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P-wave velocity structure inside the subducting Pacific plate beneath the Japan region
Physics of the Earth and Planetary Interiors, 66 (1991) 203—213 Elsevier Science Publishers By., Amsterdam
203
P-wave velocity structure inside the subducting Pacific plate beneath the Japan region Takashi Jidaka and Megumi Mizoue Earthquake Research Institute, The University of Tokyo. Yayoi 1-1-1, Bunkyo, Tokyo, Japan (Received 26 February 1990; revised and accepted 5 November 1990)
ABSTRACT lidaka, T. and Mizoue, M., 1991. P-wave velocity structure inside the subducting Pacific plate beneath the Japan region. Phys. Earth Planet. Inter., 66: 203—213. Little is known of the internal structure of the subducting Pacific plate. Previous studies suggest the existence of an intermediate boundary within the subducting slab. The low density of seismological stations in oceanic regions has prevented high-resolution studies. Recently, seismological stations in Japan have accumulated digitally recorded seismograms. Beneath the Kanto region, central Japan, the Pacific plate is subducting with a high inclination compared with that of the Tohoku region, northern Japan. The ray paths from deep earthquakes to seismological stations are expected to penetrate more inner parts of the subducting plate. This region is suitable to resolve the velocity structure within the plate. In this study, travel-time residuals and seismograms of the deep-focus earthquakes that occurred beneath the Kinki region, southern Japan, are used to constrain various parameters related to the velocity structure model within the slab. The seismograms of deep-focus earthquakes at the geographically restricted stations located in the Kanto region, central Japan, show a remarkable high-frequency later arrival of the P wave. The later arrival was studied and recognized as the reflected wave at the intermediate boundary inside the plate. The velocity structure within the plate is also studied. Our best-fit model has a velocity of Jeffreys—Bullen (J—B) model plus 1.5% in the upper layer and J—B plus 2.5% in the lower layer.
1. Introduction It is well known that a high-velocity plate subducts in the Japan region. Thus the upper mantle structure in and around the Japan region has a large-scale lateral heterogeneity. Evidence for such a structure includes the existence and the regular spatial pattern of intermediate- and deep-focus earthquakes, anomalous seismic intensity distributions, travel-time anomalies, and high-frequency spectral contents of seismograms. The velocity contrast between subducting lithosphere and the overlying asthenosphere beneath the Japan region has been calculated at between 2 and 15% (e.g. Utsu, 1967, 1975; Hirahara, 1977; Okada, 1977; Suyehiro and Sacks, 1979; Matsuzawa et al., 1986). In the oceanic region, several long-range explosion seismology experiments have been developed. 0031-9201/91/$03.50
© 1991
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As a result of these studies, a two-layered lithosphere model was proposed (e.g. Shimamura and Asada, 1976; Shimamura et al., 1983). Also, the travel-time residuals of P and S waves from local deep earthquakes were used to apply geophysical constraints to the laterally heterogeneous structure associated with the Japan subduction zone (Suyehiro and Sacks, 1979). The spatial distribution of observed and calculated residual data mdicates that the subducting lithosphere can be modelled by a two-layered structure. The two-layered slab model was also supported by Ando et al. (1989). We have studied the lateral velocity variations of compressional (P) waves inside the subducting Pacific slab beneath the Japan region. This study uses travel-time residuals (observed travel time minus Jeffreys—Bullen (J—B) travel time) from local deep earthquakes to apply constraints on van-
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T. IIDAKA AND M. MIZOUE
ous parameters related to the heterogeneous subducting Pacific plate. The seismograms of deep-focus earthquakes are also investigated. The seismograms of the deep earthquake that occurred beneath the Kinki region show a remarkable high-frequency later arrival at several seismological stations. In this paper we
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studyarrival. and identify the cause of the high-frequency later 2. Data
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It is important that the data be examined carefully to infer structural anomalies quantitatively. The data were collected according to the following criteria. Data for 26 deep-focus earthquakes that occurred in area 33.0—35.0 °N and 136.0—138.0 °E were collected for the period January 1985 to December 1987 (Fig. 1 and Table 1).
134. 0 E
142. 0 E
Fig. 1. Location of earthquakes (star) and seismological stations (triangle). The parameters of the hypocentres determined by JMA were adopted.
Seismograms from stations of the Earthquake Research Institute were used (Fig. 1). The seismometers used were of the 1 Hz velocity type.
TABLE 1 List of earthquakes Date
13 April 1 May 11 May 26 May 4 June 12 August 25 September 16 November 30 November 9 December 28 December 9 January 28 April 29 May 10 June 9 September 27 September 4 December 12 February 21 February 2 April 27 May 9 June 28 August 14 October 21 October
Time
1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1986 1986 1986 1986 1986 1986 1986 1987 1987 1987 1987 1987 1987 1987 1987
0146:54.5 0006:59.9 1157:42.1 0550:10.3 0529:07.8 1503:38.9 0758:15.8 0246:25.7 1521:54.2 2256:21.2 2311:00.7 1958:12.0 2330:39.9 1842:06.8 0800:07.5 2306:30.7 0230:13.2 1209:27.6 0150:28.9 0531:57.2 1048:03.3 0812:48.5 1510:02.2 0239:13.1 0103:58.8 0719:51.2
Location (degrees) Latitude
Longitude
34.45 33.88 34.12 34.50 33.33 33.83 33.29 33.85 34.74 33.84 33.75 34.06 33.99 34.77 33.29 34.11 34.50 33.59 33.52 33.99 34.86 34.80 33.17 33.74 33.60 33.42
137.39 137.01 137.13 136.42 137.62 137.15 137.47 137.40 136.86 137.16 137.30 137.46 136.80 137.34 136.63 136.70 137.51 137.67 137.54 137.47 136.99 136.95 137.03 137.47 137.34 136.98
Depth (km) 343 382 354 372 399 376 371 369 338 374 370 344 389 314 433 389 321 356 358 339 335 358 399 363 366 410
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P-WAVE VELOCITY STRUCTURE INSIDE SUBDUCTING PACIFIC PLATE
Deep earthquakes located by local stations using the conventional method may have systematic source errors owing to the presence of the high-velocity subducting lithosphere. The sites of deep earthquakes were relocated based on the heterogeneous upper mantle structure, but it was found that the hypocentres which were determined and those determined by Japan Meteorological Agency (JMA) and International Seismological Center (ISC) were similar to each other only in regions near the south coast of Japan (Utsu, 1975). Therefore, the location and origin time of earthquakes in the Kinki region obtained by JMA are adopted in this study.
