forearc versus backarc attenuation of earthquake ground motion

Forearc versus Backarc Attenuation of Earthquake Ground Motion

by Hadi Ghofrani and Gail M. Atkinson

Abstract Understanding of the attenuation of seismic wave amplitudes withdistance is a crucial issue for ground motion prediction equations and seismic hazardanalysis. In this study, we empirically evaluate the influence of regional geologicstructure, in particular the attenuation effects of traveling through a volcanic arc region(forearc versus backarc attenuation) in northern Japan. We perform regression analysisof Fourier amplitude spectra (FAS) of five well-recorded Japanese events that occurredvery close to the line formed (in map view) by the volcanic arc. This provides anapproximately symmetrical distribution of stations for each event relative to the vol-canic front; forearc stations lie to the east of the front, while backarc stations lie to thewest. To compare the characteristics of shallow and deep events, we have includedboth crustal and in-slab events in our dataset. Based on inspection of the data, weassume a hinged bilinear geometric spreading model with a fixed slope of �1 out toa distance of 50 km, with slope of �0:5 thereafter (for all events). Our results show,with a very high level of confidence, that high-frequency attenuation is greater in thebackarc direction. The Q values for forearc regions (Q ∼ 240 at 1 Hz, increasing toQ ∼ 3890 at 10 Hz) are about a factor of 2 larger than those for backarc regions(Q ∼ 196 at 1 Hz, increasing to Q ∼ 1669 at 10 Hz) at high frequencies, implyingmuch stronger attenuation as waves travel through the volcanic crustal structure to thebackarc stations. The separation of forearc and backarc travel paths results in a sig-nificant reduction in the standard deviation (σ) of ground motion predictions (by asmuch as 0.05 log10 units), which has important implications for hazard analyses insubduction zone regions.

Introduction

Seismic waves propagate from the earthquake hypocen-ter to the site through a heterogeneous medium in a highlycomplicated manner. A ground-motion record manifests thecharacteristics of the source, transmission path, and siteeffects, all of which are often encapsulated together in em-pirical ground-motion prediction equations (GMPEs). Manyseismologists have studied the source, path, and site effectsto model and predict strong ground motions for earthquakeengineering needs (e.g., Burger et al., 1987; Frankel et al.,1990; Boatwright, 1994; Hatzidimitriou, 1995; Del Pezzoet al., 1995; Atkinson and Chen, 1997; Frankel et al., 1999;Zhao, 2010). Generally, ground motion will decrease (attenu-ate) with distance. But wave propagation in a layered earthsuggests more complicated behavior. Multiple reflectionsand refractions of traveling wave motions result in spatialand time fluctuations of their amplitude and phase character-istics: attenuation causes frequency-dependent amplitudereduction and phase shifts; scattering produces complicatedsuperpositions of wavelets with different paths; reverberationin shallow sedimentary layers causes frequency-dependentamplification; and finally, the recording system and thesampling process produce additional signal distortions

(Scherbaum, 1994). All of these factors can be regarded asfilters or transfer functions along the path in the sense ofsignal processing.

The wave propagation terms in GMPEs commonlyexpress the effect of geometrical spreading and anelastic andscattering attenuation on ground-motion amplitudes. Due tothe trade-offs between these parameters in the adopted form ofGMPEs, it is not an easy task to estimate each of them sepa-rately. However, this interaction between the estimates of theparameters can bemitigated by some simple physical assump-tions. For example, the geometrical spreading factor at lowfrequencies is relatively unaffected by anelastic attenuationand scattering at short source-receiver distances (e.g., Atkin-son, 2004). Thus, we may estimate the geometrical spreadingfactor based on the attenuation of low-frequency groundmotions and then estimate the corresponding quality-factorthrough regression analysis with the geometric spreadingfixed. The path effect estimated by this method is an overallaverage of the factors affecting ground motions propagatingthrough the medium. A simple average model is plausible formany tectonic settings, especially at regional distances. Butin complicated geologic regimes such as subduction zones

3032

Bulletin of the Seismological Society of America, Vol. 101, No. 6, pp. 3032–3045, December 2011, doi: 10.1785/0120110067

(e.g., Cascadia, Japan, Mexico), where rays are travellingacross complex structural features, describing path effectsby simple functions may be inadequate. Knowing the trueshape of the average attenuation curve is important for tworeasons. First, we need this knowledge to reliably infer sourceproperties from distant observations. Second, the shape of thecurve is an important consideration in seismic hazard anal-yses, particularly for sites at distances important for engineer-ing purposes (<200 km) from an active seismic source. Inthis study we investigate attenuation effects due to wave pas-sage through a volcanic front in the subduction zone environ-ment of Japan. We focus on the differences in attenuationbetween forearc and backarc regions.

