Focal mechanisms of deep low-frequency earthquakes in Eastern Shimane in Western Japan

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH: SOLID EARTH, VOL. 119, 64 77, doi: /201jb010681, 2014 Focal mechanisms of deep low-frequency earthquakes in Eastern Shimane in Western Japan Naofumi Aso 1 and Satoshi Ide 1 Received 9 September 201; revised 20 November 201; accepted 21 November 201; published 7 January [1] Deep low-frequency earthquakes (LFEs) are small earthquakes (M < 2) that occur at depths of ~10 45 km with seismic wave radiation mainly in the frequency range of 2 8Hz. LFEs in western Japan are categorized into tectonic LFEs in the Nankai subduction zone, volcanic LFEs beneath active volcanoes, and semi-volcanic LFEs that occur far from active volcanoes but are otherwise similar to volcanic LFEs. While tectonic LFEs are considered to reflect shear slip on a plate boundary, the mechanisms of volcanic and semi-volcanic LFEs remain unclear. We have determined the mechanisms of 8 semi-volcanic LFEs in eastern Shimane, which is the site of the most frequent semi-volcanic LFE activity in Japan. For each event, velocity seismograms at five stations were inverted into a focal mechanism and moment rate function by a combined grid search and linear inversion analysis. Synthetic waveforms were calculated for a one-dimensional structure and the local site amplification effects were corrected using body waves from deep earthquakes. The estimated moment rate function was found to often oscillate between positive and negative values, which are unlike those of regular earthquakes. The focal mechanisms for many LFEs are dominated by a compensated linear vector dipole with symmetry axes parallel to the lineation formed by the hypocenter distribution and the direction of the minimum principal axis of regional stress. Citation: Aso, N., and S. Ide (2014), Focal mechanisms of deep low-frequency earthquakes in Eastern Shimane in Western Japan, J. Geophys. Res. Solid Earth, 119, 64 77, doi: /201jb Introduction [2] At convergent margins like those in the Japan region, various earthquakes occur, including regular interplate, intraslab, and shallow inland and volcanic earthquakes. In addition to these relatively well understood events, another category of earthquakes is also common: small earthquakes (M < 2) occurring at depths of ~10 45 km that radiate lowfrequency seismic waves (mainly 2 8 Hz). These events are referred to as deep low-frequency earthquakes (LFEs) regardless of their mechanism. The Japan Meteorological Agency (JMA) has been routinely identifying LFEs in Japan since 2002, and similar events have been detected worldwide [e.g., Obara, 2002; Rogers and Dragert, 200; Brown et al., 2009; Shelly and Hardebeck, 2010]. [] Aso et al. [201] categorized LFEs in Japan from the JMA catalog into three types: tectonic LFEs on a plate boundary; volcanic LFEs at Moho depths beneath active volcanoes; and LFEs at Moho depths distant from active volcanoes (Figure 1). Tectonic LFEs and tectonic tremors that include many tectonic LFEs have been well studied in 1 Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Tokyo, Japan. Corresponding author: N. Aso, Department of Earth and Planetary Science, Graduate School of Science, University of Tokyo, Hongo 7--1, Bunkyo-ku, Tokyo 11 00, Japan. (aso@eps.s.u-tokyo.ac.jp) 201. American Geophysical Union. All Rights Reserved /14/ /201JB Japan [e.g., Obara, 2002; Shelly et al., 2006, 2007; Ide et al., 2007] and elsewhere [e.g., Rogers and Dragert, 200; Brown et al., 2009; Shelly and Hardebeck, 2010; Ide, 2012]. Volcanic LFEs have also been recognized worldwide [e.g., Aki and Koyanagi, 1981; Ukawa and Ohtake, 1987]. By comparing seismic waveforms, magnitude frequency statistics, seismic sensitivity to tides, and hypocenter distributions, Aso et al. [2011, 201] found that the last type of LFEs is similar to volcanic LFEs and is clearly distinct from tectonic LFEs. These LFEs are termed semi-volcanic LFEs. Investigation of semi-volcanic LFEs, as well as volcanic and tectonic LFEs, is important for understanding the physical conditions that produce LFEs. [4] Volcanic LFEs have been identified to occur beneath many active volcanoes worldwide, including in Hawaii [Aki and Koyanagi, 1981] and Japan [Ukawa and Ohtake, 1987]. Most of the waveforms of volcanic LFEs have monochromatic or harmonic characteristics. Given that the rheological properties of rocks are expected to be within the ductile regime at depths of ~0 km [Shimamoto, 1986], rapid movement of magma or crustal fluids may be related to these earthquakes [e.g., Aki and Koyanagi, 1981; Hasegawa et al., 1991], while the presence of crustal fluids is considered to be related to tectonic LFEs [e.g., Shelly et al., 2006]. [5] Determination of the focal mechanisms of LFEs is important for constraining the physical mechanisms of their origins. Whilst tectonic LFEs are thought to result from shear slip on low-angle thrust faults [Ide et al., 2007; Shelly et al., 2007], the mechanisms of volcanic and semi-volcanic LFEs have not yet been firmly established. Consequently, the 64