Station corrections are used to eliminate the local crustal effects on travel-time residuals. Reading errors and non-systematic source errors are reduced by taking the mean of the travel-time residuals. Location errors were mentioned in the preceding section.
3. Method
4. Analysis for one-layered model
3.1. Travel-time residuals and errors
The upper mantle velocity structure model for the calculation is shown in Fig. 2. The velocity structure of the mantle wedge and Philippine Sea plate is assumed as J—B less 3% and 8.2 km s~, respectively (Suyehiro and Sacks, 1979; Hon et al., 1985). The hypocentres for model calculation
In comparing the calculated and the observed residuals, it is important that both sets of residuals are the result of the laterally heterogeneous structure associated with the subduction zone. We compare the spatial distribution of the observed travel-time residuals with the theoretical time residuals calculated by using a two-dimensional (2D) ray-tracing method for P waves. Such a comparison is meaningful only for regions with a high density of seismological stations, such as Japan. The velocity structure for P waves within the subducting Pacific plate is estimated by fitting the pattern of the calculated travel-time residual curves to the observed data. Travel-time residuals for various models are calculated using a 2D ray-tracing scheme SEIS83 (Cerveny and Psencik, 1983). Calculated residuals are the difference between the travel times of the rays in the plane of the lateral velocity variation and J—B travel times, which were obtained using the same program. Observed travel-time residuals, however, generally contain some errors, including: (1) local crustal effects; (2) reading errors; (3) random location errors; (4) origin-time errors; (5) systematic location errors. We must immimze these errors in order to study the lateral heterogeneity.
3.2. Station Correction A station correction, here, is defined as a correction to travel-time residuals for a given station to eliminate the local crustal effects on residuals. The station correction values are estimated from the isovalue lines of station correction obtained by Ashiya et al. (1987).
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km ______________________________________ Fig. 2. A model representing the simplified cross-section of the the subducting plate. The velocity structure of the mantle wedge and Philippine Sea plate is assumed as J—B minus 3% and 8.2 km s1, respectively. The hypocentres are located at three different depths, i.e. 325, 375 and 425 km. The distance between each hypocentre and the upper boundary of the plate is assumed as 15 km. upper mantle incorporating
206
T. IIDAKA AND M. MIZOUE
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Fig. 3. Model fitting of data at the depth range 350—400 km. The calculated travel-time residual curves for the four cases of the Velocity model within the plate are shown. The data are satisfied by those of two models, i.e. J—B plus 1% and J—B plus
Within the range of hypocentre depth, 350—400 km, the gradients of the slope of the observed data fit the calculated slope of the models with J—B plus 1—2% (Fig. 3). The value of J—B plus 1—2% is suited to the three different depth ranges (Fig. 4). We suggest from these analyses that the P-wave velocity structure of the subducting slab is about + 1.5% higher than the J—B model (Fig. 4). The P-wave velocity contrast between the subducting slab and surrounding mantle is 4.5%. This value is near to that obtained by Suyehiro and Sacks (1979).
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are located at three different depths—325, ~ and 425 km. These hypocentres are located at a distance of 15 km from the upper boundary of the plate. ________________________________________
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The seismograms show a remarkable highfrequency later arrival at several stations from the deep earthquakes that occur beneath the Kinki
range with of greater than distances about 300 km5).remarkably varies epicentral (Fig. The wave forms of deep earthquakes can be classified into the following three types. Type 1: dominantly low frequency (OKY stationType in Fig. 5). 2: low-frequency component dominant in
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5.1. Features of the X-phase
region. In this section, we investigate and identify the origin of the high-frequency later arrival. The velocity structure inside the plate is also discussed. The wave form of deep earthquakes at a depth
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5. Analysis of later phase
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Fig. 4. Model fitting of data for all depth ranges. The calculated travel-time residual curve is shown of the model with a velocity structure within the plate of J—B plus 1.5%. Classified by focal depth range.
stations in Fig. 5). Type 3: high-frequency component is dominant (TSK station in Fig. 5). This high-frequency later phase has the following characteristics. (1) The high-frequency later phase is observed
later arrival is higher than that of first arrival. (3) This phase is not observed for earthquakes shallower than about 300 km. (4) This phase suddenly appears when the epicentral distance exceeds a particular distance (Fig. 5).
207
P-WAVE VELOCITY STRUCTURE INSIDE SUBDUCTING PACIFIC PLATE
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low-frequency later First, phase. consider dominant casethe first (a). In arrival this case, and the high-frequency waves wedge thatwethe and travel high-velocity later within arrival slab, are low-velocity considered respectively. mantle as The epicentral distance recorded at a station for wave form type 2 is greater than that recorded for wave form Type 1. In the cases of type 1 and 2, the ray-path lengths of the first arrival in the mantle wedge in each type are compared; the ray-path length of type 2 is longer than that of type 1. So it is to be expected that the travel-time residual of type 2 is larger than that of type 1. However, the observed travel-time residual data of the three types are of the same trend, with travel-time residuals of type 2 being smaller than those of type 1 (Fig. 7). It is shown, however, that part of the ray path of the low-frequency initial arrival in type 2
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Fig. 5. (a) Map of the hypocentres and seismological stations
in the Kanto region. The examples of wave form in these stations are shown in (b). The isodepth lines of the subducting Pacific plate are also shown. (b) An example of the highfrequency later phase. The wave form records of deep earth. quakes occurring beneath the Kinki region are similar to this example. The wave form is dominantly low frequency at seismological stations located in the western Kanto region. At
stations located in the eastern Kanto region, the wave form is dominantly high frequency. In the intermediate region, the first arrival is dominantly low frequency and a dominant highfrequency later phase can be observed.
5.2. Origin of X phase Several possible interpretations for high-frequency later phase are as follows (Fig. 6). (a) Two-path model of one-layered slab. The first arrival travels outside the plate and the highfrequency arrival travels inside the plate. (b) Multiple reflections at superficial layers Just beneath the station. (c) A reflected wave at the lower boundary of the subducting plate.
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Fig. 6. Possible ray paths for the high-frequency later arrivals projected on the vertical section. Only the known velocity boundaries are taken into the consideration. Stars and triangles denote hypocentres and seismological stations, respectively.
