Comparison of Kramers-Krönig Relation and High-Frequency Acoustic Measurements in Water-Saturated Glass Beads

다공성 입자 매질에서 고주파 영역 음향 측정 자료와 Kramers-Krönig 관계식의 비교

Yang, Hae-Sang;Lee, Keun-Hwa;Seong, Woo-Jae

  • Received : 2011.05.24
  • Accepted : 2011.09.27
  • Published : 2011.10.31


The necessary and sufficient condition for causality of a physical system can be expressed as Kramers-Kr$\ddot{o}$nig (K-K) relation. K-K relation for acoustic wave is a Hilbert transforms pair between dispersion equations of phase speed and attenuation. In this study, we quantitatively compare the acoustic measurements in water-saturated glass beads for the frequency ranges from 400 kHz to 1.1 MHz with the predictions of differential form of K-K relation obtained by Waters et al. For media with attenuation obeying an arbitrary frequency power law, acoustic measurements show good agreements with the predictions of Kramers-Kr$\ddot{o}$nig relation.


Kramers-Kr$\ddot{o}$nig relation;porous medium;p-wave sound speed and attenuation;water-saturated glass beads


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