplitudes of long-period P-waves. The method yields reliable result and is inexpensive and convenient as seismograms of only one station are required. ACKNOWLEDGEMENTS
The authors are grateful to Dr. Hari Narain, Director, National Geophysical Research Institute, Hyderabad (India) for according permission to publish this work. We also wish to record our thanks to the Survey of India for access to the WILD-A8 autograph and Electronics Corporation of India and Regional Research Laboratory, Hyderabad for allowing us to use their computers. REFERENCES Arora, SK., 1971. A study of the Earth’s crust near Gauribidanur in Southern India. Bull. Seismol. Sot. Am., 61: 671-683. Blackman, R.D. and Tukey, J.W., 1958. The Measurement of Power Spectra. Dover Publ., New York, N.Y., 190 pp. Bonjer, K.P., Fuchs, K. and Wohlenberg, J., 1970. Crustal structure of the East African rift system from spectral response ratios of long-period body waves. Z. Geophys., 36: 287-297. Fernandez, L.M. and Careaga, J., 1968. The thickness of the crust in Central United States and La Paz, Bolivia, from the spectrum of longitudinal seismic waves. Bull. Seismol. Sot. Am., 58: 711-741. Hasegawa, H.S., 1971. Crustal transfer ratios of short- and long-period body waves recorded at Yellowknife. Bull. Seismol. Sot. Am., 61: 1303-1320. Haskell, N.A., 1953. The dispersion of surface waves on multi-layered media. Bull. Seismol. Sot. Am., 43: 17-34. Haskell, N.A., 1962. Crustal reflections of plane P and SV waves. J. Geophys. Res., 67: 4751-4767. Kaila, K.L., Reddy, P.R., Krishna, V.G., Narain, H., Subbotin, S.I., Chekunov, A.V., Kharechko, G.E. and Tripolsky, A.A., 1976. Deep crustal structure on the southwestern part of the Indian Shield. Int. Geol. Congr., 25th, Sydney (Abstr.). Kurita, T., 1970. Crustal and upper mantle structure in Japan from amplitude and phase spectra of long-period P-waves. Part 3, Chugoku region. J. Phys. Earth, 18: 53-78. Leong, L.S., 1975. Crust11 st.ucture of the Baltic Shield beneath Umea, Sweden, from the spectral behaviour of long-period P-waves. Bull. Seismol. Sot. Am., 65: 113-125. Phinney, R.A., 1964. Structure of the Earth’s crust from spectral behaviour of longperiod body waves. J. Geophys. Res., 69: 2997-3017. Rogers Jr., A.M. and Kisslinger, C., 1972. The effect of a dipping layer on P-wave transmission. Bull. Seismol. Sot. Am., 62: 301-324. Sezawa, K. and Kanai, K., 1932. Possibility of free oscillations of strata excited by seismic waves, III. Bull. Earthquake Res. Inst. (Tokyo), 10: l-18. Sezawa, K. and Kanai, K., 1937. On the free vibrations of a surface layer due to an obliquely incident disturbance. Bull. Earthquake Res. Inst. (Tokyo), 15: 375-383. Subrahmanyam, C., Qureshy, M.N., Brahmam, N.K., 1969. Crustal studies in India by gravity data. Annu. Rep. (1968-69), Nat. Geophys. Res. Inst., Hyderabad, pp. 21-22.
127 Amsterdam
-
Printed
in The Netherlands
CRUSTAL STRUCTURE OF THE PENINSULAR SHIELD BENEATH HYDERABAD (INDIA) FROM THE SPECTRAL CHARACTERISTICS OF LONG-PERIOD P-WAVES
D.D. SINGH National
and B.K.
Geophysical
(Submitted
July
RASTOGI Research
18. 1977;
Institute,
revised version
Hyderabad accepted
500007 January
(India) 25, 1978)
ABSTRACT Singh, D.D. and Rastogi, B.K., 1978. Crustal structure Hyderabad (India) from the spectral characteristics physics, 51: 127-137.
of the peninsular shield beneath of long-period P-waves. Tectono-
The crustal transfer functions have been obtained from long period P-waves of thirteen teleseismic events recorded at Hyderabad (HYB), India, The crustal structure beneath this seismograph station has been obtained after comparing these functions with the theoretical crustal transfer functions which were computed using the Thomson-Haskell matrix formulation. The method is suitable and economical for determining the fine crustal structure. The crust beneath Hyderabad is found to consist of three layers with total thickness of 36 km. The thicknesses of top, middle and bottom layers are 21 km, 8 km and 7 km, respectively.
