11:00 〜 13:00
[SSS06-P08] Investigating the impact of the free surface effect and the Hurst exponent κ to the frequency dependency of seismic wave scattering through the 3D Finite Difference simulation of plane P wave propagation
キーワード：Heterogeneity, Seismic scattering, Numerical simulation
Small-scale velocity heterogeneity in the subsurface can scatter seismic waves. As a result, teleseismic P wave energies are partitioned into transverse-component seismograms. This allows us to stochastically study the small-scale medium heterogeneity by computing the peak ratio at seismic stations. Peak ratio is defined as the ratio of the maximum P wave amplitude in the transverse envelope, over that of the 3-component sum envelope.
Analyses using the peak ratio approach have been done on a global scale (Kubanza et al. 2007) and in Japan (Nishimura 2012; Ganefianto et al. 2021). Peak ratio is observed to increase with frequency. We proposed a means to quantify this frequency dependency by estimating the frequency gradient m at a station (Ganefianto et al. 2020, SSJ). However, factors behind the apparent frequency dependency are poorly understood. Secondly, Emoto et al. (2010) studied the free surface effect on seismogram envelope of stations on the surface. However, its depth dependency especially on peak ratio is yet to be studied, which is important for borehole stations. Here, we investigate how m can be influenced by the free surface (stations depth), and the characterisation of the von Karman medium (Hurst exponent κ) by performing 3D Finite Difference simulations of seismic wave propagation using OpenSWPC.
The computational model has 512×512×512 grids spaced every 0.05 km. We consider a flat free surface. The propagating media are of the von Karman type, with background P and S wave velocities of 5 and 2 km/s, respectively; correlation distance a of 0.5 km; and rms fractional fluctuation in velocity ε of 5%. All parameters except for κ are kept unchanged, thus we are able to examine the link between κ and peak ratio frequency dependency.
We consider a vertical plane P wave originating near the bottom of the computational model. By controlling its wavelength, we simulate propagation at different frequencies. For the receivers, we set arrays of stations extending down to 10 km. We define more stations near the model's centre to counter the noted artefact where artificial reflection from the model boundaries may exist. The lateral spread of the receivers serves as a substitute for ensemble averaging. Ideally, to obtain the mean-squared (MS) envelope, we stack over many random medium realisations. But this requires too many runs of the simulation. So, envelopes at equal depth are stacked to give the MS envelope for that depth.
The free surface effect is dominant in the shallow region. The interference between the up-going (incident) and the down-going (surface-reflected) waves affects the vertical component peak amplitude, creating an apparent rise in peak ratio at λ/4 where these waves are out of phase. This causes a depth dependence of m. In the shallow region, the free surface effect creates large m fluctuations. At deeper depths (≧4 km), the up-going and down-going waves are separable, and the case is analogous to an infinite random medium.
Overall, m is decreasing with increasing κ indicating that larger κ weaken the apparent frequency dependency. Taking only the deeper depths, we linearly approximate m as a function of κ. Previous estimation based on vector wave envelope synthesis (Suzaki 2007) suggests that frequency dependency diminishes quickly and virtually disappears at large κ, presumably following the convergence to a frequency independent Gaussian model at large κ. However, we see smaller drop in m in this study. Also, we see positive m values at large κ, implying that some frequency dependency may persist at large κ.
So far, we considered only random media with a flat free surface. Next, we shall simulate the effect of topography. These results will be useful when studying peak ratio measured at borehole stations.
Acknowledgement: We thank Profs. Takuto Maeda, Shunsuke Takemura and Takashi Furumura for the OpenSWPC code. We use the EIC-ERI system at the University of Tokyo. This experiment is supported by JST SPRING Grant Number JPMJSP2114.
Analyses using the peak ratio approach have been done on a global scale (Kubanza et al. 2007) and in Japan (Nishimura 2012; Ganefianto et al. 2021). Peak ratio is observed to increase with frequency. We proposed a means to quantify this frequency dependency by estimating the frequency gradient m at a station (Ganefianto et al. 2020, SSJ). However, factors behind the apparent frequency dependency are poorly understood. Secondly, Emoto et al. (2010) studied the free surface effect on seismogram envelope of stations on the surface. However, its depth dependency especially on peak ratio is yet to be studied, which is important for borehole stations. Here, we investigate how m can be influenced by the free surface (stations depth), and the characterisation of the von Karman medium (Hurst exponent κ) by performing 3D Finite Difference simulations of seismic wave propagation using OpenSWPC.
The computational model has 512×512×512 grids spaced every 0.05 km. We consider a flat free surface. The propagating media are of the von Karman type, with background P and S wave velocities of 5 and 2 km/s, respectively; correlation distance a of 0.5 km; and rms fractional fluctuation in velocity ε of 5%. All parameters except for κ are kept unchanged, thus we are able to examine the link between κ and peak ratio frequency dependency.
We consider a vertical plane P wave originating near the bottom of the computational model. By controlling its wavelength, we simulate propagation at different frequencies. For the receivers, we set arrays of stations extending down to 10 km. We define more stations near the model's centre to counter the noted artefact where artificial reflection from the model boundaries may exist. The lateral spread of the receivers serves as a substitute for ensemble averaging. Ideally, to obtain the mean-squared (MS) envelope, we stack over many random medium realisations. But this requires too many runs of the simulation. So, envelopes at equal depth are stacked to give the MS envelope for that depth.
The free surface effect is dominant in the shallow region. The interference between the up-going (incident) and the down-going (surface-reflected) waves affects the vertical component peak amplitude, creating an apparent rise in peak ratio at λ/4 where these waves are out of phase. This causes a depth dependence of m. In the shallow region, the free surface effect creates large m fluctuations. At deeper depths (≧4 km), the up-going and down-going waves are separable, and the case is analogous to an infinite random medium.
Overall, m is decreasing with increasing κ indicating that larger κ weaken the apparent frequency dependency. Taking only the deeper depths, we linearly approximate m as a function of κ. Previous estimation based on vector wave envelope synthesis (Suzaki 2007) suggests that frequency dependency diminishes quickly and virtually disappears at large κ, presumably following the convergence to a frequency independent Gaussian model at large κ. However, we see smaller drop in m in this study. Also, we see positive m values at large κ, implying that some frequency dependency may persist at large κ.
So far, we considered only random media with a flat free surface. Next, we shall simulate the effect of topography. These results will be useful when studying peak ratio measured at borehole stations.
Acknowledgement: We thank Profs. Takuto Maeda, Shunsuke Takemura and Takashi Furumura for the OpenSWPC code. We use the EIC-ERI system at the University of Tokyo. This experiment is supported by JST SPRING Grant Number JPMJSP2114.