Seismic attenuation in a nonvolcanic swarm region beneath Wakayama, southwest Japan

Authors


Abstract

[1] Seismic attenuation in the Wakayama swarm area of southwest Japan is estimated by optimally fitting the theoretical S coda model to an average S coda envelope in the frequency range of 1–48 Hz. The average S coda envelope is confirmed to have a common decay curve independent of the source-station distance. Intrinsic attenuation is found to peak at around 4 Hz, suggesting thermal diffusion in grain size or crack length domains with dimensions of the order of 0.7–1 mm, which is reasonable for crustal rock. Scattering attenuation is well approximated by the relation 0.054f−1 in this frequency range, with an inferred peak at 0.5 Hz, suggesting that the statistical model is characterized by an exponential autocorrelation function with a correlation length of about 1 km and a fractional velocity fluctuation of 21%. Scattering is the dominant cause of attenuation at frequencies below 2 Hz, while intrinsic attenuation becomes predominant above 4 Hz. Although values of coda attenuation (Qc−1) generally lie between the total and intrinsic attenuation, the differences between these three values becomes very small above 4 Hz, indicating that the coda attenuation measurements provide a reasonably good estimate of the total attenuation. The total attenuation was found to coincide well with the total apparent attenuation estimated by a linear inversion using direct S waves from swarm earthquakes, confirming the validity of the present results.

1. Introduction

[2] Seismic waves traveling through the Earth are attenuated both by wave scattering due to various heterogeneities within the Earth and by anelastic mechanisms such as conversion of vibrational energy into heat through friction, viscosity, and thermal relaxation processes. The first effect is known as scattering attenuation and is characterized by the scattering quality factor Qs. The second effect is called intrinsic attenuation and is characterized by the intrinsic quality factor Qi. Total attenuation is defined as Qt−1 = Qs−1 + Qi−1 [Dainty, 1981]. Knowledge of the total attenuation in the Earth is important for reliably estimating not only earthquake source parameters such as stress drop and corner frequency but also site amplification factors for seismic hazard assessment. Measurements of intrinsic attenuation (Qi−1) and its frequency dependence are effective means of elucidating the properties of crustal rock. According to the thermal diffusion model for intrinsic attenuation [Zener, 1948; Savage, 1965, 1966; Leary, 1995], when a seismic wave propagates through crustal rock, significant heat dissipation occurs because of the presence of small-scale irregularities and discontinuities such as grains, microfractures, cracks, and flaws, leading to structural weakness of the crust. The magnitude and particularly the frequency dependence of this heat dissipation are strongly associated with the sizes of irregularities and discontinuities. Characterization of scattering attenuation (Qs−1) is also important, specifically with regard to the magnitude of attenuation, its frequency dependence, and the relative contribution of scattering attenuation to total attenuation, particularly at frequencies lower than 1 Hz, and is a key factor in investigating the conjecture [Aki, 1980] regarding the shape of the S wave attenuation versus frequency curve. Furthermore, the strength and average size of heterogeneities in the shallow crust, including the strongly fractured swarm region, can be inferred through the derivation of a statistical model of seismic velocity fluctuations from the frequency dependence of scattering attenuation. In this case, scattering attenuation is represented by a spatial autocorrelation function that is usually characterized as either exponential, Von Karman-like, self-similar, or Gaussian [Sato and Fehler, 1998].

[3] Many researchers have applied the multiple lapse time window analysis method [Hoshiba et al., 1991] to separate intrinsic and scattering attenuation. The method assumes a model of the Earth with uniform distribution of scattering and attenuation properties, uniform seismic velocity, isotropic scattering, and S wave–only scattering. In the present study, a very simplified method for the separation of seismic attenuation is devised and is applied to the S coda envelope of velocity seismograms from very shallow earthquakes. The separation of attenuation is performed by optimally fitting the theoretical S coda model for multiply scattered wave energies in the time domain [after Zeng, 1991] to an average S coda envelope produced by averaging the mean squared S coda envelopes over all earthquakes for all stations. In this case, the average S coda envelope is interpreted as a common envelope curve independent of the source-station distance [Aki and Chouet, 1975; Tsujiura, 1978; Rautian and Khalturin, 1978], and the decay of the common envelope curve is interpreted as a combination of scattering and intrinsic attenuation.

[4] This study investigates the intrinsic, scattering, and total attenuation of an earthquake swarm region beneath Wakayama in the northwestern part of the Kii Peninsula, southwest Japan (Figure 1). First, the S coda envelope is confirmed to have a common decay curve for all stations in the Wakayama area. The average S coda envelope is then determined for several frequency bands and is used to estimate the scattering, intrinsic, and total attenuation, along with coda Q−1 (or Qc−1) to describe S coda decay rates [Aki, 1969; Aki and Chouet, 1975]. The validity of the present results is evaluated by comparison with the total apparent attenuation estimated from linear inversions using direct S waves from swarm earthquakes and by comparing the Qc−1 values estimated using the best fit theoretical S coda envelope with those estimated using the average S coda envelope. Finally, the relative contribution of scattering and intrinsic attenuation to the total attenuation is investigated, and a physically viable attenuation mechanism explaining the obtained frequency-dependent results is discussed.

Figure 1.

(a) Wakayama area in the northwest of the Kii Peninsula, southwestern Japan. (b) Epicentral distribution of earthquakes observed for the period from 1 January 2000 to 31 December 2002 using the telemetered network for microearthquake observation. (c) Vertical distribution of earthquakes in and around the Kii Peninsula, obtained by projecting hypocenters of earthquakes located within the area indicated in Figure 1b on a vertical plane along the A–B line in Figure 1b. The earthquake swarm region is surrounded with a dotted line. Dark areas indicated by numbers 1 and 2 denote the distribution of S wave reflection points at depths of about 24 km and 40 km, respectively.