2 Figure 1. Location and distribution of semi-volcanic LFEs in eastern Shimane. (a) Map of western Japan. Blue, red, and green dots indicate tectonic, volcanic, and semi-volcanic LFEs, respectively [Aso et al., 201]. All the LFEs detected by JMA from June 2000 to December 2011 are plotted. Closed and open triangles show active and Quaternary volcanoes, respectively [Committee for Catalog of Quaternary Volcanoes in Japan, 1999]. Black rectangle shows the area of Figure 1b. (b) Eastern Shimane in map view and in latitudinal and longitudinal cross sections. Green dots indicate semi-volcanic LFEs detected by JMA from June 2000 to December 2011, and orange dots are analyzed events. Open triangles show Quaternary volcanoes [Committee for Catalog of Quaternary Volcanoes in Japan, 1999]. Crosses show Hi-net stations used in this study. Black line marks the estimated source area extent of the 2000 western Tottori earthquake [Fukuyama et al., 200] and NIED Seismic Moment Tensor solution is also shown. Black rectangle shows the area of Figure 1c. (c) Detailed distribution of the 8 semi-volcanic LFEs in eastern Shimane analyzed in this study, in map view and latitudinal and longitudinal cross sections. Colored dots and lines represent the relocated hypocenters and relocation errors with the color representing magnitude. Gray ellipses mark the original locations determined by JMA with the ellipse centers and radii representing the hypocenters and their errors, respectively. The green line is the best-fit line through the hypocenter distribution, which plunges at 26.6 toward

3 Table 1. Event List a Event ID Year Month Day Hour Min Sec M JMA VR a The 8 analyzed events are listed with their origin times, JMA magnitudes (M JMA ), and the variance reduction (VR) value of the result. ratios for a large number of events within a small cluster, using a waveform inversion method to determine the focal mechanisms. To do this, we studied 8 semi-volcanic LFEs that occurred in eastern Shimane of western Japan, which is the site of the most frequent semi-volcanic LFE activity in Japan [Aso regional tectonic and volcanic significance of volcanic LFEs remains poorly understood [Chouet, 200; McNutt, 2005]. Previous studies have estimated the focal mechanisms of volcanic or semi-volcanic LFEs in some regions using polarizations, amplitude ratios, or waveforms [Ukawa and Ohtake, 1987; Nishidomi and Takeo, 1996; Okada and Hasegawa, 2000; Ohmi and Obara, 2002; Nakamichi et al., 200]. These studies have obtained a wide range of focal mechanisms, not only in terms of the faulting mechanism but also in terms of the non double-couple component. It is presently unclear whether this range of mechanisms is actually real or if it corresponds to an artifact of data processing or the small number of analyzed events. Intuitively, it might be expected that earthquakes within a small cluster in a small region have similar mechanisms dictated by the local tectonic conditions. Our study aims to determine if a common mechanism characterizes the LFEs that occur in a small region. [6] The major difficulty in estimating LFE focal mechanisms is the low signal-to-noise (S/N) ratios of the seismic data due to the small magnitude of events and the correspondingly small amplitude of seismic waves, which results in large errors. Few previous studies have analyzed whole waveforms. Herein, we analyzed seismic signals with relatively high S/N Figure 2. Representative waveforms of semi-volcanic LFE in eastern Shimane. Raw velocity waveforms of event #1 are shown versus the time elapsed from the event origin. Vertical blue lines show P and S wave arrivals, and the gray shaded area shows the windows used for inversion. Some signals from the following event #2 that occurred ~8 s after event #1 are evident. 66

4 Table 2. Seismic Structure Used for Waveform Inversion in Eastern Shimane a Layer z (km) V P (km/s) V S (km/s) ρ (kg/m ) Q P Q S a We used a horizontally layered structure. P wave velocity (V P ), S wave velocity (V S ), density (ρ), P wave quality factor (Q P ), and S wave quality factor (Q S ) are listed. et al., 201]. This region is distant from active volcanoes, and the lack of noise from active volcanoes is an advantage in analyzing semi-volcanic LFEs rather than volcanic LFEs. The anthropogenic noise is also low in this region, and the S/N ratio of the record is relatively high. Ohmi and Obara [2002] obtained a single-force mechanism for one of these LFEs, but analysis of multiple events is necessary to robustly characterize the mechanism(s). The large number of events in the eastern Shimane area enables us to statistically analyze the distribution of solutions. Aso et al. [201] concluded that LFEs in this region are distributed in a single linear cluster with a length of 1.5 km, using the network cross-correlation (NCC) relocation method developed by Ohta and Ide [2008, 2011]. We also compare the characteristic direction of the moment tensor with the direction of the single-force mechanism determined by Ohmi and Obara [2002], and with the direction formed by the hypocenter distribution. [7] Beneath the eastern Shimane area of Japan, the Philippine Sea plate is subducting beneath the Eurasian plate. Epicenters of the LFEs are located 10 km from the 20 km long fault plane of the 2000 western Tottori earthquake (M w 6.6) and may be physically related to this larger event [Ohmi et al., 2004]. This site is also directly beneath Yokota volcano, which is a Quaternary volcanic cluster. However, there is no active volcano within 50 km of the earthquake epicenters. Resolving whether the regional tectonics, large inland earthquake, and/ or Quaternary volcanism have a relationship with the LFE activity would provide key insights into the physical conditions responsible for the LFEs. As such, reliable focal mechanisms for LFEs in this area might provide important insights into the seismology, volcanology, and geology of the region. 