Stress, strain rate and anisotropy in Kyushu, Japan strain rate and anisotropy in Kyushu, ... Kyushu...

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Earth and Planetary Science Letters 439 (2016) 129–142 Contents lists available at ScienceDirect Earth and Planetary Science Letters www.elsevier.com/locate/epsl Stress, strain rate and anisotropy in Kyushu, Japan M.K. Savage a,, Y. Aoki b , K. Unglert a,h , T. Ohkura c , K. Umakoshi d , H. Shimizu e , M. Iguchi f , T. Tameguri f , T. Ohminato b , J. Mori g a Victoria University of Wellington, New Zealand b Earthquake Research Institute, University of Tokyo, Japan c Aso Volcanological Laboratory, Kyoto University, Japan d Graduate School of Fisheries and Environmental Sciences, Nagasaki University, Japan e Institute of Seismology and Volcanology, Kyushu University, Shimabara, Japan f Sakurajima Volcano Research Center, Kyoto University, Kagoshima, Japan g Disaster Prevention Research Institute, Kyoto University, Japan h Department of Earth, Ocean, and Atmospheric Sciences, The University of British Columbia, Vancouver, Canada a r t i c l e i n f o a b s t r a c t Article history: Received 30 September 2015 Received in revised form 4 January 2016 Accepted 5 January 2016 Available online 8 February 2016 Editor: P. Shearer Keywords: seismic anisotropy stress birefringence strain rate Kyushu volcanoes Seismic anisotropy, the directional dependence of wave speeds, may be caused by stress-oriented cracks or by strain-oriented minerals, yet few studies have quantitatively compared anisotropy to stress and strain over large regions. Here we compare crustal stress and strain rates on the Island of Kyushu, Japan, as measured from inversions of focal mechanisms, GPS and shear wave splitting. Over 85,000 shear wave splitting measurements from local and regional earthquakes are obtained from the NIED network between 2004 and 2012, and on Aso, Sakurajima, Kirishima and Unzen volcano networks. Strain rate measurements are made from the Japanese Geonet stations. JMA-determined S arrival times processed with the MFAST shear wave splitting code measure fast polarisations (), related to the orientation of the anisotropic medium and time delays (dt ), related to the path length and the percent anisotropy. We apply the TESSA 2-D delay time tomography and spatial averaging code to the highest quality events, which have nearly vertical incidence angles, separating the 3455 shallow (depth < 40 km) from the 4957 deep (>=40 km) earthquakes. Using square grids with 30 km sides for all the inversions, the best correlations are observed between splitting from shallow earthquakes and stress. Axes of maximum horizontal stress (SHmax) and correlate with a coefficient c of 0.56, significant at the 99% confidence level. Their mean difference is 31.9 . Axes of maximum compressional strain rate and SHmax are also well aligned, with an average difference of 28 , but they do not correlate with each other, meaning that where they differ, the difference is not systematic. Anisotropy strength is negatively correlated with the stress ratio parameter determined from focal mechanism inversion (c =−0.64; significant at the 99% confidence level). The anisotropy and stress results are consistent with stress-aligned microcracks in the crust in a dominantly strike-slip regime. Eigenvalues of maximum horizontal strain rate correlate positively with stress ratio (c = 0.43, significant at 99% confidence). All three orientations are E–W in central Kyushu, where the compressional strain rate is highest. Both splitting and stress suggest plate-boundary-parallel maximum principal stress just off the coast of Kyushu, where strain rate measurements are sparse. South western Kyushu has the largest difference between directions of strain rate and stress. from shallow and deep earthquakes are not well aligned, suggesting that the deep earthquake waveforms are not simply split in the crust. Causes for the anisotropy may be olivine crystals aligned by drag of the subducting Philippine Sea plate in the mantle and stress-aligned microcracks in the crust. © 2016 Elsevier B.V. All rights reserved. 1. Introduction Stress in the Earth is fundamentally tied to the mechanisms of earthquakes and volcanoes. Earthquakes are usually caused by brittle failure on faults, when the accumulated stress exceeds the * Corresponding author. E-mail address: [email protected] (M.K. Savage). material strength, and subsurface magmatic activity can modify local stress fields, causing both earthquakes and eruptions. There- fore understanding stress is a critical endeavour for Earth physi- cists, and several techniques have been devised to measure stress. Kyushu Island in south-western Japan is an optimum location to compare stress measurements using different methods because there are several well-monitored volcanoes and a subduction mar- http://dx.doi.org/10.1016/j.epsl.2016.01.005 0012-821X/© 2016 Elsevier B.V. All rights reserved.

Transcript of Stress, strain rate and anisotropy in Kyushu, Japan strain rate and anisotropy in Kyushu, ... Kyushu...

Page 1: Stress, strain rate and anisotropy in Kyushu, Japan strain rate and anisotropy in Kyushu, ... Kyushu Island in south-western Japan is an optimum location to compare stress measurements

Earth and Planetary Science Letters 439 (2016) 129–142

Contents lists available at ScienceDirect

Earth and Planetary Science Letters

www.elsevier.com/locate/epsl

Stress, strain rate and anisotropy in Kyushu, Japan

M.K. Savage a,∗, Y. Aoki b, K. Unglert a,h, T. Ohkura c, K. Umakoshi d, H. Shimizu e, M. Iguchi f, T. Tameguri f, T. Ohminato b, J. Mori g

a Victoria University of Wellington, New Zealandb Earthquake Research Institute, University of Tokyo, Japanc Aso Volcanological Laboratory, Kyoto University, Japand Graduate School of Fisheries and Environmental Sciences, Nagasaki University, Japane Institute of Seismology and Volcanology, Kyushu University, Shimabara, Japanf Sakurajima Volcano Research Center, Kyoto University, Kagoshima, Japang Disaster Prevention Research Institute, Kyoto University, Japanh Department of Earth, Ocean, and Atmospheric Sciences, The University of British Columbia, Vancouver, Canada

a r t i c l e i n f o a b s t r a c t

Article history:Received 30 September 2015Received in revised form 4 January 2016Accepted 5 January 2016Available online 8 February 2016Editor: P. Shearer

