ANOMALOUS RAYLEIGH-WAVE PROPAGATION ALONG OCEANIC TRENCH KIYOSHI YOMOGIDA

Division of Earth and Planetary Sciences, Graduate School of Science, Hokkaido University, Japan1 RIKO OKUYAMA

Department of Earth and Planetary Systems Science, Faculty of Science, University of Hiroshima, Japan2 ICHIRO NAKANISHI

Department of Geophysics, Kyoto University, Japan3 ABSTRACT

A clear later phase of amplitude larger than the direct surface wave packet was observed at stations in Hokkaido, Japan, for several events of the December 1991 offUrup earthquake swarm in the Kuril Islands region. From its particle motion, this phase is likely to be a fundamental Rayleigh wave packet that arrived with an azimuth largely deviated from each great-circle direction. As its origin, Nakanishi (1992) proposed that the sea-trench topography in this area as deep as 10 km may produce a narrow zone of low velocity for Rayleigh waves of periods around 15 sec. Following this idea, we compute ray paths and estimate how Rayleigh waves would propagate if we assume that lateral velocity variations are caused only by seafloor topography. We confirm that thick sea water in the trench indeed produces the phase velocity of Rayleigh waves to be smaller than in a surrounding area by the degree over 100%. Such a low-velocity zone appears only in a period range from 12 to 20 sec. Although this strong low-velocity zone disturbs the direction of Rayleigh wave propagation from its great circle, the overall ray paths are not so affected as far as an epicentre is outside this low-velocity zone, that is, off the trench axis. In contrast, the majority of rays are severely distorted for an event within the low-velocity zone or, in other words, in the neighborhood of the trench axis. For such an event, a part of wave energy appears to be trapped in this zone and eventually propagates outwards due to the curvature or bend of trench geometry, resulting in very late arriving waves of large amplitude with an incident direction clearly different from great circles. This phenomenon is observed only at a very limited period range around 16 sec. These theoretical results are consistent with the above mentioned observation of Nakanishi (1992). 1 2 3

Sapporo 060-0810, Japan ([email protected]) Higashi-Hiroshima 739-8526, Japan (Present name: Riko Meiji, Present address: 2-43-12, Ooizumi-machi, Nerima-ku, Tokyo 178-0062, Japan) Kyoto 606-8502, Japan

Stud. Geophys. Geod., 46 (2002), 691−710 © 2002 StudiaGeo s.r.o., Prague

691

K. Yomogida et al.

K e y w o r d s : Rayleigh wave, later phase, oceanic trench, ray tracing. 1. INTRODUCTION

For last two decades, the precise phase or group velocity measurement of surface waves has enabled us to retrieve fairly detailed lateral heterogeneous features of the earth from global to regional scales, under the name of ‘seismic tomography’ (e.g., Woodhouse and Dziewonski, 1984; van Heijst and Woodhouse, 1999; Debayle and Kennett, 2000). These deterministic studies on surface wave propagation are, however, still limited in a period range of longer than 20 sec, mainly because both Rayleigh and Love waves propagate in a highly complex manner at a shorter period. Under the WKBJ approximation (e.g., Dahlen and Tromp, 1998), we can estimate relatively well how each propagation direction or ray path of surface waves is disturbed by existing lateral heterogeneities of the earth (e.g., Yomogida and Aki, 1985; Woodhouse and Wong, 1986). For example, Yomogida and Aki (1985) showed that Rayleigh waves at periods between 20 and 100 sec propagate clearly deviated from each great-circle path by the degree of the proposed lateral heterogeneities on oceanic floors as a function of their ages. Since there should be a much stronger degree of lateral heterogeneities in continents or other tectonically active areas, we expect more complicated or anomalous propagation of surface waves there. In the same manner, the phase or group velocity of Rayleigh waves of periods shorter than 20 sec is strongly affected by structures above the lithosphere, including sea water in an oceanic area. Surface waves of the short-period range propagate in such a complicated way that no quantitative studies have been conducted intensively yet. The recent progress of the dense deployment of seismic stations, particularly with broadband seismometers, are enabling us to study short-period surface waves, particularly because they are expected to be useful in the determination of source processes (e.g., Nakanishi et al., 1991). New observations at those stations encourage us to work on the complex propagation of short-period surface waves. In December 1991, a swarm with over four-hundred located events took place off Urup Island of the Kuril Islands. Fig. 1 shows the locations of large events. For some events, a clear later phase was observed after the primary wave packet of surface waves. Fig. 2 shows such an example: an event on December 19, 1991, as represented by ‘1’ in Fig. 1. Seismograms at a station named KKJ show a large later phase (or better to say, wave packet) about three minutes after the arrival of the primary surface wave packet. Records at other stations do not have such a phase. Nakanishi (1992) analyzed this later phase carefully and summarized its main characteristics as follows: 1. The phase is a fundamental Rayleigh wave mainly at periods of 15 − 20 sec, with the delay of about three minutes. 2. The phase deviates from its great-circle path, estimated from its particle motion. 3. The phase is observed only for events located inside the trench axis of the Kuril trench with sea depth of deeper than 4 km, and with the focal depth of shallower than 20 km (Fig. 1).