208
T. IIDAI(A AND M. MIZOUE
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Fig. 7. Example of travel-time residual data. Symbols of travel-time residual data are divided by wave-form type. L.F. indicates dominantly low frequency type (type 1). L.F.+H.F. indicates that the first arrival is dominantly low frequency and that a high-frequency later arrival can be seen (type 2). HF. indicates dominantly high frequency type (type 3).
propagates inside the plate; the propagated ray path is expected to follow that of minimum travel time. For the ray path of the high-frequency later phase in Type 2, another ray path has to be considered. Case (a) cannot explain the observed data. If case (b) is correct, the high-frequency later arrival should be observed also for the intermediate-depth earthquakes. In our experience, however, the later arrival was observed only for deep earthquakes, deeper than about 300 km. This multiple reflection model cannot explain, therefore, the observed data. In case (c), the calculated X—P time is much larger than that observed. The observed X—P time is <2 s, but the calculated X—P time is > 3 s at the epicentral distances where the later phase can be observed. The apparent velocity of the channel wave at the thin low-velocity layer inside the plate (i.e. case (d)) is lower than that of first arrival (Fukao et al., 1983; Hon et al., 1985). However, the observed apparent velocity of this later arrival is higher than that of the first arrival. Only two cases (i.e. (e) and (f) in Fig. 6) remain as the possible origin of the X phase. According to these analyses, a two-layered slab model is suitable to explain the observed data. This model is
also suggested in other studies (Suyehiro and Sacks, 1979; Ando et al., 1989). 5.3. Two-layer model calculation A two-dimensional ray-tracing scheme is applied to further constrain the origin of the highfrequency later arrival. Several assumptions are adopted with regard to the velocity structure of the upper mantle. The velocity structure for shallower than 70 km is taken to be as prescribed by the J—B velocity structure model. The velocity of Philippine Sea plate is assumed as 8.2 km s’ (Hori et al., 1985). The velocity structure of the asthenosphere is assumed as J—B less 3% (Suyehiro and Sacks, 1979). A thickness of 30 km is adopted for the upper layer inside the plate (Ando et al., 1989) and the velocity of J—B plus 1.5%, obtained from previous section, is adopted for the velocity structure of the upper layer inside the plate (Fig. 8). Behaviour of the branches for direct, refracted and reflected waves is shown in Fig. 9. The A—B, C—D and B—E branches are direct, refracted and reflected waves, respectively. We placed the nine hypocentres for calculation at depths of 325, 425 and 475 km (Fig. 10). At each depth, three different cases are examined. In
209
P-WAVE VELOCITY STRUCTURE INSIDE SUBDUCTING PACIFIC PLATE
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Fig. 8. Velocity structure of a two-layered slab model. The velocities of the mantle wedge and Philippine Sea plate are assumed as J—B minus 3% and 8.2 km s~, respectively (after Suyehiro and Sacks, 1979; Hon et al., 1985). The upper layer of the plate is assumed as J—B plus 1.5%. The thickness of the upper layer is given as 30 km (Ando ci al., 1989).
the three cases, the hypocentres are located at distances of 5, 15 and 25 km from the upper boundary of the plate. First, the branch C—D is investigated. The branch C—D is the residual curve of a refracted wave at the second layer. This, the behaviour of this branch is sensitive to the velocity of second layer inside the plate. The three cases at different distances from the upper boundary of the subducting plate to the hypocentre are examined, Velocity models for a second layer with three different velocities, J—B plus 2.5, 3.5 and 4.5%, are _____________________________________ —2 - -
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Fig. 10. 1-lypocentre locations for model calculation of the
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Fig. 9. Example of travel-time residual curves for a two-layered slab model. The solid line (segment A—B) denotes the direct wave, whilst the broken (segment C—D) and dashed-dotted (segment B—E) lines denote refracted and reflected waves at the intermediate boundary within the slab.
travel-time residual. Three depths (i.e. 325, 375 and 425 km) are used with three different distances (i.e. 5, 15 and 25 km) from the upper boundary of the plate.
used. These values mean velocity contrasts of 1, 2 and 3% between the upper and second layers inside the plate. For any depth range, the calculated residual curve with a velocity of J—B plus 2.5% is suitable for the observed data. From the slope of C—D branch, the P-wave velocity of the second layer is estimated to be + 2.5% (Fig. 11). As a whole, the calculated curves shift to the left of the observed data, while the distance between the upper boundary to hypocentre increases. In the other two cases, where the distances between the hypocentre and upper boundary of the plate are 5 and 25 km, the velocity model of J—B plus 2.5% also shows good fit to the observed data. It is suggested from these analyses that the P-wave velocity of second layer is J—B + 2.5%. The velocity contrast between the first and second layers is 1%. Next, the origin of the high-frequency later phase is investigated. Examples of travel-time residual curves and observed data are shown in Fig. 12. The velocity model inside a slab with a first layer of J—B plus 1.5% and second layer of J—B plus 2.5% is obtained from the preceding process. In this velocity model, the branch C—D (i.e. refracted wave) does not return back to the epicentral distance where the high-frequency waves are observed (Fig. 12). Therefore, it is difficult to explain the high-frequency wave as the refracted wave at the secondary layer. However, the branch B—E (i.e. reflected wave) fits the observation data,
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T. IIDAKA AND M. MIZOUE
and thus the reflected wave is appropriate for interpretation of the origin of the high-frequency later phase. However, two questions remain to be solved. Why is the high-frequency later phase not observed at short epicentral distances? Why are the frequencies of first and later phases different?
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To solve the preceding two questions, we estimate the attenuation effects of a heterogeneous structure on the wave form. The Q structure model is constructed after Sacks and Okada (1974), and Sekiguchi (1988) (Fig. 13).
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calculated residual data are obtained from the velocity model with an upper layer of J—B plus 1.5% and lower layer of J—B plus 2.5%.
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istence respectively. of a low Sekiguchi Q zone in(1988) the western showed partthe of exthe volcanic front to the mantle wedge. The value for this low Q zone is obtained as 150—170 using three-dimensional inversions according to the spectrum ratio method. We used the Q~value of 150 for the lowQ region. The radiation pattern of the source mechanism is assumed as the P-axis dip of 300 from the horizontal plane, after Ito and Annaka (1977). Ito and Annaka (1977) studied the source mechanisms of deep earthquakes located beneath the Japan region. The mechanism for deep earthquakes beneath the Kinki region is down-dip compression. The P-axis dip angles of these earthquakes scatter between 20 and 500, with an average dip angle of about 30 o. The hypocentre is located at a distance of 15 km from the upper boundary of the plate at a depth of 370 km. =
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Fig. 11. Observed residual data and calculated residual data,
Travel-time residual data are classified by the focal depth range. The hypocentres within each depth range are located at a distance of 15 km from the upper boundary of the plate. The circles denote the observation data, the bar means standard deviation. The calculated travel-time residual curves for the
velocity model of the slab are shown.