Keywords:seismic anisotropystressbirefringencestrain rateKyushuvolcanoes

Seismic anisotropy, the directional dependence of wave speeds, may be caused by stress-oriented cracks or by strain-oriented minerals, yet few studies have quantitatively compared anisotropy to stress and strain over large regions. Here we compare crustal stress and strain rates on the Island of Kyushu, Japan, as measured from inversions of focal mechanisms, GPS and shear wave splitting. Over 85,000 shear wave splitting measurements from local and regional earthquakes are obtained from the NIED network between 2004 and 2012, and on Aso, Sakurajima, Kirishima and Unzen volcano networks. Strain rate measurements are made from the Japanese Geonet stations. JMA-determined S arrival times processed with the MFAST shear wave splitting code measure fast polarisations (�), related to the orientation of the anisotropic medium and time delays (dt), related to the path length and the percent anisotropy. We apply the TESSA 2-D delay time tomography and spatial averaging code to the highest quality events, which have nearly vertical incidence angles, separating the 3455 shallow (depth < 40 km) from the 4957 deep (>=40 km) earthquakes. Using square grids with 30 km sides for all the inversions, the best correlations are observed between splitting from shallow earthquakes and stress. Axes of maximum horizontal stress (SHmax) and � correlate with a coefficient c of 0.56, significant at the 99% confidence level. Their mean difference is 31.9◦. Axes of maximum compressional strain rate and SHmax are also well aligned, with an average difference of 28◦, but they do not correlate with each other, meaning that where they differ, the difference is not systematic. Anisotropy strength is negatively correlated with the stress ratio parameter determined from focal mechanism inversion (c = −0.64; significant at the 99% confidence level). The anisotropy and stress results are consistent with stress-aligned microcracks in the crust in a dominantly strike-slip regime. Eigenvalues of maximum horizontal strain rate correlate positively with stress ratio (c = 0.43, significant at 99% confidence). All three orientations are E–W in central Kyushu, where the compressional strain rate is highest. Both splitting and stress suggest plate-boundary-parallel maximum principal stress just off the coast of Kyushu, where strain rate measurements are sparse. South western Kyushu has the largest difference between directions of strain rate and stress. � from shallow and deep earthquakes are not well aligned, suggesting that the deep earthquake waveforms are not simply split in the crust. Causes for the anisotropy may be olivine crystals aligned by drag of the subducting Philippine Sea plate in the mantle and stress-aligned microcracks in the crust.

© 2016 Elsevier B.V. All rights reserved.

1. Introduction

Stress in the Earth is fundamentally tied to the mechanisms of earthquakes and volcanoes. Earthquakes are usually caused by brittle failure on faults, when the accumulated stress exceeds the

* Corresponding author.E-mail address: [email protected] (M.K. Savage).

http://dx.doi.org/10.1016/j.epsl.2016.01.0050012-821X/© 2016 Elsevier B.V. All rights reserved.

material strength, and subsurface magmatic activity can modify local stress fields, causing both earthquakes and eruptions. There-fore understanding stress is a critical endeavour for Earth physi-cists, and several techniques have been devised to measure stress. Kyushu Island in south-western Japan is an optimum location to compare stress measurements using different methods because there are several well-monitored volcanoes and a subduction mar-

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130 M.K. Savage et al. / Earth and Planetary Science Letters 439 (2016) 129–142

gin with large networks of seismometers and GPS stations that have been running for over ten years. Here we systematically com-pare three methods to determine the state of stress and its regional variation.

The most direct method to determine stress in the crust is through strain measurements in boreholes (e.g., Townend, 2006); both stress magnitudes and directions can then be determined, however, drilling boreholes to seismogenic depths is difficult and expensive. Another well-established method is to invert earth-quake focal mechanisms for the direction of stress in an area (e.g., Hardebeck and Michael, 2006). Earthquake faults slip in response to the stress in a region, and the fault orientation can be de-termined from earthquake focal mechanisms. Differential stresses are more likely to cause those faults with favourable orienta-tions to slip, and inversion of many different focal mechanisms can be used to determine the stress orientations where earth-quakes occur. Global Positioning System (GPS) networks are widely used to determine strain rates in the Earth (Davis et al., 1989;Shen et al., 1996). Assuming simple linear elasticity, stress and strain should be parallel for small strains, and strain rate changes should be proportional to stress rate changes.

Seismic anisotropy, the directional dependence of wave speed, can be used to characterise mineral or crack alignment in the crust and mantle. In the crust it is thought that one of the main causes of crack alignment is anisotropic stress; cracks perpendicular to the maximum principal stress are closed, leaving only those cracks open that are parallel to the maximum principal stress (Nur and Simmons, 1969). Thus the anisotropic fast direction may lie par-allel to the maximum principal stress direction. One of the most common methods to determine seismic anisotropy is by using its birefringent effect on shear waves, often called “shear wave split-ting”. Shear waves entering anisotropic material are separated into two components, with the polarisation of the first arriving wave (φ) determined by the orientation of the anisotropic symmetry axes and the propagation direction, and the time between the first and later (nearly orthogonal) component (dt) is a non-linear prod-uct of the strength of the anisotropy and the path length through the anisotropic medium.

Ando et al. (1980) first examined seismic anisotropy in Japan. They suggested that differential arrival times of shear waves from deep earthquakes recorded on stations in central Japan were caused by either anisotropic olivine fabric or aligned melt-filled cracks in the mantle. Since then many articles have been written on anisotropy in Japan, confirming and extending their sugges-tions. Olivine orientations caused by mantle flow patterns have been used to explain shear wave splitting on large scales for paths that travel through the mantle (Long and van der Hilst, 2006;Salah et al., 2009; Terada et al., 2013; Tono et al., 2009) as well as P-wave anisotropy in the same areas (Wang and Zhao, 2013). Crustal anisotropy has been attributed to cracks and also to faulting structures and mineral alignment (Kaneshima, 1990;Salah et al., 2009). Furthermore, in regions of stress-controlled anisotropy in central Japan, an increase in normalised delay time with increasing strain rate has been used to measure a stressing rate of 3 kPa/yr, comparable to the GPS-derived rates in the region (Hiramatsu et al., 2010).

