Imaging of three-dimensional small-scale heterogeneities in the Hidaka, Japan region: coda spectral analysis

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1 Geophys. J. Int. (2004) 158, doi: /j X x Imaging of three-dimensional small-sale heterogeneities in the Hidaka, Japan region: oda spetral analysis Taka aki Taira and Kiyoshi Yomogida Division of Earth and Planetary Sienes, Graduate Shool of Siene, Hokkaido University, North 10 West 8, Kita-ku, Sapporo , Japan. s: (TT); (KY) Aepted 2004 April 13. Reeived 2004 Marh 19; in original form 2003 April 23 GJI Seismology SUMMARY While large-sale heterogeneities have been studied intensively by seismi tomography with traveltime data, small-sale heterogeneities are not fully investigated yet. We obtained the 3- D spatial distribution of small-sale heterogeneities as relative sattering oeffiients in the Hidaka, Japan, region using the spatial variation of high-frequeny oda power spetra. We analysed 530 seismograms reorded at 62 stations for nine loal earthquakes in the frequeny range of 1 32 Hz. After orreting soure, station and propagation effets, we assigned the spatial and temporal variations of erved power spetra of oda waves into the 3-D distribution of sattering oeffiient, based on single and isotropi sattering models. Small-sale heterogeneities are distributed not only in a non-uniform manner but also differently among sale lengths estimated from their frequeny dependene. An area of large relative sattering oeffiient in 2 and 16 Hz is loated at a depth shallower than 45 km in the southwest of the Hidaka Mountains, orrelating well with a highly ative area of miroearthquakes. At a depth of km, two dipping zones of large sattering oeffiient are imaged beneath the summit of the Hidaka Mountains. These zones may imply two layers of strong seismi-wave refletion, onsistent with the upper and lower planes of the double seismi zone in the subduting Paifi Plate, as determined by the hypoentral distribution in this region. Key words: ollision belt, lithosphere, sattering, seismi oda. 1 INTRODUCTION Observed seismograms of high-frequeny oda waves (>1 Hz) are attributed mainly to small-sale heterogeneities in the Earth (e.g. Aki 1969; Aki & Chouet 1975). The stohasti harateristis of heterogeneities have been studied, using the exitation of inoherent oda wave and the attenuation of high-frequeny seismi waves (e.g. Aki 1973; Jin & Aki 1986; Su & Aki 1990). On the other hand, seismi array ervation enables us to estimate the spatial distribution of heterogeneities beneath the array in a deterministi manner. Several studies based on suh array analysis tehnique [e.g. semblane analysis and frequeny wavenumber (f k) analysis] quantitatively estimated the distribution of small-sale heterogeneities from oherent arrivals in oda (e.g. Capon 1969; Neidell & Taner 1971; Nikolaev & Troitskiy 1987; Gupta et al. 1990). Using the f k analysis, Gupta et al. (1990) analysed seismograms at the EKA and NORESS arrays using a nulear explosion as a seismi soure and determined loations of several distint satterers. Matsumoto et al. (1998) applied the slant stak method to the data of a small-aperture seismi array in the soure region of the 1995 Hyogo-ken Nanbu earthquake (M7.2) and showed strong satterers onentrated just beneath the hypoentre. Regional dense seismi ervations were reently onduted and revealed the distribution of satterers in a wide area (e.g. Nishigami 1991; Revenaugh 1995; Nishigami 1997, 2000; Revenaugh 2000). For example, Nishigami (2000) used the reursive stohasti inversion to image the 3-D distribution of satterers around the San Andreas fault. He onluded that the satterer distribution is related to the geometry of the fault system. Revenaugh (2000) estimated the distribution of sattering potential by the stohasti Kirhhoff migration in southern California. He suggested that the sattering potential is highly orrelated with miroseismiity level. In order to pinpoint the loations of small-sale heterogeneities, theories and models with realisti sattering proesses must be taken further into aount. Another kind of deterministi approah to mapping small saleheterogeneities is the use of the spetral ratio of oda waves, as used for example by Aki & Ferrazzini (2000), Taira & Yomogida (2003) and Tsuruga et al. (2003). These studies showed that oda levels flutuate signifiantly and systematially within a dense seismi network. For example, Taira & Yomogida (2003) obtained oda amplifiation fators in the Hidaka region, inluding their frequeny dependene. A oda amplifiation fator was defined as the amplitude ratio of oda waves among different stations after orreting 998 C 2004 RAS

