## 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 *Q*_{s}. The second effect is called intrinsic attenuation and is characterized by the intrinsic quality factor *Q*_{i}. Total attenuation is defined as *Q*_{t}^{−1} = *Q*_{s}^{−1} + *Q*_{i}^{−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 (*Q*_{i}^{−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 (*Q*_{s}^{−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 *Q*_{c}^{−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 *Q*_{c}^{−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.