Kyushu is the southern-most island of the main Japanese archipelago. It lies at an arc–arc junction between the subduct-ing Philippine Sea Plate to the north and the Ryukyu arc to the southwest and has many subduction zone volcanoes (e.g., Mahony et al., 2011) (Fig. 1). Oblique convergence of the Philippine Sea plate occurs primarily as dip-slip movement on the subduction in-terface, at a rate of 62–68 mm/yr in the N55W direction (Heki and Miyazaki, 2001). Some dextral strike-slip motion is taken up on the Median Tectonic Line (MTL) and its extensions, which make up

Fig. 1. Map of Quaternary volcanoes (red triangles) in Kyushu. Labelled volcanoes are discussed in the text. CVR is the Central Volcanic Region, delineated by the red dashed lines. The southern-most boundary is also often considered the extension of the Median Tectonic Line (MTL). The inset shows the tectonic setting of the region, with plates labelled Eu for Europe, PhS for Philippine Sea and Pa for Pacific. Red box in inset is outline of box. Blue lines are active faults. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the southern boundary of the Central Volcanic Region (CVR) (e.g., Itoh et al., 1998).

2. Methodology and data

2.1. Anisotropy

2.1.1. Splitting analysisFor the anisotropy measurements, we used the automatic shear

wave splitting measurement tool MFAST (Savage et al., 2010b). Starting from pre-determined S-wave arrival times, the program determines the best filter from a set of fourteen filters, as mea-sured by the product of the signal-to-noise ratio and the band-width. The filters are described in Savage et al. (2010b), and range from 0.4–4 Hz at the lowest end to 4–10 Hz at the highest end. Using the best filter, the Silver and Chan (1991) 2-D eigenvalue minimisation technique is used to determine shear wave splitting parameters over a set of 75 phase arrival windows that start and end at various times before and after the S arrival. A grid search uses trial values of � and dt to correct for splitting. The eigen-values of the corrected particle motion are determined and the values of � and dt yielding the minimum of the smallest eigen-value are considered the best measurements for that window. The grid search examines � between −90 and 90 in increments of 1◦ , and between 0 and 1.0 s in increments of 0.01 s. The best window is chosen via cluster analysis (Teanby et al., 2004) and the final measurement is graded based on several factors, including whether other similar sized clusters exist with markedly different results, the signal to noise ratio of the measurement, and the formal er-ror bars of the final measurement. We use version 2.0 of MFAST, which corrects for a mistake in the previous methodology of mea-suring error bars (Walsh et al., 2013). Here we present the highest quality measurements from the best filters (AB), in which the max-imum eigenvalue on the contour plots is larger than 5 times the 95% confidence interval (emax > 5) (Savage et al., 2010b). Briefly, AB measurements are not null, i.e., � is further from than 20 de-

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grees from the measured incoming polarisation direction and its perpendicular. Dt < 0.8 times the maximum allowed delay time (here 1.0 s), the signal-to-noise ratio is >3, the standard error of φ < 25◦ , and the clustering algorithm didn’t return any clusters with significant numbers that had large differences between the average dt and � within the best cluster compared to any other cluster.

To average the data we use directional statistics for the angular variables (Berens, 2009; Gerst and Savage, 2004; Mardia and Jupp, 2000). Normalised vectors of individual values of � are multiplied by a factor of two and summed, and then the total length of the vector is divided by the number of measurements. The orientation of Rmean, the resultant vector, is twice the mean �, and its length (0 < |Rmean| < 1) is used to calculate the standard error and stan-dard deviation. A length of 1 corresponds to all values of � being the same and a length of 0 represents a random distribution. We present both standard deviations and standard errors to evaluate the spread of data as well as the reliability of the averages.

2.1.2. Data sourcesWe use data from earthquakes recorded on the NIED seismic

network, and on volcano networks at Sakurajima, Unzen, Aso and Kirishima. We corrected the HiNet borehole station component azimuths using the station orientations calculated by teleseismic waveform correlations (Shiomi, 2013). We use hand-picked S ar-rivals. For the volcano networks we examine two types of earth-quakes: Local earthquakes that occur near the volcano, and deeper regional events that occur at distances of up to a few hundred kilometres in the subducting plates underneath the volcano. The advantage of local earthquakes is that they are often numerous, and are close to the volcano, which makes their paths uncom-plicated and more likely to be caused by local stress. However, the travel paths of shallow earthquakes may be near-horizontal and many do not fulfil the criterion for near-vertical incidence, so to obtain more measurements we also examine deeper regional earthquakes. Paths for the deeper events include mantle as well as crust, so that the two possible sources of anisotropy must be carefully examined.

At Aso volcano, regional earthquakes were not saved prior to 2006, and except for data recorded at NIED stations, we only report the results from local earthquakes in that area. The arrival times we used were determined by the observatory staff. At Sakurajima and Kirishima volcanoes only regional earthquakes were examined (arrival times determined by Martha Savage). At Unzen, both local and regional earthquakes were available and were analysed. For NIED stations, the arrival times determined by the Japan Meteoro-logical Agency (JMA) were used for the S arrivals.

For rays arriving at low angles to the surface, interference be-tween direct S waves and S–P conversions at the surface can dis-rupt splitting measurements. For Poisson solids, arrival angles shal-lower than 35◦ could cause such interference, but surface velocities are usually slower than velocities at depth, and most shear wave splitting studies use arrival angles steeper than 45◦ (e.g., Booth and Crampin, 1985; Tono and Fukao, 2009). Snell’s law ensures near-vertical incidence for almost all rays arriving at areas with low surface velocities such as volcanic areas (e.g., Savage et al., 1989;Volti et al., 2005). Nonetheless, earthquakes with steep incidence angles throughout most of the path are still favoured. Paths that start near horizontally will curve strongly, so that they will pass through material with a varying propagation direction relative to the symmetry system, which will cause the splitting to vary along the path, leading to complicated waveforms. We make measure-ments on all earthquakes, and examine the effect that angle of incidence (measured with respect to the vertical) has on the re-sults. Recent tests of angle of incidence compared to measurement scatter in the Canterbury plains suggested that straight-line inci-

dence angles of 60◦ yielded similar results to those within 45◦ , but that higher values were more scattered (Holt et al., 2013).