692

Stud. Geophys. Geod., 46 (2002)

Anomalous Rayleigh-wave Propagation along Oceanic Trench

4. Since the phase is not observed at all the stations for each event, it should not be originated from its complicated source process. From these observational facts, Nakanishi (1992) proposed that this phase may be originated from a Rayleigh wave propagating along ‘a low velocity zone formed by the ocean bathymetry around a trench axis’ as a lateral heterogeneity. In other words, ‘the seatrench topography acts as a strong low-velocity zone for short-period Rayleigh waves.’ Due to a subducting oceanic plate covered with thick sediment, the subsurface structure in a subduction zone is generally very complicated. Previous seismic studies clearly detected such subduction-related lateral heterogeneities, although the type of wave propagations was different from the present one. For example, Hori et al. (1985) estimated an oceanic crust subducting deep into the mantle around Japan, using body waves. Okamoto (1993) investigated how teleseismic P waveforms are affected by sediment and bathymetry in a subduction zone. Ihmle and Madariaga (1996) found monochromatic body waves for the 1995 Chile and 1994 Kuril earthquakes, interpreting them as vertically traveling P waves in sea water. These studies mainly discussed twodimensional lateral heterogeneities perpendicular to a trench axis (i.e., a profile of vertical and subducting directions). On the other hand, Shapiro et al. (1998) studied Rayleigh waves propagating in the accretionary prism of a trench, similar to the present situation, although their waveforms showed a coda-like wave packet of long duration, in contrast with a separated and distinct wave packet of Nakanishi (1992). Shapiro et al. (2000) explained the above type of Rayleigh waves by simulations with a three-dimensional finite difference method. Kennett et al. (1990) studied a wave guide for 1-Hz Lg wave propagation, using the topography of the Baja California Peninsula as a local resonator. In this study, we shall conduct numerical simulations whether the above hypothesis of Nakanishi (1992) is valid or not, and quantitatively estimate the effect of the low-velocity zone related to the ocean bathymetry on short-period Rayleigh waves. Although very complicated propagation of surface waves in a laterally heterogeneous medium should be treated by an advanced method of wave theory, including mode-mode conversions (e.g., Kennett, 1998), we can grossly investigate such a propagation phenomenon by a simple WKBJ or ray-theoretical approach (e.g., Dahlen and Tromp, 1998; Červený, 2001). In this study, we adopt a ray-tracing scheme of Yomogida and Aki (1985), particularly in order to pay our attention to how much propagation paths of short-period Rayleigh waves are disturbed by the lateral heterogeneity formed by the sea topography around the Kuril trench. Since all the above events are shallow (< 50 km) and the contribution of higher-mode surface waves should be negligible, we shall consider only fundamental Rayleigh waves in this study. In addition, sea topography strongly affects only fundamental Rayleigh waves whose energy is concentrated near the surface. As in the previous studies mentioned above, lateral heterogeneities in the solid earth (e.g., accretionary prism, subducting crust and plate) should affect the propagation of seismic waves in a trench area. For the fundamental Rayleigh waves of periods shorter than 20 sec, however, lateral variations in phase velocity can exist as much as 200% by trench topography, as shown later. In contrast, the heterogeneities in the solid earth play a minor role in short-period Rayleigh waves because their magnitude should not exceed 10% at most. Stud. Geophys. Geod., 46 (2002)

693

K. Yomogida et al.

Fig. 1. Map of northern Japan and the Kuril islands with three stations (AIB, KKJ, and NMR) for the 1991 off-Urup swarm. The lower figure shows detail hypocentral locations with open circles for events with an anomalous later phase and solid rectangulars without it. Ocean depths are drawn for every 1,000 m, based on EPOTO5 compiled by Japan Coastal Guard (modified from Nakanishi, 1992).

