Prediction of maximum P- and S-wave amplitude distributions incorporating frequency- and distance-dependent characteristics of the observed apparent radiation patterns

Abstract

Frequency-dependent model of the apparent radiation pattern has been extensively incorporated into engineering and scientific applications for high-frequency seismic waves, but distance-dependent properties have not yet been fully taken into account. We investigated the unified characteristics of frequency and distance dependences in both apparent P- and S-wave radiation patterns during local crustal earthquakes. Observed distortions of the apparent P- and S-wave radiation patterns could be simply modeled by using a function of the normalized hypocentral distance, which is a product of the wave number and hypocentral distance. This behavior suggests that major cause of distortion of the apparent radiation pattern is seismic wave scattering and diffraction within the heterogeneous crust. On the basis of observed normalized hypocentral distance dependency, we proposed a method for prediction of spatial distributions of maximum P- and S-wave amplitudes. Our method incorporating normalized hypocentral distance dependence of the apparent radiation pattern reproduced the observed spatial distributions of maximum P- and S-wave amplitudes over a wide frequency and distance ranges successfully.[Figure not available: see fulltext.]

Takemura et al. Earth, Planets and Space (2016) 68:166 DOI 10.1186/s40623-016-0544-8

Prediction ofmaximum P- andS-wave amplitude distributions incorporating frequency- anddistance-dependent characteristics ofthe observed apparent radiation patterns

Shunsuke Takemura1*http://orcid.org/0000-0002-7511-3443

Web End = , Manabu Kobayashi2 and Kazuo Yoshimoto2

http://orcid.org/0000-0002-7511-3443

Web End = Introduction

It is well known that, as frequency increases over 1Hz, the spatial distributions of observed maximum P- and S-wave amplitudes during local earthquakes (hereafter, this is called the apparent radiation pattern) are gradually distorted from the expected four-lobe amplitude pattern of a double-couple point source (e.g., Liu and Helmberger 1985; Satoh 2002a; Takenaka et al. 2003; Takemura et al. 2009; Sawazaki et al. 2011; Kobayashi etal. 2015). The frequency-dependent characteristics of the observed apparent radiation patterns have been incorporated into various applications such as the

predictions of strong ground motions (e.g., Pitarka etal. 2000; Pulido and Kubo 2004), the estimation of high-frequency seismic energy radiation during large earthquakes (e.g., Nakahara 2013), nonvolcanic/volcanic tremors (e.g., Maeda and Obara 2009; Kumagai et al. 2010; Cannata etal. 2013; Yabe and Ide 2014), and landslides (e.g., Ogiso and Yomogida 2015), and the earthquake early warning systems (e.g., Okamoto and Tsuno 2015). Although the frequencydistance change model for S-wave radiation pattern proposed by Satoh (2002b) has been used in some applications, to achieve more accurate estimation and prediction of high-frequency seismic radiation, a precise frequency- and distance-dependent model for the apparent radiation pattern for both P and S waves is required. Relationship of the apparent radiation patterns between P and S waves has been important due to recent development real-time systems, such as urgent

*Correspondence: [email protected]

1 National Research Institute for Earth Science and Disaster Resilience, 3-1 Tennodai, Tsukuba 305-0006, JapanFull list of author information is available at the end of the article

The Author(s) 2016. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

Web End =http://creativecommons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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earthquake detection and earthquake early warning (e.g., Okamoto and Tsuno 2015).

High-quality seismograms recorded by dense regional seismic networks for various distances and wide dynamic ranges enable us to investigate frequency- and distance-dependent characteristics of the apparent radiation pattern. Takemura et al. (2009, 2015) and Kobayashi et al. (2015) reported that the apparent P- and S-wave radiation patterns are distorted with increasing distance but still preserving the original four-lobe pattern at hypocentral distances less than 40km even for high frequencies. In this study, we rstly investigated the frequency- and distance-dependent characteristics of the apparent P- and S-wave radiation patterns using dense and large number seismograms. On the basis of observed characteristics, then we propose a frequency- and distance-dependent model of the apparent radiation pattern to predict the spatial distributions of maximum P- and S-wave amplitudes of local earthquakes.