2. Seismological Background and Geological Setting

[5] The earthquake swarm activity in Wakayama is characterized by long-continuing activity in the form of shallow earthquakes in a nonvolcanic area far from the present volcanic front in Japan. There is a clear localization of earthquakes related to the geological setting in this area. Figure 1a shows the location of Wakayama in the northwest of the Kii Peninsula, southwest Japan, and Figure 1b shows the epicentral distribution of earthquakes observed for the period 1 January 2000 to 31 December 2002 by the Wakayama Seismological Observatory of the Earthquake Research Institute, University of Tokyo, using a telemetered network for microearthquake observation. Figure 1c shows the projection of hypocenters of earthquakes located within the indicated area in Figure 1b on a vertical plane along the A–B line. As shown in Figures 1b and 1c, most of the earthquakes in the upper crust are located in and around the Wakayama plain in the northwest of the Kii Peninsula, where intense swarm activity occurs. The focal mechanisms are interpreted as mainly intermediate solutions between strike-slip and reverse faulting [e.g., Mizoue et al., 1983]. The pressure axes of the earthquakes are stably concentrated in the east-west direction, while the tension axes are more or less randomly oriented on a plane perpendicular to the pressure axis.

[6] Figure 2 shows the relationship between the epicentral distribution of shallow earthquakes with focal depths of <10 km and the geological setting in the northwest of the Kii Peninsula. Swarm activity appears to be localized in the area of the Sambagawa metamorphic belt (SMB) and the Mikabu metamorphic belt (MMB). The swarm activity terminates abruptly to the north at the median tectonic line. This border of activity coincides with the northern limit of the SMB, and the southern limit coincides roughly with the border between the MMB and the Shimanto Terrane (ST), which is characterized by very low seismic activity. It is difficult to identify a geologically clear border around the eastern limit of the active area. However, the SMB thins significantly to the east, disappearing east of the eastern limit of swarm activity, where the seismically inactive ST becomes predominant. Thus seismic activity is extremely low in the east of the Wakayama area. The sea to the west obscures any geological features related to the western limit of the swarm activity. As shown in Figure 1c, focal depths of the swarm earthquakes are clearly limited to about 10 km. The vertical limit of activity can be explained by the existence of the relatively seismically inactive ST beneath the seismically active SMB and MMB. Thus the clear localization of earthquakes is expected to be strongly related to the distribution of the SMB and MMB.

Figure 2.

Epicentral distribution of shallow earthquakes with focal depths <10 km and geological setting in the northwest of the Kii Peninsula. Black circles, events in Figure 1; red circles, events used for the coda and direct S wave analyses in this study; blue solid triangles, seismic stations; M.T.L., median tectonic line; RG, Ryoke granites; IG, Izumi group; SMB, Sambagawa metamorphic belt; MMB, Mikabu metamorphic belt; and ST, Shimanto Terrane. From north to south, the stations are Kishi-josui (KSJ), Wakayama-jo (WYJ), Okazaki (OKZ), Wakayama (WKY), Shobo-gakko (SBG), and Shiotsu-sho (STS).

3. Observations and Data

[7] Seismic observations with three-component velocity seismometers have been carried out at six stations in the Wakayama area for the period 1 January 1997 to 21 December 2002. Hypocenters and magnitudes of the earthquakes were determined by the Wakayama Seismological Observatory. Figure 2 shows the locations of the stations and the epicenters of the 130 events with S-P times shorter than 1 s selected for the coda analysis in this study. The magnitudes of the analyzed events ranged from 1.9 to 3.8, and their focal depths are 2–6 km. Five of the six stations, Okazaki (OKZ), Shobo-gakko (SBG), Shiotsu-sho (STS), Wakayama-jo (WYJ), and Wakayama (WKY), are on metamorphic rocks, while Kishi-josui (KSJ) is on a thin soil site. The seismometers have a flat amplitude response between 0.025 and 30 Hz. Waveform data digitized at a sampling rate of 100 Hz were stored on a digital memory card and are used here to estimate seismic attenuation in the low-frequency range of 1–16 Hz (hereinafter referred to as low-frequency observations).

[8] Another seismic observation was performed simultaneously at station WKY using a three-component seismometer with flat amplitude response in the high-frequency range of 2–55 Hz. Waveform data obtained by this system were digitized at a sampling rate of 200 Hz and were stored on hard disk and are used in this study to estimate seismic attenuation in the high-frequency range of 4–48 Hz (high-frequency observations).

4. Analysis

4.1. Coda Waves

4.1.1. S Coda Envelopes With a Spatially Common Decay Curve

[9] In the present study, the average S coda envelope is used to separate scattering and intrinsic attenuation. However, before determining the average S coda envelope, it should be determined whether the S coda envelopes have a common decay curve for all source-station pairs, that is, whether coda Q−1 (Qc−1) to describe S coda decay rates is the same for all stations.

[10] According to Sato and Fehler [1998] the coda energy decay curve normalized against the energy at a reference lapse time tref in the latter portion of the S coda is expressed as

display math

where C is the normalized coda energy, K(x) = x−1 ln [(x + 1)/(x − 1)], f is the target frequency, vs is the S wave velocity, r is the source-station distance, and t is the lapse time measured from the source origin time. The coda quality factor Qc is determined by the best fit of equation (1) to observed or synthesized coda. Fitting is performed by taking the logarithms of both sides of equation (1) and applying a least squares fit.

[11] Figure 3 shows a comparison of Qc−1 for all stations as the average over all events at each station. Values of Qc−1 at frequencies of 1–16 Hz from the low-frequency observation at the five stations are plotted in Figure 3, along with the values of Qc−1 at frequencies of 4–48 Hz from the high-frequency observation at WKY. The time window used for determining Qc−1 was 4–9 s, the same as was used for separating scattering and intrinsic attenuations. It is obvious from Figure 3 that there is good agreement between stations at all frequencies, indicating the presence of a spatially common coda decay in the Wakayama area. It should be noted, in particular, that the high-frequency observations are consistent with the low-frequency observations in the region of overlap (4–16 Hz) and that the differences in Qc−1 values between stations may decrease with increasing frequency from 4 to 16 Hz. Thus it is considered that the average S coda envelope at WKY can be used to represent the average S coda envelope for the other five rock site stations at frequencies higher than 16 Hz. The consistency of Qc−1 among the five stations suggests that source-generated surface waves confined to the uppermost crust have negligible effect on the S coda envelope decay. Therefore it is expected that the average attenuation of the shallow crust can be reliably estimated by the present method using the average S coda envelope.

