Spatial variations in the frequency-magnitude distribution of earthquakes in the southwestern Okinawa Trough

The relations between the frequency of occurrence and the magnitude of earthquakes are established in the southern Okinawa Trough for 2823 relocated earthquakes recorded during a passive ocean bottom seismometer experiment. Three high b-values areas are identified: (1) for an area offshore of the Ilan Plain, south of the andesitic Kueishantao Island from a depth of 50 km to the surface, thereby confirming the subduction component of the island andesites; (2) for a body lying along the 123.3◦E meridian at depths ranging from 0 to 50 km that may reflect the high temperature inflow rising up from a slab tear; (3) for a third cylindrical body about 15 km in diameter beneath the Cross Backarc Volcanic Trail, at depths ranging from 0 to 15 km. This anomaly might be related to the presence of a magma chamber at the base of the crust already evidenced by tomographic and geochemical results. The high b-values are generally linked to magmatic and geothermal activities, although most of the seismicity is linked to normal faulting processes in the southern Okinawa Trough.


Introduction
Located east of Taiwan, the southern Okinawa Trough (OT) is a portion of a young continental backarc basin that is at the end of the rifting stage (Sibuet et al., 1998) (Fig. 1(a)). Normal faulting is a common tensional process evidenced by seismic reflection data (Sibuet et al., 1998) and focal mechanism analyses (Fournier et al., 2001;Kao and Jian, 2001;Kubo and Fukuyama, 2003). In the southern OT, the volcanic front of the Ryukyu subduction zone is located within the backarc basin (Sibuet et al., 1998;Wang et al., 2000) (Fig. 1(a)). The most obvious cluster of seamounts, which consists of more than 70 volcanoes, is located in the vicinity of 24.8 • N; 122.8 • E and is named the "Crossbackarc volcanic trail" (CBVT) (Sibuet et al., 1998;upperleft inset in Fig. 1(a)). Based on the relocated hypocenter locations (Engdahl et al., 1998), magnetic anomaly distributions (Hsu et al., 2001) and depths of the magnetic basement (Lin et al., 2004a), a slab tear has been identified along the 123.3 • E meridian ( Fig. 1(a)). However, despite the microseismicity in the southern Okinawa Trough being very high, the surrounding land stations are too distant to record this stab tear. Consequently, with the objective of gaining a better understanding of the nature and role of tectonic features in this region, we conducted a passive seismic ocean bottom seismometer (OBS) experiment in November 2003. Ishimoto and Ida (1939) and Gutenberg and Richter (1944) introduced the relation between the frequency of oc-Copyright c The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. currence and the magnitude of earthquakes. The commonly used form is log 10 N = a − b M, where N is the cumulative number of earthquakes with a magnitude equal or larger than M, and a and b are constants. The parameter 'b' is the slope of the best fitting line between the observed number of earthquakes at a given magnitude and the magnitude (e.g. Fig. 2(d)). Since its first formulation, many studies of the frequency-magnitude distribution (FMD) as a function of time and space have been performed. For example, volcanic areas are commonly associated with high b-values (Warren and Latham, 1970), and underlying magma chambers are also characterized by anomalously high b-values (Wiemer and Wyss, 1997;Wiemer et al., 1998;Murru et al., 1999). The b-value has been shown to be inversely proportional to stress in laboratory (Scholz, 1968) and in mines experiments (Urbancic et al., 1992). Stress and indirectly confining pressure are parameters which strongly control the type of faults and b-values.
For example, normal faulting events (tensional stress) have systematically the highest b-values and thrust events (compressional stress) have systematically the lowest (Frohlich and Davis, 1993;Wiemer and Wyss, 1997;Schorlemmer et al., 2005). The presence of melt and normal faults that induce the distribution of high b-values are both present in the southern OT (e.g. Sibuet et al., 1998;Shinjo, 2003a, b). We have calculated the spatial distribution of b-values in order to gain an understanding of how these may account for this complex tectonic regime and compare these results with a V p/V s ratio and P-and S-velocity tomographic inversion performed with the same earthquakes (Lin et al., 2006a, accepted).  Sibuet and Hsu (2004). Upper-left corner inset: detailed bathymetric map (isobathic spacing, 100 m) of the cross-backarc volcanic trail (CBVT) (Sibuet et al., 1998)