INTRODUCTION
The local crustal structure in the Hyderabad area is not known, though, the regional structure of the peninsular shield of India has been determined by regional gravity data (Subrahmanyam et al., 1969). The knowledge of the local crustal structure is of considerable scientific value. In view of this we attempted to obtain the local crustal structure beneath Hyderabad. A first order seismograph station, equipped with seismographs conforming to WWSSN standards is operating at Hyderabad since 1968. As there are not enough local earthquakes, short-distance travel-time study is not possible to determine the local crustal structure around Hyderabad. Phinney (1964) has given a method of determining the crustal layering beneath a seismograph station using the teleseismic earthquakes. The method utilizes frequency dependent polarization properties of teleseismic P-waves. Phinney has defined the ratio of the vertical spectrum to the horizontal spectrum of longperiod P-wave as crustal transfer ratio - a function which depends on structure beneath the station. The spectral ratio response is due to the narrow
128
cone of structure beneath the receiving station as body waves traverse at a small angle of incidence under the station for the teleseismic events. Therefore, as pointed out by Fernandez and Careaga (1968), it is possible to determine the crustai layering with great horizontal resolution using this method. This property is specially significant as gravity study gives the average picture over the entire structure and surface wave dispersion study gives the average structure over hundreds or thousands of kilometers. Moreover, the spectral ratio method does not require the knowledge of earthquake origin time. The seismic travel time method is very sensitive to the accuracy of origin time determination. However, body wave spectral ratios appear to be most critical with respect to structure in the lower half of the crust considering the period range of 5-50 sec. This method has been applied by Phinney (1964) and afterwards by several workers (Fernandez and Careaga, 1968; Bonjer et al., 2970; Kurita, 1970; Hasegawa, 1971; Rogers and Kisslinger, 1972; Leong, 1975). We have applied this method to determine the crustal structure beneath Hyderabad. THEORETICAL
BACKGROUND
The frequency response of the layers of the crust and upper mantle to the seismic waves is a function of some of the physical parameters of the layered system. The response of layered media to body waves has been studied as early as in 1932 by Sezawa and Kanai (1932, 1937). The use of matrix algebra provided a significant simplification in the numerical calculations involved in the problem (Haskell, 1953). Haskell (1962) considered the effect of the layers on the incident P-waves as a transfer function affecting either the vertical or the horizontal component of motion and gave the following expressions for the vertical and horizontal components of motion at the free surface (1) w,(w) = A(w)Wp(o~, ~1 where A(w) is the spectrum of the incident wave and Ur and Wp are spectral transfer functions. Haskell gave a method of computing the transfer functions if the model is composed of homogeneous parallel layers; in that case Up and Wp depend only on the frequency and apparent velocity of the wave. From eq. 1 division yields: ?!!?= $= UO
Tp(0, c)
(2)
This implies that by dividing the observed spectrums we obtain a function which is independent of the spectrum of the incident pulse. Therefore Phinney (1964) proposed to employ Tp for the determination of crustal
129