Figure 3.

Comparison of Qc−1 between five rock site stations at 1, 2, 4, 8, 16, 32, and 48 Hz. Circles, OKZ; squares, SBG; diamonds, STS; triangles, WYJ; and stars, WKY.

4.1.2. Determination of Average S Coda Envelope

[12] The average S coda envelope with a common decay curve independent of the source-station distance is determined using velocity seismograms with S-P times shorter than 1 s. The procedure for determining the average S coda envelope is as follows. An S coda envelope at a given station and for a given event is produced by using band-pass-filtered, mean squared three-component seismograms; summing all the components; and then normalizing the composed seismogram envelope against the amplitude at a reference lapse time tref (30 s in this case) in the S coda portion. The average S coda envelope is then produced by averaging the normalized seismogram envelopes over all stations for all events. In the present case, the band-pass filters have center frequencies (fc) of 1, 2, 4, 8, 16, 32, and 48 Hz and bandwidths of 0.8 fc to 1.2 fc. The amplitude at a lapse time of 30 s used for amplitude normalization is more than 3 times greater than the noise level.

[13] The average S coda envelope dependent on lapse time, frequency, and reference lapse time is defined as NormMSEnv(f, t, tref). As an example, Figure 4 shows the normalized seismogram envelopes and average S coda envelopes for f = 1, 2, 4, and 8 Hz. The average S coda envelopes obtained for f = 1, 2, 4, 8, 16, 32, and 48 Hz are summarized in Figure 5. As seen in Figure 5, the average S coda envelope decays smoothly at lapse times of about 4–10 s for all frequencies but becomes affected by several peaks at lapse times longer than 11 s. The peaks are particularly conspicuous at lapse times of 11–15 and 18–26 s for frequencies of 4, 8, and 16 Hz, as indicated by arrows in Figure 5. The early S coda portion with a smoothly decaying curve is used in this study to estimate seismic attenuation of the shallow crust. The causes of the two peak regions are examined in detail in section 6.4 by applying a normal moveout (NMO) correction as employed in seismic reflection surveys to the seismograms.

Figure 4.

Examples of normalized seismogram envelopes (blue curves) and average S coda envelopes NormMSEnv(f, t, tref) (thick white curves) for f = 1, 2, 4, and 8 Hz. Thin white curves denote the standard deviations. To show a decaying behavior of coda envelope in later portions of S coda, a reference time (tref) of 40 s for normalized coda energy was used in these examples.

Figure 5.

Average S coda envelopes NormMSEnv(f, t, tref) (curves from 0 to 19 or 30 s) and best fit theoretical coda envelopes NormEthe(Qs, Qi, f, r, t, tref) (curves from 4 to 9 s) for f = 1, 2, 4, 8, 16, 32, and 48 Hz using a time window (gray lines) of 4–9 s. Arrows indicate peaks disturbing the smooth decay of the coda envelopes. Reference time (tref) for normalized coda energy is 30 s.

[14] The lapse time window for the best fit of the theoretical model to the observation is chosen to correspond to the S coda portion containing scattered waves sampling the earthquake swarm region of the crust. Usually, S coda portions at lapse times longer than twice the S wave travel time are expected to be composed of incoherent waves scattered by various heterogeneities in the lithosphere [Lacoss et al., 1969; Spudich and Bostwick, 1987; Scherbaum et al., 1991]. The present study follows this criterion. As the average S wave travel time of the seismograms used is about 1.9 s, the lapse time window is chosen to start at a lapse time of 4 s (2ts) and to end at 9 s, given an S wave velocity of 3.0 km/s and the shallow crust objective (<15 km). As is shown in Figure 5, the S coda portion corresponding to the lapse time window of 4–9 s chosen for determining the model parameters consists of scattered waves sampling the shallow crust, which includes the swarm activity region down to about 10 km depth.

4.1.3. Model Fitting

[15] Assuming isotropic scattering and the uniform random distribution of scatterers in the propagation medium, Zeng [1991] introduced an approximate solution for multiply scattered wave energy by combining the single-scattering model and the diffusion model. It was also shown that this hybrid single-scattering diffusion solution agrees quite well with the exact solution [Zeng et al., 1991] for both strong and weak scattering for close sources and receivers. The hybrid solution Ethe is expressed as

display math

where

display math

Here Ethe(Qs, Qi, f, r, t) is the energy detected at distance r at time t in a medium with intrinsic attenuation Qi−1, scattering attenuation Qs−1, and the S wave velocity vs; E0 is the total incident wave energy; and G is the site term for the observational station. The first term on the right-hand side of equation (2) is the contribution of the direct wave pulse. The second term is the energy of singly scattered waves, and the last term includes all energies contributed by scattered waves of order 2 or higher. Equation (1) defining S coda decay rates (coda Q−1, or Qc−1) is based on the single-scattering approximation. Therefore equation (1) is similar to the second term on the right-hand side of equation (2) describing the energy of singly scattered waves. The relationships between the three attenuations Qs−1, Qi−1, and Qc−1 were discussed theoretically by Hoshiba [1991]. Normalizing Ethe(Qs, Qi, f, r, t) to the energy Ethe(Qs, Qi, f, r, tref) at reference time tref to remove the contribution of total incident wave energy E0 and the site term G, the normalized energy NormEthe(Qs, Qi, f, r, t, tref) can be written as

display math

[16] Intrinsic attenuation and scattering attenuation are estimated by optimally fitting the theoretical model NormEthe(Qs, Qi, f, r, t, tref) to the average S coda envelope NormMSEnv(f, t, tref). In this study, the model parameters of Qs and Qi for minimizing the variance Var (Qs, Qi, f) between logarithms of NormMSEnv(f, t, tref) and NormEthe(Qs, Qi, f, r, t, tref) are determined by a grid search technique. The variance Var (Qs, Qi, f) is written as

