Velocity Dispersion and Amplitude Attenuation of Rayleigh Waves Across the Philippine Sea

The fundamental-mode interstation group and phase velocities and attenuation coefficients of Rayleigh waves along four paths across the Phil­ ippine Sea are determined to have periods of between 20 and 110 seconds by the two-station method. The values of group and phase velocities are quite consistent with the results of previous studies using the single�station method. Group and phase velocities vary significantly with different wave­ paths at periods of less than 50 seconds, but for longer periods, the phase velocities are quite close. The inversion results show that the thickness of the lithosphere is about 60 km in the Philippine Sea, except in the area of the eastern volcanic islands where a slightly thinner lithosphere (about 50 km) is deduced. The attenuation coefficients observed in the Philippine Sea are higher than the values obtained in the Pacific. This result simply re­ flects that the Philippine Sea plate is younger than that of the Pacific. Lat­ eral variation in attenuation coefficient is not as clear as it is in velocity because of its large variance. However, the vertical distribution of Qj/ is quite similar to that for the shear velocity model. (


INTRODUCTION
In seismology, there are two approaches often used to study the structure of the Earth.One is to derive the velocity model from travel-time data and the other is to derive the Q model from attenuation observations.In the past, surface wave amplitude attenuations have been widely used to study the anelasticity properties of the crust and upper mantle (e.g., Mitchell, 1973Mitchell, , 1975;;Mitchell et al., 1976;Yacoub and Mitchell, 1977;Canas and Mitchell, 1978;Hwang and Mitchell, 1986;Al-Khatib and Mitchell, 1991).These studies have also provided good results for regional velocity variations of the crust and upper mantle.
Previous studies in the Philippine Sea have devoted much effort to the determination of velocity structure (e.g., Seekins and Teng, 1977; Yu, 1982; Yu and Chang, 1991; Oda and  Senna, 1994), but none to amplitude attenuation.However, the Q structure, as derived from the attenuation observations, would provide us with some other important properties of the media which cannot be deduced from velocity data.In this study we try to determine the interstation amplitude attenuation, as well as velocity dispersions, of Rayleigh waves along four paths across the Philippine Sea using the two-station method.

2.METHOD
In this study, the two-station method was used to determine the interstation group and phase velocities and attenuation coefficients of Rayleigh waves at periods between 20 and 110 seconds.Although this method could eliminate errors coming from the source (e.g., mislocation of the source and uncertainties in origin time ), it requires each station pair to lie on the same great circle with the source and their records should also have high enough signal to noise ratio.In this case, there are few seismograms that meet these conditions.In order to get more data, a maximum deviation of 5° in azimuths between each station pair is accepted.
The spectral amplitudes and group velocities of the fundamental Rayleigh waves at periods between 20 and 110 seconds are first determined by the multiple-filter method (Dziewonski et al., 1969) and then refined by frequency-variable filtering (Russell et al., 1988) for each seis mogram.A frequency-domain Wiener filter (Taylor and Toksoz, 1982;Hwang and Mitchell, 1986) is applied to determine the interstation Green's function ,G(f), between the station pairs according to the relation where H(f) is the cross-correlation matrix between the input signal (at station 1) and output signal (at station 2), and R(f) is the auto-correlation matrix of the input signal.As stated by Al Khatib and Mitchell (1991), frequency-domain Wiener filtering guarantees the removal of random noise and provides more stable and accurate estimates of group and phase velocities and attenuation coefficients than other methods do.
From the Green's function, the interstation group and phase velocities are calculated from the group delay and phase spectra of the transfer functions (Taylor and Toksoz, 1982) using the following formula (2) and (3) where X1 and X2 are epicentral distances in kilometers for stations 1 and 2, respectively, t1 and t2 are arrival times, t0 is the first time point of the Green's function, <P(f) is the phase of the Green's function in cycles, and N is an integer which provides the reasonable phase velocities for periods longer than 60 seconds.The interstation attenuation coefficients are calculated using the formula (Hwang and Mitchell, 1986) y( f );;: -ln l G( f ) j �s in 8 2 /si n 8 1 , X2-X1 (4 ) where �1 and �2 are the epicentral distances in degrees for stations 1 and 2, respectively, and G(f) is the interstation Green's function.The uncertainties in the measurements of phase and group velocities and attenuation coefficients have been discussed in detail by several authors (Forsyth, 1975;Kijko and Mitchell, 1983).Systematic errors may be caused by interference from other phases, incomplete separation of modes, or lateral refraction.Russell et al. (1988) showed that use of a phase-matched and frequency-variable filter will guarantee removal of the phase of interest mode and will minimize spectral distortions due to phase fluctuation.
Other systematic errors, such as mislocation of the source and uncertainties in origin time, will be canceled by using the two-station method.