2.1.3. Spatial averagesWe calculate average values of anisotropy in grids by using

the two-dimensional tomography and spatial averaging program TESSA (Johnson et al., 2011), summarised here. This code is de-signed to create a first-order approximation of lateral variations in anisotropy. It provides approximate values for anisotropy strength and for fast directions and uses the results from the MFAST codes. For the delay time inversion, it solves a constrained linear least squares problem (Gill et al., 1981). The algorithm solves for the anisotropy strength in each block, defined as delay time per km. The program determines an initial solution by first solving the linear least-squares problem, then iteratively converges to a final solution subject to bounding constraints. These constraints are set so that the minimum strength of anisotropy is above 0 s/km and the maximum is the maximum dt observed applied to a single block (i.e., dtmax/Lmin(b) , where Lmin(b) is the width of the smallest block in the grid). The anisotropy parameters are weighted accord-ing to their measurement uncertainties. The tomography method assumes that dt is simply additive. This is a simplification of the non-linear relationship between heterogeneous anisotropy and the observed apparent dt at the surface and does not account for depth dependence of the anisotropy. The residuals considered “good” for the delay time tomography are those in which the square-root of the diagonal elements of the model variance matrix are greater than 5. That value is chosen because it includes most of the grid blocks with more than 10 rays and includes the features from the checkerboard test that are best reconstructed (Johnson et al., 2011). As expected, it encompasses the region where most of the stations are located (see section 3.3).

The spatial averaging uses the method of Audoine et al. (2004)on the same grid used for the delay time averages, and suffers from the same approximations as the dt tomography. We used weighting of 1/d2 where d is the distance of the specific grid block from the station. This weighting scheme accounts for the fact that � will be influenced a greater amount by anisotropic media closest to the station (e.g., Rümpker and Silver, 1998). For each grid block, circular statistics are used to calculate the mean fast directions, if the standard deviation of the data passing through the blocks is less than 30◦ and the standard error of the mean is less than 10◦ .

Although the TESSA method allows quad-tree gridding to deter-mine values on the most suitable grid for each area, we chose the constant grid-size option so that we could more easily compare to stress and strain rate inversions. We use square boxes with 30 km on each side. If there are less than 10 rays in any box the calcu-lation is not made for that box. The node spacing is 3 km, which indicates the spacing of points used to divide each ray.

To compare the results with stress and strain rate we mainly use the earthquakes shallower than 40 km, with straight-line inci-dence angles less than 60◦ .

2.2. Strain rate

We estimate the spatial distribution of strain rates from the GPS measurements by GEONET (Sagiya, 2004) between January 2006 and December 2010. By default, GEONET offers daily solutions for each site, from which we first determine velocities by assuming that the velocity of each site is constant in time. This assumption is justified because no earthquakes or slow-slip transients exist to perturb the time series during the time period we chose.

We then estimate the spatial variation of strain rates from this obtained velocity field. To suppress short-wavelength oscillations of strain rates fictitiously generated by velocity uncertainties, we apply a Gaussian filter following Shen et al. (1996). At a given point

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in the strain rate field we define velocity components ux and u y . Strain-rate components are exx , exy , e yy , and w where the first three represent the strain tensor and the last represents rotation. The velocities at the ith GPS site, vi

x and viy , are related to the

values of the strain rate field as

vix = ux + xiexx + yiexy + yi w + εi

x

viy = u y + xiexy + yie yy − xi w + εi

y

where xi and yi denote the x and y component of the vector connecting the point where the strain rate is calculated and the coordinate of the ith GPS site, and εi

x and εiy are the errors of the

corresponding velocity components. Given N GPS sites, the strain-rate components for each point are thus derived by solving a set of 2N equations. These observation equations are weighted by the distance between the spot in which the strain-rate is obtained and the GPS site. The weighting is given by

Eij = Cij exp((

R2i + R2

j

)/L2)

where Cij is the covariance matrix of the velocity estimation errors obtained from the geodetic data adjustment between the ith and jth stations, Ri and R j represent the distance from the spot for which the strain rate is to be estimated and the ith and jth GPS sites, and L is a correlation length decay constant, which we fixed to 35 km in this case. This weighting works as a spatial low-pass filter of the strain rates.

This length is chosen to be larger than the average GPS site spacing of 20–25 km. Visual examination of maps using correla-tion lengths of 25 and 45 km are very similar to the 35 km length chosen here, with the difference that the 25 km correlation length has somewhat larger extension in the central eastern offshore re-gion (Supplementary Figs. S1, S2).

2.3. Stress

The stress field is estimated by inverting focal mechanism solu-tions using a method developed by Hardebeck and Michael (2006). The slip vector of the ith earthquake, si1, si2, and si3, can be re-lated to the stress tensor components at a given point, σi j = σ ji , as (see Eq. (4) of Hardebeck and Michael, 2006)

si1 = (ni1 − n3

i1 + ni1n2i3

)σ11 + (

ni2 − 2n2i1ni2

)σ12

+ (ni3 − 2n2

i1ni3)σ13 + (

ni1n2i3 − ni1n2

i2

)σ22

− 2ni1ni2ni3σ23

si2 = (ni2n2

i3 − ni2n2i1

)σ11 + (

ni1 − 2n2i2ni1

)σ12 − 2ni1ni2ni3σ13

+ (ni2 − n3

i2 + ni2n2i3

)σ22 + (

ni3 − 2n2i2ni3

)σ23

si3 = (n3

i3 − ni3n2i1 − ni3

)σ11 − 2ni1ni2ni3σ12

+ (ni1 − 2n2

i3ni1)σ13 + (

n3i3 − ni3n2

i2 − ni3)σ22

+ (ni2 − 2n2

i3ni2)σ23

where ni1, ni2 and ni3 denote components of the fault normal direction. Note that we assume σ33 = σ11 + σ22 because it is im-possible to estimate the isotropic part of the stress tensor from fault plane solutions. Given N fault plane solutions and M spots for the stress tensor to be estimated, we solve a linear equation to invert for 5M model parameters from 3N data.

We additionally impose damping to require neighbouring stress tensors to be similar. We used a value of 1, which we determined subjectively according to the following criteria: a stronger damp-ing favours a spatially smoother solution with an expense of worse fit to fault plane solutions. A weaker damping favours a solution that is more consistent with the fault plane solutions but it can be

unrealistically rough in space. Supplementary Fig. S3 shows quan-titatively the trade-offs for different damping parameters.

We use the JMA focal mechanisms from Jan. 1997–Oct. 2011. We define σ1, σ2 and σ3 as the maximum, intermediate and minimum compressive stresses, respectively. We report the maxi-mum horizontal stress, SHmax, the stress regime of thrust faulting (where σ3 is vertical), strike-slip (where σ2 is vertical) or normal (σ1 is vertical) and the stress parameter RATIO, defined as

RATIO = (σ2−σ3)/(σ1 − σ3). (1)

RATIO is always positive and less than one because σ1 ≥ σ2 ≥ σ3. RATIO is 0 when σ2 = σ3 and is singular if the medium is isotropic.