The volcanic front is defined by the geological forma-tion of volcanoes in subduction zones, generally above theslab and parallel to the trench axis (Sugimura, 1960). It iswell-known that the volcanic structures in the crust and man-tle may affect attenuation in subduction zones by dividingthe region into forearc and backarc regions; for example, innorthern Japan, the volcanic front acts as a natural boundaryand results in heterogeneous attenuation structure beneaththis region (e.g., Hasegawa et al., 1994; Yoshimoto et al.,2006). The mantle wedge in the backarc regions has lowseismic velocity and a low quality factor (Q), where Q is theinverse of anelastic attenuation. This wedge filters out thehigh-frequency content of motions propagating from deep-focus in-slab events that traverse the wedge (Kanno et al.,2006; Zhao, 2010). Figure 1 is a schematic illustration of theproblem. In this figure, the shaded area represents the hot andlow-Q zone due to the volcanic zone. To date, GMPEs havetried to introduce correction factors to take the heterogeneousattenuation structure causing the anomalous intensity innorthern Japan into consideration (Morikawa et al., 2006;Kanno et al., 2006; Dhakal et al., 2008; Zhao, 2010). In this

study, we aim to improve on previous approaches by analyz-ing data that are optimal in terms of their potential to definethe attenuation differences quantitatively.

We use Fourier amplitude data to examine the shape ofthe attenuation curve for selected crustal and in-slab eventspropagating in forearc and backarc regions. We developseparate Q models to describe the ground motions in forearcand backarc regions in Japan and show that this path distinc-tion reduces aleatory variability in ground motions.

Data

To study the behavior of ground motions in forearc andbackarc regions, we have selected 22 events of moment mag-nitude �M� > 5:0 that lie close to the volcanic arc in Japan,and thus provide an approximately symmetrical distributionof stations for each event relative to the volcanic front, asshown in Figure 2. To compare the characteristics of shallowand deep events, we have included both crustal and in-slabevents in our dataset. The total number of records for the 14selected in-slab events is 2992 and for the 8 well-recordedcrustal events is 1052 (overall 4044). After applying cut-off distance criteria (as discussed in Regression Analysis),

Figure 1. Schematic illustration of sample ray paths from twoevents within the subducting slab. Amplitudes at A1 will be lowerthan those at station B1, for the same hypocentral distance. Seismicwaves registered at backarc stations (A1) experienced crossingthrough a low-velocity, high-attenuation mantle wedge shown byshaded areas. The bright gray area surrounded by a dashed linerepresents the extended low-velocity, low-Q structure underneathbackarc regions due to the spreading of volcanoes to the westerncoastlines in the central part of Japan. (Modified from Hasegawaet al., 1994.)

Figure 2. Epicenters of crustal (squares) and in-slab (circles)study events. Sizes of symbols represent the magnitudes of theevents.

Forearc versus Backarc Attenuation of Earthquake Ground Motion 3033

the total number of records is reduced to 2244, whichincludes 575 records for crustal and 1669 records for in-slabevents. Details of the selected events are summarized inTable 1.

Strong ground-motion time-series were downloadedfrom the Kyoshin network (K-NET; see Data and Re-sources). Focal depth information is adopted from K-NETreports. The assigned M for each event is that reported bythe Global CMT catalog. As the soil profiles are generallyavailable for only the top 10 or 20 m, the time-averaged ve-locity to a depth of 30 m (VS30) for each site is calculatedfrom the site velocity profile extended to 30 m using themodel given by Boore (2004). VS30 has become the mostcommon parameter for the simplified classification of a sitein terms of its seismic response (National Earthquake Ha-zards Reduction Program [NEHRP], 2000; Eurocode 8,2004; National Building Code of Canada [NBCC], 2005).Variability of ground motion due to site amplification is con-sidered by a linear function of VS30. Any stations for whichthe shear-wave velocity profile is not available are not used inthe analysis.

The data processing procedure for all records includesbaseline correction (removing dc and trend) and band-passfiltering. Signals are zero-padded at both ends to a sufficient

duration for reliable processing, considering the corner fre-quency of the filter (Converse and Brady, 1992). We haveapplied noncausal, band-pass Butterworth filters with anorder of 4. The selected frequency range of analysis is 0.1 to15 Hz. The lower frequency limit was selected after inspect-ing many records and determining that this value is appro-priate to provide well-shaped displacement time-series, anddisplacement spectra with a flat portion at low frequencies.The upper band is chosen considering the cut-off frequencyof the seismograph response spectrum (15 Hz). To make theenergy of the signal zero at the beginning and the end, a 5%cosine taper is applied to both ends. For each record, the geo-metric-mean horizontal-component peak ground accelera-tion (PGA) and Fourier amplitude spectrum (FAS) arecalculated. Log (10) amplitudes of the spectra are tabulatedat frequencies having a spacing of 0.1 log frequency units,where the log(10) amplitudes were averaged within each fre-quency bin centered about the tabulated frequency.