694

Stud. Geophys. Geod., 46 (2002)

Anomalous Rayleigh-wave Propagation along Oceanic Trench

Fig. 2. Three-component velocity seismograms at three stations in Hokkaido for an event on December 19, 1991 whose hypocenter is marked as ‘1’ in Fig. 1 (modified from Nakanishi, 1992).

2. VELOCITY MODELS

Based on the WKBJ approximation, Woodhouse (1974) and later Yomogida and Aki (1985) formulated surface-wave propagation in a laterally heterogeneous earth. One important result is that a propagation path is determined by the lateral variation of phase velocity or 2-D phase-velocity map at a given period, while the wave propagates along the ray with the speed of group velocity. For this reason, we shall consider the spatial distribution of phase velocities at a given period carefully, rather than that of group velocities, in this study, in order to understand the characteristics of the anomalous phase analyzed by Nakanishi (1992). While Rayleigh waves of periods longer than 20 sec in ocean are mainly controlled by the structure of the lithosphere and the asthenosphere, those of shorter periods are largely affected by sea water as a surface layer of very low velocity. Although there are a certain degree of lateral heterogeneous structures in this subduction area, we assume the crust and the upper mantle to be laterally homogeneous. Since the maximum degree of these lateral Stud. Geophys. Geod., 46 (2002)

695

K. Yomogida et al.

heterogeneities should be less than several percent, this simplification does not affect our results in this study, compared with the lateral heterogeneities caused by the ocean bathymetry in this region. For continental areas or islands, we adopt the Gutenberg’s classical earth model with 23 layers (e.g., Box 7.5 of Aki and Richards, 1980). For oceanic areas, a classical oceanic model named ‘8099’ with seven layers (Dorman et al., 1960) is used as the reference model. The original 8099 model sets the sea depth to be 4 km. Since we study the effect of ocean topography, we vary the thickness of the first layer, that is, sea water, following the five-degree mesh data of ocean depths from the data set ETOPO5 compiled by Japan Coast Guard. The deepest sea depth is 9,067 m in the Kuril Trench in the region of Fig. 1. We also vary the thickness of the second layer of the model 8099, that is, a sedimentary layer, roughly simulating thick sediment in the island side of the trench. As shown later, however, the variation of this layer by several kilometers as a realistic value does not alter the gross feature of phase velocity maps. Phase and group velocities were calculated by the subroutine package ‘DISPER80’ made by Saito (1988). Fig. 3 shows their dispersion curves for the models used in this study. Phase and group velocities are plotted for ocean models of various sea depths by every kilometer. Phase velocities in a long period range are nearly constant to be about 4 km/s, up to 50 sec. As ocean depth increases, the period becomes shorter where phase velocity starts decreasing abruptly. Near the axis of the Kuril trench with the maximum ocean depth of nearly 9 km, we can expect that phase velocity between 12 and 25 sec is much smaller than in the surrounding ocean with sea depth of about 4 km. Phase velocities of Fig. 3 do not decrease monotonically with ocean depth because we slightly vary the thickness of the sedimentary layer, as mentioned above. This figure shows that the effect of the sedimentary later is very minor, compared with that of ocean bathymetry. The general tendency and the degree of variations for group velocity are similar to those for phase velocity. Fig. 4 shows phase velocity maps at various periods for the present models. Besides the difference between ocean and continent, lateral heterogeneities in this figure are purely originated from ocean bathymetry, except for a very minor effect of the sedimentary layer. In a period range of longer than 24 sec, the degree of lateral heterogeneities in phase velocity in this region is only up to 10%. The Kuril trench does not yield any noticeable lateral heterogeneities there. At periods around 20 sec, the effect of ocean bathymetry in the Kuril trench starts appearing in phase velocity maps. At a period of 18 sec, there is a narrow low velocity area along the trench axis with less than 2.4 km/s, compared with about 3.8 km/s in the other oceanic area. As the period decreases, the velocity at the trench axis is reduced. The velocity in the surrounding area, however, decreases more rapidly, resulting in a wider but not stronger low velocity zone in the trench. Finally, at periods shorter than 14 sec, the reduction of phase velocity around the trench axis gradually stops, as predicted by the dispersion curves in Fig. 3, while the velocities in the other parts of the ocean (shallower than 4 km) continues to decrease. As a result, a narrow zone of low phase velocity virtually disappears in the trench while the contrast in the ocean-continental boundary becomes prominent. In summary, the Kuril trench is likely to behave as if it were a very strong low phasevelocity zone of Rayleigh waves, due to the deep sea water there at the surface. For example, the minimum phase velocity at the trench axis is less than 2 km/s at a period of 16 sec while about 3.5 km/s in most of oceanic areas. This narrow and strong low-velocity zone is noticeable only in the periods between 14 and 18 sec.

