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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Shear wave ： ウィキペディア英語版 S-wave S-waves, secondary waves, or shear waves (sometimes called an elastic S-wave) are a type of elastic wave, and are one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves. The S-wave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation. The wave moves through elastic media, and the main restoring force comes from shear effects. These waves do not diverge, and they obey the continuity equation for incompressible media: :$\backslash nabla\; \backslash cdot\; \backslash mathbf\; =\; 0$ Its name, S for secondary, comes from the fact that it is the second direct arrival on an earthquake seismogram, after the compressional primary wave, or P-wave, because S-waves travel slower in rock. Unlike the P-wave, the S-wave cannot travel through the molten outer core of the Earth, and this causes a shadow zone for S-waves opposite to where they originate. They can still appear in the solid inner core: when a P-wave strikes the boundary of molten and solid cores, S-waves will then propagate in the solid medium. And when the S-waves hit the boundary again they will in turn create P-waves. This property allows seismologists to determine the nature of the inner core. As transverse waves, S-waves exhibit properties, such as polarization and birefringence, much like other transverse waves. S-waves polarized in the horizontal plane are classified as SH-waves. If polarized in the vertical plane, they are classified as SV-waves. When an S- or P-wave strikes an interface at an angle other than 90 degrees, a phenomenon known as mode conversion occurs. As described above, if the interface is between a solid and liquid, S becomes P or vice versa. However, even if the interface is between two solid media, mode conversion results. If a P-wave strikes an interface, four propagation modes may result: reflected and transmitted P and reflected and transmitted SV. Similarly, if an SV-wave strikes an interface, the same four modes occur in different proportions. The exact amplitudes of all these waves are described by the Zoeppritz equations, which in turn are solutions to the wave equation. ==Theory== The prediction of S-waves came out of theory in the 1800s. Starting with the stress-strain relationship for an isotropic solid in Einstein notation: :$\backslash tau\_=\backslash lambda\backslash delta\_e\_+2\backslash mu\; e\_$ where $\backslash tau$ is the stress, $\backslash lambda$ and $\backslash mu$ are the Lamé parameters (with $\backslash mu$ as the shear modulus), $\backslash delta\_$ is the Kronecker delta, and the strain tensor is defined :$e\_\; =\; \backslash frac\backslash left(\; \backslash partial\_i\; u\_j\; +\; \backslash partial\_j\; u\_i\; \backslash right)$ for strain displacement u. Plugging the latter into the former yields: :$\backslash tau\_\; =\; \backslash lambda\backslash delta\_\backslash partial\_ku\_k\; +\; \backslash mu\; \backslash left(\; \backslash partial\_i\; u\_j\; +\; \backslash partial\_j\; u\_i\; \backslash right)$ Newton's 2nd law in this situation gives the ''homogeneous equation of motion'' for seismic wave propagation: :$\backslash rho\backslash frac\; =\; \backslash partial\_j\backslash tau\_$ where $\backslash rho$ is the mass density. Plugging in the above stress tensor gives: :$\backslash begin$ \rho\frac &= \partial_i\lambda\partial_k u_k + \partial_j\mu\left(\partial_i u_j + \partial_j u_i \right) \\ &= \lambda\partial_i\partial_k u_k + \mu\partial_i\partial_j u_j + \mu\partial_j\partial_j u_i \end Applying vector identities and making certain approximations gives the seismic wave equation in homogeneous media: :$\backslash rho\; \backslash ddot)\; -\; \backslash mu\backslash nabla\; \backslash times\; (\backslash nabla\; \backslash times\; \backslash boldsymbol)$ where Newton's notation has been used for the time derivative. Taking the curl of this equation and applying vector identities eventually gives: :$\backslash nabla^2(\backslash nabla\backslash times\backslash boldsymbol)\; -\; \backslash frac\backslash frac\backslash left(\backslash nabla\backslash times\backslash boldsymbol\backslash right)\; =\; 0$ which is simply the wave equation applied to the curl of u with a velocity $\backslash beta$ satisfying :$\backslash beta^2\; =\; \backslash frac$ This describes S-wave propagation. Taking the divergence of seismic wave equation in homogeneous media, instead of the curl, yields an equation describing P-wave propagation. The steady-state SH waves are defined by the Helmholtz equation :$(\backslash nabla^2+k^2\; )\backslash boldsymbol=0$ where k is the wave number. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「S-wave」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.