[S-SS11] Strong Ground Motion and Earthquake Disaster

[SSS11-P09] Reproduction study of the phase characteristics of a transfer function at a vertical array observation on a slope

*Kentaro Kasamatsu¹, Takashi Nozawa¹, Tetsushi Watanabe², Yoshiyuki Takahashi¹ (1.Kajima Corporation, 2.Kobori Research Complex Inc.)

Keywords:Slope, Vertical Array Observation, Transfer Function, Phase Characteristics

Transfer functions at vertical array observatories installed on slopes might not be reproduced by a one-dimensional ground response analysis with a vertically incident plane wave (1D analysis). In this study, we tried to reproduce phase characteristics of the observed transfer function with a two-dimensional ground response analysis (2D analysis) while considering the slope of the topography at a KiK-net station of Tatsuyama-Higasi (SZOH32). SZOH32 has two vertically arranged seismometers in Tatsuyama-cho, Shizuoka Prefecture. The sensors are installed at ground level (GL) and at a depth of 103m (GL-103m). The S-wave velocity at GL-103m is estimated to be 1600m/s by PS logging. The averaged transfer function of the radial component with observation records of 7 earthquakes that occurred east of SZOH32 is shown in Figure A with a black line and circles. A blue dashed line and circles in Figure A indicate the theoretical transfer function calculated by the 1D analysis with an S-wave velocity structure model by PS logging. Attenuation was assumed to be 5% for all frequencies. The amplitude characteristics are largely reproduced, but the observed and 1D analyzed phase transitions are distributed in opposite directions at frequencies around 3 and 4Hz, where the trough is formed at GL-103m. The observed phase transitions at these frequencies cannot be reproduced by the 1D analysis. The S-wave velocity structure model used in our 2D analysis is shown in Figure B. The topographic model was constructed by incorporating elevation data measured around SZOH32 into DEM whose resolution is 10m. S-wave velocity, P-wave velocity, and thickness were set based on PS logging of SZOH32. The distribution of velocity boundaries was assumed to be parallel to the topographic model. We conducted the 2D analysis with the finite difference method. The S-wave velocity structure model in Figure B was discretized with square grids with a spacing of 0.5m. The 2D analysis consisted of the P-SV wave field and the SV plane wave with an incidence angle of 40 degrees. The attenuation was assumed to be approximately half the value of the result of an optimized analysis based on the 1D analysis with the amplitude characteristics of the transfer function. The theoretical transfer function from the 2D analysis is shown with a red line and circles in Figure A. Although the amplitude at frequencies around 3 and 4Hz is slightly overestimated, the overall amplitude characteristics could be largely reproduced. The phases at frequencies around 3 and 4Hz also have good agreement with the observed ones. We performed another 2D analysis with the plane SV wave having a vertical incidence. In addition to the observed phases around 3 to 4Hz, the observed amplitudes at all frequencies were not well reproduced. The simulated velocity waveform at GL-103m is shown in Figure C. The Ricker wave was used for a source-time function with a central frequency of 3Hz. The result of a multiple-filter analysis is arranged vertically. Incident and reflected waves from the surface are found at 0.7 and 0.9 seconds, respectively. According to the multiple-filter analysis result at frequencies of 2 and 4Hz near 3Hz, the maximum amplitude can be found during the time at which the reflected wave arrives. This waveform's characteristics could be related to the overlapping of reflected wavefronts caused by differences in surface elevation, as indicated by Uetake et al. (2024). We found that the observed phase transitions at frequencies around 3 and 4Hz are due to the amplitude difference between the incident and the reflected waves, and this wave propagation can be reproduced by the 2D analysis considering oblique incidence. At vertical array observatories with significant topographical unevenness, it is important to focus not only on the amplitude characteristics but also the phase ones.