display math

where equation image is the mean hypocentral distance, ts is the S wave travel time, Δt is the sampling interval of the data, and Ndat is the number of data. In the search procedure, values of both Qs and Qi from 1 to 4000 are tested independently in increments of 1 to calculate the variance. Optimal total attenuation optQt−1 can be determined from the definition [Dainty, 1981] as

display math

Seismic albedo B0, introduced by Wu [1985] to represent the ratio of scattering attenuation to total attenuation, can be expressed as

display math

[17] The F test is used to assess the uncertainty of the estimates of Qs−1 and Qi−1. This method was also used by Jin et al. [1994], Akinci et al. [1995], and Adams and Abercrombie [1998]. According to the F test the ratio of the variance Var1−α with a confidence level of 1 − α with regard to the minimum variance Varmin can be written as

display math

where Var is the unbiased estimate of variance, F is the F distribution, ϕ is the degree of freedom, and α is the level of significance in percent. All pairs of Qs−1 and Qi−1 with Var1−α are searched for, and the contour of a confidence level of 1 − α is determined in the Qs−1Qi−1 plane. From the range of the contour along the Qs−1 and Qi−1 axes the positive (Δ+Qs,i−1) and negative (ΔQs,i−1) errors in Qs−1 and Qi−1 are calculated as follows:

display math

where subscripts max and min represent the maximum and minimum values of Qs,i−1 on the contour of the 1 − α confidence level. Thus the Qs−1 and Qi−1 values can be estimated as

display math

The values of Qt−1 (= Qs−1 + Qi−1) and B0 (= Qs−1/Qt−1) at the 1 − α confidence level are estimated using the pairs of Qs−1 and Qi−1 with Var1−α, and errors are determined in the same way as for Qs−1 and Qi−1 above. A significance level of 5% was adopted for α, giving a confidence level of 95%.

[18] The resolution of scattering and intrinsic attenuation estimated by this method was evaluated by applying the method to coda envelopes synthesized using given values of scattering and intrinsic attenuation. From comparisons of the given and estimated values the errors of estimation of scattering and intrinsic attenuation were found to be at most 25% and 33%, respectively, at f = 1 Hz, and this error was found to decrease with increasing frequency. The errors were comparable to or smaller than those estimated from the F test using equation (8). Therefore the errors determined from the F test are adopted for error analysis in this study.

4.2. Total Apparent Attenuation of Direct S Waves

[19] The validity of the results obtained by the present method was checked by examining the coincidence between the total attenuation Qt−1 estimated using the S coda and the total apparent attenuation Qd−1 estimated using direct S waves from swarm earthquakes. The estimate of total apparent attenuation was performed by linear inversion using S wave spectra by the same procedure used by Matsunami et al. [2003]. The inversion was preliminarily performed using 2-s, 3-s, and 4-s time windows of S waves to examine the effect of a length of the time window on the total apparent attenuation Qd−1. From comparisons of their results it was found that similar values of Qd−1 were obtained for the three different time windows. Therefore a 3-s time window was used here to extract S waves, and a 5% Hanning taper was applied to the time window. Because S-P times for events analyzed here were shorter than about 3.5 s, P coda just before direct S wave arrival could not be used to examine the noise level. Therefore a 3-s time window before P wave arrival was used to examine the noise level, and only data with a signal-to-noise ratio of greater than 3 was used in the analysis. Only the horizontal component was analyzed here. The amplitude spectrum of the horizontal component can be calculated by

display math

where ANS and AEW represent the north-south (NS) and east-west (EW) components of the seismograms and AH is the horizontal component. For all spectra, smoothing was performed using a Hanning window with a bandwidth of 0.6 Hz.

[20] Assuming that S waves are radiated spherically from a point source in the same medium as in the study by Zeng [1991], the Fourier amplitude spectrum of the observed S wave can be expressed as

display math

where Oij(f) is the S wave Fourier amplitude spectrum of the ith event recorded at the jth station, Si(f) is the source term for the ith event, Gj(f) is the site term for the jth station, Rij is the hypocentral distance for the ith event and the jth station, and Qd−1 and Vs denote the total apparent attenuation and the velocity of the S waves in the medium, respectively. Equation (11) is equivalent to the first term (direct wave pulse) on the right-hand side of equation (2). Qd−1 is expected to be equal to the total attenuation Qt−1 (= Qs−1 + Qi−1) from equation (2). The spectral ratio between the jth station and the reference station is obtained by

display math

where the subscript r denotes the reference station. By taking the logarithm, equation (12) can be rewritten at a fixed frequency as

display math

where gj = ln [Gj(f)/Gr(f)], rij = ln (Rij/Rir), and oij = ln (Oij/Oir), oij = ln (Oij/Oir), and rij = ln (Rij/Rir). Denoting αij = πf(RirRij)/Vs and dij = oij + rij, equation (13) becomes

display math

[21] For all events and all stations, equation (14) can be expressed in matrix form by

display math

where m is a vector in the model space, d is a vector in the data space, and G is a matrix relating m to d. The unknown parameters of the model space are the reciprocal of the average quality factor of the medium Qd−1 and the site effect relative to the reference site gj for each frequency. The inversion was executed by finding a solution of m that minimized the prediction error, ∣Gmd2. A least squares solution was obtained using the singular value decomposition method [Lawson and Hanson, 1974]. The standard deviations of the model parameters were estimated from diagonal elements of the covariance matrix [Menke, 1989] according to

display math

where σd2 is the variance of the data.