Apparent radiation pattern forcrustal earthquakes

We analyzed velocity waveforms recorded by Hi-net (high-sensitivity seismograph network operated by the National Research Institute for Earth Science and Disaster Resilience (NIED); Okada etal. 2004) during 13 earthquakes occurred in the crust of Chugoku region, Japan (Events 113 of Fig.1a and Additional le1: Table S1). The mechanisms of these earthquakes were characterized by strike-slip faulting and reported consistently by both the moment tensor (MT) solutions of F-net (full range seismograph network by NIED; Fukuyama et al. 1998) and the rst-motion focal mechanisms in the unied hypocenter catalog of the Japan Meteorological Agency.

In some previous studies, energy partition of S wave in each horizontal component was analyzed in order to eliminate the eects of dierences in site amplication and source size. However, Sawazaki et al. (2011) pointed out that spatial distribution of maximum amplitudes and energy partitioning in each component show dierent frequency-dependent properties. Therefore, on the basis of the method by Kobayashi etal. (2015), we measured coda-normalized maximum P- and S-wave amplitudes (hereafter, these are referred to as the P-wave amplitude and S-wave amplitude, respectively) from three-component root-mean-square (RMS) envelopes for the following different frequency bands: 0.51, 12, 24, 48, and 816Hz.

Additional le1: Figure S1 shows examples of ltered velocity seismograms and RMS vector envelopes normalized by averaged coda amplitudes to eliminate the eects of dierences in site amplication and source size (e.g., Yoshimoto et al. 1993). Since coda normalization technique is applicable in the seismograms with hypocentral distance less than approximately 150km (e.g., Sato etal.

2012 Ch. 3; Takemoto etal. 2012), we employ the lapse times of 6070 s for calculating averaged coda amplitudes. The time windows of -seconds, which represent the averaged pulse durations of P and S waves measured from the displacement waveforms at four F-net stations (lled triangles in Fig.1a), were used to measure P- and S-wave amplitudes.

After measuring P- and S-wave amplitudes, we estimated the master attenuation curves of P- and S-wave attenuations by using the following equation:

where Aijmax is the P- or S-wave amplitude at a hypo-central distance of Li km, Qj is the quality factor for the apparent P- or S-wave attenuation, fC is the central frequency of each band, Vj is the seismic velocity for P or S waves in the upper crust (assuming 6.00 and 3.55km/s, respectively), and B is a constant. Since hypocentral distance Li is widely used in empirical attenuation functions of ground motions (e.g., Si and Midorikawa 1999; Boatwright 2007; Yabe et al. 2014), we simply assumed geometrical spreading 1/Li of body waves, rather than inverse of exact ray-path length. Figure 1b shows the apparent attenuations for P and S waves estimated by least square tting.

Figure1c, d shows the measured P- and S-wave amplitudes and master attenuation curves as a function of the hypocentral distance for frequencies of 0.51 and 48Hz. The color scale represents the magnitude of the P- and S-wave radiation pattern coefficients (|FP| and |FS|; Aki and Richards 2002) estimated from MT solutions in the one-dimensional (1D) crustal velocity structure (Ukawa et al. 1984), which is used in the Hi-net routine hypo-center analysis. The S-wave radiation pattern coefficient |FS| was calculated by RMS of SV- and SH-wave radiation pattern coefficients. Wavelengths in Fig.1c, d (P and S, respectively) were calculated by using the central frequencies of each band and seismic velocities in the crust. Observed amplitudes are scattered around master attenuation curves, reecting the eects of non-isotropic source radiation and uctuation of amplitude due to small-scale velocity inhomogeneity along propagation path (e.g., Hoshiba 2000; Yoshimoto etal. 2015).

The scatter due to non-isotropic source radiation is most evident in the P-wave amplitudes for the lowest frequency (0.51Hz; left side of Fig.1c). We conrmed that P-wave amplitudes with larger/smaller |FP| values tend to distribute above/below the master attenuation curve, respectively. As the frequency increased (48 Hz; right of Fig.1c), this tendency become unclear, implying that P-wave amplitudes at higher frequencies do not show a clear four-lobe apparent radiation pattern. Although

ln

~LiAmax ij

= ~fC

QjVj Li

+ B

j = P, S

,

(1)

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similar behaviors appeared in the S-wave amplitudes (Fig. 1d), the four-lobe patterns become unclear more rapidly compared to the P-wave ones (Fig.1c).