Overall Characteristics of Data in Forearc andBackarc Regions

To gain an initial impression of the ground motions inforearc and backarc regions, we compare the FAS for two

Table 1Selected In-Slab and Crustal Events

Date(yyyy/mm/dd)*

Time(local time; hh:mm:ss)

Latitude(°N)

Longitude(°E) M Depth (km)† Sites‡ Strike (Φ ) (°) Dip (δ ) (°)

Length(km)

Width(km)

In-Slab Events1996/12/04 00:49:00 37.44 139.61 5.6 146 86 – – – –1996/12/21 10:29:00 36.13 139.87 5.5 53 170 – – – –1997/11/15 16:05:00 43.65 145.08 6.0 130 92 – – – –1999/05/13 02:59:00 42.95 143.91 6.2 101 202 – – – –2001/12/02 22:02:00 39.40 141.26 6.4 119 330 – – – –2003/05/26§ 18:24:00 38.81 141.68 7.0 74 (52) 412 192 68 17 192004/10/06 23:40:00 35.99 140.09 5.7 65 207 – – – –2004/11/27 07:42:00 42.33 143.08 5.6 53 121 – – – –2007/01/16 03:18:00 34.94 138.89 5.9 180 189 – – – –2007/04/19 00:07:00 42.67 141.95 5.5 135 167 – – – –2007/07/01 13:12:00 43.54 144.91 5.8 140 143 – – – –2008/04/17 04:19:00 39.04 140.23 5.8 165 279 – – – –2008/07/24∥ 00:26:00 39.73 141.63 6.8 104 (120) 462 176 75 25 252008/09/22 16:32:00 41.54 140.56 5.6 150 132 – – – –

Crustal Events1996/08/11 03:12:00 38.92 140.63 5.9 7 82 – – – –1996/08/11 08:10:00 38.90 140.70 5.7 10 93 – – – –1997/03/04 12:51:00 34.95 139.16 5.6 2 76 – – – –1998/05/03 11:09:00 34.95 139.18 5.5 3 78 – – – –1998/09/03 16:58:00 39.80 140.91 5.8 10 66 – – – –2003/07/26§ 00:13:00 38.43 141.16 5.5 12 129 – – – –2003/07/26§ 07:13:00 38.40 141.17 6.2 12 (3.7) 199 11 40 13.6 5.12008/06/14§ 08:43:00 39.00 140.90 7.2 8 (0.4) 329 198 31 20 12

*Events in bold are highlighted study events.†The depth values in parentheses are those estimated through fault plane modeling.‡Total number of stations that recorded the event where known (not the number of records used for the regression analysis).§Fault plane solution is based on the reports by Geographical Survey Institute (GSI). For the GSI’s reports, latitude, longitude, and depth correspond to a

corner of the fault plane, whereas for the EIC notes, latitude, longitude, and depth correspond to the center of the fault plane.∥Fault plane solution is based on the EIC Seismological Note by M. Kikuchi and Y. Yamanaka (see Data and Resources).

3034 H. Ghofrani and G. M. Atkinson

such stations at equal epicentral distance from a given earth-quake, as shown in Figure 3. Because the epicenter of theevent is very close to the volcanic front, these two stationsare also at about the same distance from the arc. It is clearfrom Figure 3 that the station located on the forearc siderecords much higher energy at high frequencies comparedwith the backarc station, due to a difference in the slopeof the spectra versus frequency. Both stations are NEHRPClass C. While the backarc station, AKT023, is slightlysofter (VS30 � 429 m=s) than the forearc station, IWT010(VS30 � 668 m=s), this modest difference in shear-wavevelocity would not likely account for the pronounced differ-ences (factor of 4) in high-frequency amplitudes and spectralshape. We conclude that the observed differences are notlikely to be due to site effects.

We plot the geometric mean of the horizontal-component FAS for two well-recorded sample events as afunction of distance in Figure 4. The data have been normal-ized to a common VS30 � 300 �m=s� and a common sourceamplitude. The normalization is performed based on theterms of the regression analysis for these parameters, asdescribed in the next section. The different distance-decayrates for the forearc and the backarc stations can be clearlyseen in this figure, for both the crustal and in-slab events.Ground motions at low frequency (0.5 Hz) show similarlevels of FAS, but at high frequency (7 Hz), the ground-motion decay trends diverge. As expected, high-frequencyground motions decay more rapidly with distance than dolow-frequency motions, especially for backarc stations.