5. Results

5.1. Estimated Model Parameters

[22] Best fit theoretical curves for the average S coda envelope are plotted along with the observed curves NormMSEnv(f, t, tref) in Figure 5. The theoretical model produces a very good fit to the observed curves for all frequency bands, despite simplifications such as the assumption of a uniform random distribution of scatterers for seismic waves. Table 1 lists the best fit model parameters Qs−1 and Qi−1 and the equivalent parameters B0 and Qt−1 for all the frequency bands. For frequency bands centered around 4 and 8 Hz, the results from the high-frequency observation at WKY are also listed in Table 1 and can be seen to agree with the results from low-frequency observations with the five rock site stations.

Table 1. Best Fit Model Parameters
Frequency, HzQs−1Qi−1Qt−1B0Expected Qc−1Observed Qc−1
  • a

    High-frequency observation at WKY.

10.0526 + 0.0191/−0.01440.0030 + 0.0077/−0.00100.0556 + 0.0263/−0.01540.9474 + 0.0130/−0.07240.0234 + 0.0049/−0.00490.0251 + 0.0049/−0.0049
20.0270 + 0.0050/−0.00470.0128 + 0.0027/−0.00230.0400 + 0.0076/−0.00700.6757 + 0.0231/−0.01830.0228 + 0.0025/−0.00250.0234 + 0.0025/−0.0025
40.0137 + 0.0040/−0.00420.0179 + 0.0019/−0.00200.0313 + 0.0059/−0.00530.4384 + 0.0387/−0.09370.0228 + 0.0012/−0.00120.0231 + 0.0012/−0.0012
4a0.0128 + 0.0025/−0.00210.0175 + 0.0008/−0.00070.0303 + 0.0034/−0.00270.4231 + 0.0294/−0.03730.0232 + 0.0009/−0.00090.0234 + 0.0009/−0.0009
80.0065 + 0.0014/−0.00120.0076 + 0.0006/−0.00050.0141 + 0.0019/−0.00170.4581 + 0.0299/−0.04390.0102 + 0.0006/−0.00060.0103 + 0.0006/−0.0006
8a0.0065 + 0.0018/−0.00150.0078 + 0.0007/−0.00060.0143 + 0.0024/−0.00200.4545 + 0.0402/−0.06100.0106 + 0.0004/−0.00040.0107 + 0.0004/−0.0004
16a0.0032 + 0.0006/−0.00050.0045 + 0.0002/−0.00020.0077 + 0.0008/−0.00070.4180 + 0.0290/−0.03780.0059 + 0.0002/−0.00020.0060 + 0.0002/−0.0002
32a0.0016 + 0.0004/−0.00030.0031 + 0.0002/−0.00010.0047 + 0.0005/−0.00040.3349 + 0.0376/−0.04340.0037 + 0.0001/−0.0001/0.0038 + 0.0001/−0.0001
48a0.0010 + 0.0002/−0.00020.0023 + 0.0001/−0.00010.0034 + 0.0003/−0.00030.3098 + 0.0368/−0.0447/0.0027 + 0.0001/−0.00010.0028 + 0.0001/−0.0001

[23] The errors of Qs−1 and Qi−1 estimated by the F test are shown in Figure 6, along with the variability of B0 and Qt−1 for f = 1, 2, 4, and 8 Hz. The range of model parameters at the 95% confidence level was calculated by equations (7)(9) as measures of the uncertainties of Qs−1 and Qi−1. In general, the confidence areas are asymmetrical around the best fit estimation, and therefore the errors are not symmetric, as shown in Table 1.

Figure 6.

Examples showing the variability of the best fit model parameters at the 95% confidence level for f = 1, 2, 4, and 8 Hz. Optimal model parameters (a) optQs−1 and optQi−1 and (b) optB0 and optQt−1 are represented by stars. The area outlined by open circles represents the 95% confidence area.

[24] The estimated model parameters are plotted as a function of frequency in Figure 7. Qs−1 and Qt−1 decrease (Qs and Qt increase) monotonically with increasing frequency, while Qi−1 peaks at around 4 Hz and decreases with increasing and decreasing frequency. Assuming a functional form of Q−1 = βfγ to fit the Q−1 values, the Qs−1 and Qt−1 values are approximated by 0.054f−1 (Qs ≅ 19f) and 0.071f−0.8 (Qt ≅ 14f0.8) for the frequency range of 1 to 48 Hz, and the Qi−1 values are approximated by 0.030f−0.7 (Qs ≅ 33f0.7) for frequencies higher than 8 Hz.

Figure 7.

Comparisons of (a) Qs−1, Qi−1, Qt−1, and Qc−1 for the frequency range of 1–48 Hz and (b) frequency-dependent seismic albedo B0 = Qs−1/Qt−1. Qs−1 and Qt−1 values are approximated by 0.054f−1 (solid line) and 0.071f−0.8 (dashed line) for the frequency range of 1–48 Hz. Qi−1 values are approximated by 0.030f−0.7 (dotted line) for frequencies higher than 8 Hz. Errors are estimated for the 95% confidence level.

[25] The relationships between the four attenuations, Qs−1, Qi−1, Qt−1, and Qc−1, are also examined in Figure 7 in terms of the frequency dependences (Figure 7a) and frequency-dependent seismic albedo B0 (= Qs−1/Qt−1) (Figure 7b). Qs−1 is larger than Qi−1 (Qs is smaller than Qi) at frequencies below 2 Hz, is similar to Qi−1 at frequencies of 4–16 Hz, and is smaller than Qi−1 (Qs is larger than Qi) at high frequencies above 32 Hz. As can be seen in Figure 7b, the seismic albedo B0 decreases with increasing frequency, 0.9–0.6 at 1–2 Hz, 0.5–0.4 at 4–16 Hz, and 0.4–0.3 at 32–48 Hz, which indicates the dominance of scattering attenuation at frequencies below 2 Hz, a gradual increase in the relative strength of intrinsic attenuation from 4 to 16 Hz, and the dominance of intrinsic attenuation at frequencies above 32 Hz.

[26] The intrinsic, scattering, and total attenuation can also be compared with Qc−1 in Figure 7a. In general, Qc−1 is less than Qt−1 and larger than Qi−1 (Qc is larger than Qt and less than Qi). Although Qc−1 lies between Qt−1 and Qi−1, these three attenuations approach each other very closely with increasing frequency above 4 Hz. Qc−1 is also sensitive to changes in Qi−1, particularly at frequencies higher than 2 Hz.