2. Data and Theoretical Waveforms [8] A total of 121 events was detected in eastern Shimane by the JMA from 2002 to We selected 8 of these events larger than M JMA of 1.2 (local magnitude determined by JMA; Table 1). We used three-component velocity seismograms from five stations of Hi-net, which was deployed by the National Research Institute for Earth Science and Disaster Prevention (NIED), Japan (Figure 1b). The original data were resampled to 20 samples per second after anti-alias filtering. No additional filtering was applied. For each seismogram, we extracted a 1.5 s time window beginning 0.2 s before the arrival of either the P wave in the vertical component or the S wave in the horizontal component (Figure 2). Either P or S arrivals at all five stations were determined by the JMA for all selected events, but for the present analysis, we require both P and S arrivals. Arrival times were manually picked, so that systematic errors on the hypocenter location or velocity structure did not strongly affect our results. [9] We assumed a horizontally layered structure (Table 2) for the calculation of theoretical waveforms. The velocity structure is identical to that used by the local observatory [Ohmi et al., 2001], apart from a thin high-attenuation layer at the top, which was introduced to provide consistency with logging data at the Hi-net stations. The density and quality factors of each layer are similar to the values used in previous studies [e.g., Pulido and Dalguer, 2009]. Other velocity models have been proposed or used previously, but we obtained similar results even when using these different structure models, which suggest that the results are not sensitive to the assumed structure. The theoretical Green function was calculated using the method developed by Takeo [1985], which is a combination of the reflection-transmission matrix [Kennet and Kerry, 1979] and the discrete wave number integration method [Bouchon, 1981] with correction for inelastic attenuation using a complex number of velocity. The wave number domain used in our study is k <. km 1, which encompasses the frequency range of LFEs. [10] Previous studies of volcanic earthquakes have found it difficult to calculate the Green function because of the strong effect of attenuation or heterogeneity in volcanic regions. Although our study region is distant from active volcanoes and heterogeneity effects are expected to be relatively small, near-surface heterogeneity may be large and control site amplification. Therefore, we modified the amplitude of the Figure. Deep events used for estimating the relative quality factor. Blue dots represent the 84 deep events used to calculate the relative quality factor. Red dots are the semivolcanic LFEs in eastern Shimane analyzed in this study; the black crosses are stations. The black rectangle indicates the area of Figure 1b. 67

5 Table. Attenuation Factor Ratios a ASO AND IDE: MECHANISMS OF LFES IN EASTERN SHIMANE Station U (P Wave) E (S Wave) N (S Wave) HKTH 0.51 ( ) 0.60 ( ) 0.69 ( ) HINH NITH 0.6 ( ) 0.71 ( ) 0.72 ( ) MZKH 0.59 ( ) 0.55 ( ) 0.54 ( ) SGOH 0.92 ( ) 0.92 ( ) 0.86 ( ) a Amplitude ratios between stations were calculated for deep earthquakes and are treated as a differential attenuation factor. Median values are shown, along with 25% and 75% quartile values. Green function that was calculated for the one-dimensional structure. Near the surface, the raypath from each LFE to each station is similar to a raypath from a deep earthquake in the subducting Pacific plate beneath the Eurasian and Philippine Sea plates, given that both raypaths are almost vertical. Assuming that site amplification near the surface is common to both LFEs and deep intraslab earthquakes, we used the relative amplitude differences in the seismograms of deep earthquakes to correct for relative site amplification amongst stations. To account for the differences in dominant frequencies between LFEs and deep earthquakes, we focused on site amplification at the characteristic frequency of LFE waves and approximated it as a constant. For this purpose, we measured the maximum amplitude of the P wave for the vertical component and the S wave for the horizontal component, after band-pass filtering between 2 and 8 Hz, for 84 deep earthquakes observed at the five stations (Figure ). We ignored the radiation pattern of these earthquakes, as the stations are located at almost the same points on a focal sphere. Amplitude ratios were calculated relative to the HINH station for each event, and the median for all events was taken as the constant for site amplification (Table ). We used this relative quality factor as a multiplier applied to a synthetic waveform before the inversion, which reduces potential bias in the solutions.. Methods [11] We consider that a LFE has a point source due to its small magnitude and deep location. Given that the waveforms we analyzed are short, we assumed that the mechanism type and principal axes of the moment tensor are temporally invariant and that the amplitude changes as a function of source time. We allow the moment tensor to be of any mechanism type, including double-couple, compensated linear vector dipole (CLVD), and isotropic deformation. Solving for the mechanism type and principal axes of the moment tensor and source time function simultaneously is a nonlinear