696

Stud. Geophys. Geod., 46 (2002)

Anomalous Rayleigh-wave Propagation along Oceanic Trench

Fig. 3. Phase and group velocity dispersion curves for continent and oceans with various sea depths (the numbers denote the sea depths in kilometer). The structure of the continent is based on the classical Gutenberg model and the oceanic structure follows the model 8099 of Dorman et al. (1960), with slight modification of a sedimentary layer.

Stud. Geophys. Geod., 46 (2002)

697

K. Yomogida et al.

Fig. 4.

698

Phase velocity maps at various periods in the area of Fig. 1. Stud. Geophys. Geod., 46 (2002)

Anomalous Rayleigh-wave Propagation along Oceanic Trench

Fig. 4.

(continued)

Stud. Geophys. Geod., 46 (2002)

699

K. Yomogida et al.

Fig. 4.

700

(continued)

Stud. Geophys. Geod., 46 (2002)

Anomalous Rayleigh-wave Propagation along Oceanic Trench 3. METHOD

Since surface waves are dispersive, the propagation characteristics analyzed by the asymptotic ray theory are slightly different from those for body waves which are nondispersive. Under the assumption that the structure varies slowly in lateral directions, we can apply the WKBJ approximation to the surface-wave propagation in the medium. Surface wave of a given mode and a given frequency (or period in a conventional manner) propagates in a horizontal direction as if an eigenfunction, corresponding to a local vertical structure, propagated in a two-dimensional heterogeneous medium, as derived by Kirpichnikova (1969), Woodhouse (1974), and Yomogida (1984). As summarized in Chapter 3.12 of Červený (2001), ray tracings of surface waves are conducted for the corresponding two-dimensional phase velocity map. The sphericity of the earth can be taken into consideration by introducing the Mercator projection of a phase velocity map (Jobert and Jobert, 1983). We may be able to compute synthetic seismograms based on either the paraxial ray approximation or the Gaussian beam method (Yomogida and Aki, 1985), representing a generalization of the ray approach. As shown in Fig. 4, however, the difference between the maximum and the minimum of phase velocities is nearly twice or 200% in some of the present cases. Conventional ray-theoretical approaches cannot properly deal with wave propagations in such a highly heterogeneous medium, considering the adopted assumption, that is, a medium must be ‘laterally slowly varying’. More advanced methods or numerical approaches such as the finite difference method (e.g., Boore, 1972; Zahradník and Moczo, 1996) are required to obtain accurate seismograms in such a case. Mode-mode conversions must take place severely, so this effect must be fully considered (e.g., Kennett, 1998) if one uses an analytical method. Nevertheless, ray paths computed in this study will surely help us to understand the gross feature of surface-wave propagations in this region and to estimate the origin of the anomalous later phase pointed out in the Introduction. We use the ray approach in this study and leave the use of more sophisticated methods in future. 4. RAY PATH CONFIGURATIONS

Fig. 5 shows the result of ray tracings of Rayleigh waves at three periods for the event on December 19, 1991 (epicenter: 45.17.N, 151.20.E) whose epicenter was represented by ‘1’ in Fig. 1 and seismograms were shown in Fig. 2. The total of one-hundred rays is computed for take-off angles between N80°W and S with the interval of one degree. Since this event is located near the trench axis, as shown in Fig. 1, the source can be considered to be located in the center of a very strong low-velocity zone at periods between 14 and 18 sec. At a period of 24 sec, all the rays propagate not significantly deviated from their greatcircle paths. Rays taking off in the SW direction are distorted relatively largely, forming a kind of shadow zones, in the northern part of Honshu Island (i.e., an area where no rays arrive). The gradient of phase velocities is strong enough perpendicular to the direction of the trench axis even in this period range that some rays crossing the inland boundary of the trench are bent back to the trench. Nevertheless, we can expect only amplitude and phase variations of the primary Rayleigh wave packet at 24 sec period if we observe in the northern part of Japan.