structure beneath a recording station. Observed values of T, can be obtained by Fourier analysis of long-period P-waves from teleseismic earthquakes, the practical details for which are given in the next section. Theoretical curves of Tp(o) can be calculated for a broad class of earth models for various values of c. Instead of c we can take the angle of incidence i, as the two quantities are uniquely related to each other. By variation of the parameters, a theoretical curve can be found which matches the observed one. This theoretical model will represent the crustal structure beneath the station. Hereafter, in this paper we will refer IR(f) lo as observed crustal transfer function ratio and [R(f) IT as theoretical transfer ratio. Referring to Haskell (1962), the expression for the latter quantity can be written as: (3) The right-hand side of this expression consists of the elements of the matrix J which is the (4 X 4) matrix product obtained in solving the boundary value problem of the layered system. More specifically the matrix J is given by Haskell’s (1953) relation (2.19) as: J = E,‘a,_,a,_,
. . . a,
(4)
where each submatrix a, depends on the transmission coefficients ness, density, rigidity, velocity) of the corresponding mth layer. DATA
(thick-
ANALYSIS
We have determined the observed crustal transfer function ratios of thirteen teleseismic events recorded by the three matched component, longperiod, WWSSN type seismographs at Hyderabad. The details of the seismograph station are given in Table I. Details of the earthquakes are given in TABLE Station
I and instrument
characteristics
Station Code Name Latitude Longitude Height above M.S.L. Bedrock Seismographs
Hyderabad HYB 17’25’02”N 78’33’11”E 510 mts Granite Long-period
Seismometer period Galvanometer period Maximum dynamic magnification Mode of recording Damping ratio Run and maintained by
Z, N, B 15 set 100 set 1500 Photographic paper Critical National Geophysical
Press-Ewing
Research
Institute
II
20:47:17.4
Mar. 23,197l
Apr. 12, 1971
Apr. 17, 1972
Sept. 05,1972
Sept. 07,1972
Sept. 24, 1972
Jan. 31, 1973
Feb. 06,1973
Jun. 26,1973
Sept. II,1973
Dec. 19,1973
Jul. 04, 1974
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
19:30;42.1
04:43:01.5
23:18:50.8
22~32100.2
10:37:10.1
20:55:53.1
20:09:35.6
02:55:00.1
17:18:29.5
10:49:42.7
19:03:25.9
17:13:15.1
May 15,197O
1.
28.3 55.6 24.2 122.5 1.9 128.2 1.9 68.1 6.3 131.2 28.2 139.2 31.4 100.6 43.2 146.6 25.6 124.5 9.4 119.5 45.1 94.0
N; E N; E N; E s; E S; E N; E N; E N; E N; E s; E N; E
41.5 N; 79.3 E
50.2 N; 91.3 E
Epicenter
used in the study
Origin time G.M.T.
of earthquakes
Date
Event
Parameters
TABLE
Is.
Mongolia
Sumba
Taiwan Is.
Szechwan Province Kuril Is.
Bonin
Carlsberg Ridge Tanimbar
Halmahera
Taiwan
USSRMongolia Br. KirgizSinkiang Br. S. Iran
Region
Is.
N
58
141
50
N
498
N
47
132
35
44
N
-
6.1
6.0
5.8
5.8
6.1
6.0
6.1
5.6
7.0
5.8
6.0
6.0
5.9
(mb)
(km)
N
Magnitude
Focal depth
30.4
48.4
43.4
62.3
24.4
56.5
56.7
22.0
51.1
41.4
23.0
24.0
34.0
(deg)
Epicentral distance
-
36.5
34.2
37.0
27.3
39.0
40.3
28.3
47.6
33.7
33.4
45.2
39.6
21.7 Average
123.4
70.9
49.8
50.9
67.3
109.8
209.1
110.9
72.9
301.4
01.4
14.5
(deg)
(ded 35.6
Back azimuth (stationepicenter)
Angle of incidence
33 36
38
34
34
36
37
30
34
38
38
37
38
36
(km)
Crustal thickness
131
,J”c l@USSR-MONGOLIA
0
2E
KIRGIZ
10
- SINKIANG ,
to
.o IO
0
HALMAHERA
r %
IO S
CARLSBERG
70
80
RIDGE
90
IO0
110
120
130
I40
E
Fig. 1. Location of the station (closed circle) and earthquakes (open circle). Table
II. The locations of these earthquakes and the recording station are shown in Fig. 1. The first 3-4 min of P-wave long-period trace is reproduced in Fig. 2 for two earthquakes. The long-period P-waves were digitized at the time interval of 0.40 set starting from the onset to a sample length of 45-55 sec. We have digitized our records with the help of WILD-A8 Autograph. This instrument is used for photogrammetric work at Survey of India (C.S.T. and M.P.), Hyderabad, and can be used for digitizing the records with good accuracy. It has a resolution of 10 microns and has a drawing table of large surface area on which the seismograms can be directly placed and digitized. The x- and y-coordinates are printed on a paper and the same figures are displayed on the WILD-EKS system. The discrete amplitude values are then transferred to computer cards. From this digitized data Fourier spectrum was obtained after the application of a hamming window (Blackman and Tukey, 1958). Following considerations have to be kept in mind while obtaining spectra of P-wave.
