## Estimation of *Q*-Values in the Seismogenic and Aseismic Layers in the Kinki Region, Japan, by Elimination of the Geometrical Spreading Effect Using Ray Approximation
### by Anatoly Petukhin, Kojiro Irikura, Shiro Ohmi, and Takao Kagawa
#### Abstract
The *Q*-value is one of the parameters controlling attenuation of seismic waves with distance. Attenuation relations in crust used in the earthquake engineering applications usually consider models with uniform *Q* and geometrical spreading. In this work we try to estimate a nonuniform *Q*-value based on the ray geometrical spreading in a nonuniform velocity model. We estimate *Q*-values in the seismogenic and aseismic zones of the Kinki region (Japan) using Hi-net data. The Hi-net network consists of high-sensitivity seismometers in 100–200 m boreholes. We assumed a two-layer model of *Q*(*f*) (seismogenic and aseismic zones), with uniform *Q* in each layer, and we applied a method for the separation of source, path, and site effects. Path lengths in the layers were calculated using raytracing. A geometrical spreading term was calculated for a realistic 1D velocity model (consisting of three layers over the Moho). Inversion was performed in two steps. (1) The *Q* value in the seismogenic layer was estimated using shallow earthquake data (depth < 20 km), assuming a one-layer *Q* model. (2) Data from subduction zone earthquakes covering the aseismic zone (with depths 20–70 km) and two-layer *Q* model (0–20 and 20–70 km) were used to calculate *Q* in the aseismic zone, where the *Q*-value for the upper layer was constrained by results of step 1. The total number of records used was 628. Only direct *S*-wave data were used to calculate Fourier amplitude spectra in the high-frequency range 1–10 Hz. Validation of the method and inversion results were made by inversion of synthesized data. We discuss in detail several possible sources of errors of the estimation of *Q*-values. The results of inversion showed a higher *Q* in the upper layer, *Q*(*f*) = 180*f*^{0.7} for the seismogenic layer, than that in the lower, *Q*(*f*) = 90*f*^{0.8} for the aseismic zone. This result supports the model of the crust containing a brittle seismogenic layer and a ductile aseismic zone. We proposed amplitude versus distance attenuation model for Kinki region, Japan, based on estimated *Q*-values and geometrical spreading.
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