Stud. Geophys. Geod., 46 (2002)

701

K. Yomogida et al.

Fig. 5. Ray paths at three periods for the event of Fig. 2. Take-off angles of rays are from south to N80°W with the interval of one degree. The letter ‘A’ at 16 sec period denotes rays that may correspond to the anomalous phase analyzed by Nakanishi (1992), and rays propagating along the Japan Trench in the south are represented by ‘B’.

702

Stud. Geophys. Geod., 46 (2002)

Anomalous Rayleigh-wave Propagation along Oceanic Trench

Fig. 5.

(continued)

At a period of 10 sec, the computed rays are highly deviated from their great-circle paths. As shown in Fig. 4, the trench does not behave as a low velocity zone, but the contrast in phase velocity between the oceanic area and the island area is so large that most of rays are bent back to the oceanic area and cannot propagate into islands or inland areas such as Hokkaido. Since we did not have oceanic stations at that time (they are very rare even under the current situation), we cannot check this phenomenon in a quantitative manner by comparing the spectra, for example, between a station in Hokkaido and a station in ocean. This example clearly shows that Rayleigh waves of very small amplitude may be observed at an inland station in the period range of shorter than 10 sec, and the effect of diffraction may be included to explain it. Nevertheless, our result shows that the wave packet or phase of Rayleigh waves in this period range should be not anomalous in appearance but only its amplitude would be very small. At a period of 16 sec, rays behave in a more complicated manner than in the previous two cases. Rays taking off in both western and southern directions propagate not so differently from those at 24 sec, although the deviation from each great-circle path becomes more noticeable. A quite surprising result is observed in rays taking off in the direction close to the trench axis, that is, in the southwest. These rays are largely bent where they are about to leave the trench zone. Some rays are bent sharply several times in both sides of the trench zone, as if they are trapped in the zone. We pointed out in Fig. 4 that there is a narrow and strong low-velocity zone along the trench axis, due to the existence of deep sea water at the surface, at periods around 16 sec. The above behavior of Stud. Geophys. Geod., 46 (2002)

703

K. Yomogida et al.

rays is originated from this low-velocity zone. If this low-velocity zone were of a onedimensional structure or the boundaries in both sides were flat, rays would be trapped in the zone forever, never propagating outwards because the epicenter is within the zone. This principle is similar to that of T-phase or the wave propagating through the SOFAR channel in a certain depth of the ocean (e.g., Ewing et al., 1952). Since trenches are not straight but curved and/or segmented, the geographical complication of trenches leads to a highly complicated feature of Rayleigh-wave propagation in this period range. In the example at 16 sec of Fig. 5, some of trapped rays in the trench-related low velocity zone (represented by ‘A’ in the figure) finally run away from the Kuril trench, and propagate in Hokkaido with the propagation direction from ESE to WNW, quite different from the primary rays that propagate not far from their great-circle paths. As Nakanishi (1992) analyzed, the anomalous later phase was observed for this event and the phase appeared to arrive from nearly east while the primary Rayleigh wave arrived not far from each great-circle path, which is consistent with our result. Since the energy of the observed phase is the largest at 15 − 20 sec, the period dependency of computed rays in Fig. 5 can also explain why the anomalous phase was observed only in a limited period range. Since Rayleigh waves along each ray propagates with group velocity and the group velocity around the trench is also very slow (~ 1.2 km/s, compared with 3.5 km/s in the average ocean of 4 km deep, as shown in Fig. 3), the travel time of the above rays is longer than that of the primary Rayleigh wave packet by several minutes. The amount of this delay is also consistent with the observation of Nakanishi (1992). 5. EFFECT OF SOURCE POSITION