[27] The ratios of Qt−1, Qs−1, and Qi−1 to Qc−1 are plotted against frequency in Figure 8 to examine quantitatively the relationships between the intrinsic, scattering, total, and coda attenuation. The ratio Qt−1/Qc−1 very gradually decreases with increasing frequency above 4 Hz, 1.35 at 4 Hz, and 1.2 at 48 Hz, whereas Qi−1/Qc−1 very gradually increases with frequency above 4 Hz, 0.7 at 4 Hz, and 0.85 at 48 Hz. Thus Qc−1 is close to the total attenuation Qt−1 at frequencies higher than 4 Hz and provides a reasonably good estimate of the total attenuation, although it underestimates the total attenuation by at most 26%. At least 70% of Qc−1 at frequencies higher than 4 Hz is due to intrinsic attenuation. This large contribution of intrinsic attenuation above 4 Hz (Figure 8) and the sensitivity of Qc−1 to change in intrinsic attenuation above 2 Hz (Figure 7a) demonstrate that Qc−1 is dominated by intrinsic attenuation. Similar results were reported by Matsunami [1991] on the basis of laboratory experiments using ultrasonic waves. The observed or experimental results of the dominance of intrinsic attenuation in coda attenuation Qc−1 for the case of large intrinsic attenuation is consistent with the prediction from the radiative transfer theory [Hoshiba, 1991; Wennerberg, 1993; Sato and Fehler, 1998].

Figure 8.

Ratios of Qt−1, Qs−1, and Qi−1 to Qc−1 as a function of frequency.

[28] The observed close agreement between the total (Qt−1) and coda attenuation (Qc−1) above 4 Hz can be explained by the fact that both the total and the coda attenuation are dominated by intrinsic attenuation in the frequency range. The close agreement between S wave attenuation and coda attenuation reported by Aki [1980] is also expected to be due to the dominance of intrinsic attenuation in the S wave attenuation, as argued by Wennerberg [1993].

5.2. Reliability

[29] Direct S wave attenuation Qd−1 was estimated by linear inversion using S wave spectra for the events and stations listed in Table 2. A total of 16 events observed simultaneously at more than four stations was used. In choosing the events, the alignment of observation stations with respect to the epicenter was taken into account as far as possible to avoid the source radiation effect. Figure 9 plots the estimated Qd−1 along with Qt−1 estimated using coda waves. The two values agree well for all frequencies. The observed Qc−1 estimated using NormMSEnv(f, 4 ≤ t ≤ 9, tref) and the expected value calculated by the best theoretical fit of the coda envelope using the same lapse time window are compared in the last columns in Table 1. These two values also agree very well for all frequencies. These results confirm the reliability of the model parameters determined by the present method.

Figure 9.

Comparisons of direct S wave attenuation (Qd−1) with the total attenuation (Qt−1) estimated using coda waves. Stars denote values of Qt−1, solid curves represent the average Qd−1, and dotted curves are the standard deviations.

Table 2. Parameters for Earthquakes and Recording Stations Used for Estimating Direct S Wave Attenuation
EventCodeDateMagnitudeLatitude, degLongitude, degDepth, kmStationa
OKZSBGSTSKSJWYJWKY
  • a

    A value of 1 indicates that that station recorded the corresponding earthquake.

10184 June 19973.734.22586135.148384.1011110
202920 July 19972.634.23015135.271484.3111001
304411 Oct. 19973.834.04379135.266455.0011101
40551 Jan. 19983.934.13400135.160003.4111100
50656 May 19984.234.21312135.268605.3111101
60762 July 19983.134.09623135.203604.6011011
709324 Oct. 19983.134.16166135.147204.5011101
809725 Nov. 19983.034.09494135.132603.9011110
912327 Feb. 19992.634.21350135.182603.9110100
1012512 March 19993.434.13659135.205206.4111100
111482 Aug. 19994.134.43740135.344509.7111101
1215312 Aug. 19993.434.23340135.189905.4111010
131732 Nov. 19993.734.02732135.303104.4011101
141753 Nov. 19993.134.18196135.227404.4110101
1524325 Jan. 20013.934.05340135.105906.7011110
1628811 Dec. 20013.334.10730135.08737.1010111

6. Discussion

6.1. Comparison With Previous Results

[30] Intrinsic and scattering attenuation have been separated by many researchers by applying the multiple lapse time window analysis method [Hoshiba et al., 1991]. Many regions of the world have been satisfactorily treated in this way, including Japan [Fehler et al., 1992; Hoshiba, 1993], Hawaii and Long Valley in the Sierra Nevada in eastern California [Mayeda et al., 1992], southern California [Jin et al., 1994; Adams and Abercrombie, 1998], southern Spain, and western Anatolia (Turkey) [Akinci et al., 1995]. The previous studies considered window lengths that were up to 60 s past the origin time and hypocentral distances up to 70 km. Therefore the medium model is considered to be closer than the present case to the assumptions of Zeng's [1991] model. Figure 10 summarizes the results of these measurements along with those of the present study. The results indicate that the relationship between scattering and intrinsic attenuation varies widely, although the general trend is that scattering and intrinsic attenuation decrease with increasing frequency from 1 to about 100 Hz. The attenuation in the present case is markedly higher than in the other cases. This is considered to be due to the fact that the result of the present study represents the average attenuation in the shallow crust alone, including the strongly heterogeneous swarm region, whereas the results of other studies take the average over a much greater range of depth and time to include weakly heterogeneous lower crust and upper mantle.

Figure 10.