2 Imaging of three-dimensional small-sale heterogeneities 999 for eah the site amplifiation fator that reflets the surfae geology (e.g. Quaternary sediment) of eah station. They found systemati spatial variations of oda amplifiation fators, revealing a highly non-uniform distribution of small-sale heterogeneities in this region. As one of their important results, the oda is relatively amplified for paths rossing the Hidaka Mountains in a high-frequeny range (>16 Hz). They did not, however, relate the deteted oda amplifiation fators with the spatial distribution of satterers in the Earth quantitatively. In this paper, we shall propose a new imaging method, using power spetra of oda waves of high frequeny (>1 Hz) as a funtion of lapse time. We shall also attempt to detet the loation of small-sale heterogeneities with large sattering oeffiient beneath the Hidaka Mountains, in order to explain the harateristis of oda amplifiation fators obtained by Taira & Yomogida (2003). Sattering oeffiient in this study is defined as the frational loss of energy of inident seismi wave as a result of sattering by heterogeneities in a medium (Aki & Chouet 1975). We shall disuss the orresponding regional tetonis, suh as the subduting Paifi Plate, in the Hidaka ollision zone, using frequeny dependene in spatial distribution of sattering oeffiients. 2 MAPPING OF SMALL-SCALE HETEROGENEITIES As one of the promising reent researh movements, the distribution of small-sale heterogeneities has been gradually revealed with the use of dense seismi networks. For example, Matsumoto et al. (1998), Nishigami (2000), and Revenaugh (2000) estimated the spatial distribution of heterogeneities in ative seismi areas from high-frequeny oda waves. Although these studies adopted some sophistiated approahes, all of them were based on the following two fundamental assumptions in the sattering proess: single and isotropi sattering models. In this study, we shall also employ theses two assumptions in the relative sattering oeffiients. Beause the erved seismograms are involved in various omplex proesses, the following additional assumptions are introdued: sattering in a 3-D half-spae with a onstant S-wave veloity, only S-to-S wave onversion and isotropi radiation of S waves ateah soure. Heterogeneities are expressed as relative sattering oeffiient loated at eah blok of the volume δv (Fig. 1a). The free surfae is treated as a perfet seismi refletor of S waves for whih the refletion oeffiient is one. In order to take this effet into aount, sattered waves generated by a mirror image soure are introdued in addition to the sattered waves from the original soure (Fig. 1b). Beause all the hypoentres in this study are relatively deep (>30 km) and loated within the model spae, the effet of omplex veloity struture in this area should be minor. Using the radiative transfer theory, on the one hand, Sato et al. (1997) showed that the effet of non-isotropi radiation of seismi waves (i.e. a double ouple soure) beomes unimportant as the lapse time of oda waves inreases, beause of the averaging effet of sattered waves. Beause we use the oda part of relatively large lapse time (i.e. after the time twie the S-wave traveltime) in this study, the assumption of isotropi radiation at eah soure should not affet the loations and magnitudes of satterers signifiantly. In summary, all the additional assumptions in the present analysis should not severely alter our final result of the loations and magnitudes of satterers. In ontrast with the previous studies that normalized eah seismogram by its maximum in the first stage of their data analyses, our present approah tries to map the power spetrum of eah oda into sattering oeffiients in a medium after the orretions of soure, station and overall propagation effets (e.g. the effet of oda Q). As for Taira & Yomogida (2003), the relative site amplifiation fator (RSAF) ofeah station is estimated by the oda-normalization method with regional earthquakes and oda Q is determined by the maximum likelihood method, respetively. The oda power spetra are then mapped into the relative sattering oeffiient at eah blok by the following three steps. First of all, we attempt to remove the propagation effet for a given soure to eah station. The erved amplitude in oda is affeted by the energy loss resulting from anelasti or intrinsi attenuation, together with the averaged or bakground sattering attenuation, along eah ray path. We normalize amplitude in oda, using the values of oda Q, asobtained in Taira & Yomogida (2003), with the referene starting time of oda wave t : v k ( τ ; f ) ( = v k τ ; f ) [ ( π f τ exp t ) Q ( f ; k) ], (1) where v k (τ ; f ) indiates the veloity amplitude in oda for the ith earthquake at the jth station in the kth omponent for the lapse time τ after being passed through a bandpass filter of the entre frequeny f. t is defined as the maximum lapse time of all the data for eah earthquake. Q ( f ; k) isthe oda Q averaged over all the seismograms in the kth omponent. v k (τ ; f )may be onsidered as the normalized veloity amplitude of oda waves beause it is already orreted by the overall propagation effet. Next, we alulate the running power spetrum of v k (τ ; f ) with an appropriate time window δ t (1.28 s in this study) around τ,whih is expressed by E k ( f, τ ). This proess smoothes the highly ompliated temporal variation of the oda level that Figure 1. Model geometry and sattering ray path of a single sattered wave by the pth blok of volume δv in a homogeneous half-spae for the jth station with (a) the ith real and (b) the mirror image soures. v s is the share wave veloity and δt is the time window.