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The behaviour of the wave forms, based on this structure model, is examined at those stations
211
P-WAVE VELOCITY STRUCTURE INSIDE SUBDUCTING PACIFIC PLATE 2
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The wave form with a frequency of 1 Hz does not attenuate remarkably in two cases (i.e. direct and reflected waves) at locations where the highfrequency later phase can be observed. However, the wave form with a frequency of 10 Hz attenuates remarkably in direct wave (Fig. 13) in this position, because the direct wave travels within the low Q zone. The reflected wave, however, does not pass through the low Q region and therefore does not attenuate remarkably. At the western side of this position, the wave form with a frequency of 10 Hz attenuates rapidly. The existence of a low Q zone in the western area means that the high-frequency wave is not observed at this location, but the high-frequency later phase can be observed. The results of this simulation also show the difference of frequencies between the direct wave and reflected wave.
6. Discussion [i~’~1
In the western Pacific region, an intermediate
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DISTANCE IN Km Fig. 13. The Q structure model for the synthetic wave form calculation. The Q values are assumed after Sekiguchi (1988) and Sacks and Okada (1974). The frequency of 10Hz is cxamined, which is the same as the dominant frequency of the high-frequency later phase at stations where this phase can be
observed. The source mechanism is assumed to have a P-axis dip angle of 300 from the horizontal plane. Triangles denote the stations where the high-frequency later arrival can be observed. The arrows show the position of these stations.
where the high-frequency later phase is observed. From observation data, the dominant frequency of the first arrival is 1 Hz. The dominant frequency of the later arrival is 8—10 Hz. The difference between these predominant periods is remarkable, The two frequencies of 1 Hz and 10 Hz are used in this examination.
boundary within the plate has been suggested already from oceanic seismological experiments (e.g. Shimamura and Asada, 1976; Shimamura et al., 1983). Suyehiro and Sacks (1979) also suggested a two-layered slab model beneath the Japan region. Ando et al. (1989) indicated the existence of a boundary within the plate from observation of S waves converted to P waves. There is much evidence for the existence of an intermediate boundary within the plate. In addition, a double seismic plane has been observed beneath the Tohoku region. The hypocentres of the Wadati Benioff zone beneath the Tohoku region are located within these two narrow belts. The upper plane of the double seismic zone is located just beneath the upper boundary of the subducting Pacific plate (Hasegawa et al., 1978; Matsuzawa et al., 1986). The cause of the double seismic zone has been discussed by many researchers, but no consensus has been reached as yet. The existence of an intermediate boundary may contribute to an understanding of the cause of a double seismic zone. However, the depth of the intermediate boundary
212
obtained by this study is deeper than 250 km, whereas beneath the Tohoku region, the double seismic zone continues to a depth of about 150 km, but is not clear deeper than 150 km. It is therefore difficult to relate these two phenomena, and this problem has been left unexplained in this study. The velocity contrast between the upper and lower layers has been reported as being about 5% in the western Pacific Ocean (Shimamura et al., 1983), but the contrast obtained in this study is only 1%. To discuss this discrepancy of the contrast, it is necessary to consider the thermal structure within the plate, and a more detailed analysis is necessary to solve the problem. The thickness of the first layer within the plate is assumed as being 30 km, after Ando et al. (1989). This value is obtained from the analysis of S waves converted to P waves. The use of the converted phases on the seismograms proved to be a practical and highly promising method for the detection of the boundary. For the present situation, this value appears the most accurate cornpared with those obtained from analysis of refracted waves,
7. Conclusions The seismograms for deep earthquakes located beneath the Kinki region show a remarkable high-frequency later phase at geographically restricted stations. The origin of the high-frequency later phase is identified as a reflected wave at the intermediate boundary within the subducting plate. Previous studies, for example, Suyehiro and Sacks (1979), suggested a two-layered slab model beneath the Japan region and this study verifies this model. The spatial distribution of the travel-time residuals is compared with that of the calculated travel-time residuals. The velocity structure of the lower layer is also estimated in this study. The velocities of P waves at the upper and lower layers within the plate are J—B plus 1.5% and J—B plus 2.5%, respectively. The velocity contrast between the upper layer and lower layer is about 1%.
T. LIDAKA AND M. MIZOUE
Acknowledgements We thank Dr. Takashi Miyatake for providing his computer programs and for helpful discussions. Discussions with Drs. T. Urabe, S. Kaneshima, M. Takeo, T. Tsukuda were valuable and helpful. We thank colleagues for helpful cornments and suggestions.
References Ando, M., Kaneshima, S., Ohtaki, T. and Okura, T., 1989. S to P converted phase from the lower plane of the doubleplaned deep-seismic
zone. Eos. (Trans. Am. Geophys.
Union), October 24, Vol. 70, pp. 1228. Ashiya, K., Asano, S., Yoshii, T., Ishida, M. and Nishiki, T., 1987. Simultaneous determination of three-dimensional crustal structure and
hypocenters beneath Kanto-Tokai
Distnct, Japan. Tectonophysics, 140: 13—27. Cerveny, V. and Psencik, I., 1983. SEIS83, a three-dimensional seismic ray package, Charles University, Prague. Fukao, Y., Hori, S. and Ukawa, M., 1983. A seismological constraint on the depth of basalt—eclogite transition in a subducting oceanic crust. Nature, 303: 413—415. Hasegawa, A., Umino, N. and Takagi, A., 1978. Double-planed deep seismic zone and upper mantle structure in the northeastern Japan arc. Geophys. JR. Astron. Soc., 54: 281—296. Hirahara, K., 1977. A large-scale three dimensional seismic structure under the Japan islands and the Sea of Japan. J. Phys. Earth, 25: 393—418. Hori, S., Inoue, H., Fukao, Y. and Ukawa, M., 1985. Seismic detection of the untransformed basaltic oceanic crust subducting into the mantle. Geophys. J. R. Astron. Soc., 83: 169197. Ito, K. and Annaka, T., 1977. Spatial clustering and focal mechanisms of deep earthquakes in central Japan. Zisin, 30: 201—212 (in Japanese). Matsuzawa, T., Umino, N., Hasegawa, A. and Takagi, A., 1986. Upper mantle velocity structure estimated from PSconverted wave beneath the north-eastern Japan Arc. Geophys. J. R. Astron. Soc., 86: 767—787. Okada, H., 1977. Fine structure of the upper mantle beneath Japanese island arcs as revealed from body wave analyses. Ph.D. Thesis, Hokkaido University, 129 pp. Sacks, IS. and Okada, H., 1974. A comparison of the anelasticity structure beneath western South America and Japan. Phys. Earth Planet Inter., 9: 211—219. Sekiguchi, S., 1988. The upper mantle Q structure beneath the Kanto-Tokai region with 3D block inversion methods. Abstracts of the Fall Meeting of the Seismological Society of Japan (in Japanese), Sept. 16: 74. Shimamura, H. and Asada, T., 1976. Apparent velocity measurements on an oceanic lithosphere. Phys. Earth Planet Inter., 13: 15—22.