problem. However, by assuming the moment tensor, the source time function can be estimated by a linear inversion. To obtain the best combination of the moment tensor and time function, we conducted a linear inversion for the time function using each assumed moment tensor and a grid search for the moment tensor. [12] The moment tensor (M ij ) is a symmetry qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tensor. With a constraint of a unit scalar moment ij M 2 ij =2 ¼ 1½NmŠ, five parameters are estimated. Assuming the five parameters of the moment tensor, the observation equation used in this study is as follows: Figure 4. Comparison of observed and synthetic waveforms. Three-component waveforms around P and S wave arrival times at five stations for event #1. Each waveform is 1.5 s long and starts 0.2 s before the arrival time. Black and red lines indicate the observed and synthetic waveforms, respectively. The amplitude is normalized for each P and S wave. We used the windows around P wave arrivals for vertical components and around S wave arrivals for horizontal components for the inversion. The time windows not used are shaded. 68

6 0 u 1 u i 1 0 ¼ C B A 1 A i 10 CB A@ m 1 m j 1 0 þ C B e 1 e i 1 ; (1) C A u N cmp A N cmp m N bf e N cmp Figure 5. Distribution of variance reduction values. Histogram of variance reduction (VR) values from analyses of real data (red) and noise data (blue). The vertical axis shows the event number of each bin normalized by the total number. A dashed line shows the reliability thresholds with VR = 22% with a confidence interval of 90%, which was obtained using the distribution from noise analysis. where u i is the displacement seismogram of the ith component, e i is the error vector, m j is the released scalar moment for the jth temporal basis function, and the matrix A i is the response of the ith component for sets of released scalar moment for each basis function. N bf is the number of basis functions. When the basis functions are distributed by steps of Δt, then we have 0 1 g i ð0þ g i ð ΔtÞ g i N bf 1 Δt B C A i g i ðδtþ g i ð Δt þ δtþ g i N bf 1 Δt þ δt A; (2) where g i ðþis t the response of the ith component at time t for a basis function and δt is the sampling rate. The response for the basis function g i ðþ t is related to the displacement due to an impulsive unit seismic moment (G i (t)) as follows: Figure 6. Representative results for semi-volcanic LFEs in eastern Shimane. Moment tensor solution for event #1 shown as beach ball plots and a scalar moment rate function. The moment tensor at each time step is shown separately as isotropic and deviatoric components, and the rightmost beach ball plots indicate the cumulative moment tensor, which was obtained by summing all the moment tensors at every time step. The size of each beach ball plot corresponds to the moment magnitude of each isotropic or deviatoric component. The moment magnitude of the full moment tensor is also given. Station distribution is also shown on the lower hemisphere. In the bottom panel, the red line is the moment rate normalized by the maximum value and the blue lines are its estimated error. 69

7 Figure 7. Temporal distribution of semi-volcanic LFE focal mechanisms in eastern Shimane. Moment tensors for all 8 events plotted on a time axis. Each moment tensor is shown separately as beach ball plots of the isotropic and deviatoric components. The size of each beach ball plot corresponds to the moment magnitude of each isotropic or deviatoric component, and the color represents the VR value of each event. Solutions with VR > 22% are marked with thick outlines. Black stars on the time axis represent the total activity of LFEs in eastern Shimane as determined by the JMA. The event identification is also annotated on the figure. g ðþ¼ṁt i t ðþg iðþ; t () where Mt ðþ is the normalized moment rate function of the basis function as Ṁ ðþdt t ¼ 1 ½ Nm Š. [1] For the observation equation (u = Am + e), we estimated the model parameter vector (m) to minimize the error e 2 = u Am 2. To quantify how well the synthetic waveforms represent the observed waveforms, we defined the variance reduction (VR) value as follows: VR ¼ juj2 ju Amj 2 juj 2 : (4) Generally, a large VR value is considered to be reliable, but this value also depends on the statistical nature of the data and background noise; we provide more information about the VR values in the following section. [14] In this study, the source time function is a 1 s first-order spline curve at intervals of 0.1 s, and each of the nine basis functions is a single triangle wave with a width of 0.2 s aligned every 0.1 s (Δt = 0.1 s; N bf = 9). For each event, we estimated 14 parameters, including 5 for the moment tensor and 9 for the time function. Since the moment tensor has only 5 degrees of freedom (for a fixed magnitude), a grid search is likely, in most cases, to find a global minimum. [15] Given that monochromatic waveforms (Figure 2) are potentially caused by an oscillating source, the assumption of unidirectional slip, as in the analysis of regular earthquakes, is not appropriate here and was not adopted as a constraint for the inversion. 