Summary of total attenuation (Qt−1), seismic albedo (B0 = Qs−1/Qt−1), scattering attenuation (Qs−1), and intrinsic attenuation (Qi−1) estimated for various regions in the world. Regions are ktj, Kanto-Tokai, Japan [Fehler et al., 1992]; km, Kumamoto in Kyusyu, Japan; wy, Wakayama, southwestern Japan [Hoshiba, 1993]; lv, Long Valley in eastern California; cc, central California; h, Hawaii [Mayeda et al., 1992]; svd, southern California; pas, southern California [Jin et al., 1994]; sp, southern Spain, for 0–170 km distance range [Akinci et al., 1995]; cjp, Cajon Pass borehole (2900 m depth) in southern California; csp, Cedar Springs of the Southern California Seismic Network [Adams and Abercrombie, 1998]; this study, Wakayama in southwestern Japan.

[31] The present result indicating the predominance of scattering attenuation below 2 Hz and intrinsic attenuation above 16 Hz is similar to the observation of larger scattering attenuation below 6 Hz near fault zones in southern California [Jin et al., 1994] and the predominance of scattering attenuation below 4 Hz and intrinsic attenuation above 8 Hz reported for southern Spain [Akinci et al., 1995]. The peak in intrinsic attenuation observed in Wakayama is similar to observation in Hawaii [Mayeda et al., 1992], where the intrinsic attenuation appears to exhibit a peak at around 6 Hz. As a contrasting result, Adams and Abercrombie [1998] revealed a weak frequency dependence of scattering attenuation above 10 Hz (f−0.04) over a wide frequency range of 1–100 Hz, suggesting wave scattering in a self-similar medium on scales smaller than the correlation distance of 0.1 km. The weak frequency dependence above 10 Hz is similar to the frequency dependence of total attenuation Qt−1 in the tectonically stable region of the northeastern United States and southeastern Canada [e.g., Benz et al., 1997]. Therefore observations of Qt−1 at over 10 Hz in a stable continental area were considered in that study to be useful in attempting to understand the weak frequency dependence above 10 Hz.

6.2. Mechanism of Intrinsic Attenuation

[32] Aki [1980] preferred the thermoelastic effect, studied by Zener [1948], as the most viable model to explain intrinsic attenuation at lithospheric temperatures on the basis that the required scale of rock grains and cracks and the attenuation caused by thermoelasticity are in closest agreement with observations among the various hypotheses. However, there is as yet no seismic evidence to support the frequency dependence of thermoelastic attenuation, such as evidence to associate the peak frequency with grain size or crack length, or to describe the change in behavior with increasing frequency.

[33] Leary [1995] identified a frequency dependence of f−0.57 for intrinsic attenuation Qi−1 on the basis of wideband seismic observations in the frequency range of 5–200 Hz at a depth of 2.5 km in the Cajon Pass borehole in granitic crust in southern California. The observed frequency dependence is in good agreement with the theoretical prediction of f−0.5 [Leary, 1995] based on the thermal diffusion process.

[34] The results of the present study for the Wakayama swarm area suggest that the thermoelastic effect is an important mechanism for seismic intrinsic attenuation. The intrinsic attenuation obtained in the present study exhibited a peak at around 4 Hz, decreasing with both increasing and decreasing frequency. In addition, Qi−1 can be approximated by the relation 0.030f−0.7 in the frequency range 8–48 Hz. According to the thermal diffusion model for intrinsic attenuation [Zener, 1948; Savage, 1965, 1966] the predicted thermoelastic attenuation peaks around a frequency of fpDT/a2, where a is the characteristic dimension of the heterogeneities (i.e., grain size or crack half length) and DT is the thermal diffusivity. Assuming DT = 0.02–0.05 cm2/s, which is typical for granitic rock [Hodgman et al., 1959; Clark, 1966], and fp = 4 Hz for the present case, a is estimated to be 0.7–1.1 mm, which is a reasonable value for grain size in the present case. The thermoelastic theory also predicts the S wave Qi−1 to have values on the order of 10−3 (e.g., about 0.003 for granitic rock). For the present case, although the Qi−1 observed around the peak frequency (at 2 and 4 Hz) is 0.01–0.02, the values above and below the peak frequency are consistent with the theoretical prediction, of the order of 10−3. Although the observed frequency dependence in this study (f−0.7) was approximated for a relatively narrow frequency band of 8–48 Hz, the present result is qualitatively similar to the frequency dependence of f−0.5 predicted by Leary [1995] for a sufficiently high frequency range. Thus the peak frequency corresponding to a domain size that is plausible and the high-frequency behavior qualitatively similar to the theoretical prediction are considered as evidence to support the hypothesis of thermal diffusion on the scale of grains, cracks, or microfractures in crustal rock as an explanation for seismic intrinsic attenuation in the upper crust.

6.3. Statistical Model for Scattering Attenuation

[35] Aki [1980] noted that the S wave total attenuation Qt−1 peaked at around 0.5 Hz and decreased with both increasing and decreasing frequency. This was confirmed observationally by Kinoshita [1994] from spectral decay analysis of strong motion records of earthquakes with focal depths of less than 50 km in southern Kanto, Japan. In addition, Adams and Abercrombie [1998] identified a peak in Qt−1 at around 0.5 Hz after combining their results by the multiple lapse time window analysis method [Hoshiba et al., 1991] with the results of previous studies using data for southern California [Jin et al., 1994; Mitchell, 1995; Benz et al., 1997]. In the present study, the scattering attenuation (Qs−1) decreased with increasing frequency (0.054f−1) in the frequency range 1–48 Hz.

[36] According to theoretical models of isotropic wave scattering, particularly for a medium characterized by an exponential autocorrelation function for spatially random velocity fluctuation [Sato and Fehler, 1998], S wave scattering attenuation Qs−1 (f) peaks at fVsa and decreases with increasing frequency according to 4.6ɛ2(Vs/2πaf), where Vs is the S wave mean velocity, a is the correlation length, and ɛ2 is the mean square fractional velocity fluctuation. The observed frequency dependence agrees very well with the frequency dependence of f−1 for the exponential autocorrelation case. Assuming that the scattering attenuation has a peak at around 0.5 Hz, the scale length (correlation length) and the mean square fractional velocity fluctuation can be estimated from a comparison of the observed and theoretical scattering attenuation Qs−1. The estimated values are about 1 km and 21%, respectively. The high mean square fractional velocity fluctuation represents a strongly inhomogeneous swarm region in the shallow crust.