P-WAVE VELOCITY STRUCTURE INSIDE SUBDUCTING PACIFIC PLATE
Shimamura, H., Asada, T., Suyehiro, K., Yamada, T. and Inatani, H., 1983. Long shot experiments to study velocity anisotropy in the oceanic lithosphere of the northwestern Pacific. Phys. Earth Planet Inter., 31: 348—362. Suyehiro, K. and Sacks, IS., 1979. P- and S-wave velocity anomalies associated with the subducting lithosphere determined from travel-time residuals in the Japan region. Bull. Seismol. Soc. Am., 69: 97—114.
213 Utsu, T., 1967. Anomalies in seismic wave velocity and attenuation associated with a deep earthquake zone, 1. J. Fac. Sci., Hokkaido Univ., Ser. 7: 1—25. Utsu, T., 1975. Regional variation of travel-time residuals of P waves from nearby deep earthquakes in Japan and vicinity. J. Phys. Earth, 23: 367—380.
203
P-wave velocity structure inside the subducting Pacific plate beneath the Japan region Takashi Jidaka and Megumi Mizoue Earthquake Research Institute, The University of Tokyo. Yayoi 1-1-1, Bunkyo, Tokyo, Japan (Received 26 February 1990; revised and accepted 5 November 1990)
ABSTRACT lidaka, T. and Mizoue, M., 1991. P-wave velocity structure inside the subducting Pacific plate beneath the Japan region. Phys. Earth Planet. Inter., 66: 203—213. Little is known of the internal structure of the subducting Pacific plate. Previous studies suggest the existence of an intermediate boundary within the subducting slab. The low density of seismological stations in oceanic regions has prevented high-resolution studies. Recently, seismological stations in Japan have accumulated digitally recorded seismograms. Beneath the Kanto region, central Japan, the Pacific plate is subducting with a high inclination compared with that of the Tohoku region, northern Japan. The ray paths from deep earthquakes to seismological stations are expected to penetrate more inner parts of the subducting plate. This region is suitable to resolve the velocity structure within the plate. In this study, travel-time residuals and seismograms of the deep-focus earthquakes that occurred beneath the Kinki region, southern Japan, are used to constrain various parameters related to the velocity structure model within the slab. The seismograms of deep-focus earthquakes at the geographically restricted stations located in the Kanto region, central Japan, show a remarkable high-frequency later arrival of the P wave. The later arrival was studied and recognized as the reflected wave at the intermediate boundary inside the plate. The velocity structure within the plate is also studied. Our best-fit model has a velocity of Jeffreys—Bullen (J—B) model plus 1.5% in the upper layer and J—B plus 2.5% in the lower layer.
1. Introduction It is well known that a high-velocity plate subducts in the Japan region. Thus the upper mantle structure in and around the Japan region has a large-scale lateral heterogeneity. Evidence for such a structure includes the existence and the regular spatial pattern of intermediate- and deep-focus earthquakes, anomalous seismic intensity distributions, travel-time anomalies, and high-frequency spectral contents of seismograms. The velocity contrast between subducting lithosphere and the overlying asthenosphere beneath the Japan region has been calculated at between 2 and 15% (e.g. Utsu, 1967, 1975; Hirahara, 1977; Okada, 1977; Suyehiro and Sacks, 1979; Matsuzawa et al., 1986). In the oceanic region, several long-range explosion seismology experiments have been developed. 0031-9201/91/$03.50
© 1991
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Elsevier Science Publishers B.V.
As a result of these studies, a two-layered lithosphere model was proposed (e.g. Shimamura and Asada, 1976; Shimamura et al., 1983). Also, the travel-time residuals of P and S waves from local deep earthquakes were used to apply geophysical constraints to the laterally heterogeneous structure associated with the Japan subduction zone (Suyehiro and Sacks, 1979). The spatial distribution of observed and calculated residual data mdicates that the subducting lithosphere can be modelled by a two-layered structure. The two-layered slab model was also supported by Ando et al. (1989). We have studied the lateral velocity variations of compressional (P) waves inside the subducting Pacific slab beneath the Japan region. This study uses travel-time residuals (observed travel time minus Jeffreys—Bullen (J—B) travel time) from local deep earthquakes to apply constraints on van-
204
T. IIDAKA AND M. MIZOUE
ous parameters related to the heterogeneous subducting Pacific plate. The seismograms of deep-focus earthquakes are also investigated. The seismograms of the deep earthquake that occurred beneath the Kinki region show a remarkable high-frequency later arrival at several seismological stations. In this paper we
A 37 0 E
studyarrival. and identify the cause of the high-frequency later 2. Data
A
32. 0 N
______________________________________________________
It is important that the data be examined carefully to infer structural anomalies quantitatively. The data were collected according to the following criteria. Data for 26 deep-focus earthquakes that occurred in area 33.0—35.0 °N and 136.0—138.0 °E were collected for the period January 1985 to December 1987 (Fig. 1 and Table 1).
134. 0 E
142. 0 E
Fig. 1. Location of earthquakes (star) and seismological stations (triangle). The parameters of the hypocentres determined by JMA were adopted.
Seismograms from stations of the Earthquake Research Institute were used (Fig. 1). The seismometers used were of the 1 Hz velocity type.