4. Results 4.1. How Can We Treat Low-VR Results? [16] The observed waveforms are well matched by the synthetic waveforms in most of the windows used for the inversion (Figure 4). Moreover, even in the windows not used for the inversion, the synthetic waveforms are consistent with the observed waveforms. For the representative event #1 that occurred at 0:40:6 on 19 July 2002 (JST), the VR value is 44.6% (Table 1). [17] Although the VR values for these events are not particularly high, the reliability of the inversions should not only be assessed from VR values, as these are highly dependent on various properties such as the S/N ratio, frequency component, filtering, time window length, sampling rate, and assumed basis functions. Even though the VR values cannot be high for low-s/n data, one would expect that the VR values from real data are higher than those from background noise. Therefore, the relative VR value of analyzed data to that of the noise is more important than the absolute VR value. In addition, when the results of many events have similar characteristics and are not recognizable from the results of analyzing noise, we can consider that the characteristics are from signal. These two aforementioned points highlight the importance of comparing results from real data with those from noise. [18] To determine the distribution of VR values and results for analyzing background noise, we analyzed waveforms that did not include any known events. We prepared 120 sets of noise waveforms starting every minute from 00:00:00 on 1 August 2004 (JST) and applied the same procedure as that 70

8 Figure 8. Spatial distribution of semi-volcanic LFE focal mechanisms in eastern Shimane. Moment tensors for all 8 events shown in map view. Colored stars represent the location and each moment tensor is shown separately as beach ball plots of isotropic and deviatoric components, with their size corresponding to the moment magnitude of each isotropic or deviatoric component. The colors of the stars and beach ball plots represent the VR value. Solutions with VR > 22% are marked with thick outlines. The event identification is also annotated on the figure. described in the previous section. The analyses of noise data produced VR values up to 7%, and relatively high VR values were produced when tidal noise happened to be in the same phase for many windows. In total, 109 of 120 imaginary events estimated from the noise waveforms have VR values <22%, indicating that VR values >22% are reliable with a confidence interval of 90%, when neglecting the small sample size (Figure 5) Source Time Functions and Magnitudes [19] The source time functions of semi-volcanic LFEs determined from our inversions oscillate between positive and negative values with a dominant frequency of ~2 Hz (Figure 6), which is different from ordinary earthquakes. This characteristic is not found when analyzing noise, and we regard this as a real source feature. Semi-volcanic LFEs in eastern Shimane appear to have a cyclic source, with the forward and reversal mechanisms mutually occurring at frequencies of ~2 Hz. This oscillation implies that some resonance is occurring in the source region. [20] Given that the source time function is oscillating, the cumulative moment, which is a scalar moment of the moment tensor obtained by summing all the moment tensors at every time step, tends to be small. Therefore, we focus on the released moment at the point when the highest moment was released. The corresponding moment magnitude can be used 71

9 Figure 9. Source-type diagram of semi-volcanic LFE focal mechanisms in eastern Shimane. (a) Source type of semi-volcanic LFEs in eastern Shimane. Colors represent VR values. Solutions with VR > 22% are marked with thick outlines. The solid green lines are the area where double-couple (DC), compensated linear vector dipole (CLVD), and isotropic deformation (ISO) dominate. We refer to the source type as being dominated by one component when that component is larger than the other two combined. (b) Results of analyzing 120 imaginary events within the background noise record shown in the same manner as Figure 9a. as an index of the event size, although these events are not slip events. We focus on the orientation of the moment tensor in the following subsections. 4.. Mechanisms [21] We now investigate the LFE source mechanisms, which are the mechanism type (double-couple, CLVD, and isotropic deformation) and principal axes, using the eigenvalues and eigenvectors of the estimated moment tensor, respectively. We first discuss the basic features of the temporal and spatial variations of the moment tensor in section 4..1 and then statistically evaluate the type and principal axes in sections 4..2 and 4.., respectively Temporal and Spatial Variability of Mechanisms [22] Many events have a similar mechanism, with the CLVD directed north-northeast without any clear temporal or spatial variations (Figures 7 and 8). Therefore, we focus on the overall characteristics of the results of all events. 72