Data and Method
Fifteen OBSs were deployed in the southern OT from November 19 to December 1, 2003. More than 3300 microearthquakes were recorded during this 12-days passive seismic experiment ( Fig. 1(b); Lin et al., 2006b, revised). All P-and S-arrival times were picked by hand. As the amplitudes of the seismograms recorded by the OBS instruments were not calibrated, the magnitudes of the earth-quakes were evaluated using the duration of seismic waves (Md) of other measurements (e.g. M L , Md, Ms and Mw). The duration of each event was determined manually. The magnitudes of most of the earthquakes (Md) range from 1 to 2, although the whole range consists of magnitudes from 0.9 to 4 ( Fig. 1(b)). This range in magnitude, dominated by small-magnitude earthquakes, provides an appropriate dataset to calculate b-values because the use of smallmagnitude earthquakes increases the precision of b-values estimation (Wiemer and Wyss, 2002). In order to obtain accurately locate the hypocenters, all of the earthquakes were relocated using the SIMUL2000 program (Thurber and Eberhart-Phillips, 1999). The layered model from the best VELEST solution was used (Kissling et al., 1994) as the starting one-dimensional (1-D) model, and a minimal grid spacing of 15 km is used for the SIMUL2000 program. Following the tomographic inversion, a detailed 3-D velocity model was obtained (Lin et al., 2006a, accepted), and all of the earthquakes were relocated using this 3-D velocity model. Only hypocenters determined at an accuracy lower than 10 km in the three directions were chosen for the FMD calculations. In total, 2823 earthquakes were relocated. After relocation, the average rms residual decreases from 0.242 to 0.151 s, showing a better determination of hypocenters. Wiemer and Wyss (2002) have demonstrated that using earthquakes of different magnitudes (e.g. M L , Md, Ms and Mw) may induce systematic errors. To avoid this problem, we only used the Md magnitude determined from the OBS stations, even if the available magnitude of the same earthquakes was calculated separately from the Taiwanese and Japanese networks.
Several areas with a V p/V s higher than 1.78 are can be determined based on the tomographic results (Lin et al., 2006a, accepted). Since the presence of melt or H 2 Oenriched material is characterized by low V p, low V s and high V p/V s (Watanabe, 1993;Reyner et al., 2006), we have highlighted such areas on Fig. 2(b) in white dashed contours. These high V p/V s anomalies rise obliquely from a depth of 50 km through the slab tear in three directions (Fig. 3): a first branch rises northwesterly and feeds the CBVT; a second branch rises in a northerly direction above the slab tear to a depth of 15 km; a third branch rises to the north of Irimote Island (24.5 • N; 123.9 • E). The resolution estimates for the tomographic inversion are relatively high (>0.6) in the central part of the southern OT at a shallow depth (5-km). For the deeper part, the resolution decreases, but it is still acceptable beneath the Ryukyu Arc (>0.5).
Zmap software (Wiemer, 2001;Wiemer andWyss, 1994, 1997) is used to estimate b-values at the nodal points of a 2-D grid using the 50 nearest earthquakes. The shape of the sampling volume is a vertical cylinder, and the grid spacing is 0.05 • . The height of each sampling cylinder is 5 km, and the center of the cylinder corresponds to the depth of each estimated layer. The high-density hypocenter distribution allows us to use a grid spacing as small as 5 km in order to increase the spatial resolution. The resolution map corresponds to the radii of each circle of sampling (Fig. 2(c)): the larger the radius, the lower the chance of analyzing small sub-volumes. The magnitude of completeness (Mc) is a factor used to calculate the b-and a-values, which should  (Aki, 1965;Bender, 1983) and the weighted least squares methods. In this case, the results are independent of the method (Bender, 1983).