Regression Analysis

We use regression analysis to quantify the effects seen inFigures 3 and 4. Japan’s K-NET strong-motion seismicnetwork provides an invaluable opportunity to study theseeffects. However, the K-NET database may need filtering toremove weak-motion data at distance (which are not reliablyrecorded), in order to prevent a biased estimate of attenuation.From visualizing the database, it appears there is a flatteningof amplitudes around 70 km for moderate events, which hasbeen interpreted as due to instrument limitations (Strasser andBommer, 2005; Kanno et al., 2006), or alternatively as a biasdue to untriggered stations (Zhao et al., 2006). This may beequivalent to the low-amplitude quantization noise problemmentioned by Atkinson (2004). The potential bias is greatestat large distances from the source, where accelerations arelow. To determine the cut-off distances to use to ensure reli-able amplitude data, we examined the five best-recordedevents (which contain ∼40% of the total number of records).For each event, we went through all the records visually andselected the S-wavewindow; we used only those records withenough preevent memory to estimate the background noiselevel and establish acceptable signal-to-noise ratio (> 2).We plot the attenuation of amplitudes to establish the distancebeyond which the average acceleration level is predicted tobe less than the minimum-resolvable level plus one standarddeviation. Because this distance is magnitude-dependent(with larger events producing reliable amplitudes to largerdistances), the prediction is made by inspecting the trend ofpeak ground accelerations for each event versus hypocentral

Figure 3. Comparison of horizontal-component Fourier Amplitude Spectrum (FAS) of an in-slab event (2 December 2001, 22:02:00,M 6.4, h � 119 km) at two stations. AKT023 is a backarc station at 55 km, and IWT010 is a forearc station at 53 km from the epicenter.VS30 � 429 m=s and VS30 � 668 m=s at AKT023 and IWT010, respectively. The spectra of the strongest shaking part of the signals, asshown by the black window, are compared.


distance. Figure 5 illustrates how this procedure is used todetermine a cut-off distance of Rmax � 100 and 250 for theM 5.4 and M 6.9 events, respectively (see also Fig. 4). Thecut-off distances used for each event in the regressionanalysis are given in Table 2.

Functional Form

A general empirical attenuation form for a specific eventis often written as:

logA � A0 � b logR � cR; (1)

where A0 is source amplitude, b is the apparent geometricspreading, c is the anelastic attenuation coefficient and R is

a distance measure. Theoretically b � 1 for body wavesin a whole-space, and c � 0 for a perfectly elastic earth.Generally, c increases with frequency, while b is approxi-mately frequency-independent. The regional quality factor,Q, is proportional to the inverse of anelastic attenuation (c)(Trifunac, 1976):

c�f� � πf log10�e�Q�f�β ; (2)

where β is the velocity of shear-wave along the propagationpath, assumed here to be 3:5 �km=s�. The frequency depen-dence of Q can be generally expressed in an exponentialform as Q � Q0f

n (e.g., Rautian and Khalturin, 1978),although a polynomial form is sometimes used to better

Figure 4. Comparison of forearc and backarc attenuation for representative crustal and in-slab events at frequencies of ∼0:5 and 7.0 Hz.All the records are normalized (as explained in the text) to a common source amplitude and a common reference site condition withVS30 � 300 m=s.


accommodate the trend of Q values often observed at lowerfrequency (e.g., Aki, 1980; Cormier, 1982; Boore, 1983,2003; Atkinson, 2004).

Assuming that low frequencies are relatively unaffectedby anelastic attenuation and scattering at short source-receiver distances (Atkinson, 2004), one can estimate thegeometrical spreading from the apparent decay slope at lowfrequencies. Explanatory plots of ground motion parametersversus distance, as shown on Figure 4, suggested that ahinged bilinear geometrical spreading function will describethe behavior of the data for crustal events (e.g., Ordaz andSingh, 1992; Castro et al., 1996). For in-slab events, data aresparse in the direct-wave distance range (<70 km), so thefunctional form cannot be reliably discerned.

In Figure 6 we have plotted two representative eventsto illustrate the decay characteristics of different types ofevents. Data are normalized to a specific reference site con-dition (VS30 � 300 m=s) as follows:

log obsnormal � log obs � log pred� log prednormal; (3)

where obs is the observed amplitude of ground motion,obsnormal is the normalized amplitude, pred is the predictedvalue for identical values of the predictive variables as in theobserved data, and prednormal is the predicted value under thenormalization conditions (Fukushima et al., 2003). The pre-dicted values are those given by the regression equationsdescribed in the following. For both types of events, we havededuced by inspection that a bilinear geometrical spreading

Figure 5. Average trends of PGA for events ofM 5.4 andM 6.9.Small symbols are individual records, while large symbols aregeometric-mean values in log-distance bins. Note apparent flatten-ing for M 5.4 at R > 100 km. Amplitudes for M 6.9 are reliable toR≅250 km.