10 8 2 2ðλ 1 2λ 2 þ λ Þ λ 6 λ 7 λ 1 þ λ þ λ 2 þ λ 5 u >< λ ¼ 2 v 2ð λ 1 þ 2λ 2 λ Þ λ λ 1 þ λ 2 þ λ 5 λ 1 þ λ 0 >: λ 1 (5) Figure 10. Polar plot of semi-volcanic LFE focal mechanisms in eastern Shimane. (a) Directions of semi-volcanic LFEs in eastern Shimane plotted in the lower hemisphere. Colors represent VR values. Solutions with VR > 22% are marked with thick outlines. The blue star marks the direction of the hypocenter lineation. (b) Results of analyzing 120 imaginary events within background noise record shown in the same manner as Figure 10a. Given that the source time functions are oscillating, the CLVD polarity can be both positive and negative. The polarity of CLVD is defined by the polarity of the eigenvalue of the deviatoric moment tensor in the symmetry axis direction. The most common symmetry axis direction is north-northeast, which is parallel to the hypocenter distribution (Figure 8), as discussed further in section Mechanism Type [2] We calculated eigenvalues (λ 1 λ 2 λ ) of each moment tensor and plotted a point (u,v) on the source type diagram (Figure 9) developed by Hudson et al. [1989] defined as follows: [24] Figure 9a shows the distribution of points corresponding to all the obtained moment tensors (colors represent VR values) and the subregions dominated by double-couple (DC), CLVD, or isotropic (ISO) deformation. Any source type can be expressed as a combination of three components: DC, major CLVD ( CLVD or + CLVD for u 0oru 0, respectively), and major isotropic deformation ( ISO or + ISO for v 0orv 0, respectively). When one component is larger than the combination of the other two, we note that the source type is dominated by the largest component. [25] Despite the wide scatter in the moment tensors, the number of points in the CLVD-dominant region is larger than that in the DC-dominant region. Most of isotropic components (v) are small and weakly correlate with the corresponding deviatoric components (u). These characteristics are pronounced for 20 events with VR values >22%, which as noted previously is a reliability threshold. Within these 20 events, 10 fall into the CLVD-dominant region, into the DC-dominant region, 1 into the ISO-dominant region, and 6 into marginal regions. Given that 7 of the 120 imaginary events within the noise data fall into the CLVD-dominant region (Figure 9b), we conclude that the most probable physical mechanism for the LFEs is CLVD rather than DC or ISO deformation Characteristic Direction of CLVD [26] The CLVD component has a single symmetry axis that is dominant for many events; consequently, it is possible to discuss the principal symmetry axis direction, which corresponds to the maximum amplitude of the eigenvalues of the deviatoric component. In doing this, the deviatoric component is divided into the major CLVD (the closest CLVD) and major DC (the closest DC) components as follows: 20 p 2= ffiffi p B 1= ffiffi 1 1= ffiffi C B C7 p 4 p 1= ffiffi 0 A5 or 1= ffiffi 1 6B C B C7 4@ p 1 2= ffiffi 0 A5: (6) 1 However, many previous studies have divided the deviatoric component into the major DC (the closest DC) and minor CLVD (the CLVD orthogonal to the closest DC) components as follows [e.g., Shearer, 2009]: p 1 1= ffiffi 1 6B C B 0 A; 2= ffiffiffi C7 p 1 1= ffiffi A5: (7) These two approaches lead to a different CLVD symmetry axis. Given that the dominant mechanism is likely to be the CLVD, we use the method that maximizes the CLVD component. 7

11 Figure 11. Test result for the variable orientation model. Example of a test solution with temporally variant orientation. The moment tensor solution for event #1 is shown by beach ball plots and scalar moment rate functions. The moment tensor at each time step is shown by separate beach ball plots of isotropic and deviatoric components, and the rightmost beach ball plots indicate the cumulative moment tensor. The radius of each beach ball plot corresponds to the moment magnitude of each isotropic or deviatoric component; also shown is the moment magnitude of the full moment tensor. In the bottom panel, red lines are the magnitude of the moment rate normalized by the maximum value, and the blue lines correspond to the estimation error of the moment tensor at each time step. [27] The principal symmetry axis direction in the obtained moment tensors is typically oriented north-northeast with a small dip angle, which is close to the lineation direction formed by the source distribution (Figure 10). This plot statistically supports the qualitative features noted in Figure 8. The consistency of the lineation formed by the source distribution and the characteristic direction of the mechanisms implies that there is an underlying causal physical relationship between these two parameters. This observation may be a potentially important constraint for the physical modeling of semi-volcanic LFEs. Figure 12. Test result for selected stations. Example of a jackknife test for events #1, #1, #18, and #, with VR values >5%. The results obtained when sequentially removing each station are shown, along with the original result. The moment tensor corresponding to the maximum amplitude is shown by separate beach ball plots of the isotropic and deviatoric components. The size of each beach ball plot corresponds to the moment magnitude of each isotropic or deviatoric component, but the total magnitude is normalized for each solution. 5. Discussion 5.1. Tests of Solution Stability [28] The moment tensor orientation may change temporally during the source duration, although for simplicity we assumed that this was invariant and that only the amplitude changes temporally. To verify this assumption, we applied another inversion method with temporally variant orientation to the same data sets. We estimated the shape of a 1 s firstorder spline curve with 0.1 s node intervals (nine unknown parameters) for each of the six components of the moment tensor. Therefore, 54 independent model parameters were simultaneously solved by a linear inversion. Figure 11 shows the solution of temporally variable moment tensors for event #1. Comparing this with the fixed orientation solution (Figure 6), the moment tensor orientations at high-amplitude points (0.6, 0.8, and 0.9 s) are similar. The final cumulative moment or timing of the maximum amplitude (0.6 or 0.9 s) is different between these two models, although these values can fluctuate for an oscillating source. Given this, we only discuss the orientation at maximum amplitude and regard completely reverse orientations as representing the same 74