We calculated the observed amplitude uctuation Aj

by the following equation:

where Aj(Li) is the P- and S-wave amplitude at a hypocentral distance of Li and A0j(Li) is the prediction from the master attenuation curve (Eq. 1). Theoretical amplitude uctuations were dened as |Fj| uctuations from the azimuthal average of |Fj| at a hypocentral distance of Li.

Figure 2 shows the comparison of azimuthal dependence of the observed and theoretical amplitude uctuations (lled and open symbols, respectively) at frequencies of 0.51 and 48Hz. Despite of the continuous four-lobe azimuthal variations of theoretical amplitude uctuations, observed uctuations are scattered around the theoretical ones. As wavelengths decrease, observed amplitude uctuations are widely scattered and large amplitude uctuations also appeared in the nodal directions. We conrmed that one of the key parameters for distortions of the observed P- and S-wave apparent radiation patterns is the wavelength of the seismic waves.

Frequency anddistance dependences inthe apparent radiation pattern

To quantify distortion of the apparent radiation pattern from double-couple point source predictions, we simply calculated the cross-correlation coefficient (CCC) between the observation and theoretical amplitude uctuations using moving hypocentral distance windows (4070, 5080, 6090, 70100, 80110, 90120, and 100130km).

distances (log(kL)>2.85), showing almost dissipation of non-isotropic source radiation eect. Considering typical correlation length a of crustal heterogeneities (e.g., Takemura etal. 2009; Kobayashi etal. 2015), this feature appears in the strong scattering domain of kakL diagram (Fig.13.11 of Aki and Richards 1980), in where conventional ray theory does not stand.

To characterize observed kL dependence of CCC, a linear tting approach was applied by using the following equation:

The values of r and CCC0 were determined as

0.380.023 and 1.350.053, respectively, by a least squares estimation for the range of log(kL) < 2.85. The observed CCC could be described by using resultant Eq.(3) (blue line in Fig.3). We here introduce a set of values k1L1, k2L2, and k3L3 from log(kiLi)=0.92, 2.85, and 3.55 (i=1, 2, 3), respectively, from Fig.3, for the following discussions.

Apparent radiation pattern modeling andamplitude predictions

Pulido and Kubo (2004) proposed a simple linear frequency-dependent model of S-wave radiation pattern coefficients for strong ground motion prediction. On the basis of the observed linear decay of CCCs against log(kL), we revisited their approach and proposed a new model, which includes the frequency- and distance-dependent characteristics of the P- and S-wave apparent radiation pattern. Our frequency- and distance-dependent apparent radiation pattern coefficient Rj (j=P, S) at a station with a takeo angle and azimuth ~ is described by the following equation:

~Aj(Li) = Aj(Li)

A0j(Li)

A0j(Li)

~j = P, S

,

(2)

CCC = rlog(kL) + CCC0.

(3)

Fj(S, , [notdef], , ), if kL k1L1 Fj(S, , [notdef], , ) log(kL)

log(k1L1) log(k3L3)log(k1L1)

Rj(, , kL) =

Favej Fj(S, , [notdef], , )

, if k1L1 kL k2L2

Fj(S, , [notdef], , ) log(k2L2)log(k1L1)log(k3L3)log(k1L1)

,

(4)

Favej Fj(S, , [notdef], , )

, if k2L2 kL

Figure3 shows the estimated CCCs as a function of the normalized hypocentral distance kL, where k is the wave number (k=2/=2f/V) and L is the average hypo-central distance of each distance range. Observed CCCs showed linear decay from 0.75 to 0.25 with increasing log(kL) from 1.64 to 2.85 and no signicant dierences in decay patterns between P and S waves. These results suggest that major causes of the frequency- and distance-dependent distortion of the apparent radiation pattern are seismic wave scattering and diraction in the heterogeneous crust and that eects of crustal heterogeneity are not dierent for both P and S waves. Saturation of CCC decay was found at greater normalized hypocentral

where Fj is the radiation pattern coefficient of a double-couple point source in the 1D crustal velocity structure (Ukawa et al. 1984). The focal mechanism is characterized by using angles of strike ~S, dip , and rake . Fjave

is the average radiation pattern coefficient for P and S waves of a double-couple point source (Boore and Boat-wright 1984). Takeo angle was also evaluated in the 1D structure model (an example shown in Fig.4d). The modeled apparent radiation pattern coefficient introduced here is identical to the double-couple point source radiation pattern at small normalized hypocentral distances (<k1L1) and diminishes non-isotropy as increasing normalized hypocentral distance. Furthermore, our