Table 2Q Values at Specific Frequencies of f � 0:5, 1.0, 5.0, and 10.0 (Hz) in Forearc and Backarc Regions for All In-Slab

and Crustal Events

Forearc Q at f � Backarc Q at f �Date (yyyy/mm/dd) Time (local time; hh:mm:ss) M h (km) Rmax* 0.5 1.0 5.0 10.0 0.5 1.0 5.0 10.0

In-Slab Events1996/12/04 00:49:00 5.6 146 500 53 122 1499 12994 45 105 609 10831996/12/21 10:29:00 5.5 53 250 61 122 557 722 67 130 375 4871997/11/15 16:05:00 6.0 130 300 122 229 4873 12994 177 244 1772 29991999/05/13 02:59:00 6.2 101 250 244 650 2436 4873 325 557 1026 16952001/12/02 22:02:00 6.4 119 300 139 390 3898 3898 177 354 1772 19492003/05/26 18:24:00 7.0 74 400 217 487 1083 2166 177 354 722 12572004/10/06 23:40:00 5.7 65 200 70 139 672 1147 50 108 390 6392004/11/27 07:42:00 5.6 53 150 67 122 780 1856 61 111 527 10832007/01/16 03:18:00 5.9 180 500 85 229 4873 9746 57 134 886 12992007/04/19 00:07:00 5.5 135 250 89 195 1772 5569 89 150 591 13442007/07/01 13:12:00 5.8 140 300 130 354 6497 12994 108 260 1772 25992008/04/17 04:19:00 5.8 165 300 103 300 6497 9746 93 244 975 14992008/07/24 00:26:00 6.8 104 250 122 260 1499 2999 93 186 750 13442008/09/22 16:32:00 5.6 150 500 150 278 NA† NA 195 300 9746 4331

Crustal Events1996/08/11 03:12:00 5.9 7 150 25 78 780 1083 31 100 812 8471996/08/11 08:10:00 5.7 10 100 16 55 975 736 23 115 1949 7091997/03/04 12:51:00 5.6 2 100 41 95 1499 812 30 71 609 6391998/05/03 11:09:00 5.5 3 100 70 83 1299 736 49 71 453 5821998/09/03 16:58:00 5.8 10 100 63 186 1299 1344 162 229 591 6722003/07/26 00:13:00 5.4 12 150 40 70 1772 3249 278 115 696 8472003/07/26 07:13:00 6.0 12 200 32 134 1624 1344 72 130 390 5342008/06/14 08:43:00 6.9 8 250 150 260 696 764 108 150 390 513

*Rmax is the applied cut-off distance.†NA, not applicable.


factor with a crossover distance of 50 km will adequatelydescribe the decay.

For crustal events, the slope of FAS values versus distanceappears to follow the theoretical value of �1 correspondingto attenuation of the direct wave in a whole-space at<50 kmat low frequency; the amplitudes at distances beyond 50 kmdecrease more slowly, as the direct wave joined by postcriticalreflections off the base of the crust. This is due to theMoho-bounce effect, which has been shown to be importantin characterizing ground motions at regional distances(e.g., Burger et al., 1987; Somerville and Yoshimura, 1990;Somerville et al., 1990; Campbell, 1991; Atkinson and Mer-eu, 1992; Somerville et al., 2001; Bay et al. 2003; Atkinson,2004). We assume that the geometric spreading rate is �0:5

beyond 50 km. This rate is appropriate for the decay ofamplitudes for postcritical reflected waves and Lg phase ina half-space at regional distances (Hasegawa et al., 1985;Chun et al., 1987; Shin and Herrmann, 1987). The dominantpart of the signal at these distances is multiply reflected andrefracted shear waves that attenuate as surface waves becausethey are trapped within the crustal waveguide (Ou and Herr-mann, 1990). With the slopes fixed, we find the best value forthe crossover distance is ∼50 km. This distance providesminimal attenuation residuals and near-source spectral ampli-tudes in reasonable agreement with expected values based onthe seismic moment.

For the in-slab events, most of the records are at dis-tances greater than ∼100 km. In concept, we might expect

Figure 6. Comparison of PGA in forearc and backarc regions. In this figure, symbols represent normalized observed ground motions forVS30 � 300 m=s. The geometrical spreading factor in the adopted bilinear form is fixed to �1 for Rij ≤ 50 km and �0:5 for Rij > 50 km.

Figure 7. Attenuation (Fourier acceleration spectrum at 7 Hz, in cm=s) and Q for M 7.0 in-slab event of 26 May 2003. (a) Solid line isbest fit for forearc motions; dashed line is best fit for backarc motions. (b) Symbols showQ values from this study; lines showQ values fromprevious studies in Japan.


the crossover distance to be larger for the in-slab events dueto their greater focal depth, or we might not establishLg-spreading at all for deep events. However, there areinsufficient data at <100 km to establish the behaviorempirically. Therefore, we assume the same hinged bilinearform as used for crustal events for consistency in derivingthe anelastic attenuation. We note, though, that the decaywithin 100 km is not constrained by data for in-slabevents, and that the assumed crossover distance of 50 kmmight bias source-parameter estimates for in-slab events,if the actual geometrical spreading is different from thatassumed. Furthermore, the estimated anelastic attenuationcoefficients for the in-slab events are referenced to a geo-metric spreading coefficient of �0:5; different Q valueswould be obtained if a spreading rate of �1 were assumedfor all distances.