6.4. Effect of Reflections From Discontinuities at Depth

[37] As shown in Figure 5, the average S coda envelope decays smoothly at lapse times of about 4–10 s for all frequencies yet exhibits two conspicuous peaks at lapse times of 12–16 and 21–27 s, particularly for frequency bands centered around 4, 8, and 16 Hz. This is tentatively attributed to reflections from discontinuities at depth. To examine this, a normal moveout correction as employed in seismic reflection surveys is applied to the seismograms corrected for wave attenuation (Q) and geometrical spreading. In the present analysis, an NMO correction is applied, taking into account differences in focal depths for the shallow earthquakes [Inamori et al., 1992]. The NMO and focal depth corrections transform the waveform data from time (Tz) to depth (z) in the seismic section. The phase at a lapse time of Tz is assumed to represent an S wave reflection phase from a reflector at depth z. Amplitudes before the arrival of a direct S wave are removed in this transformation, and amplitudes at the arrival time of a direct S wave are plotted at the depth corresponding to the focal depth of the event.

[38] An NMO correction is applied to seismograms from 23 events, with epicenters as shown in Figure 11a along with the stations that observed those events. Assuming an S wave velocity of 3.2 km/s and Q = 600, the NS and EW component seismograms after attenuation, geometrical spreading, and NMO corrections are plotted in Figure 11b. In Figure 11b, seismograms are aligned in the order of epicentral location of each event in the northwest-southeast (NW-SE) direction. The traces are spaced equally on the vertical axis for convenience; the actual events were not evenly distributed along this line. Two clear phases at depths of around 22–24 and 37–42 km appear after correction, and the depth of the latter phase decreases slightly toward the northwest. The emergence times of these two phases agree well with the timing of the two peaks in the S coda. The possible origins of these reflections are discussed below.

Figure 11.

(a) Locations of events used for normal moveout (NMO) correction and stations observing these events. (b) Examples of NMO-corrected seismograms for an S wave velocity of 3.2 km/s and Q of 600. Seismograms are aligned in the order of epicentral location of each event in the northwest-southeast (NW-SE) direction. Although the actual distribution of events is not linear, the traces are spaced equally on the vertical axis for clarity. Two clear phases at depths of around 24 and 37–42 km can be identified after correction.

[39] To compare the distribution of reflection points at depths of about 24 and 40 km with seismic activity beneath the western part of the Kii Peninsula, vertical distributions of the reflection points and hypocenters are shown in Figure 1c (the region of interested is indicated in Figures 1a and 1b). A previous study on the crustal structure beneath the Kii Peninsula [Mizoue et al., 1983] suggested that the Conrad discontinuity is located at a depth of 20–24 km below the Wakayama plain and that the Moho discontinuity is located at a depth of about 30 km below the northern part of the Kii Peninsula. Therefore the peak at lapse times of 12–16 s in the S coda is confidently attributed to reflections from the Conrad discontinuity below the Wakayama plain. However, the peak at 21–27 s is not likely to be caused by reflections from the Moho discontinuity, which is too shallow to be responsible for these observations. Rather, the reflections at lapse times of 21–27 s may be due to molten material in the upper mantle immediately below the crust as an S wave reflector, as supposed by Wakita et al. [1987]. Examination of the structure of the reflector at a depth of about 40 km is a very interesting and important problem in the discussion of the formation processes related to tectonic activity beneath the Kii Peninsula. Similar to the approach adopted in a previous study [e.g., Matsumoto and Hasegawa, 1996], one way to examine the structure is to estimate the frequency-dependent reflection coefficients of the reflector because the peak at 12–16 s in the S coda is predominant at 8 Hz, whereas the peak at 21–27 s is predominant at 4 Hz.

7. Conclusions

[40] Scattering is the dominant cause of attenuation at frequencies below 2 Hz, while intrinsic attenuation becomes predominant above 4 Hz. Intrinsic attenuation (Qi−1) peaks at around 4 Hz, which, under the assumption of a thermal diffusion process for intrinsic attenuation, predicts a grain size or crack length on the order of 0.7–1 mm, reasonable for crustal rock.

[41] Scattering attenuation (Qs−1) can be well approximated by the relation 0.054f−1 in the frequency range of 1–48 Hz, suggesting that the shallow crust can be modeled statistically by spatial velocity fluctuation with an exponential autocorrelation function. Assuming that the scattering attenuation has a peak at around 0.5 Hz, the scale length and mean square fractional velocity fluctuation are estimated to be about 1 km and 21%, respectively. The high-velocity fluctuation is expected to correspond to a strongly inhomogeneous swarm region in the shallow crust.

[42] Although the value for coda attenuation (Qc−1) generally lies between the values for the total and intrinsic attenuation, these three attenuations approach each other very closely with increasing frequency above 4 Hz, indicating that the coda attenuation measurements provide a reasonably good estimate of the total attenuation, although it is underestimated by at most 26%. The total attenuation Qt−1 (= Qs−1 + Qi−1) was found to be in good agreement with the total apparent attenuation Qd−1 estimated by a linear inversion using direct S waves from swarm earthquakes, supporting the basic hypothesis that the S coda is composed mostly of scattered S waves and confirming the validity of the present results.

[43] Later parts of the average S coda envelope were found to exhibit peaks (4–16 Hz). NMO correction applied to the seismograms showed the two peaks to be produced by reflections from a horizontal Conrad discontinuity at 24 km and a gently northwest dipping discontinuity in the upper mantle at 37–42 km.

Acknowledgments

[44] The authors would like to express their sincerest gratitude to the late Norihiko Seto for valuable discussion and helpful observations on strong ground motions in Wakayama. Gratitude is also extended to Jim Mori for helpful comments concerning revision of the manuscript, Kunihiro Shigetomi for valuable discussion, and all those who assisted with the observations.

Ancillary