3. Results

From 161 stations, we obtained 85,361 splitting measurements, with 25,187 of those with AB quality and emax > 5. The Sup-plementary spreadsheet contains all the station average measure-ments separated into different incidence angle criteria. The average dominant frequency of the waveforms used for shear-wave split-ting measurements is 2.1 Hz for the deep earthquakes and 2.8 Hz for shallow earthquakes.

3.1. Station averages of shear wave splitting

The true angles of incidence for all the ray paths are likely to be considerably smaller than the straight-line angles, since low velocities near the surface usually bend the ray paths towards near-vertical. Rather than consider separate velocity structures un-der each station, we compare whether the results differ when re-stricting the straight-line ray paths to 45◦ or 60◦ (Supplementary spreadsheet, Table 1, Fig. 2). There are only 20% fewer measure-ments for the narrow incidence angles for deep events, so the averages are similar. For shallow earthquakes, less than half the measurements fulfil the stricter criteria. When less than 5 mea-surements are available at a given station, the averages for differ-ent criteria differ by a large amount and the scatter of the data is large. For stations with more than 5 measurements, the scatter is not significantly different as a function of incidence angle cri-teria, but the shallow earthquakes are significantly less scattered (Rmean = 0.61 ± 0.08) than the deep ones (Rmean = 0.39 ± 0.05) (Table 1, Supplementary spreadsheet). Among these stations, the difference between the means for the two incidence angle crite-ria depends strongly on Rmean. Considering only the 23 stations with Rmean > 0.4 for incidences angles <60◦ , only two have significant differences greater than 10◦ between the average �

for incidence <45◦ and 60◦: N.TMNH differs by 19◦ , and HDK differs by 13◦ . From this we conclude that when the fast direc-tions are well-aligned, results do not depend strongly on incidence angle.

For shallow earthquakes the fast directions in the regions near Aso and Unzen volcano are aligned roughly E–W or NW/SE (Figs. 2, 3) and in other regions they are aligned more NE–SW, par-allel to faults or to previously published estimates of SHmax from focal mechanism inversions (Townend and Zoback, 2006) (Fig. 3). Measurements for deep earthquakes are more abundant and also more scattered, particularly near the volcanic areas of Sakurajima and Kirishima. General trends seem to confirm the E–W fast di-rections near Aso and NNE–SSW directions in Eastern Kyushu. Stations in southwest Kyushu have strong E–W or NW/SE align-ment.

S-waves from deep earthquakes may be re-split when they reach the crust. Some studies have found quite different behaviour between shallow and deep earthquakes (Gerst and Savage, 2004), and splitting from deep local earthquakes has often been inter-

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M.K. Savage et al. / Earth and Planetary Science Letters 439 (2016) 129–142 133

Table 1Summary for different path combinations.

Angle of incidence/depth criteria

Number of high-quality measurements

Number of stations with measurements

Average Rmean and 95% conf. limit for stations with >5 measurements

Number of stations with >5 measurements

<60, shallow 3459 106 0.52 ± 0.08 79<60, deep 5167 142 0.38 ± 0.04 109<45, shallow 1506 73 0.61 ± 0.08 36<45, deep 4259 136 0.39 ± 0.05 97

Fig. 2. Rose diagrams (circular histograms) of fast directions for earthquakes less than or equal to 40 km in depth (top; a, b) and deeper than 40 km (bottom: c, d) (Supplementary spreadsheet). Rose diagrams include the best measurements made at each station, using the criteria emax > 5, AB quality measurement. Roses with less than ten measurements are half the length of the others. Left (a, c) have straight-line incidence angle <45◦ and right (b, d) have straight-line incidence angle <60◦ . Blue bars are SHmax measurements from Townend and Zoback (2006), with thin bars being lower quality and thick bars higher quality measurements. The yellow roses in the labelled boxes in a) and c) are enlarged in Fig. 3. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

preted to represent mantle anisotropy (e.g., Long and van der Hilst, 2006) while others concluded that splitting from shallow and deep events is similar and have used all depths to determine the stress field (Johnson et al., 2011).

There are only 5 stations with Rmean > 0.4 and more than 5 measurements on both shallow and deep sets of earthquakes with straight-line angles of incidence less than 45◦ . Relaxing the criterion to allow up to 60◦ angles of incidence yielded

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Fig. 3. Rose diagrams from Fig. 2 a) and c) for monitored volcanic areas. Unzen and Aso include only shallow earthquakes (<40 km deep). Sakurajima and Kirishima include only deep earthquakes (>=40 km deep). Topography is denoted in grey scale. SHmax measurements are as in Fig. 2. Black triangles show quaternary volcanoes. Active faults are thin blue lines. Yellow roses in boxes are enlarged in insets with roses colour-coded to match the triangles at the station locations. SHmax are blue lines in the online version and dashed lines in the print version. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

only 10 stations (two overlapping) (Supplementary spreadsheet). Deeper earthquakes had larger delay times at all but one station, with an average difference of 0.16 ±0.06 s. Fast directions for shal-low earthquakes are rotated counter-clockwise compared to those for deep earthquakes for all but three stations, and the median ro-tation was 22◦ counter-clockwise.

3.2. Time variations of parameters

Each of the volcanic regions was initially examined to see if time variations correlate with volcanic eruptions, as had previ-ously been observed at several volcanoes (e.g., Asama volcano (Savage et al., 2010a), Ruapehu volcano (Gerst and Savage, 2004), Mt. Vesuvius (Bianco et al., 2006)). Aso volcano showed statisti-cally significant variation of splitting parameters with time, but the variation was different for different stations (Unglert et al.,

2011). Data on Sakurajima was too scattered to see strong trends with time. One station at Kirishima volcano (EV.TKN) showed a change in average fast direction at the time of the eruption for the deep earthquakes examined. Measurements at Unzen volcano yield variations with time, but they are different for shallow and deep events, and delay times did not correlate with levelling data. This suggests that the variations may have been related to move-ment of earthquakes over time rather than changes in stress con-ditions. Therefore here we examine spatial variations, assuming that time variations are negligible compared to the spatial varia-tions.