To examine attenuation differences between forearcand backarc regions, we used separate anelastic attenuationfactors. Thus, the following functional form is adoptedfor the regression of ground-motion amplitudes, Y (Booreet al., 2009):

log10 Y � c1 � c2 log10�Rij� � c4�Rij�� c5 log10�VS30=Vref�;

for Rij < R0

log10 Y � c1 � c2 log10�R0� � c3 log10�Rij=R0�� c4�Rij� � c5 log10�VS30=Vref�;

for Rij ≥ R0 c4 ��

c41 �1 � ARC�c42 ARC

; (4)

Figure 8. Attenuation (7 Hz) and Q for M 6.8 in-slab event of 24 July 2008. (a) Solid line is best fit for forearc motions; dashed line isbest fit for backarc motions. (b) Symbols show Q values from this study; lines show Q values from previous studies in Japan.

Figure 9. Attenuation (7 Hz) and Q for M 5.4 crustal event of 26 July 2003. (a) Solid line is best fit for forearc motions; dashed line isbest fit for backarc motions. (b) Symbols show Q values from this study; lines show Q values from previous studies in Japan.


where Rij is the hypocentral distance from event i to station jand R0 is the fixed crossover distance (� 50 km). The coeffi-cients c2 and c3 are fixed at �1 and �0:5, respectively. Theanelastic coefficients c41 and c42 are for forearc and backarcregions, respectively. ARC is a dummy variable that is set to 1for forearc and 0 for backarc stations. The site amplification isassumed to be linearly dependent on VS30 and is specified re-lative to motions that would be recorded on an NEHRP B-Csite condition (Vref � 760 m=s).

Results

We performed the regression analysis separately foreach event of the database to gain insight into the variabilityof the attenuation. Figures 7 to 11 show the attenuation

results for five well-recorded events. Higher Q values andlesser attenuation are readily apparent for the forearc stationsat high frequencies (≥2 Hz) for all events. Table 2 listsattenuation results for all events, while Table 3 providesall regression coefficients. It may be noted in Figures 7 to 11that the Q values of this study tend to differ significantlyfrom those of previous studies (Kobayashi et al., 2000; Zhaoet al., 2006; Macias et al., 2008). This may be largely due tothe use of 1=R attenuation at all distances in the previousstudies, whereas in this study we use 1=

pR attenuation

beyond 50 km. Because anelastic attenuation and geometricspreading are coupled, the Q values in this study are notdirectly comparable with those of the previous studies.Different distance ranges for the analysis will also affect theresults. Finally, the differences could also be partly due to the

Figure 11. Attenuation (7 Hz) and Q forM 6.9 in-slab event of 14 June 2008. (a) Solid line is best fit for forearc motions; dashed line isbest fit for backarc motions. (b) Symbols show Q values from this study; lines show Q values from previous studies in Japan.

Figure 10. Attenuation (7 Hz) and Q forM 6.0 crustal event of 26 July 2003. (a) Solid line is best fit for forearc motions; dashed line isbest fit for backarc motions. (b) Symbols show Q values from this study; lines show Q values from previous studies in Japan.


Figure 12. (a) Displacement spectra and (b) acceleration spectra of five well-recorded events compared with the Brune source model atRref � 1 km. The spectrum at each station is corrected back to the source considering geometrical spreading and the average quality factorestimated from all crustal and in-slab events in the dataset. The long-period level is fixed by the known seismic moment. The stress-parameterwhich best matches the high-frequency flat part of the acceleration spectrum is inferred for each event.

Table 3Regression Coefficients for the Five Well-Recorded Events Considering the Fixed Geometrical Spreading

of �1:0�R ≤ 50 km� and �0:5�R > 50 km�Date

(yyyy/mm/dd)Time (local time;

hh:mm:ss)Stress Drop

ΔσHypocentral Cut-OffDistance (Rmax) M h (km) f (Hz) c1 c41 c42 c5

2003/05/26

18:24:00 300 bars 250 km 7.0 71 0.5 2.8277 �0:0011 �0:0009 �0:6918:24:00 300 bars 250 km 7.0 71 1.0 2.8079 −0:0011 �0:0008 �0:8718:24:00 300 bars 250 km 7.0 71 5.0 3.2123 �0:0027 �0:0018 �0:3118:24:00 300 bars 250 km 7.0 71 15.0 3.0988 �0:0031 �0:0018 0.4618:24:00 300 bars 250 km PGA 3.8337 �0:0025 �0:0018 �0:53