TABLE 1 List of earthquakes Date
13 April 1 May 11 May 26 May 4 June 12 August 25 September 16 November 30 November 9 December 28 December 9 January 28 April 29 May 10 June 9 September 27 September 4 December 12 February 21 February 2 April 27 May 9 June 28 August 14 October 21 October
Time
1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1985 1986 1986 1986 1986 1986 1986 1986 1987 1987 1987 1987 1987 1987 1987 1987
0146:54.5 0006:59.9 1157:42.1 0550:10.3 0529:07.8 1503:38.9 0758:15.8 0246:25.7 1521:54.2 2256:21.2 2311:00.7 1958:12.0 2330:39.9 1842:06.8 0800:07.5 2306:30.7 0230:13.2 1209:27.6 0150:28.9 0531:57.2 1048:03.3 0812:48.5 1510:02.2 0239:13.1 0103:58.8 0719:51.2
Location (degrees) Latitude
Longitude
34.45 33.88 34.12 34.50 33.33 33.83 33.29 33.85 34.74 33.84 33.75 34.06 33.99 34.77 33.29 34.11 34.50 33.59 33.52 33.99 34.86 34.80 33.17 33.74 33.60 33.42
137.39 137.01 137.13 136.42 137.62 137.15 137.47 137.40 136.86 137.16 137.30 137.46 136.80 137.34 136.63 136.70 137.51 137.67 137.54 137.47 136.99 136.95 137.03 137.47 137.34 136.98
Depth (km) 343 382 354 372 399 376 371 369 338 374 370 344 389 314 433 389 321 356 358 339 335 358 399 363 366 410
205
P-WAVE VELOCITY STRUCTURE INSIDE SUBDUCTING PACIFIC PLATE
Deep earthquakes located by local stations using the conventional method may have systematic source errors owing to the presence of the high-velocity subducting lithosphere. The sites of deep earthquakes were relocated based on the heterogeneous upper mantle structure, but it was found that the hypocentres which were determined and those determined by Japan Meteorological Agency (JMA) and International Seismological Center (ISC) were similar to each other only in regions near the south coast of Japan (Utsu, 1975). Therefore, the location and origin time of earthquakes in the Kinki region obtained by JMA are adopted in this study.
Station corrections are used to eliminate the local crustal effects on travel-time residuals. Reading errors and non-systematic source errors are reduced by taking the mean of the travel-time residuals. Location errors were mentioned in the preceding section.
3. Method
4. Analysis for one-layered model
3.1. Travel-time residuals and errors
The upper mantle velocity structure model for the calculation is shown in Fig. 2. The velocity structure of the mantle wedge and Philippine Sea plate is assumed as J—B less 3% and 8.2 km s~, respectively (Suyehiro and Sacks, 1979; Hon et al., 1985). The hypocentres for model calculation
In comparing the calculated and the observed residuals, it is important that both sets of residuals are the result of the laterally heterogeneous structure associated with the subduction zone. We compare the spatial distribution of the observed travel-time residuals with the theoretical time residuals calculated by using a two-dimensional (2D) ray-tracing method for P waves. Such a comparison is meaningful only for regions with a high density of seismological stations, such as Japan. The velocity structure for P waves within the subducting Pacific plate is estimated by fitting the pattern of the calculated travel-time residual curves to the observed data. Travel-time residuals for various models are calculated using a 2D ray-tracing scheme SEIS83 (Cerveny and Psencik, 1983). Calculated residuals are the difference between the travel times of the rays in the plane of the lateral velocity variation and J—B travel times, which were obtained using the same program. Observed travel-time residuals, however, generally contain some errors, including: (1) local crustal effects; (2) reading errors; (3) random location errors; (4) origin-time errors; (5) systematic location errors. We must immimze these errors in order to study the lateral heterogeneity.
3.2. Station Correction A station correction, here, is defined as a correction to travel-time residuals for a given station to eliminate the local crustal effects on residuals. The station correction values are estimated from the isovalue lines of station correction obtained by Ashiya et al. (1987).
L~E~
8.2 km/s 70
—
—
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—~i~
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600
- -
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k
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km ______________________________________ Fig. 2. A model representing the simplified cross-section of the the subducting plate. The velocity structure of the mantle wedge and Philippine Sea plate is assumed as J—B minus 3% and 8.2 km s1, respectively. The hypocentres are located at three different depths, i.e. 325, 375 and 425 km. The distance between each hypocentre and the upper boundary of the plate is assumed as 15 km. upper mantle incorporating
206
T. IIDAKA AND M. MIZOUE
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- -
— - —
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- -
-
- —
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Fig. 3. Model fitting of data at the depth range 350—400 km. The calculated travel-time residual curves for the four cases of the Velocity model within the plate are shown. The data are satisfied by those of two models, i.e. J—B plus 1% and J—B plus
Within the range of hypocentre depth, 350—400 km, the gradients of the slope of the observed data fit the calculated slope of the models with J—B plus 1—2% (Fig. 3). The value of J—B plus 1—2% is suited to the three different depth ranges (Fig. 4). We suggest from these analyses that the P-wave velocity structure of the subducting slab is about + 1.5% higher than the J—B model (Fig. 4). The P-wave velocity contrast between the subducting slab and surrounding mantle is 4.5%. This value is near to that obtained by Suyehiro and Sacks (1979).
2%.
are located at three different depths—325, ~ and 425 km. These hypocentres are located at a distance of 15 km from the upper boundary of the plate. ________________________________________
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The seismograms show a remarkable highfrequency later arrival at several stations from the deep earthquakes that occur beneath the Kinki
range with of greater than distances about 300 km5).remarkably varies epicentral (Fig. The wave forms of deep earthquakes can be classified into the following three types. Type 1: dominantly low frequency (OKY stationType in Fig. 5). 2: low-frequency component dominant in
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5.1. Features of the X-phase
region. In this section, we investigate and identify the origin of the high-frequency later arrival. The velocity structure inside the plate is also discussed. The wave form of deep earthquakes at a depth
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5. Analysis of later phase
________
in both (2) The vertical apparent and velocity horizontal of components. the high-frequency
_
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stations in Fig. 5). Type 3: high-frequency component is dominant (TSK station in Fig. 5). This high-frequency later phase has the following characteristics. (1) The high-frequency later phase is observed
later arrival is higher than that of first arrival. (3) This phase is not observed for earthquakes shallower than about 300 km. (4) This phase suddenly appears when the epicentral distance exceeds a particular distance (Fig. 5).