As Nakanishi (1992) emphasized in his analysis, the anomalous later phase was not observed for all the events around Urup Island. The anomalous phase was observed only for events whose epicentres are very close to the trench axis or where their sea depths are deeper than 4,000 m (open circles in Fig. 1). If events were located at an oceanic area shallower than 2,000 m, such an anomalous later phase was not observed. In Fig. 6, we show ray paths for another event on December 19, 1991, whose epicenter is slightly different from the one of Fig. 5. Its epicenter is closer to Urup Island than the previous one, and the ocean depth above the event is less than 2,000 m, represented by ‘2’ in Fig. 1 (45.82°N, 150.37°E). Compared with the result in Fig. 5, we can easily recognize the effect of source position on the Rayleigh-wave propagation in this period range. At a period of 24 sec, ray paths are more severely distorted than in the example of Fig. 5. A strong focus of rays appears along the ocean-continental boundary because the event is now located near the corresponding phase-velocity contrast. A similar focusing phenomenon is observed at a period of 10 sec, which marks quite different propagation features from the example of Fig. 5. In contrast with the bending of almost all the rays at the inland slope of the trench in the previous example, rays can propagate into the inland side, although the distortion of rays is strong. Nevertheless, this pattern of rays does not predict the existence of any anomalous later phases but the large variation in the amplitude of the primary Rayleigh wave packet.

704

Stud. Geophys. Geod., 46 (2002)

Anomalous Rayleigh-wave Propagation along Oceanic Trench

Fig. 6. Same as Fig. 5 except for another event on December 19, 1991 whose hypocenter is marked as ‘2’ in Fig. 1.

Stud. Geophys. Geod., 46 (2002)

705

K. Yomogida et al.

Fig. 6.

(continued)

At a period of 16 sec, in which many rays are trapped in the low-velocity zone related to the trench in the example of Fig. 5, only a few rays are trapped in the low velocity zone for the event of Fig. 6. Since the event is located near the boundary of the low velocity zone, most of rays propagate outwards although some of them are severely distorted. No rays are trapped in the Kuril trench, although there are rays trapped in a trench area in the south (i.e., the Japan trench). This result supports the observation that the event of Fig. 6 did not show any anomalous later phases at stations in Hokkaido. In summary, the effect of the trench-related low-velocity zone on the later phase is proved to be extremely important only for events near the trench axis. 6. CONCLUSIONS

Assuming the cause of lateral heterogeneities to be ocean bathymetry, we first modelled phase and group velocity maps for relatively short-period (from 10 to 24 sec) Rayleigh waves around the northern part of Japan, including Hokkaido and southern Kuril islands. Lateral heterogeneities in phase velocity are about 10% at a period longer than 24 sec, but as much as 200% at a shorter period. In a period range from 14 to 18 sec, the Kuril trench with the deepest point close to 10 km behaves as a very strong low-velocity zone for Rayleigh waves. At a period shorter than 12 sec, however, the ocean bathymetry of the trench turns to be unimportant, and a strong lateral heterogeneity in phase velocity exists only along ocean-continent boundaries.

706

Stud. Geophys. Geod., 46 (2002)

Anomalous Rayleigh-wave Propagation along Oceanic Trench

Based on the asymptotic ray theory of Yomogida and Aki (1985), we calculated ray paths for the swarm events that occurred near Urup Island in 1991. When an event is located inside the Kuril trench, ray paths are severely distorted and deviated from each great-circle path. Ray paths at a period about 16 sec particularly behave in a highly complicated manner. Since the trench topography forms a very strong low-velocity zone of phase velocity, many rays are trapped in this zone and propagate to a long distance along the trench. Due to the curvature or bend of trenches, a part of trapped Rayleigh waves eventually escapes from the zone, arriving at some stations in the inland area. These rays arrive at the stations from a direction very different from that of the primary or direct Rayleigh wave, and their travel times are greater than the travel times of the direct wave. This result can qualitatively explain the anomalous later phase observed at stations in Hokkaido, as analyzed by Nakanishi (1992): the later phase comes from east, or different arrival direction from great-circles, with the delay of about 3 minutes compared with the primary Rayleigh wave. The dominant period of this phase is 15 to 20 sec. This study also implied that such a later phase is likely to exist only if an event is located close to the trench axis. This is consistent with another observational result of Nakanishi (1992). Besides the minor correction of sedimentary thickness, we considered only the effect of ocean bathymetry on the phase-velocity distribution of Rayleigh waves. Although the effect of lateral heterogeneities in the other parts of the earth such as the crust and the uppermost mantle is minor, we need to take it into consideration in future studies. For example, the anomalous rays at 16 sec period of Fig. 5 (represented by ‘A’) do not arrive exactly at the station KKJ where the later phase was clearly observed (Fig. 2). This discrepancy may be due to the lateral heterogeneity in the solid earth. Because the dense coverage of seismic stations has been rapidly improved in Japan, we may resolve detailed conditions in which such a later phase is observed. Together with the updated structural information in both inland and oceanic areas, more quantitative investigations on this phenomenon should be conducted. The present study suggests an additional new type of anomalous phases. Some rays at 16 sec period of Fig. 5 propagate not only in the Kuril trench but also farther in the south along the Japan trench (i.e., the trench in the east of Honshu), as represented by ‘B’. An anomalous later phase, similar to the one in Fig. 2, was observed at a station named Ogasawara, more than 1,000 km away from its epicenter in the south of the Japan trench (I. Nakanishi, unpublished data). Since surface waves trapped along a trench zone to a long distance should be strongly affected by detailed lateral variations, any further quantitative analyses may be too speculative. Since the Kuril trench is connected with the Japan trench in the south with a different strike angle, several rays at 16 sec period in both Figs. 5 and 6 propagate in a trapped manner along the Japan trench to the south. Since the geometry of the corresponding low velocity zone is very complicated in this region, anomalous later phases may be observed even for an event located outside the low velocity zone if a station is in a special position relative to the zone. With a dense seismic observation, we will be able to discuss this type of complicated surface-wave propagation in an oceanic area. No anomalous later phases that seemed to correspond to Love waves were observed for the present swarm events. Since Love waves are not affected by oceanic topography, and the subsurface structure in ocean is generally much more laterally homogeneous than in continent, the possibility of anomalous propagation of Love waves may be less than in Stud. Geophys. Geod., 46 (2002)