3 1000 T. Taira and K. Yomogida Figure 2. Shemati view of the proedure to obtain CSF k ( f, τ ). (a) Bandpass filtered (with the entre frequeny of 2 Hz) seismogram after the orretion of oda Q. (b) Power spetra of HIC (left) and the average over all the stations (entre) for the earthquake, 1999 Deember 18. Relative site amplifiation fator (RSAF)ofHIC (right) was obtained formerly by Taira & Yomogida (2003). () CSF k ( f, τ ), that is, running power spetra after orretion of soure, station and propagation effets. annot be expressed by the present disretization sale of the model spae. The seletion of δt is based on the relationship of δt < 2(δV ) 1/3 /υ s,where υ s is the S-wave veloity, so that the isohronal sattering shell at eah lapse time τ always overs multiple bloks (Fig. 1). Using the single sattering model (e.g. Aki & Chouet 1975; Sato & Fehler 1998), the running power spetrum an be related to the intensity of sattering term P k ( f, τ ) for the orresponding portion of oda as follows: ( ) E k f,τ = S ik ( f ) 2 G jk ( f ) 2 P k ( f,τ ) exp ( 2π f τ Q ( f ; k) ), (2) where S ik ( f )isthe soure term of the ith earthquake, G jk ( f )isthe station term of the jth station and τ is the maximum lapse time for the ith earthquake. Beause G jk ( f ) an be replaed by the relative site amplifiation fator [RSAF jk ( f ) for the jth station in the kth omponent at frequeny f ], as already obtained from regional earthquakes (Taira & Yomogida 2003), the remaining task is to suppress the soure term S ik ( f ). Analogous to oda duration magnitude (e.g. Sato & Fehler 1998), we define the oda soure fator (hereafter alled CSF) as the ratio of the power spetrum of oda E k ( f, τ )tothe average over all the stations for a given ith earthquake Ẽ ik ( f,τ )atthe fixed lapse time τ, using the orresponding relative site amplifiation

4 fator: RSAF jk ( f ) 2 E ( ) k f,τ Ẽ ik ( f,τ ) ( ) S ik ( f ) 2 P k f,τ exp ( 2π f τ ) Q = ( f ; k) ( S ik ( f ) 2 P ik ( f,τ ) exp 2π f τ ) Q ( f ; k) P ( ) k f,τ ( ) CSF k f,τ. (3) P ik ( f,τ ) Fig. 2 shows a shemati view of the proedure to obtain CSF. Note that the above proedure is presented for eah omponent, then we shall use the sum of the three omponents of CSF: CSF ( f,τ ) 3 k=1 ( ) CSF k f,τ. (4) Finally, we estimate the spatial distribution of relative sattering oeffiient. Coda waves from loal earthquakes are assumed to be omposed of single and isotropially sattered body waves over the model spae V with a sattering oeffiient g(f, p)atthepth blok. P ( f, τ )isthen expressed by ( ) P f,τ g( f, p) = rip 2 r δv, (5) pj 2 p Imaging of three-dimensional small-sale heterogeneities 1001 where r ip and r pj indiate the distanes from the entre of the pth blok to the ith earthquake and to the jth station, respetively. The summation is done over all the p th blok that satisfies the traveltime τ al (p) δ t/2. We alulate the traveltime τ al to be τ (p)ofsattered waves responsible for the erved oda spetrum as the sum of that from the ith earthquake to the pth blok τ ip plus that from the satterer to the jth station τ pi, inluding the free surfae refletion as an additional ontribution from the mirror image soure of the ith earthquake: τ al (p) = τ ip + τ pj. (6) In order to estimate relative sattering oeffiient at eah blok, CSF ( f, τ ) defined by eq. (4) as a funtion of lapse time, τ, is mapped into the spatial variation of relative sattering oeffiient (Fig. 3b). The sattering oeffiient g i j( f, p)ofthepth blok in frequeny f is estimated from the erved power spetra of oda waves, CSF i j( f, τ ), for a given earthquake station pair (i.e. ith earthquake and jth station) by distributing the energy in an isohronal sattering shell with eq. (5) (Fig. 3b): g ( f, p) = r 2 ip r 2 pj CSF ( ) f,τ δv Ṽ ( ), (7) τ where Ṽ (τ )isthe volume of the ellipsoidal shell over the given time interval (τ δt/2, τ + δt/2).wealulate g ( f, p) for all the earthquake station pairs (i.e. all the erved ombinations of i and j) and average them for a given pth satterer (Fig. 4): g( f, p) = 1 N M N i=1 M g ( f, p), (8) j=1 where N and M are the earthquake and station numbers, respetively. As a result, g( f, p) represents the relative sattering oeffiient in the pth blok at frequeny f. Figure 3. Shemati view of dividing CSF ( f, τ ). (a) One value of CSF ( f, τ ) for the ith earthquake of the jth station. (b) Ellipsoidal shell for the given time interval (τ those imaged from the given CSF ( f, τ ). δt/2, τ + δ t/2). Bloks in