Abstract

We first compare two apparently dissimilar expressions for the quality factor Q of inhomogeneous plane waves in isotropic viscoelastic media, where Q is defined as the result of an energy-balance relation. In this case, it is the ratio of twice the strain energy to the dissipated energy. Both expressions give the same Q for P-waves and Q for S-waves is independent of the inhomogeneity angle γ (isotropic media). Then, we consider the more general balance equation, which holds for anisotropic viscoelastic media, where anomalous behaviors are observed when γ exceeds some critical value (forbidden directions of propagation). This problem has already been solved analytically for SH-waves. Here, we consider the qP–qS case, which requires a numerical solution of the dispersion equation to obtain the wavenumber and attenuation factor, i.e., the real and imaginary parts of the wave vector, respectively. The forbidden directions appear when the phase velocity approaches a zero value. Generally, the phase velocity of homogeneous waves (γ = 0) exceeds that of inhomogeneous waves, while the latter show stronger attenuation (lower quality factor). In the vicinity of the forbidden directions, the opposite behavior may occur.

中文翻译：

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非均匀平面波的品质因数

摘要

我们首先比较各向同性粘弹性介质中非均匀平面波的品质因数Q的两个明显不同的表达式，其中Q被定义为能量平衡关系的结果。在这种情况下，它是应变能与耗散能的两倍。这两个表达式对P波给出相同的Q，对S波给出Q，与不均匀角度γ（各向同性介质）无关。然后，我们考虑更通用的平衡方程，该方程适用于各向异性粘弹性介质，其中当γ超过某个临界值（传播的禁止方向）时，观察到异常行为。该问题已通过解析解决SH波。在这里，我们考虑qP – qS情况，这需要色散方程的数值解来获得波数和衰减因子，即波矢量的实部和虚部。当相速度接近零值时，出现禁止方向。通常，均匀波（γ= 0）的相速度超过非均匀波的相速度，而后者显示出较强的衰减（较低的品质因数）。在禁止方向附近，可能会发生相反的行为。