3.3. Inversions for splitting parameters

The differences between results at common stations for deep and shallow earthquakes, and the larger variation of fast directions

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Fig. 4. Two-dimensional inversion and spatial averaging for the 4957 measurements from deep earthquakes (depth > 40 km) with angle of incidence <60◦ and emax > 5. a) Checkerboard used in TESSA (Johnson et al., 2011) and station distribution (triangles). b) Delay time tomography. The black contour surrounds the region with the highest resolution, as discussed in the text. c) Ray paths used in the inversion. d) Rose diagrams (orange) of fast polarisation spatial averages on the grids. Blue bars: average fast directions for those grids that had the standard deviation less than 30◦ and standard error of the mean of less than 10◦ . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

for deep earthquakes suggest that the waves from deep earth-quakes are not simply being split in the crust near the station in the same region where splitting is observed for shallow earth-quakes, hence the waves may be affected by anisotropy along the entire path length. We first consider the TESSA (Johnson et al., 2011) inversion and spatial averaging results for the deep earth-quakes with angles of incidence less than 60◦ (Fig. 4). The delay times tend to be higher in those regions with better-aligned rose diagrams and lower where the rose diagrams are variable (e.g., dark blue region in Fig. 4b with stations near Kirishima at 32N, 131E). The spatial averages further emphasise the E–W fast direc-tions in southwest Kyushu, rotating clockwise from west to east, and the NNE–SSW fast directions along the central coastline. Mea-surements in the volcanic regions show greater scatter than in the rest of the region (cf. diagrams near high-density stations at

31.75N and 31.5N and near Aso volcano at 33N). There is also large scatter in northeast Kyushu. There is some tendency for the fast directions around Unzen to be transverse to the central crater (around 32.7N, 130.2E). Several grid points show two well-aligned populations of fast directions.

Comparing rose diagrams for deep and shallow earthquakes, again for incidence angles <60◦ , there are fewer well-defined grid points for shallow earthquakes but where they exist, they have less scatter than the deep events (compare Figs. 4d and 5), as was also found for station averages. Central Kyushu particularly has well-aligned fast directions for shallow earthquakes, which are E–W near latitudes 32.5–33.5◦ . Close to the sheared MTL region at the southern boundary of the CVR, the fast directions parallel that boundary.

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Fig. 5. Spatial average of fast directions for the 3455 measurements of shallow earthquakes with angle of incidence <60◦ and emax > 5, coloured as in Fig. 4d. The dashed lines give the borders of the central volcanic region. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.)

3.4. Stress and strain rate measurements

Fig. 6 shows the inversions of focal mechanisms and GPS for stress and strain rate. The focal mechanisms yield mostly strike-slip faulting, with some normal faulting off the southwest and east-central coasts of Kyushu, and thrust faulting off the southeast coast. Maximum horizontal stress directions are mainly ENE–WSW to E–W for strike-slip, NW–SE for thrust fault and NE–SW for nor-mal fault regions. There are several regions without earthquakes where the stress regime is not determined.

Velocities determined from GPS show a circular pattern in southeast Kyushu, with larger velocities east of the CVR. Strain rate has mainly E–W compression, with the largest values in the north and northeast. N–S extension is strong in southern Kyushu. As seen in the stress inversions, plate-boundary parallel extension off the east coast of central Kyushu gives way to plate-boundary perpen-dicular compression to the south.

3.5. Numerical comparison of measurements

To quantitatively compare the three sets of measurements, we compare the angles by using circular statistics. Because each pro-gram had slightly different parameterisation, we used grids that are close, but not identical to each other, to calculate the values for each inversion. For splitting fast directions we only consider grid points for which the standard deviation of the fast directions is less than 30◦ and the standard error of the mean is less than 10◦ . For numerical comparisons, we compare angles at one set of grid points to the measurements of a different angular parameter from the nearest of a second set of grid points, for those points that are less than the minimum distance away (set to 0.1◦ here). The dif-ference between the two angles is calculated as the cosine. These are contoured using the GMT functions grdsample and grdimage (Wessel and Smith, 1998) (Fig. 7).

The Directional Statistics package (Berens, 2009) is used to cal-culate correlation coefficients and p-values for the relation be-tween the two sets of parameters, using l2 norms. We also calcu-late S , the average absolute value of the cosine of the differences between the angles, using an l1 norm (Table 2).

For these spatially averaged data, the highest correlation coef-ficient (0.56) is between splitting fast azimuth and stress SHmax, meaning that when one changes, the other changes in the same di-rection (Table 2). This is highly significant, with a p-value of 0.005 (99.5% confidence level). However, the average difference between the two measures is 31.9◦ . The average differences between fast azimuths from deep and shallow earthquakes differed substantially (34.5◦) as noted also above for the comparisons of station averages, but they are correlated (c = 0.46; significant at the 99.8% confi-dence level). Conversely, the smallest difference between azimuths is 28.1◦ for strain rate and stress, but they are not well correlated, meaning that when they differ, that difference is not systematic. Fast azimuths from deep earthquakes also correlate to maximum horizontal stress orientations (c = 0.46, p = 0.056); but their av-erage difference of 50.8◦ is large. Splitting does not correlate well with strain rate.

The regions that differ most for the stress versus strain rate case are only in small patches on the western edge between Un-zen and Sakurajima (around 32N, 130E) and off the east coast of Kyushu (32.5N, 132E) (Fig. 7b). Splitting fast directions from shallow earthquakes compare better with stress than with strain rate, partly because the region that is most rapidly changing in the splitting does not have many stress inversion results (compare Fig. 6a and c). Overall, the regions with the worst matches (dark-est) for all types of measurements are off the central east coast of Kyushu, where the stress field changes between thrust, strike-slip and normal, and in the northwest, where there are not many earthquakes and the GPS velocity and strain rate is small (compare Figs. 6 and 7).