RESULT AND DISCUSSION
Thirteen events along four path-pairs, GUA-MAT(GUMO-MAJO), GUA-SHK, GUMO TATO, and GU A-DAV, across the Philippine Sea, have been selected to determine the funda mental Rayleigh wave interstation group and phase velocities and attenuation coefficients at the periods between 20 and 110 seconds (Table 1 and Fig. 1).The mean observed values and their standard deviations for each path are shown in Figs. 2, 3, and 6, respectively.Figs. 2 and 3 show that the group and phase velocities along the paths for GU A-MAT and GUMO-MAJO are significantly lower than those for the other paths, especially for the period range of less than 50 seconds.This significant path-dependent variation agrees with the lateral variation statements o _ f previous studies (Yu and Chang,1991;Oda and Senna, 199 4 ).By inversion of    the group and phase velocity data for each path, respectively, a lithosphere thickness of about 60 km is obtained for most parts of the Philippine Sea, except in the area of the eastern volca nic islands where a slightly thinner lithosphere thickness (about 50 km) gives a better fit (Fig. 4).This result is different from the studies by Seekins and Teng (1977) and Yu and Chang (1991).However, the values of shear velocity, in our study, vary from 4.4 to 4.55 km/sec in the lithosphere and from 4. 1 to 4.3 km/sec in the asthenosphere agree well with their results.  Anderson, 1975; Seekins and Teng,  1977; Yu and Chang, 1991).Similarly, unexpected high attenuations at the periods between 36 and 70 seconds for the GUA-DAV path (Fig. 4) are also found.These unreasonable results may be affected by energy enhan�ed by multipathing interferences of wave propagation to stations MAT (or MAJO) and DAV, since these paths lie close to the plate boundary.Unfortu nately, we cannot find more appropriate events for these paths.Moreover, low attenuation values observed at the periods between 24 and 40 seconds along several paths seem to need a high shear velocity layer at a shallow depth just below the Moho, but according to the velocity dispersion inversion result, there is no such high_ shear velocity layer at a shallow depth.Thus the model derived from velocity dispersion data is more reliable than that from attenuation values because we can measure velocity more accurately.0 1 00 :; Frequency (Hz) Frequency (Hz) Yu et al.
Figure 7 shows the vertical distribution of Q"(/ along each path.These distribution pat terns match well with the velocity distributions.The average Q values in the Philippine Sea are about 200 for the lithosphere and about 30 for the asthenosphere, respectively.These values are lower than the observations in the Pacific (Mitchell et al., 1976;Canas and Mitchell, 1977).This fact reflects the younger age of the plate and softer asthenosphere of the Philippine Sea compared to the Pacific (Seekins and Teng, 1977;Seno and Maruyama, 1984;Yu and Chang, 1991;Oda and Senna,1994).The average attenuation coefficients as well as their standard deviations of Rayleigh waves across the Philippine Sea are shown in Fig. 8. Also shown is the comparison with observations in the Eurasia and Pacific plates.

CONCLUSIONS
After analysis of the interstation group and phase velocities and attenuation coefficients along four paths of Rayleigh waves across the Philippine Sea using the two-station method, a number conclusions can be drawn.

PERIOD (SEC)
Fi g . 8. The average attenuation coefficients and their standard deviations ob tained for the fundamental Rayleigh waves obtained in this study com pared with observations made in the Pacific (Mitchell et al., 1976) and in Eurasia (Yacoub and Mitchell, 1977).
( 1) The thickness of the Philippine Sea plate is about 60 km, except in the area of the eastern volcanic islands where 50 km is more likely.
(2) Shear velocities vary from 4.4 to 4.55 km/sec in the lithosphere and from 4.1 to 4.3 km/sec in the asthenosphere of the Philippine Sea.
(3) Attenuation coefficients observed in the Philippine Sea are higher than those obtained in the Pacific, but lower than the observations in Eurasia.In the Philippine Sea, the average Q values are about 200 for the lithosphere and 30 for the asthenosphere, respectively.Lateral variation in attenuation is not as clear as the velocity because of the large variance.

Fig. 1 .
Fig. 1.Map showing the four paths of Rayleigh waves across the Philippine Sea.Triangles denote the seismograph stations.

Fig. 2 .
Fig. 2. Group velocity dispersion curves of the fundamental Rayleigh waves along four paths across the Philippine Sea.

Fig. 3 .
Fig. 3. Phase velocity dispersion curves of the fundamental Rayleigh waves along four paths across the Philippine Sea.

Fig. 4 .
Fig. 4. Shear velocity models derived by inversion of the group and phase veloc ity dispersion data.

Fig. 6 .Fig. 7 .
Fig. 6.Attenuation coefficients of the fundamental Rayleigh waves along four paths across the Philippine Sea.