132
USSR-MONGOLIA
BORDER
PP I J
NS
EW
l$IRGIF
-S INKI fNG
FORDER I
NS
EW
v..
Fig. 2. The first few minutes of long-period P-waves recorded at Hyderabad by PressEwing Seismographs.
The selection of the sample length of the record to be used is very critical. The length should be sufficient to include important reverberations of the crust, since these reverberations are the physical reason of the transfer functions, The length should not be too long so as to avoid the later phases such as PP or PcP. If these later phases with different angles of incidence are included the resultant spectrum will be the superposition of several elementary spectra. Considering these factors a sample length of about 50 set is optimum. The superposition of the later phases can be avoided by the selection of epicentral distances at which these phases arrive at a considerable time after the initial P-wave. For the events we have studied, the later phases arrive only after a minute. Phases such as pP and sP may be considered as part of the P package with
133
the same angle of incidence and transfer function. The inherent transient character of the seismic signal is another limitation which allows only a statistical estimation of the true spectrum of the phase. The short length of the available record limits the frequency resolution of the spectrum. This resolution is a function of the sample length TL of the seismogram used and is given by Blackman and Tukey (1958). Resolution in cps = l/TL. For a sample length of 50 set, the resolution is 0.02 cps. This means that a statistically independent observation is obtained for every increment of the frequency of 0.02 cps. This increment is sufficient to observe the fine details of the theoretical curves. CALCULATION
OF OBSERVED
The observed IE(f)l,
CRUSTAL
crustal transfer
TRANSFER
function
FUNCTION
RATIO
ratio is given by:
= IV(f)lllMf)l
(5)
where I V(f) I and lH(fi I are the Fourier amplitudes of vertical and horizontal components of P-wave trace motion, respectively. This ratio is nothing but the tangent of the frequency-dependent apparent angle of emergence of the P-wave. If u( tK ), v(tK) and r(tK) are discrete P-wave trace motion amplitudes of vertical, NS and EW components, respectively, at certain time tK = KAt (K = 0,1,2, . . . . N - l), the vertical and horizontal P-wave amplitude spectra are given by: N-l
lV(f)l=
N-l
K 1 cos 27rfKAt]* + [ c
I[K~04t
u(tK) sin 2nfKAt]*]“*
K=O N-l
Wf)l = 1 c p. ii
(6)
N--l cos
4k)
2~fKAt] * + [KGo w( tK) sin BnfHAt] *) I’*
(7)
in the range 0 < f < fN where fN = :At is the Nyquist frequency. The horizontal trace amplitude tu(tK) at any instant tK can be determined as the horizontal component of the total vector field from the relations: 6K
= a=t~[r(tK)/v(tK)l
W(tK)
= v(tK)/cos
@K
Equations 6 and 7 yield the amplitude response spectra of two truncated data sequences. A hamming window was applied to the digitized data which was then used to obtain smoothed spectra. Dividing the smooth spectra of the vertical and horizontal components of the motion, we obtain the observed crustal transfer-function ratio of the crust beneath the receiving station as in eq. 5. The summation in eq. 6 and 7 was done by the Simpson’s method. The methodical procedure described so far consists of the following steps.