Comparisons of parameter magnitudes are in Fig. 8 and Table 2. There are fewest well-resolved blocks for delay times of shallow earthquakes (Fig. 8a), less than for those matching the direction criteria. In central Kyushu there is a larger delay time per km for the shallow earthquakes, smaller compressional strain rate (Fig. 8d) and smaller stress ratio (Fig. 8e). Using the same algorithm to com-pare the grid points that are nearest each other but no more than 0.1◦ apart, and only using grid boxes with resolution matrix di-agonals >5, gives the correlation coefficients in Table 2. The only significant correlations are between the delay time/km for shallow earthquakes versus stress ratio and between maximum compres-sional strain rate and stress ratio. The negative correlation between shallow splitting delay time/km and stress ratio is consistent with the map comparison of higher dt/km and smaller stress ratio in central Kyushu. The correlation between compressional strain rate and stress ratio is also consistent with the lower stress ratio and strain rate in central Kyushu. However, despite both splitting and strain rate being correlated with stress ratio, they are not cor-related significantly with each other. Nor are anisotropy strength from shallow and deep earthquakes correlated.

4. Discussion

Stress measurements are similar to previous measurements in the region, although the most recent study has higher res-olution than ours and therefore shows more detailed variations (Matsumoto et al., 2015). Likewise, GPS strain rate values are simi-lar to those determined earlier (e.g., Takayama and Yoshida, 2007). Salah et al. (2009) determine splitting for both shallow and deep events in Kyushu (see especially their Fig. 14), reporting that shal-low splitting reflects SHmax. They do not have as many stations as we do because they do not include the volcano networks. They have many fewer measurements from shallow (<50 km deep) events than in our study, but those that are reported have similar fast directions to ours. Their measurements from deep earthquakes are similar to ours in eastern Kyushu. In northwest Kyushu they present single measurements at most stations, with most showing

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Fig. 6. Inversions for stress and strain rate in Kyushu. a) Focal mechanisms. b) Inversion for SHmax orientation. c) GPS velocity vectors. d) Inversion for strain rate orientations: compression (inward pointing arrows) and extension (outward pointing arrows) with amplitude given by arrow length.

Table 2Correlations between gridded parameters.

Comparison values Correlation coefficient c

p-value Sn S S(deg)

Shallow splitting/strain 0.23 0.11 36.5 0.73 43.0Strain/stress 0.14 0.38 44.1 0.88 28.1Shallow split/stress 0.560 0.0049 24.6 0.85 31.9Shallow split/deep split 0.46 0.0021 36.3 0.82 34.5Deep split/stress 0.46 0.056 11.4 0.63 50.8Shallow dt/km vs RATIO −0.637 0.008Deep dt/km vs RATIO 0.0003 0.999Shallow dt/km vs strain max eigenvalue −0.105 0.58Strain max eigenvalue/RATIO 0.434 0.0016Shallow dt/km vs deep dt/km 0.125 0.60Shallow dt/km vs extensional strain −0.072 0.62Deep dt/km vs extensional strain −0.0003 0.999

Sn = sum of absolute values of cosines of residuals (residuals are differences between the angles), for well-resolved blocks. S is the average absolute value of the cosine of differences. S (deg) is that value in degrees. The p-value is a statistical measure that determines how significant a value is. It tells the probability that a particular correlation would have occurred by chance from two Gaussian distributions. For example, a p-value of 0.05 says that a similar correlation would occur 5 times in 100 tests, and values less than 0.05 are considered statistically significant.

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Fig. 7. Comparison of estimates of maximum stress direction. The bars in each panel are from the inversions of two sets of angular parameters, except for d) where only stress is given. The background colour is a contour of the average absolute value of the cosine of the difference between the directions, coloured by the scale at the bottom. Shallow splitting measurements are dark blue bars, deep splitting measurements are light blue bars, SHmax are red bars, and maximum strain rate directions are purple bars. The value of S printed at the bottom right of each map is the sum of squares of the difference between measurements at the closest grid points, provided that the distance was less than 0.1◦ . a) Fast direction of shallow earthquakes versus maximum compressional strain rate. b) Maximum compressional strain rate versus SHmax. c) Splitting fast directions from shallow earthquakes versus SHmax. d) SHmax by itself for reference. e) Shallow splitting measurements compared to the deep splitting measurements. f) Splitting measurements from deep earthquakes compared to SHmax. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 8. Comparison of magnitudes of parameters. a) Splitting delay time per km for shallow earthquakes. b) Splitting delay time per km for deep earthquakes. c) Extensional eigenvalue from the strain rate inversion. d) Compressional eigenvalue from the strain rate inversion. e) Stress ratio from the stress inversion. Black circles are the points with best resolved values; they are used for numerical comparisons, and to contour the data. Highlighted regions in a) and b) encircle the points with best resolution. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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NW/SE fast directions, at odds to many of our measurements. But several of their stations yield NE/SW or E–W fast directions, similar to our results. Other published shear-wave splitting measurements in Kyushu have mainly been in local studies (Kaneshima, 1990;Unglert et al., 2011) or were used to study mantle processes (e.g., Long and van der Hilst, 2006). Comparing Fig. 5 with Fig. 10 of the P-wave anisotropy inversion of Wang and Zhao (2013)for crustal depths of 10 and 25 km, the change from margin-perpendicular fast directions offshore southern Kyushu to margin-parallel anisotropy in central Kyushu is common to both studies. In general the shear wave splitting seems to better match the 10 km depth slice in the P-wave anisotropy than the deeper slices, sug-gesting shallow anisotropy controls both. The E–W anisotropy in central Kyushu in this study is more coherent than in the P-wave anisotropy, but the rapid rotation “star pattern” in fast direc-tions centred at (33N, 131.25E) is seen in both studies, as are the boundary-parallel fast directions at stations near the CVR bound-ary.

It has long been assumed that shear wave splitting from shal-low earthquakes is caused by stress and therefore that its measure-ment can yield stress directions. However, some studies have found that there are areas where the anisotropy is better explained by structures such as fault fabric (e.g., Kaneshima, 1990) and mineral orientation (e.g., do Nascimento et al., 2004). This study shows that in central Kyushu, stress and anisotropy correlate with each other overall, although there are exceptions in some regions. As far as we are aware, this is the first study to show that strength of anisotropy is correlated with stress ratio. If we make the assumption that one of the three stresses is sub vertical (Zoback and Zoback, 2002), and that most of the area is in a strike-slip regime (green bars are most common in Fig. 6), then σ2 is vertical and hence SHmax is in the σ1 direction and RATIO decreases when the difference between σ1 and σ3 increases (Eq. (1)). So a larger SHmax will close more vertical cracks with planes perpendicular to σ1, making a larger anisotropy, and smaller RATIO. Thus both the good correlation be-tween splitting fast direction and SHmax, and the good negative correlation between strength of shallow anisotropy and stress ratio are consistent with stress-controlled cracks in a largely strike-slip regime.