2003/07/26

00:13:00 100 bars 150 km 5.5 12 0.5 1.6664 �0:0007 �0:0049 �0:2900:13:00 100 bars 150 km 5.5 12 1.0 1.8484 �0:0034 �0:0056 �0:7800:13:00 100 bars 150 km 5.5 12 5.0 2.3069 �0:0028 �0:0011 �0:1400:13:00 100 bars 150 km 5.5 12 15.0 2.4471 �0:0046 �0:0012 0.5500:13:00 100 bars 150 km PGA 3.4486 �0:0063 �0:0036 0

2003/07/26

07:13:00 150 bars 200 km 6.2 12 0.5 2.2557 −0.0027 −0.0061 −0.4307:13:00 150 bars 200 km 6.2 12 1.0 2.2997 �0:003 �0:0029 �0:8107:13:00 150 bars 200 km 6.2 12 5.0 2.7457 �0:005 �0:0012 �0:1207:13:00 150 bars 200 km 6.2 12 15.0 2.8848 �0:0073 �0:0029 0.6307:13:00 150 bars 200 km PGA 3.6299 �0:0057 �0:0021 �0:1

2008/06/14

08:43:00 140 bars 250 km 7.2 8 0.5 2.5727 �0:0018 �0:0013 �0:7108:43:00 140 bars 250 km 7.2 8 1.0 2.6734 �0:0026 �0:0015 �0:808:43:00 140 bars 250 km 7.2 8 5.0 3.1297 �0:005 �0:0028 �0:208:43:00 140 bars 250 km 7.2 8 15.0 3.324 �0:0076 �0:0051 0.508:43:00 140 bars 250 km PGA 3.8967 �0:0052 �0:0031 �0:27

2008/07/24

00:26:00 300 bars 250 km 6.8 108 0.5 2.7719 �0:0021 �0:0016 �0:6900:26:00 300 bars 250 km 6.8 108 1.0 2.8614 �0:0021 �0:0015 �0:8900:26:00 300 bars 250 km 6.8 108 5.0 3.0988 �0:0026 �0:0013 �0:3800:26:00 300 bars 250 km 6.8 108 15.0 2.9966 �0:0029 �0:0013 0.4800:26:00 300 bars 250 km PGA 3.7989 �0:0026 �0:0015 �0:48


fact that the anelastic attenuation rates derived from responsespectra are not necessarily the same for the Fourier spectra.The important result obtained here is not the absolute valuesof Q, but rather its dependence on whether the travel pathrepresents forearc or backarc attenuation. It should be notedthat we are looking at Q values for single events, whereasthe other studies have determined combined Q values for

multiple events. For this reason, we have not attempted todefine error bars for our single-event Q values; they are in-herently different kinds of estimates than those obtainedfrom a multiple-event regression.

The attenuation for each event can be used to play backeach recording to a reference near-source distance, allowingan average apparent source spectrum to be obtained for eachevent. Figure 12 compares these apparent source spectra witha theoretical Brune model spectrum (Brune, 1970, 1971) forthe known seismic moment; the stress drop is chosen toprovide a match to the high-frequency level of the accelera-tion spectrum (Boore, 1983). The apparent source spectra oftwo crustal events (M 5.5 and M 6.2) show a slump at inter-mediate frequencies (∼0:4 Hz), compared with the theoreti-cal Brune model. We examined possible factors that could beresponsible for this feature by looking at time-series and theirspectra. As seen in Figure 13, the same feature is apparent atindividual stations across a wide range of distances andazimuths and is thus unlikely to be a propagation effect. Themost likely explanation is source complexity, or there mightbe two slip patches close together that make up the totalmoment of the event (possible double-event). Inspection ofthe time series at the closest stations suggests that this mightbe the case; there is a suggestion of two pulses at some near-by stations, but not all.

Discussion and Conclusion

Our results show, with a very high level of confidence,that attenuation is greater in the backarc than in theforearc direction, especially at higher frequencies. Theseresults are summarized in Figure 14. The regional qualityfactor can be expressed as Q�f� � �0:0504 log10�f�2�1:0096 log10�f� � 2:3771 for forearc regions, in compar-ison with Q�f� � �0:0394 log10�f�2 � 0:7888 log10�f��2:2987 for backarc regions, considering all in-slab events

Figure 13. The double-bump feature in the spectrum (26 July2003, 07:13:00) is persistent across a wide range of distances andazimuths (Az.).

Figure 14. Comparison of quality factors for all (a) in-slab events and (b) crustal events in the dataset. A quadratic polynomial function isfitted to forearc (solid line) and backarc (dashed line) attenuation results. Symbols are the average values of quality factors; error bars showstandard deviation (�1σ) around the mean.