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model includes not only S-wave radiation pattern but also P-wave one, which would be important for the earthquake early warning.

Figure4a, b shows the spatial distributions of modeled apparent radiation pattern coefficients for frequencies of 0.51 and 48Hz, respectively. We also show the spatial distribution of the radiation pattern coefficient for a double-couple point source in a homogeneous medium as a reference (Fig.4c), where amplitude nodes (Rj=0.00)

clearly exist. The azimuthal dierence of modeled apparent radiation pattern coefficients became unclear with increasing distances and wave numbers.

By using the estimated master attenuation curves and modeled apparent radiation pattern coefficients, we here propose a representation for the prediction of

coda-normalized maximum amplitudes for both P and S waves [Ajmax(,~,kL)] during local crustal earthquakes as follows:

where R0j(kL) is the azimuthal average of the modeled apparent radiation pattern coefficient.

Figure5 shows the comparisons between the observed and predicted spatial distributions of P- and S-wave amplitudes during Events 11 and 14 for low (0.51Hz) and high (48Hz) frequencies. The latter event was not

Amaxj(, , kL) =

Rj(, , kL)di exp[notdef]

kL

+ B

2Qj(k)

Rj(, , kL) = Rj(

, , kL) R0j(kL)

R0j(kL)

(5)

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used in the analyzes of the apparent radiation patterns in the previous sections, and its source parameters are shown at the bottom of Additional le1: Table S1. The

eects of rupture directivity (e.g., Boatwright 2007; Pacor etal. 2016) and uctuation of maximum amplitudes (e.g., Hoshiba 2000; Yoshimoto et al. 2015) were not taken into consideration within our method. Actually, for some earthquakes, directivity amplications were found in the southsoutheast direction from the source even for high frequencies (48Hz). Recent observation study by Pacor et al. (2016) demonstrated that some earthquakes with Mw of 3.54 show directivity eects and that weakening of directivity starts at a frequency of approximately 10 Hz. Despite this, our predictions reproduced the observed spatial distributions of P- and S-wave amplitudes for both low- and high-frequency bands reasonably. Since seismograms with hypocentral distances less than 150 km were used in our analysis, practical applicability of our method is limited within same distance range. As the wave number (k=2/=2f/V) and distance (L)

increased, both the observed and predicted maximum amplitude distributions became gradually distorted from the original four-lobe pattern of the double-couple point source.

Satoh (2014) employed frequency- and distance-dependent S-wave radiation pattern coefficient for the stochastic Greens function method based on empirical model of Satoh (2002a, b), which showed very weak distance dependency for frequencies of 25 Hz and an

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isotropic radiation pattern for higher (>6 Hz) frequencies irrespective of distance. Satoh (2002b) constructed this model via observed energy partitioning of S waves in each horizontal component to reduce source and site amplication eects, rather than spatial distribution of maximum amplitude. Although our model does not include directivity eects, our model practically succeeds in reproducing observed spatial distribution of maximum amplitude of small-to-moderate local crustal earthquakes

compared to Satoh (2002b)s model (Additional le 1: Figure S2). This dierence may be caused by dierence in the method for model construction.

Conclusions

We investigated the frequency and distance dependences in the apparent radiation pattern for both P and S waves during local crustal earthquakes. We demonstrated how the four-lobe apparent radiation pattern, which is

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expected from a double-couple point source, is gradually distorted with increasing frequency and distance. The observed distortions have common decay pattern for P and S waves and could be characterized by the normalized hypocentral distance kL. These results suggest that major causes of frequency- and distance-dependent distortion of the apparent radiation pattern are seismic wave scattering and diraction in the heterogeneous crust.