134
(1) Calculation of the observed crustal transfer function ratio /R(f) lo from digitized trace amplitudes of long-period P-waves of 50 set duration from teleseismic events. (2) Computation of the theoretical crustal transfer function ratio I R(f) IT from some assumed model parameters, (3) Determination of the thickness of the crust at the recording station from that theoretical curve which matches the observed one. DISCUSSION
Figure 3 shows the observed crustal transfer function ratio computed with the relations mentioned earlier for six of the events listed in Table II. We tried to find out the crustal model which fits best with the observed curves. This is an arduous process. A large number of crustal models have to be considered for this purpose. Theoretical transfer functions have to be determined for these models and after comparison with the observed ones, the best-fitting model has to be selected, The crust may consist of several layers and the layer parameters which have to be changed are P-velocity (oL), Svelocity (p), density (p) and layer-thickness (h). The theoretical crustal transfer function curve depends upon these parameters as well as the incidenceangle of the P-wave. The angle of incidence of P-waves in our study ranges from 27.3” to 47.6”. As a first-degree approximation, we have assumed that the S-velocity (0) and density (p) are related to P-velocity (LY) and the Poisson’s ratio (a) through the following relations and have varied only the P-velocity, Poisson’s ratio and layer thickness: fl= a (!2_%)
1’2
p = 2.35 + 0.036 (LY- 3.00)2 In the finally selected model, the S-velocity and density of each layer is varied from the values thus determined in the range of +0.3 unit with an increment of 0.1 to get the best-fitting value. The values of Poisson’s ratio (u) are selected in the range of 0.24-0.27. A P-wave velocity of 8.1 km/set has been assumed below the Moho for all the models. For the three-layered model the P-wave velocities were taken in the ranges of 5.6-6.2 for the first layer, 6.3-6.8 in the second layer and 6.57.5 km/see in the third layer. The velocities were varied with an increment of 0.1. The velocities for one-layer, two-layer and four-layer crustal models were taken from the ranges mentioned above. The total crustal thickness was varied in the range of 30-42 km. The thickness of individual layers was suitably varied. The crustal thickness affects the peak position of the crustal transfer function curve. The increase in the crustal thickness shifts the peak position towards the lower-frequency side. This criterion has been much useful in arriving at the correct model. The variations of P velocity, Poisson’s
f:\\ LA
IO
USSR
MONGOLIA BORDER f,
6
’ I
!
4
:
i
I
2
KIRGIZ - SINKIANG
16
I 1
6
_-
.
-.
‘./
4’
0
135
--l-J
0
:
CARLSBERG
RIDGE
4
r
TANIMBAR
-
oex Observed
- - -
Theoretical
IN
in J
4 3 2
I OU
IS.
I
/ i I ’ I I 1
:
,/---‘,_I
0
004
:
I
0 I2
-FREQUENCY
0 20
0
004
0.12
0,20
HZ-
Fig. 3. Observed (continuous line) and theoretical (broken line) crustal transfer functions for six of the earthquakes listed in Table II.
ratio and thickness of layers in the ranges mentioned above would give several hundreds of combinations but we stopped proceeding further in the directions in which we started to get bad fit between theoretical and observed curves. In this way we have calculated theoretical crustal transfer function curves for about 100 models and matched these with the observed ones. A one-layer model, with 6.25 km/set velocity above Moho, showed a reasonably good fit yielding the average crustal thickness of 35 km. The three-layer mod& showed better fit but two and four layer models did not
136 h FREE SURFACE
(Km)
d
A
(KmlSsc)
P
o(m/Sec)
tgm/C.Cf
21
5.81
3.12
2.66
8
6,41
3.62
2.75
7
6.66
3.94
2.91
6.10
4.61
3.34
CONRAD
MOtiO
oc
Fig. 4. The selected three-layered erustai model.
fit with the observed curves. The three-layer model which fitted best is given in Fig, 4, For the individual events the thickness of the top layer was varied till the best match was obtained between observed and theoretical curves. The value of crustal thickness obtained for each event for this three-layer model is given in Table II. The average crustal thickness obtained from all the events is 36 km. From Fig. 4 the average density of the crust is 2.74 g/cm3. For six of the events the theoretical transfer functions are shown by dashed curves in Fig. 3, along with the observed curves which are shown by continuous lines. We observe that the form, amplitude and periodicity of the two curves do not depart significantly. From Table II, we find that the crustal thickness is increasing systematically from about 34 to 38 km with the increase of azimuth from about 15” to 120”. This observation can not be substantiated in absence of other pertinent geophysical data in the vicinity of the NGRI seismic station. The two earthquakes, Tanimbar Island (event number 7) and Taiwan region (event number ll), are showing less crustal thickness values in comparison to other events of the similar azimuth and this may be due to the poor signal to noise ratio. The average crustal thickness in the peninsular shield of India has been inferred from the gravity data to be 34 km (Subrahmanyam et al., 1969). The travel-time study of the earthquake sources at short distances has given a crustal thickness of 35 km near the Gauribidanur array, which is 430 km south of Hyderabad (Arora, 1971). The deep seismic sounding studies 300 km south of Hyderabad have given a crustal thickness of about 35-40 km (Kaila et al., 1976). It can be seen that all these methods have given a crustal thickness of about 34-40 km in this region. Hence the crustal structure found by us beneath Hyderabad is consistent with the average erustal structure of the Peninsular shield found by gravity method and the crustal structure in the southern parts of the Peninsular shield found by seismic methods.