707

K. Yomogida et al.

the case of Rayleigh waves. In contrast, short-period Love waves may propagate anomalously in continent, for example, when they pass through a thick sedimentary basin or a high-mountain range with deep root (e.g., Petersen et al., 1998; Yoshida, 2000). The only candidate to cause anomalous Love-wave propagation in ocean may be the variation of sedimentary thickness. If we observe anomalous phases of Rayleigh and Love waves in ocean simultaneously, the independent information of lateral heterogeneities in ocean topography and sediment will be obtained. Surface waves in a period range of shorter than 20 sec have not been studied quantitatively yet, probably because their propagation is too complex to conduct any deterministic study. Recent dense seismic arrays being deployed around the world are enabling us to study short-period surface waves, in a similar manner to conventional studies on surface waves of longer periods. Not only the effect of ocean trenches may be very important, but also it should be the first target to investigate because we can assign a quite reliable laterally heterogeneous model from ocean bathymetric data, compared with lateral heterogeneities in the solid earth. In addition, events near a trench axis are very important for studying earthquake source problems because some of them have been reported very anomalous, clearly lacking high-frequency waves (Wadati, 1928; Fukao and Kanjo, 1980). Since they may be related to Tsunami-genic events, detailed studies on the propagation effect in a trench region are very important in terms of natural disaster prevention. Acknowledgments: The authors wish their sincere thanks to Japan Oceanographic Data Center of Japan Coast Guard for providing us with a bathymetry data set named ETOPO5 of the studied area. Continuous encouragement from Ivan Pšenčík was the driving force for us to complete this study. Comments by Anatoli Levshin, Ivan Pšenčík, and an anonymous reviewer were appreciated very much. Finally, the first author (K.Y.) greatly honors Prof. Vlastislav Červený with his profound contribution to not only high-frequency but also low-frequency seismic wave problems, important in global seismology, from which the idea of the present study was evolved. Received: May 3, 2002;

Accepted: August 1, 2002

References Aki K. and Richards P.G., 1980. Quantitative Seismology: Theory and Methods. W.H. Freeman, San Francisco. Boore D.M., 1972. Finite difference methods for seismic wave propagation in heterogeneous materials. In: B.A. Bolt (Ed.), Seismology: Surface Waves and Earth Oscillations (Methods in Computational Physics, vol. 11) (ed. by B.A. Bolt), New York, Academic Press. Červený V., 2001. Seismic Ray Theory, Cambridge University Press, Cambridge. Dahlen F.A. and Tromp J., 1998. Theoretical Global Seismology. Princeton University Press, Princeton.