The observed frequency and distance dependences in the apparent radiation patterns for both P and S waves could be simply modeled by using a linear function of log(kL). On the basis of this, we proposed a method for prediction of the spatial distributions of maximum P-and S-wave amplitudes. Our method, which incorporates frequency- and distance-dependent characteristics of the observed apparent radiation pattern, successfully reproduced the observed spatial distributions of P- and S-wave amplitudes during small-to-moderate local crustal earthquakes.

Our method could also provide better insights into source rupture process and practical correction for the eects of the apparent radiation pattern. In future study, this would enable us to estimate the radiated source energy precisely and to obtain better insights into high-frequency seismic sources, such as small earthquakes and non-volcanic/volcanic tremors and the other eects, especially rupture directivity and uctuation of maximum amplitudes, will be taken into consideration within our method.

and conducting the signal processing work, respectively. We also thank two anonymous reviewers and the editor Prof. H. Takenaka for careful reading and constructive comments that improved the manuscript.

Competing interests

The authors declare that they have no competing interests.

Received: 29 April 2016 Accepted: 8 October 2016

References

Aki K, Richards P (1980) Quantitative seismology. University Science Books,

Freeman, San FranciscoAki K, Richards P (2002) Quantitative seismology, 2nd edn. University Science

Books, Freeman, San FranciscoBoatwright J (2007) The persistence of directivity in small earthquakes. Bull

Seismol Soc Am 97:18501861. doi:http://dx.doi.org/10.1785/0120050228

Web End =10.1785/0120050228 Boore DM, Boatwright J (1984) Average body-wave radiation coefficients. Bull

Seismol Soc Am 74:16151621Cannata A, Frazia DG, Aliotta M, Cassisi C, Montalto P, Patane D (2013)

Monitoring seismo-volcanic and infrasonic signals at volcanoes: Mt. Etna case study. Pure appl Geophys 170:17511771. doi:http://dx.doi.org/10.1007/s00024-012-0634-x

Web End =10.1007/ http://dx.doi.org/10.1007/s00024-012-0634-x

Web End =s00024-012-0634-x Efron B, Tibshirani R (1986) Bootstrap methods for standard errors, condence intervals, and other measures of statistical accuracy. Stat Sci 1(1):5477 Fukuyama E, Ishida M, Dreger DS, Kawai H (1998) Automated seismic moment tensor determination by using on-line broadband seismic waveforms. Zisin 51:149156 (in Japanese with English abstract)

Hoshiba M (2000) Large uctuation of wave amplitude produced by small uctuation of velocity structure. Phys Earth Planet Int 120:201217. doi:http://dx.doi.org/10.1016/S0031-920(99)00165-X

Web End =10.1016/S0031-920(99)00165-X Kobayashi M, Takemura S, Yoshimoto K (2015) Frequency and distance changes in the apparent P-wave radiation pattern: eects of seismic wave scattering in the crust inferred from dense seismic observations and numerical simulations. Geophys J Int 202:18951907. doi:http://dx.doi.org/10.1093/gji/ggv263

Web End =10.1093/ http://dx.doi.org/10.1093/gji/ggv263

Web End =gji/ggv263 Kumagai H, Nakano M, Maeda T, Yepes H, Palacios P, Ruiz M, Arrais S, Vaca M,

Molina I, Yamashita T (2010) Broadband seismic monitoring of active volcanoes using deterministic and stochastic approaches. J Geophys Res 115:B08303. doi:http://dx.doi.org/10.1029/2009JB006889

Web End =10.1029/2009JB006889 Liu H, Helmberger DV (1985) The 23:19 aftershock of the 15 October 1979

Imperial Valley earthquake: more evidence for an asperity. Bull Seismol Soc Am 75:689708Maeda T, Obara K (2009) Spatiotemporal distribution of seismic energy radiation from low-frequency tremor in western Shikoku, Japan. J Geophys Res 114, B00A09, doi:http://dx.doi.org/10.1029/2008JB006043