207
P-WAVE VELOCITY STRUCTURE INSIDE SUBDUCTING PACIFIC PLATE
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wave at the intermediate subducting plate. wave at the intermediate subducting plate.
low-frequency later First, phase. consider dominant casethe first (a). In arrival this case, and the high-frequency waves wedge thatwethe and travel high-velocity later within arrival slab, are low-velocity considered respectively. mantle as The epicentral distance recorded at a station for wave form type 2 is greater than that recorded for wave form Type 1. In the cases of type 1 and 2, the ray-path lengths of the first arrival in the mantle wedge in each type are compared; the ray-path length of type 2 is longer than that of type 1. So it is to be expected that the travel-time residual of type 2 is larger than that of type 1. However, the observed travel-time residual data of the three types are of the same trend, with travel-time residuals of type 2 being smaller than those of type 1 (Fig. 7). It is shown, however, that part of the ray path of the low-frequency initial arrival in type 2
__________
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(d) The channel model for a high-frequency
38N
I
Fig. 5. (a) Map of the hypocentres and seismological stations
in the Kanto region. The examples of wave form in these stations are shown in (b). The isodepth lines of the subducting Pacific plate are also shown. (b) An example of the highfrequency later phase. The wave form records of deep earth. quakes occurring beneath the Kinki region are similar to this example. The wave form is dominantly low frequency at seismological stations located in the western Kanto region. At
stations located in the eastern Kanto region, the wave form is dominantly high frequency. In the intermediate region, the first arrival is dominantly low frequency and a dominant highfrequency later phase can be observed.
5.2. Origin of X phase Several possible interpretations for high-frequency later phase are as follows (Fig. 6). (a) Two-path model of one-layered slab. The first arrival travels outside the plate and the highfrequency arrival travels inside the plate. (b) Multiple reflections at superficial layers Just beneath the station. (c) A reflected wave at the lower boundary of the subducting plate.
e
Fig. 6. Possible ray paths for the high-frequency later arrivals projected on the vertical section. Only the known velocity boundaries are taken into the consideration. Stars and triangles denote hypocentres and seismological stations, respectively.
208
T. IIDAI(A AND M. MIZOUE
sec
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propagates inside the plate; the propagated ray path is expected to follow that of minimum travel time. For the ray path of the high-frequency later phase in Type 2, another ray path has to be considered. Case (a) cannot explain the observed data. If case (b) is correct, the high-frequency later arrival should be observed also for the intermediate-depth earthquakes. In our experience, however, the later arrival was observed only for deep earthquakes, deeper than about 300 km. This multiple reflection model cannot explain, therefore, the observed data. In case (c), the calculated X—P time is much larger than that observed. The observed X—P time is <2 s, but the calculated X—P time is > 3 s at the epicentral distances where the later phase can be observed. The apparent velocity of the channel wave at the thin low-velocity layer inside the plate (i.e. case (d)) is lower than that of first arrival (Fukao et al., 1983; Hon et al., 1985). However, the observed apparent velocity of this later arrival is higher than that of the first arrival. Only two cases (i.e. (e) and (f) in Fig. 6) remain as the possible origin of the X phase. According to these analyses, a two-layered slab model is suitable to explain the observed data. This model is
also suggested in other studies (Suyehiro and Sacks, 1979; Ando et al., 1989). 5.3. Two-layer model calculation A two-dimensional ray-tracing scheme is applied to further constrain the origin of the highfrequency later arrival. Several assumptions are adopted with regard to the velocity structure of the upper mantle. The velocity structure for shallower than 70 km is taken to be as prescribed by the J—B velocity structure model. The velocity of Philippine Sea plate is assumed as 8.2 km s’ (Hori et al., 1985). The velocity structure of the asthenosphere is assumed as J—B less 3% (Suyehiro and Sacks, 1979). A thickness of 30 km is adopted for the upper layer inside the plate (Ando et al., 1989) and the velocity of J—B plus 1.5%, obtained from previous section, is adopted for the velocity structure of the upper layer inside the plate (Fig. 8). Behaviour of the branches for direct, refracted and reflected waves is shown in Fig. 9. The A—B, C—D and B—E branches are direct, refracted and reflected waves, respectively. We placed the nine hypocentres for calculation at depths of 325, 425 and 475 km (Fig. 10). At each depth, three different cases are examined. In
209
P-WAVE VELOCITY STRUCTURE INSIDE SUBDUCTING PACIFIC PLATE
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—
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___
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Fig. 8. Velocity structure of a two-layered slab model. The velocities of the mantle wedge and Philippine Sea plate are assumed as J—B minus 3% and 8.2 km s~, respectively (after Suyehiro and Sacks, 1979; Hon et al., 1985). The upper layer of the plate is assumed as J—B plus 1.5%. The thickness of the upper layer is given as 30 km (Ando ci al., 1989).
the three cases, the hypocentres are located at distances of 5, 15 and 25 km from the upper boundary of the plate. First, the branch C—D is investigated. The branch C—D is the residual curve of a refracted wave at the second layer. This, the behaviour of this branch is sensitive to the velocity of second layer inside the plate. The three cases at different distances from the upper boundary of the subducting plate to the hypocentre are examined, Velocity models for a second layer with three different velocities, J—B plus 2.5, 3.5 and 4.5%, are _____________________________________ —2 - -
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Fig. 9. Example of travel-time residual curves for a two-layered slab model. The solid line (segment A—B) denotes the direct wave, whilst the broken (segment C—D) and dashed-dotted (segment B—E) lines denote refracted and reflected waves at the intermediate boundary within the slab.
travel-time residual. Three depths (i.e. 325, 375 and 425 km) are used with three different distances (i.e. 5, 15 and 25 km) from the upper boundary of the plate.
used. These values mean velocity contrasts of 1, 2 and 3% between the upper and second layers inside the plate. For any depth range, the calculated residual curve with a velocity of J—B plus 2.5% is suitable for the observed data. From the slope of C—D branch, the P-wave velocity of the second layer is estimated to be + 2.5% (Fig. 11). As a whole, the calculated curves shift to the left of the observed data, while the distance between the upper boundary to hypocentre increases. In the other two cases, where the distances between the hypocentre and upper boundary of the plate are 5 and 25 km, the velocity model of J—B plus 2.5% also shows good fit to the observed data. It is suggested from these analyses that the P-wave velocity of second layer is J—B + 2.5%. The velocity contrast between the first and second layers is 1%. Next, the origin of the high-frequency later phase is investigated. Examples of travel-time residual curves and observed data are shown in Fig. 12. The velocity model inside a slab with a first layer of J—B plus 1.5% and second layer of J—B plus 2.5% is obtained from the preceding process. In this velocity model, the branch C—D (i.e. refracted wave) does not return back to the epicentral distance where the high-frequency waves are observed (Fig. 12). Therefore, it is difficult to explain the high-frequency wave as the refracted wave at the secondary layer. However, the branch B—E (i.e. reflected wave) fits the observation data,
210
T. IIDAKA AND M. MIZOUE
and thus the reflected wave is appropriate for interpretation of the origin of the high-frequency later phase. However, two questions remain to be solved. Why is the high-frequency later phase not observed at short epicentral distances? Why are the frequencies of first and later phases different?