137 CONCLUSION
The fine crustal structure has been obtained beneath Hyderabad, India, using spectral amplitudes of long-period P-waves. The method yields reliable result and is inexpensive and convenient as seismograms of only one station are required. ACKNOWLEDGEMENTS
The authors are grateful to Dr. Hari Narain, Director, National Geophysical Research Institute, Hyderabad (India) for according permission to publish this work. We also wish to record our thanks to the Survey of India for access to the WILD-A8 autograph and Electronics Corporation of India and Regional Research Laboratory, Hyderabad for allowing us to use their computers. REFERENCES Arora, SK., 1971. A study of the Earth’s crust near Gauribidanur in Southern India. Bull. Seismol. Sot. Am., 61: 671-683. Blackman, R.D. and Tukey, J.W., 1958. The Measurement of Power Spectra. Dover Publ., New York, N.Y., 190 pp. Bonjer, K.P., Fuchs, K. and Wohlenberg, J., 1970. Crustal structure of the East African rift system from spectral response ratios of long-period body waves. Z. Geophys., 36: 287-297. Fernandez, L.M. and Careaga, J., 1968. The thickness of the crust in Central United States and La Paz, Bolivia, from the spectrum of longitudinal seismic waves. Bull. Seismol. Sot. Am., 58: 711-741. Hasegawa, H.S., 1971. Crustal transfer ratios of short- and long-period body waves recorded at Yellowknife. Bull. Seismol. Sot. Am., 61: 1303-1320. Haskell, N.A., 1953. The dispersion of surface waves on multi-layered media. Bull. Seismol. Sot. Am., 43: 17-34. Haskell, N.A., 1962. Crustal reflections of plane P and SV waves. J. Geophys. Res., 67: 4751-4767. Kaila, K.L., Reddy, P.R., Krishna, V.G., Narain, H., Subbotin, S.I., Chekunov, A.V., Kharechko, G.E. and Tripolsky, A.A., 1976. Deep crustal structure on the southwestern part of the Indian Shield. Int. Geol. Congr., 25th, Sydney (Abstr.). Kurita, T., 1970. Crustal and upper mantle structure in Japan from amplitude and phase spectra of long-period P-waves. Part 3, Chugoku region. J. Phys. Earth, 18: 53-78. Leong, L.S., 1975. Crust11 st.ucture of the Baltic Shield beneath Umea, Sweden, from the spectral behaviour of long-period P-waves. Bull. Seismol. Sot. Am., 65: 113-125. Phinney, R.A., 1964. Structure of the Earth’s crust from spectral behaviour of longperiod body waves. J. Geophys. Res., 69: 2997-3017. Rogers Jr., A.M. and Kisslinger, C., 1972. The effect of a dipping layer on P-wave transmission. Bull. Seismol. Sot. Am., 62: 301-324. Sezawa, K. and Kanai, K., 1932. Possibility of free oscillations of strata excited by seismic waves, III. Bull. Earthquake Res. Inst. (Tokyo), 10: l-18. Sezawa, K. and Kanai, K., 1937. On the free vibrations of a surface layer due to an obliquely incident disturbance. Bull. Earthquake Res. Inst. (Tokyo), 15: 375-383. Subrahmanyam, C., Qureshy, M.N., Brahmam, N.K., 1969. Crustal studies in India by gravity data. Annu. Rep. (1968-69), Nat. Geophys. Res. Inst., Hyderabad, pp. 21-22.