12 mechanisms in this study. For most of the other events, we verified the similarities between the moment tensor at maximum amplitude obtained by the original method with that of the variable orientation method, suggesting that our assumption of invariant orientation is valid. Therefore, we always adopt the results of the invariable orientation method with fewer model parameters to obtain stable results for peak moment release for every event. [29] Given that we only used data from five stations, it is possible that the solutions might change drastically by removing one of these stations. We used a jackknife test to check the robustness of solutions in which three-component waveforms at each station were not used in each trial. Figure 12 compares the isotropic and deviatoric components at maximum amplitude for the original and jackknifed solutions for four major events. The solutions are all similar and typical of CLVD. Note that the difference in the case of removing data from station SGOH for event #1 is apparently due to the slight time function change in which the timing of the maximum amplitude is shifted to the timing of the second peak with an opposite sign from the original solution. Taking into account the oscillating nature of LFEs, we can neglect this type of difference. Similar opposite mechanisms are found for the solution removing HINH or MZKH for event #18 and HKTH, HINH, or SGOH for event #. Therefore, the results of every trial were generally similar and we conclude that the results are comparable and independent of the choice of stations. Although the sampling points of P waves at five stations are concentrated at the center on the focal sphere (Figure 6), we used whole waveforms that yield stable results Effects of Heterogeneities [0] Highly heterogeneous structure would generate complicated seismic waves. However, for the following reasons, we consider that heterogeneity does not significantly control our results. First, this source region is distant from active volcanoes, although some Quaternary volcanoes are present in the studied region (Figure 1b). Therefore, we might expect less heterogeneity in the structure of our studied area as compared with that in the vicinity of active volcanoes. This is one of the advantages of analyzing semi-volcanic LFEs. A further line of evidence is provided by the jackknife tests, where we estimated focal mechanisms with reduced data sets and obtained similar results. Moreover, we verified that the results are insensitive to the assumed 1-D structure. For these reasons, we consider that the effects of heterogeneity do not significantly influence our results. [1] Indeed, if the exact heterogeneous structure was available, it should be possible to calculate theoretical waveforms using the complex real structure. However, no such heterogeneity has been reported or is expected in our studied region. In addition, poorly defined -D structures may yield results that are as inaccurate as those using a 1-D structure. Therefore, we used a simple structure in our study. 5.. Toward a Physical Model [2] Our inversion analysis revealed that the dominant focal mechanism of the LFEs in eastern Shimane is CLVD with a symmetry axis that plunges gently toward the northnortheast. In this region, the Yokota Quaternary volcanic cluster, which last erupted at 1 2 Ma, is located directly above the LFEs. Although there might be still minor magmatic activity at the depth of the LFEs, it is difficult to constrain the physical properties of the materials. As such, we discuss the probable physical model from a macroscopic viewpoint, which is discernible from seismic analysis. [] The principal symmetry axis of the focal mechanism is parallel not only to the lineation of hypocenters but also to the T axis of the focal mechanism of the western Tottori earthquake in 2000 and to the minimum principal axis of the regional stress field in southwestern Japan [Fukuyama et al., 200]. This common direction at various scales implies the dominance of a regional stress field (~500 km scale) over smaller-scale phenomena and that this field influences not only large inland earthquakes (~0 km scale) but also the distribution of LFEs (~1 km scale) and the source of LFEs (possibly ~100 m scale). [4] Ohmi and Obara [2002] analyzed one LFE in eastern Shimane using S to P wave (S/P) amplitude ratios and the polarization patterns of S waves. These authors concluded that the source mechanism is most likely to be a single force rather than a tensile crack or double-couple. Although a single force cannot be expressed by a moment tensor, the polarizations of the single force, linear vector dipole (LVD), which are a pair of single forces in opposite directions, and CLVD are similar. In this sense, their result is consistent with our results. Moreover, the direction of the single force estimated by Ohmi and Obara [2002] is also north-northeast. [5] Given that there are few studies on the mechanisms of semi-volcanic LFEs, it is informative to compare our results with those of previous studies of volcanic LFEs. Ukawa and Ohtake [1987] analyzed a LFE beneath