708

Stud. Geophys. Geod., 46 (2002)

Anomalous Rayleigh-wave Propagation along Oceanic Trench Debayle E. and Kennett B.L.N., 2000. The Australian continental upper mantle: Structure and deformation inferred from surface waves. J. Geophys. Res., 105, 25243−25450. Dorman J., Ewing M. and Oliver J., 1960. Study of shear-velocity distribution in the upper mantle by mantle Rayleigh waves. Bull. Seismol. Soc. Amer., 50, 87−115. Ewing M., Press F. and Worzel J.L., 1952. Further study of the T phase. Bull. Seismol. Soc. Amer., 42, 37−51. Fukao Y. and Kanjo K., 1980. A zone of low-frequency earthquakes beneath the inner wall of the Japan trench. Tectonophysics, 67, 153−162. 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, 169−197. Ihmle P.F. and Madariaga R., 1996. Monochromatic body waves excited by great subduction zone earthquakes. Geophy. Res. Lett., 23, 2999−3002. Jobert N. and Jobert G., 1983. An application of ray theory to the propagation of waves along a laterally heterogeneous spherical earth. Geophys. Res. Lett., 10, 1148−1151. Kennett B.L.N., 1998. Guided waves in three-dimensional structures. Geophys. J. Int., 133, 159−174. Kennett B.L.N., Bostock M.G. and Xie J.-K., 1960. Guided-wave tracking in 3-D: A tool for interpreting complex regional seismograms. Bull. Seismol. Soc. Amer., 80, 633−642. Kirpichnikova N.Y., 1969. Rayleigh wave concentrated near a ray on the surface of an inhomogeneous elastic body. In: Mathematical problems in wave propagation theory, part II, Seminar in Mathematics, 15, 49−62, Steklov Mathematical Institute, Nauka, Leningrad (in Russian, English translation by Consultants Bureau, New York, 1971). Nakanishi I., 1992. Rayleigh waves guided by sea-trench topography. Geophy. Res. Lett., 19, 2385−2388. Nakanishi I., Hanakago Y., Moriya T. and Kasahara M., 1991. Performance test on long-period moment tensor determination for near earthquakes by a sparse local network. Geophy. Res. Lett., 18, 223−226. Okamoto T., 1993. Effects of sedimentary structure and bathymetry near the source on teleseismic P waveforms from shallow subduction zone earthquakes. Geophys. J. Int., 112, 471−490. Petersen H., Avouac J.P. and Campillo M., 1998. Anomalous surface waves from Lop Nor nuclear explosions: Observations and numerical modelling. J. Geophys. Res., 103, 15051−15068. Saito M., 1988. DISPER80: A subroutine package for the calculation of seismic normal-mode solutions. In: D.J. Doornbos (Ed.), Seismological Algorithms, Academic Press, London. Shapiro N.M., Campillo M., Singh S.K. and Pacheco J., 1998. Seismic channel waves in the accretionary prism of the Middle America Trench. Geophy. Res. Lett., 25, 101−194. Shapiro N.M., Olsen K.B. and Singh S.K., 2000. Wave-guide effects in subduction zones: evidence from three-dimensional modelling. Geophy. Res. Lett., 27, 433−436. Van Heijst H.J. and Woodhouse J.H., 1999. Global high-resolution phase velocity distributions of overtone and fundamental-mode surface waves determined by mode branch stripping. Geophys. J.. Int., 137, 601−620. Wadati K., 1928. Unusual nature of deep-sea earthquakes − on the three types of earthquakes. Kishoshushi, 6, 1−43 (in Japanese). Stud. Geophys. Geod., 46 (2002)

709

K. Yomogida et al. Woodhouse J.H., 1974. Surface waves in a laterally varying layered structure. Geophys. J.R. Astron. Soc., 37, 461−490. Woodhouse J.H. and Dziewonski A.M., 1984. Mapping the upper mantle: Three-dimensional modelling of Earth structure by inversion of seismic waveforms. J. Geophys. Res., 37, 5953−5986. Woodhouse J.H. and Wong Y.K., 1986. Amplitude, phase and path anomalies of mantle waves. Geophys. J.R. Astron. Soc., 87, 753−773. Yomogida K., 1984. Gaussian beams for surface waves in laterally slowly-varying media. Geophys. J.R. Astron. Soc., 82, 511−533. Yomogida K. and Aki K., 1985. Waveform synthesis of surface waves in a laterally heterogeneous Earth by the Gaussian beam method. J. Geophys. Res., 90, 7665−7688. Yoshida M., 2000. Fluctuation of group velocity of Love waves across a dent in the continental crust. Earth, Planets Space, 52, 393−402. Zahradník J. and Moczo P., 1996. Hybrid seismic modelling based on discrete-wavenumber and finite-difference methods. Pure Appl. Geophys., 148, 21−38.

710

Stud. Geophys. Geod., 46 (2002)