Web End =10.1029/2008JB006043 Maeda T, Obara K, Furumura T, Saito T (2011) Interference of long-period seismic waveeld observed by the dense Hi-net array in Japan. J Geophys Res 116:B10303. doi:http://dx.doi.org/10.1029/2011JB008464

Web End =10.1029/2011JB008464 Nakahara H (2013) Envelope inversion analysis for high-frequency seismic energy radiation from the 2011 MW 9.0 O the Pacic Coastof Tohoku earthquake. Bull Seismol Soc Am 103:13481359.

doi:http://dx.doi.org/10.1785/0120120155

Web End =10.1785/0120120155 Ogiso M, Yomogida K (2015) Estimation of locations and migration of debris ows on Izu-Oshima Island, Japan, on 16 October 2013 by distribution of high frequency seismic amplitude. J Volc Geotherm Res 298:1526. doi:http://dx.doi.org/10.1016/j.jvolgeores.2015.03.015

Web End =10.1016/j.jvolgeores.2015.03.015 Okada Y, Kasahara K, Hori S, Obara K, Sekiguchi S, Fujiwara H, Yamamoto A

(2004) Recent progress of seismic observation networks in Japan Hi-net, F-net, K-NET and KiK-net. Earth Planets Space, 56, xvxxviii, doi:http://dx.doi.org/10.1186/BF03353076

Web End =10.1186/BF03353076 Okamoto K, Tsuno S (2015) Investigation on relationship between epicentral distance and growth curve of initial P-wave propagating in local heterogeneous media for earthquake early warning system. Earth Planets Space 67:167. doi:http://dx.doi.org/10.1186/s40623-015-0339-3

Web End =10.1186/s40623-015-0339-3 Pacor F, Gallovi F, Puglia R, Luzi L, DAmico M (2016) Diminishing high-frequency directivity due to a source eect: empirical evidence from small

Additional le

Authors contributions

ST developed basic idea of this work, proposed a new method for amplitude prediction, and drafted this manuscript. MK analyzed Hi-net/F-net waveform data and examined the characteristics of the apparent radiation pattern. KY made comments on seismic wave scattering and helped drafting. All authors read and approved the nal manuscript.

Author details

1 National Research Institute for Earth Science and Disaster Resilience, 3-1 Tennodai, Tsukuba 305-0006, Japan. 2 Department of Material System Science, Graduate School of Nanobioscience, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan.

Acknowledgements

Hi-net and F-net waveform data and the MT solutions from the F-net are available via the Web site of the National Research Institute for Earth Science and Disaster Resilience, Japan. We used the unied hypocentral catalog provided by the Japan Meteorological Agency (JMA), which is available via the JMA server. The frequency response of the short-period Hi-net sensors with a natural frequency of 1 Hz was corrected to make a broadband record using the program of Maeda et al. (2011). Generic Mapping Tools (Wessel and Smith 1998) and Seismic Analysis Code (SAC) were used for making the gures

Takemura et al. Earth, Planets and Space (2016) 68:166

Page 9 of 9

earthquakes in the Abruzzo region Italy. Geophys Res Lett 43:50005008. doi:http://dx.doi.org/10.1002/2016GL068546

Web End =10.1002/2016GL068546 Pitarka A, Somerville P, Fukushima Y, Uetake T, Irikura K (2000) Simulation of near-fault strong-ground motion using hybrid Greens functions. Bull Seismol Soc Am 90:566586. doi:http://dx.doi.org/10.1785/0119990108

Web End =10.1785/0119990108 Pulido N, Kubo T (2004) Near-fault strong motion complexity of the 2000

Tottori earthquake (Japan) from a broadband source asperity model. Tectonophysics 390:177192. doi:http://dx.doi.org/10.1016/j.tecto.2004.03.032

Web End =10.1016/j.tecto.2004.03.032 Sato H, Fehler M, Maeda T (2012) Seismic wave propagation and scattering in the heterogeneous earth structure, 2nd edn. Springer, BerlinSatoh T (2002a) Empirical frequency-dependent radiation pattern of the 1998

Miyagiken-Nanbu earthquake in Japan. Bull Seismol Soc Am 92:1032 1039. doi:http://dx.doi.org/10.1785/0120010153