Izu-Ooshima volcano and concluded that a traction force induced by a magma flow, which can be treated as a single unidirectional force, is superior to a DC source. Nishidomi and Takeo [1996] analyzed a LFE in western Tochigi and obtained a strike-slip focal mechanism with a slight non-dc component. Okada and Hasegawa [2000] analyzed LFEs beneath Naruko volcano, finding that these events had significant non-dc components. Nakamichi et al. [200] analyzed LFEs beneath Iwate volcano and proposed an origin related to a tensile crack, coupled with either a shear crack or an oblate spheroid magma chamber. Like our study, most of these previous studies identified the existence of a non-dc component, indicating that volcanic and semi-volcanic LFEs may be mechanically different from ordinary earthquakes that are mostly pure double-couple in origin. [6] The CLVD mechanism with oscillating source time functions is mainly constrained by the large amplitude phases in the LFE signals. Similarly, the hypocenters shown in Figure 1c are dependent on the major oscillating phases rather than arrival times, as we used waveform correlations for relocation. Therefore, this linear hypocenter distribution may represent an elongated source volume that radiates large oscillating waves. The fundamental mode of oscillation in an elongated volume filled with magma is consistent with the characteristic frequency of the source time function. For example, using a bulk modulus of Pa, Poisson ratio of 0.25, density of kg/m,andp wave velocity of 10 m/s, the fundamental oscillation in a 1500 m long pipe is 2 Hz. Although there is no active volcanism at the surface in this region, there may still be magma at depths of 0 km. If the LFE represents the oscillation of magma, then 75

13 some mechanism is required to induce the oscillation. For shallow volcanic low-frequency events, some studies have invoked fluid movement for inducing these oscillations [Julian, 1994; Fujita and Ida, 200], which is also a probable mechanism for deep events. Nevertheless, the uncertainties are large and the development of a physical model of deep volcanic and semi-volcanic LFEs is an important topic for future research. 6. Conclusions [7] We have examined the physical processes responsible for producing volcanic or semi-volcanic LFEs using focal mechanisms. However, this approach is challenging due to the low S/N ratio of seismic data and given that most previous studies have only analyzed a small number of events in a region using a small part of the waveforms. In our study, we sought to determine the statistically dominant focal mechanism in a small region by analysis of many events in eastern Shimane, where the data have a high S/N ratio. [8] Using waveform inversion for body wave signals, we determined a source time function with a temporally invariant focal mechanism for each event. To compute synthetic waveforms at relatively narrow frequencies, we corrected site amplification effects using seismic waves from deep intraslab events. Typically, the source time functions oscillate between positive and negative values, which is a behavior unlike regular earthquakes. The focal mechanisms for many LFEs are dominated by a CLVD component with north-northeast symmetry axes parallel to the lineation formed by the hypocenter distribution. These results may provide constraints on physical models of LFEs, which potentially (but not exclusively) represent the oscillation of magma induced by fluid movement. [9] Our study has only involved analysis of LFEs in eastern Shimane; further analysis of other volcanic and semi-volcanic LFEs is required to reveal the regional variety of dominant mechanisms and their connections to regional stress fields. The comparison between shallow (<5 km) and deep (20 40 km) events and between low- and high-frequency events is another interesting avenue for future research. Some previous studies of shallow earthquakes in volcanic or geothermal regions have invoked CLVD-like mechanisms [Ross et al., 1996; Julian et al., 1997] and, therefore, there may be similarities between shallow and deep events, although it is unclear why there are so few events at intermediate depths. [40] Acknowledgments. Kazuaki Ohta is thanked for discussions throughout this work and for providing his original code to relocate hypocenters. We are grateful to Kazushige Obara, Minoru Takeo, Hitoshi Kawakatsu, Emily E. Brodsky, and Victor C. Tsai for constructive discussions on this research. Comments from Aurélie Guilhem, an anonymous reviewer, and the Associate Editor were helpful to improve the manuscript. We used waveform data from the NIED Hi-net data server. This work was supported by JSPS KAKENHI (12J0915, ) and MEXT KAKENHI ( ). References Aki, K., and R. Koyanagi (1981), Deep volcanic tremor and magma ascent mechanism under Kilauea, Hawaii, J. Geophys. Res., 86, , doi: /jb086ib08p Aso, N., K. Ohta, and S. Ide (2011), Volcanic-like low-frequency earthquakes beneath Osaka Bay in the absence of a volcano, Geophys. Res. Lett., 8, L080, doi: /2011gl Aso, N., K. Ohta, and S. Ide (201), Tectonic, volcanic, and semi-volcanic deep low-frequency earthquakes in western Japan, Tectonophysics, 600, 27 40, doi: /j.tecto Bouchon, M. (1981), A simple method to calculate Green s function for layered media, Bull. Seismol. Soc. Am., 71(4), Brown, J., G. C. Beroza, S. Ide, K. Ohta, D. R. Shelly, S. Y. Schwartz, W. Rabbel, M. 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