grey indiate 3 TECTONIC SETTING AND DATA The rustal struture in Hokkaido, Japan, is dominated by a series of aretion and ollision proesses from late Jurassi to the present (e.g. Kimura 1994). There are several ative seismi zones around the Hidaka region, a high mountain area in entral South Hokkaido, forming two seismi planes (i.e. double seismi zone) in the subduting Paifi Plate (e.g. Hasegawa et al. 1978; Suzuki et al. 1983; Katsumata et al. 2003). In order to estimate its detailed rustal struture, seismi refletion/refration experiments (e.g. Iwasaki et al. 1998; Moriya et al. 1998; Tsumura et al. 1999) and magnetotelluri (MT) surveys (e.g. Ogawa et al. 1994; Uyeshima et al. 2001) have been onduted. 3-D seismi tomography studies have been also onduted in this area (e.g. Zhao & Hasegawa 1993; Miyamahi et al. 1994; Murai et al. 2003). Moriya et al. (1998) estimated the P-wave veloity struture of the upper rust in this area, using seismi refletion/refration exploration tehnique. They suggested that the ontinental rust of the Kurile Outer Ar overthrusts that of the Northern Honshu Outer Ar as a result of their ollisional movement. Taira & Yomogida (2003) obtained the 2-D spatial variation of high-frequeny oda amplitude levels in this region. They onluded that strong heterogeneities with the sale of km should be loated in the west of the Hidaka Mountains although their loations and magnitudes were not fully onstrained. We applied the imaging method explained in Setion 2 to the seismograms reorded by a dense seismi network in this area

5 1002 T. Taira and K. Yomogida Figure 4. Shemati view of obtaining relative sattering oeffiients. operated by the Researh Group of Hidaka Collision Zone and the Institute of Seismology and Volanology, Hokkaido University (e.g. Katsumata et al. 2003). Most of the stations were equipped with a three-omponent 1 Hz veloity seismometer. The sampling rate of all the seismograms was 100 Hz. We used hypoentral parameters determined by Katsumata et al. (2003). We seleted seven loal earthquakes of magnitude greater than 5, in order to obtain seismograms to be analysed under the following riteria: (i) high signalto-noise ratio and (ii) reorded at most of the stations for a given earthquake. In addition, our data set inludes seismograms for the additional two earthquakes used by Taira & Yomogida (2003), in order to ompare their 2-D spatial variation of oda levels. Fig. 5 shows 62 stations and epientres of nine earthquakes used in this study. We analysed seismograms in six frequeny bands: 1, 2, 4, 8, 16 and 32 Hz. We used a oda part with a lapse time greater than twie the S-wave traveltime. The total time window of s is onsidered for sattered waves to be mapped in our model spae (Fig. 2a). The extent of the model spae is shown by the solid square in Fig. 5: km in horizontals and 150 km in depth. The size of eah blok δv is km in horizontals and 15 km in depth. We alulated the running power spetrum with a time window (δt) of1.28 s (Fig. 2). In order to determinate suh a running power spetrum aurately even in a short-time window, we applied an autoregressive (AR) modelling method (e.g. Akaike 1969; Kanasewih 1973). S-wave veloity was set to be 4.0 km s 1. This value is nearly equal to the average S-wave veloity down to 100 km in this area (Suzuki et al. 1988). Beause most hypoentres are loated within the area overed by our seismi array (Fig. 5), all the ray paths in this study are not far from straight, so that the introdution of any realisti veloity struture will not alter the resulting loation of heterogeneities signifiantly. To evaluate the spatial resolution of the above approah applied to the present data set, we onduted a so-alled hekerboard test. Large ( g = 0.1) and small ( g = 0.01) relative sattering oeffiients are assigned to bloks that are arranged alternately in the model spae. We synthesized oda envelopes for the nine analysed earthquakes, using the same modelling proedure, as explained in Setion 2. The syntheti data were added Gaussian white noise of 20 per ent of the average signal level. Figs 6 and 7 show the result of this resolution test in horizontal and vertial ross-setions, respetively. We normalized relative sattering oeffiients g( f, p) of eq. (8) by the logarithmi average value. The resolution is high in the entral part of the model spae. It is espeially good 0 90 km deep, exept for near edges of the model spae. Near edges and the part deeper than 120 