Web End =10.1785/0120010153 Satoh T (2002b) Radiation pattern and fmax of the Tottori-ken Seibu earthquake and the aftershocks inferred from KiK-net strong motion records. J. Struct

Constr Eng AIJ 556:2534 (in Japanese with English abstract)

Satoh T (2014) Generation method of stochastic Greens function considering into surface waves and scattering waves using records of moderate-size interplate earthquakes along the Sagami Trough. J Struct Constr Eng AIJ 705:15891599 (in Japanese with English abstract)

Sawazaki K, Sato H, Nishimura T (2011) Envelope synthesis of short-period seismograms in 3-D random media for a point shear dislocation source based on the forward earthquakes in southwestern Japan. J Geophys Res 116:B08305. doi:http://dx.doi.org/10.1029/2010JB008182

Web End =10.1029/2010JB008182 Si H, Midorikawa S (1999) New attenuation relationships for peak ground acceleration and velocity considering eects of fault type and site condition. J Struct Constr Eng AIJ 523:6370 (in Japanese with English abstract)

Takemoto T, Furumura T, Saito T, Maeda T, Noguchi S (2012) Spatial- and frequency-dependent properties of site amplication factors in Japan derived by coda normalization method. Bull Seismol Soc Am 102:1462 1476. doi:http://dx.doi.org/10.1785/0120110188

Web End =10.1785/0120110188

Takemura S, Furumura T, Saito T (2009) Distortion of the apparent

S-wave radiation pattern in the high-frequency waveeld: Tottoriken Seibu, Japan, earthquake of 2000. Geophys J Int 178:950961. doi:http://dx.doi.org/10.1111/j.1365-246X.2009.04210.x

Web End =10.1111/j.1365-246X.2009.04210.x Takemura S, Furumura T, Maeda T (2015) Scattering of high-frequency seismic waves caused by irregular surface topography and small-scale velocity inhomogeneity. Geophys J Int 201:459474. doi:http://dx.doi.org/10.1093/gji/ggv038

Web End =10.1093/gji/ggv038 Takenaka H, Mamada Y, Futamure H (2003) Near-source eect on radiation pattern of high-frequency S waves: strong SHSV mixing observed from aftershocks of the 1997 Northwestern Kagoshima, Japan, earthquakes. Phys Earth Planet Int 137:3143. doi:http://dx.doi.org/10.1016/S0031-9201(03)00006-2

Web End =10.1016/S0031-9201(03)00006-2 Ukawa M, Ishida M, Matsumura S, Kasahara K (1984) Hypocenter determination method of the Kanto-Tokai observational network for microearth-quakes. Res Notes Natl Res Cent Disaster Prev 53:188 (in Japanese with English abstract)

Wessel P, Smith WHF (1998) New, improved version of generic mapping tools released, EOS. Trans Am Geophys Union 79:579. doi:http://dx.doi.org/10.1029/98EO00426

Web End =10.1029/98EO00426 Yabe S, Ide S (2014) Spatial distribution of seismic energy rate of tectonic tremors in subduction zones. J Geophys Res 119:81718185. doi:http://dx.doi.org/10.1002/2014JB011383

Web End =10.1002 http://dx.doi.org/10.1002/2014JB011383

Web End =/2014JB011383 Yabe S, Baltay A, Ide S, Beroza G (2014) Seismic-wave attenuation determined from tectonic tremor in multiple subduction zones. Bull Seismol Soc Am. doi:http://dx.doi.org/10.1785/0120140032

Web End =10.1785/0120140032 Yoshimoto K, Sato H, Ohtake M (1993) Frequency-dependent attenuation of P and S waves in the Kanto area, Japan, based on the coda-normalization method. Geophys J Int 114:165174. doi:http://dx.doi.org/10.1111/j.1365-246X.1993.tb01476.x

Web End =10.1111/j.1365-246X.1993. http://dx.doi.org/10.1111/j.1365-246X.1993.tb01476.x

Web End =tb01476.x Yoshimoto K, Takemura S, Kobayashi M (2015) Application of scattering theory to P-wave amplitude uctuations in the crust. Earth Planets Space 67:199. doi:http://dx.doi.org/10.1186/s40623-015-0366-0

Web End =10.1186/s40623-015-0366-0