Results and Discussion
The 3-D mapping of b-values in the southern OT shows that within the crust the background b-value is approximately 1.1, with three embedded volumes characterized by b>2.0 ( Fig. 2(b)). One of these major anomalies is located offshore the Ilan Plain, south of Kueishantao Island, at depths ranging from 0 to 50 km. The feeding process of the volcanic Kueishantao Island with melt and/or H 2 Oenriched material rising from the Ryukyu slab edge has already been established from a previous tomographic study using earthquakes recorded by the Taiwanese network (Lin et al., 2004b). We suggest that the high b-values correspond to the feeding channels imaged by tomographic results, Fig. 3. Geophysical distribution of areas with V p/V s values higher than 1.78 and low V p and low V s values, extracted from slices of Figs. 6-8 and ranging from 10 km (light gray) to 50 km (dark gray) (Lin et al., 2006a, accepted). Dashed lines are the isobaths of the Wadati-Benioff zone (adapted from Font et al. (1999)). Light-colored arrows show the upward propagation trends. V are the locations of detected hot vents (Lee, 2005). The black square indicates the cross-backarc volcanic trail (CBVT).
which rises up from a depth of 50 km to the surface in the direction of Kueishantao Island (Lin et al., 2004b). However, the ∼40 km spatial resolution in this area (Fig. 2(c)) does not allow us to discuss this correspondence in more detail. The most prominent anomaly in b-values corresponds to a volume of relatively high b-values located above the N-S trending slab tear in the vicinity of the 123.3 • E meridian ( Fig. 2(b)). This anomaly in high b-values (>2.3) is imaged at depths ranging from 0 to 50 km ( Fig. 2(b)). At a depth of 50 km, part of this anomaly deviates eastward of the slab tear beneath the northern slope of OT. Glasby and Notsu (2003) reported the presence of a high heat potential along this N-S trending slab tear area. As mentioned previously, magmas and hot fluids in geothermal systems may induce high b-values (Wiemer and Wyss, 2002). We suggest that the high temperature of the inflowing mantle through the slab tear and the wedge may provide a high geothermal potential in this area. The anomalous heat originating from the slab tear may be transmitted to the overlying crust. In addition, such a heat transfer may also follow a magma conduit. This point will be discussed in the following section.
A vertical cylindrical body with high b-values, about 15 km in diameter, occurs at a shallow depth (0 15 km) beneath the CBVT (light-gray square, Fig. 2(a), (b)). The FMDs inside (red triangles) and outside (green squares) of this vertical cylinder show a large difference in b-values (∼2 and ∼1, respectively; see slices from 5 to 15 km in Fig. 2(d)), emphasizing the fact that b-values beneath volcanoes are generally smaller than previously thought and are distributed in pockets of anomalously high b-values embedded in a crust characterized by a mean b-value of ∼1 (e.g. Wiemer and Wyss, 2002;Power et al., 1998;Murru et al., 1999). According to the tomographic results, the low V p, low V s and and high V p/V s anomalies at depths between 10 and 15 km suggest the existence of a magma chamber located beneath the CBVT area (Figs. 2(a) and 3) (Lin et al., 2006a, accepted). Earthquakes are not generated within the magma chambers but around it. We thus interpreted the envelope of high b-values anomalies beneath the CBVT as the contours of the magma chambers. The mapped anomaly of b-values actually does include both the surrounding parts of magma chambers and the magma conduits to the surface (Fig. 3); however, it is located in the upper crust (0-10 km) and may also be linked to the presence of geothermal systems, as evidenced by tremor sources located in this area (Chang et al., 2006, submitted) and by the distribution of hot vents in the southern OT (Lee, 2005;Chang et al., 2006, submitted).
High V p/V s and low V p, V s anomalies have been identified in the southern OT (dashed contours in Fig. 2(a)-(c); Lin et al., 2006a, accepted) and linked to the presence of melt and/or fluid-enriched material. At depths of less than 20 km, the distribution of the high b-values corresponds to the volumes surrounding the high V p/V s and low V p, V s anomalies. At larger depths (>30 km), the correlation between high b-values and high V p/V s anomaly disappears. As mentioned in several former studies, stress is an important factor that affects the distribution of the b-values (Scholz, 1968;Wyss, 1973;Shaw, 1995) and may explain this discrepancy. Based on tomographic images, three subchannels corresponding to melt and/or H 2 O-enriched material rising from the slab tear have been identified (Lin et al., 2006a, accepted). Two of the three conduits reach the upper crust of the southern OT (Fig. 3): one rises towards the northwest in the direction of the CVBT to a depth of 10 km where a magma chamber has been suggested from geochemical analyses of dredged rocks (Shinjo et al., 2003a, b); the second rises to the north along the slab tear in the direction of the northern OT slope, to a depth of 15 km. The anomalies of high b-values mapped in our study at a shallow depth (<30 km) are in good agreement with the position of the two chambers. Hence, this comparison gives more credit to the fact that magmatic and/or geothermal activities might be the main factors controlling the distributions of high b-values. In addition, most of the anomalies of high b-values anomalies are not systematically located in the axial part of the southern OT, where numerous E-W trending normal faults account for the present-day extension in the OT (Sibuet et al., 1998). High b-values underline features of volcanic or geothermal origin rather than the presence of numerous normal faults.

Conclusion
The distribution of small-magnitude earthquakes has been established from a passive seismic experiment in the southwestern OT. b-values were computed by using 2823 relocated earthquakes selected from this earthquakes dataset. Three volumes of high b-values were identified: (1) a first body characterized by b∼2 is located offshore of the Ilan Plain, south of Kueishantao Island, and rises from the edge of the slab at a depth of 50 km to the surface, thereby confirming that the andesitic nature of rocks presents a subduction component (Chen et al., 1995); (2) a second anomaly lies along the 123.3 • E meridian, at depths ranging from 0 to 50 km, above the Ryukyu slab tear, suggesting that high b-values are related to this feature; High temperature inflow passing through the slab tear might affect the overlying mantle and crust, and the heat anomaly might accelerate the generation of hot fluid in the geothermal system, resulting in high b-values; (3) a third body with a cylinder shape of about 15 km in diameter is identified beneath the CBVT, at depths ranging from 0 to 15 km; This anomaly is related to a magma chamber located at the base of the crust (10-15 km), as already suggested both by the tomographic results and the geochemical interpretation of dredged rocks. Though the seismicity in the southern OT is mainly controlled by normal faulting, high b-values are linked to volcanic and geothermal activities.