km, however, the assigned pattern is not orretly reonstruted. Fig. 8 shows the histogram of retrieved relative sattering oeffiients. Although we set sattering oeffiients with high ontrast into eah blok (i.e. 0.1 and 0.01), retrieved sattering oeffiients are only slightly different between maximum and minimum values. Relative sattering oeffiients with the atual data set in this study overed larger and/or smaller than log average by 0.3, muh larger than the test with syntheti data (Fig. 8). Beause theses large (and small) values are the result of artifiial anomalies with poor resolution reated by our imaging proess, we removed bloks of suh a large (and small) sattering oeffiient in our mapping heterogeneities, as shown in the next setion.

6 Imaging of three-dimensional small-sale heterogeneities study area epienters stations km 0 50 Figure 5. Distribution of epientres (stars) and stations (irles). The model spae for imaging heterogeneities is indiated by the solid square. Topographi ontour interval is 200 m. 4 THREE-DIMENSIONAL DISTRIBUTION OF HETEROGENEITIES IN THE HIDAKA REGION If the size of heterogeneities is muh smaller than the wavelength of the inident wave, the amplitude of sattered waves dereases rapidly, as frequeny dereases, for example, the power spetrum dereases as f 4,where f is the frequeny of sattered wave, whih is alled Rayleigh sattering. On the other hand, if the size is larger than the wavelength, the amplitude of sattered waves hanges weakly with frequeny although their azimuthal dependeny beomes strong (e.g. Sato & Fehler 1998). These onsequenes make the erved sattered waves most sensitive to heterogeneities with a size omparable to the wavelength orresponding to the dominant frequeny onsidered. To study the spatial distribution of relative sattering oeffiient in terms of satterers of different sizes, it is important to pay our attention to its frequeny dependene. Using the proedures and the data explained in the previous setions, we obtained g( f, p), that is, the 3-D distribution of relative sattering oeffiient in the Hidaka region. Fig. 9 shows horizontal distributions at 2, 4 and 16 Hz at a depth shallower than 45 km. The most remarkable feature in the obtained distributions of sattering oeffiient is a zone of large sattering oeffiient in the southwest of the Hidaka Mountains at 2 and 16 Hz. This zone is onsistent with the result of Taira & Yomogida (2003), as an area of large oda amplitude fator (CAF). On the other hand, the distribution at 4 Hz does not show suh speifi anomalies, whih also agrees with the result of relatively uniform CAF distributions at 4 Hz, ompared with those at 2 and 16 Hz (Taira & Yomogida 2003). In other words, this loated heterogeneous zone an satter less seismi waves in the intermediate frequeny range (4 Hz). Yomogida et al. (1997) omputed syntheti sattered waves from several distributions of seismi satterers, using the boundary integral method. They found that a loalized zone of many satterers generates two spetral peaks of sattered waves. They onluded that the spetral peak in a low-frequeny range is originated from the entire zone of satterers while a high-frequeny peak is generated by individual satterers. The erved oda waves in the southwest of the Hidaka region (Fig. 9) may imply suh a loalized zone omposed of many small heterogeneities, in analogy to Yomogida et al. (1997). In addition, the present loation of large relative sattering oeffiient agrees very well with the lear lustering of miroearthquakes that extends down to the depth 0 45 km. This suggests that the distribution of these shallow heterogeneities shows the overall orrelation with the seismi ativity in this region, as shown in Figs 9(a) and (). Fig. 10 shows N S vertial setions of g( f, p) aross the Hidaka Mountains in three frequenies ranges. We fous our attention to three areas of large relative sattering oeffiients, as represented in Fig. 10(a), in order to disuss their relationship with the tetonis in this region, for example, the subduting Paifi Plate. Area 1 indiates the upper interfae of the subduting Paifi Plate or the upper plane of the double seismi zone, while area 2 orresponds to an intraplate setion or the lower plane of the double seismi zone, as determined by the hypoentral distributionshownin Fig.10 (Katsumata et al. 2003). Large sattering oeffiients in area 1 are erved only at 16 Hz (Fig. 10), while sattering oeffiients at 2 and 4 Hz are large in area 2 (Figs 10a and b).