(depth range from 60 to 150 km). For crustal events, the qual-ity factor can be described by Q�f� � �0:7805 log10�f�2 �1:6918 log10�f� � 2:1838 for forearc regions and Q�f� ��0:3280 log10�f�2 � 1:0714 log10�f� � 2:0668 for backarcregions. An interesting feature is that the quality factor satu-rates at high frequencies for crustal events (∼1000), whileit continues to increase with frequency for in-slab events.Attenuation studies in other regions (Leary and Abercrombie,1994; Abercrombie, 1995; Castro et al., 2004) have also

found that Q has weak frequency dependence at highfrequencies. Castro et al. (2004) associated the change infrequency dependence of Q at high frequencies with thepresence of faults in the crust. By contrast with the crustalattenuation, in-slab events show efficient propagation ofhigh-frequency radiation.

The apparent efficiency of high-frequency propagationfor in-slab events, as evidenced by the quality factor, in-creases with focal depth as shown in Figure 15. Furthermore,the greater the depth of the event, the greater is the differencebetween the quality factors for forearc and backarc paths.

A possible mechanism for the difference between theQ-values for forearc and backarc travel paths, for in-slabevents, is the portion of wave propagation path within thehigh-Q slab, as shown schematically in Figure 1 and sup-ported by the results in Figure 15. Deep-focus in-slab eventshave greater path lengths within the high-Q, high-velocityslab, for the forearc stations (Zhao, 2010). For crustal andin-slab events recorded by stations in the backarc region,the decrease in Q value along the wave travel path maybe caused by the hot melted rocks below the volcanoes.For events having a mixed travel path, it is possible to esti-mate the additional anelastic attenuation for the estimatedlength of the wave path within the low Q volcanic zone(Zhao, 2010).

The dependence of Q on travel path type has implica-tions for seismic hazard analysis. In probabilistic seismichazard analysis, generally two types of uncertainty are dis-tinguished: epistemic uncertainty (due to lack of data andknowledge) and aleatory uncertainty (random variability)(Toro et al., 1997). In ground-motion prediction equations(GMPEs), the standard deviation of the residuals (wherethe residual is the difference between the logarithm of an ob-servation and the logarithm of an estimated value), denotedby σ, is treated as aleatory variability and integrated across in

Figure 15. Empirical relation between quality factors as afunction of focal depth. Symbols represent Q-values for eachevent at 10 Hz. The solid line is the best fit for the forearc re-gion [log10 Q�10 Hz� � 0:1827 log�h�2 ��0:1894 log�h� � 2:8]and the dashed line is the relation describing the trend of Qversus focal depth for the backarc region [log10 Q�10 Hz� �0:3303 log�h�2 � 0:2342 log�h� � 2:8].

Figure 16. Illustration of reduction of intraevent variability in (a) crustal events and (b) in-slab event by considering separate qualityfactors for forearc and backarc regions. The symbols are the mean value of σ for two cases. The open horizontal squares are average residualsat each frequency considering a single quality factor. The filled black vertical squares are the average residuals using separate forearc andbackarc anelastic attenuation terms.


the hazard analysis. Sigma has a significant influence on theresults of seismic hazard analyses, particularly for low prob-abilities (Atkinson and Charlwood, 1983; Restrepo-Vélezand Bommer, 2003; Bommer and Abrahamson, 2006).

To examine the component of σ associated with the dis-tinction of forearc versus backarc paths, we calculated thestandard deviation of residuals for each event in the dataset,separately. The separation of forearc and backarc travel pathsresults in a significant reduction in the standard deviation (σ)of ground-motion predictions. In Figure 16 the intraeventvariability of crustal and in-slab events is shown. The sym-bols represent the average value of residuals at each fre-quency for all the events. It can be clearly seen from thisfigure that using separate quality factors for forearc/backarcregions reduces σ, particularly for in-slab events at higher-frequencies, which are most greatly affected by the hetero-geneous attenuation structures of subduction zones. It is alsonoted that the intraevent variability is greater at high frequen-cies for in-slab events, in comparison with that for crustalevents. This may be because the apparent in-slab attenuationat high frequencies depends on focal depth (Fig. 15), so thatthe mixing of focal depths within the in-slab database leadsto increased variability.

Data and Resources

Strong ground motion data used in this study werecollected from Kyoshin Network (K-NET; www.k‑net.bosai.go.jp/, last accessed July 2011) of National ResearchInstitute for Earth Science and Disaster Prevention (NIED).Focal depth information is adopted from K-NET reports. Theassigned moment magnitude (M) for each event is thatreported by the Global Centroid Moment Tensor Catalog(www.globalcmt.org/, last accessed July 2011). Fault planesolutions are based on the EIC notes by Kikuchi and Yama-naka (http://www.seis.nagoya-u.ac.jp/sanchu/Seismo_Note/,last accessed July 2011) and reports by the GeographicalSurvey Institute (www.gsi.go.jp/, last accessed July 2011).

Acknowledgments

Wewould like to thank John Zhao and Raœl Castro for their thoughtfulreviews.

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Department of Earth SciencesUniversity of Western OntarioLondon, Ontario N6A 5B6Canada

Manuscript received 1 March 2011


forearc versus backarc attenuation of earthquake ground motion

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