Wave-induced fluid flow (WIFF) between cracks and micropores is one of the major mechanisms causing attenuation and dispersion within seismic frequency ranges. Previous non-interaction-approximation (NIA) models often assume that the distribution of cracks is dilute, neglecting the influences of interacting cracks on dispersion and attenuation. To overcome this restriction, we have investigated the interaction between coplanar cracks and their influences on seismic dispersion and attenuation. First, a scattering problem for a longitudinal (P) wave normally impinging on a plane with equally distributed coplanar cracks in a porous medium is solved using an integral transform approach. Then, based on the solution, an effective wavenumber is derived for P-wave propagation in a porous material with coplanar cracks. It is found that the magnitude of dispersion and attenuation can significantly increase when the spacing between adjacent cracks decreases even if the crack density is unchanged. Moreover, frequency-dependent asymptotic behavior of inverse quality factor is also different from that of the NIA models at frequencies lower than the WIFF relaxation frequency. Specifically, the inverse quality factor scales with the square root of the frequency at low frequencies. When the spacing between adjacent cracks is large, an additional frequency-dependent scale occurs at relatively higher frequencies (but still lower than the WIFF relaxation frequency) with inverse quality factor scales with the first power of frequency. When the spacing becomes much larger so that the interaction between the adjacent cracks is negligible, the present model exactly reduces to an NIA model for the distribution of aligned slit cracks and the first power scale can maintain attenuation within low frequencies.

中文翻译：

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具有共面裂纹分布的饱和流体岩石中P波的衰减和弥散—散射法

裂缝和微孔之间的波诱导流体流（WIFF）是引起地震频率范围内衰减和弥散的主要机制之一。以前的非相互作用近似（NIA）模型通常假定裂纹的分布很稀疏，而忽略了相互作用的裂纹对弥散和衰减的影响。为了克服这一限制，我们研究了共面裂纹之间的相互作用及其对地震波频散和衰减的影响。首先，使用积分变换方法解决了通常撞击在多孔介质中具有均匀分布的共面裂纹的纵向（P）波的散射问题。然后，基于该解，得出有效波数，用于在具有共面裂纹的多孔材料中进行P波传播。已经发现，即使裂纹密度不变，当相邻裂纹之间的间距减小时，色散和衰减的幅度也会显着增加。此外，在低于WIFF弛豫频率的频率下，逆品质因数的频率相关渐近行为也不同于NIA模型。具体而言，逆品质因数与低频频率的平方根成比例。当相邻裂纹之间的间距较大时，在相对较高的频率（但仍低于WIFF弛豫频率）处会出现附加的频率相关标度，而质量因数标度与频率的一阶幂成反比。当间距变得更大时，相邻裂纹之间的相互作用可忽略不计，