If two directions (e.g., splitting and stress) are random, we ex-pect S = 2/π = 0.6366. All the average S values are higher than this except for splitting from deep events compared to stress (Ta-ble 2), suggesting some relationships, but the only statistically significant relationship (p < 0.05) between angles is for shal-low anisotropy fast direction versus SHmax and for deep versus shallow fast azimuths. The high S (0.88) yielding a low aver-age difference of 28◦ between strain rate and SHmax also sug-gests a strong relationship between the two. In areas of high topography, topographic stresses, which are nearly constant over time, can control the stress regime (e.g., Araragi et al., 2015;Yoshida et al., 2015). Strain rate from GPS is largely controlled by tectonic stresses, and hence the coincidence of stress and strain rate suggests that the tectonic strain from plate motions is also controlling the stress, and hence that they are not out of align-ment, as occurred before the Tohoku earthquake (Hasegawaa et al., 2012).

In central Japan, shear wave splitting fast directions were de-termined to be parallel to strain rate compressional orientations determined from GPS data, and a linear increase in normalised de-lay time with increasing strain rate in regions of stress-controlled anisotropy was also observed (Hiramatsu et al., 2010). However, here neither the orientations nor magnitudes of anisotropy cor-relate well to the strain rate. The region in central Japan was highly strained in a compressional regime and Kyushu is mostly in a strike-slip regime (Fig. 4), so the type of regime may explain the differences. Alternatively, the lack of correlation could be due

to structural effects dominating the areas where the strain and stress correlate poorly, such as the “star” pattern in the splitting fast directions (Figs. 5, 7) and P-wave fast directions (Wang and Zhao, 2013) at around 33N, 131.25E, and the boundary-parallel �near the shear zone at the southern boundary of the CVR (Fig. 5). Another factor could be differing effective smoothing making the regions of margin-parallel fast directions and margin-parallel max-imum horizontal strain rate mis-match to each other in the east (Fig. 7, 32N, 132E). The Hiramatsu et al. study only compared strain rate to delay times at locations where the directions co-incided. We were only able to find four points in the shallow inversion grid that fulfilled the strict criteria of well-aligned fast directions that also met the criteria of Hiramatsu et al. for fast di-rections within 30 degrees of the maximum strain rate direction, so we did not do the same comparison.

For the deep earthquakes, the trench-perpendicular fast direc-tions in southwest Kyushu are similar to those determined in two other studies of S waves passing through the mantle wedge (Salah et al., 2009; Terada et al., 2013). Trench-perpendicular fast direc-tions in the mantle wedge in the back-arc region west of the volcanic front were also determined further north by analysing ScS waves (Tono et al., 2009) and direct S waves (Nakajima and Hasegawa, 2004). Trench-perpendicular fast directions in the back-arc may be caused by mantle flow induced by drag above the down going lithospheric plate. A large-scale survey of surface wave anisotropy in Japan yields strong anisotropy of V SH > V SV in this area (Yoshizawa et al., 2010). If the flow is horizontal, then ac-cording to the relationships between olivine fabrics and seismic anisotropy as presented by Table 2 in Karato et al. (2008), the com-bination of splitting fast directions parallel to flow and V SH > V SVanisotropy is most likely caused by A- or D-type olivine. These types are both observed mainly in olivine with low water-content (H/Si < 100–200 ppm), which would suggest that the olivine has become dehydrated by water joining the melt, which is about 1% as estimated by 3-D electromagnetic images of the region (Hata and Uyeshima, 2015). Alternatively, if the flow is steeply dipping then C-type olivine fabric could exist with trench-parallel b-axes and trench-normal c-axes dipping 60◦ to the west (Terada et al., 2013), but this fabric should yield weak values of V SH compared to V SV. A more detailed study of V SH compared to V SV in this re-gion would be helpful.

Measurements of fast directions from deep earthquakes east of the volcanic arc are more trench-parallel than those to the west, as observed in previous studies (Nakajima and Hasegawa, 2004;Tono et al., 2009). However the results in northern Kyushu for this study are not as trench-perpendicular as those from the ScS study (Tono et al., 2009), suggesting that waves are being affected by more complex structures in the crust as well as in the mantle. The larger variance of the deep compared to shallow measurements also suggests interaction between splitting in the crust and mantle. The correlation between splitting directions of shallow and deep events, despite differing average values, suggests that the shallow anisotropy may be rotating the waveforms split from the deeper earthquakes, rather than simply re-splitting the waveforms. But the rotation is not complete enough to align the deep and shallow events. The waveforms may contain enough information so that a 3-D inversion could determine the deeper anisotropy.

In some of the volcanic regions we have determined that there may be some change in splitting as a function of time (Unglert et al., 2011). Such time variation is probably part of the variance that we observe in our measurements.

5. Conclusions

Statistically significant correlations are found between the di-rections of fast orientation � measured on shallow earthquakes

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and maximum horizontal stress directions measured from focal mechanism inversions, and also between the strength of anisotropy and stress ratio. These two facts are consistent with a strike-slip stress regime in which stress-controlled cracks cause the anisotropy. Similarly, stress and strain rate are well-correlated, sug-gesting that the present plate motions may be causing the stress orientations.

In the CVR of central Kyushu, E–W compressional stress and strain-rate align with E–W anisotropic fast directions. There arealso high anisotropy, low stress ratio and low compressional strain rate eigenvalues in that region, consistent with a tectonic exten-sion regime in the volcanic region.

Acknowledgements

This work was started while Savage was a Visiting Professor on the Earthquake Research Institute International Investigators pro-gram and a Visiting Fellow at Kyoto University through the Grant S08712 from the Japan Society for the Promotion of Science and the Royal Society of New Zealand International Science and Tech-nology Linkages Fund. Support was also provided from the JSPS Grants-in-Aid for Young Scientists (B) 25800244, the New Zealand Marsden Fund VUW0904 and a VUW strategic research grant. We would like to thank K. Nishida for help accessing the JMA data, S. Kinoshita for information about the orientation corrections, Y. Kohno for discussions, and GeoNet, JMA and NIED for data. H. God-frey helped with preparing the figures.

Appendix A. Supplementary material

Supplementary material related to this article can be found on-line at http://dx.doi.org/10.1016/j.epsl.2016.01.005.

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