7 1004 T. Taira and K. Yomogida A' B' C' D' E' F' Hidaka Mountains A B C D E F relative sattering oeffiients Figure 6. Result of a hekerboard test for horizontal setions. The depth range is shown in above eah map. Areas of poor resolution are shown by dashed ellipses. Cirles in grey indiate those removed from our final result with the data. The magnitude of eah relative sattering oeffiient is shown by the irle size, as shown along the bottom of the figure. This lear frequeny dependene suggests the existene of two kinds of heterogeneities with different sizes around the subduting Paifi Plate. The harateristi sizes of heterogeneities in areas 1 and 2 are estimated to be approximately 0.08 and 0.32 km respetively (i.e., the orresponding wavelengths of 16 and 4 Hz), assuming the strongest frequeny range of sattering to be kd 2 (Yomogida et al. 1997), where k is the wavenumber and d is the size of heterogeneities. The large zone of relative sattering oeffiient inlines roughly northwards in both areas 1 and 2. These results may be explained by the existene of a strong seismi refletor along the subduting Paifi Plate rather than many point-like satterers. The distribution of oda level anomalies estimated by Taira & Yomogida (2003) at high frequenies also supports suh refletor-type heterogeneities in area 1. Several studied have deteted refleted/sattered waves by a subduting plate. Obara (1997) simulated S-oda envelopes, in order to explain the anomalous envelope erved in the Kanto area, using a hybrid model with refletors and satterers. He suggested that S-oda envelopes are omposed of refleted waves from the upper boundary of the subduting Paifi Plate and sattered waves by a two-layered random medium. On the other hand, there appear to exist relative large sattering oeffiients at all frequeny ranges in area 3, deeper than 50 km in the southwest of the Hidaka Mountains. However, it is diffiult to

8 Imaging of three-dimensional small-sale heterogeneities 1005 A A' B B' C C' D D' E E' F F' relative sattering oeffiients Figure 7. Same as Fig. 6 exept for vertial ross-setions. disuss this feature beause of the lak of the other geophysial and geologial information on the physial properties in this area. As depth inreases, relative sattering oeffiients beome larger in all frequeny ranges, probably as a result of the poor resolution there (Fig. 7) and the overestimated effet of Q 1 ( f ). Note that we used average Q 1 ( f ) for the orretion of the overall propagation effet in our model spae, as estimated by Taira & Yomogida (2003). Sattering oeffiient therefore has large error if Q 1 has signifiant and systemati variations in depth and lateral diretions and the orresponding ray path is very long. The large relative sattering oeffiients in area 3 may be artefats beause of the overestimated effet of Q 1 ( f ) and depth (or lateral) dependene in oda Q, disussed above. Although it is extremely diffiult to orret detail variations of Q 1 ( f ), we are urrently developing a method to remove the first-order ompli of this effet in atual reords as the next step of the present study. 5 CONCLUSIONS We investigated the 3-D distribution of oda satterers in the Hidaka region from spatial and temporal variations of oda spetra reorded by adense seismi array. We analysed three-omponent seismograms in a frequeny range from 1 to 32 Hz. After the orretion of soure, station and over all propagation effets, oda levels were signifiantly varied, strongly suggesting non-uniform distribution of heterogeneities in this region. In order to pinpoint the loations of heterogeneities, power spetra of oda waves as a funtion of lapse time were mapped into spatial variations of sattering oeffiient, frequeny N= normalized relative sattering oeffiients Figure 8. Histogram of normalized relative sattering oeffiients for the hekerboard test of Figs 6 and 7. under the following assumptions: spherial radiation from seismi soures, single and isotropi sattering, onstant S-wave veloity and only S-to-S wave onversion. We revealed the following remarkably non-uniform harateristis in the distribution of relative sattering oeffiient in the Hidaka region. (i) Sattering oeffiients at shallow depth (0 45 km) are large in the southwest of the Hidaka Mountains at both 2 and 16 Hz, while any speifi pattern anomalies do not appear at 4 Hz. This area orresponds to an area of high miroearthquake seismiity, our result suggests several onentrations of many small heterogeneities or probably fratures. (ii) A lustering of satterers dipping to the north is loated in the two depth ranges, (area 1) and km (area 2), beneath the Hidaka Mountains. Areas 1 and 2 are omposed of