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To solve the preceding two questions, we estimate the attenuation effects of a heterogeneous structure on the wave form. The Q structure model is constructed after Sacks and Okada (1974), and Sekiguchi (1988) (Fig. 13).
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calculated residual data are obtained from the velocity model with an upper layer of J—B plus 1.5% and lower layer of J—B plus 2.5%.
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istence respectively. of a low Sekiguchi Q zone in(1988) the western showed partthe of exthe volcanic front to the mantle wedge. The value for this low Q zone is obtained as 150—170 using three-dimensional inversions according to the spectrum ratio method. We used the Q~value of 150 for the lowQ region. The radiation pattern of the source mechanism is assumed as the P-axis dip of 300 from the horizontal plane, after Ito and Annaka (1977). Ito and Annaka (1977) studied the source mechanisms of deep earthquakes located beneath the Japan region. The mechanism for deep earthquakes beneath the Kinki region is down-dip compression. The P-axis dip angles of these earthquakes scatter between 20 and 500, with an average dip angle of about 30 o. The hypocentre is located at a distance of 15 km from the upper boundary of the plate at a depth of 370 km. =
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Travel-time residual data are classified by the focal depth range. The hypocentres within each depth range are located at a distance of 15 km from the upper boundary of the plate. The circles denote the observation data, the bar means standard deviation. The calculated travel-time residual curves for the
velocity model of the slab are shown.
Q
The behaviour of the wave forms, based on this structure model, is examined at those stations
211
P-WAVE VELOCITY STRUCTURE INSIDE SUBDUCTING PACIFIC PLATE 2
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The wave form with a frequency of 1 Hz does not attenuate remarkably in two cases (i.e. direct and reflected waves) at locations where the highfrequency later phase can be observed. However, the wave form with a frequency of 10 Hz attenuates remarkably in direct wave (Fig. 13) in this position, because the direct wave travels within the low Q zone. The reflected wave, however, does not pass through the low Q region and therefore does not attenuate remarkably. At the western side of this position, the wave form with a frequency of 10 Hz attenuates rapidly. The existence of a low Q zone in the western area means that the high-frequency wave is not observed at this location, but the high-frequency later phase can be observed. The results of this simulation also show the difference of frequencies between the direct wave and reflected wave.
6. Discussion [i~’~1
In the western Pacific region, an intermediate
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DISTANCE IN Km Fig. 13. The Q structure model for the synthetic wave form calculation. The Q values are assumed after Sekiguchi (1988) and Sacks and Okada (1974). The frequency of 10Hz is cxamined, which is the same as the dominant frequency of the high-frequency later phase at stations where this phase can be
observed. The source mechanism is assumed to have a P-axis dip angle of 300 from the horizontal plane. Triangles denote the stations where the high-frequency later arrival can be observed. The arrows show the position of these stations.
where the high-frequency later phase is observed. From observation data, the dominant frequency of the first arrival is 1 Hz. The dominant frequency of the later arrival is 8—10 Hz. The difference between these predominant periods is remarkable, The two frequencies of 1 Hz and 10 Hz are used in this examination.
boundary within the plate has been suggested already from oceanic seismological experiments (e.g. Shimamura and Asada, 1976; Shimamura et al., 1983). Suyehiro and Sacks (1979) also suggested a two-layered slab model beneath the Japan region. Ando et al. (1989) indicated the existence of a boundary within the plate from observation of S waves converted to P waves. There is much evidence for the existence of an intermediate boundary within the plate. In addition, a double seismic plane has been observed beneath the Tohoku region. The hypocentres of the Wadati Benioff zone beneath the Tohoku region are located within these two narrow belts. The upper plane of the double seismic zone is located just beneath the upper boundary of the subducting Pacific plate (Hasegawa et al., 1978; Matsuzawa et al., 1986). The cause of the double seismic zone has been discussed by many researchers, but no consensus has been reached as yet. The existence of an intermediate boundary may contribute to an understanding of the cause of a double seismic zone. However, the depth of the intermediate boundary
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obtained by this study is deeper than 250 km, whereas beneath the Tohoku region, the double seismic zone continues to a depth of about 150 km, but is not clear deeper than 150 km. It is therefore difficult to relate these two phenomena, and this problem has been left unexplained in this study. The velocity contrast between the upper and lower layers has been reported as being about 5% in the western Pacific Ocean (Shimamura et al., 1983), but the contrast obtained in this study is only 1%. To discuss this discrepancy of the contrast, it is necessary to consider the thermal structure within the plate, and a more detailed analysis is necessary to solve the problem. The thickness of the first layer within the plate is assumed as being 30 km, after Ando et al. (1989). This value is obtained from the analysis of S waves converted to P waves. The use of the converted phases on the seismograms proved to be a practical and highly promising method for the detection of the boundary. For the present situation, this value appears the most accurate cornpared with those obtained from analysis of refracted waves,
7. Conclusions The seismograms for deep earthquakes located beneath the Kinki region show a remarkable high-frequency later phase at geographically restricted stations. The origin of the high-frequency later phase is identified as a reflected wave at the intermediate boundary within the subducting plate. Previous studies, for example, Suyehiro and Sacks (1979), suggested a two-layered slab model beneath the Japan region and this study verifies this model. The spatial distribution of the travel-time residuals is compared with that of the calculated travel-time residuals. The velocity structure of the lower layer is also estimated in this study. The velocities of P waves at the upper and lower layers within the plate are J—B plus 1.5% and J—B plus 2.5%, respectively. The velocity contrast between the upper layer and lower layer is about 1%.
T. LIDAKA AND M. MIZOUE
Acknowledgements We thank Dr. Takashi Miyatake for providing his computer programs and for helpful discussions. Discussions with Drs. T. Urabe, S. Kaneshima, M. Takeo, T. Tsukuda were valuable and helpful. We thank colleagues for helpful cornments and suggestions.
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