9 1006 T. Taira and K. Yomogida (a) 2 Hz (b) 4 Hz () 16 Hz Figure 9. Horizontal distributions of relative sattering oeffiient for three depth ranges, 0 15, and km, at (a) 2, (b) 4 and () 16 Hz. Areas of large relative sattering oeffiient are shown by solid ellipses. Dots indiate the hypoentres in eah depth range (modified after Katsumata et al. 2003). heterogeneities with a size of 0.08 and 0.32 km, respetively, from their dominant frequenies. In addition, suh zones of strong sattering appear to orrespond to heterogeneous zones with the upper and lower planes of the double seismi zone in the subduting Paifi Plate, respetively. There are several previous studies to interpret an area of strong sattering as a distinguished seismi refletor. Nishigami (1997) estimated the distribution of satterers around Mt Ontaka, an ative volano in Japan, by the reursive stohasti inversion analysis. He onluded the obtained image of strong satterers to be a kind of refletive struture. He also found that this image shared a ommon loation and dip with the seismi refletor estimated by the Normal Move-Out (NMO) orretion analysis (Inamori et al. 1992). Although we have adopted only the single isotropi model in this study, the above harateristis of the distribution of satterers are onsistent with the distribution of heterogeneities as anomalous features of oda amplifiation fator formerly estimated by Taira & Yomogida (2003). We an utilize our sattering images in eluidating deep small-sale heterogeneous strutures of the Hidaka region. This study employed several assumptions on the sattering proess, seismi soure radiation and veloity struture. Future studies inluding more omplex phenomena, suh as non-isotropi sattering and multiple sattering, will provide lear physial insight into these small-sale heterogeneities in this region. Additional kinds of data, suh as polarization and semblane, should also enhane the resolving power of the distribution of heterogeneities. ACKNOWLEDGMENTS The authors thank Dr Kei Katsumata at Hokkaido University for his help in proessing of seismi reords and providing us with

10 Imaging of three-dimensional small-sale heterogeneities 1007 (a) 2 Hz C C' D D' E E' area 1 area 3 area 2 (b) 4 Hz C C' D D' E E' () 16 Hz C C' D D' E E' relative sattering oeffiients Figure 10. Vertial distributions of relative sattering oeffiient along the profiles of C C, D D and E E in Fig. 6 at (a) 2, (b) 4 and () 16 Hz. Three areas of relative sattering oeffiients are shown by solid ellipses. Dots indiate the hypoentres in eah setion (modified after Katsumata et al. 2003). hypoentral parameters used in this paper. The authors also wish to thank Dr Kazunori Yoshizawa at Hokkaido University for onstrutive omments. Valuable omments by Dr John A. Goff at the Institute for Geophysis, University of Texas, an anonymous reviewer and the editor-in-harge (Dr M. Sambridge) are greatly appreiated. The authors are grateful to the Researh Group of Hidaka Collision Zone for their permission for us to use seismi waveform data and to the members of its analysing ommittee for pre-proessing the data. The orresponding ervation was onduted by Hokkaido University, Tohoku University, the Earthquake Researh Institute, University of Tokyo, Nagoya University, Disaster Prevention Researh Institute Kyoto University and Kyushu University, as a part of the new Program of the Study and Observation for Earthquake Predition. A software pakage, Generi Mapping Tools (GMT), was used to plot the figures (Wessel & Smith 1995). The present study was partially supported by the Earthquake Researh Institute Cooperative Researh Program (2000-B-07 and 2001-B-02). REFERENCES Akaike, H., Fitting autoregressive models for predition, Ann. Inst. Statist. Math., 21,

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