岩石的粘弹性谐振Q模型

实验表明,在应变小于10^-6范围内,砂岩对地震波的吸收主要由孔隙流体的局部运动引起,而且Q值随频率的变化出现谐振现象。据此,作者认为,地壳上部地震波能量的耗损可以表示为以下两种成分的线性组合:1.由滑动摩擦、热弹性驰豫、位错运动等引起的能量消散,它们主要与岩石的固相成分有关,可近似地用恒Q模型描述;2.由孔隙流体运动引起的能量消散,可以用谐振公式描述。根据这一认识,利用描述因果关系的Kramers-Krnig关系式可推导出表示地壳上部岩石粘弹性（复弹性模量,相速度频散和衰减函数）的公式,它们综合地描述了由各种机制引起的波的频散和吸收,并在谐振Q值等于参考常数Q值时退化为目前常用的Futterman模型。作为这种谐振Q模型的应用,介绍了它用于Q值测量结果外推和频散一吸收研究以及粘弹性介质中反射地震道合成的结果。

A RESONANCE Q MODEL FOR VISCOELASTIC ROCKS

It has been suggested that the dominant mechanism of attenuation of seismic waves in sa-turaled sandstone is the pore fluid flows if strains are not greater than 10^-6, while Q is frequency dependent with a resonance at some frequency6-9]. Based on the published experimental results, I suggest that the energy dissipation of seismic waves travelling in the upper part of the Earth's crust may be expressed by the linear combination of the following two components: （1） dissipation due to frictional sliding at cracks and grain boundaries, thermoelastic attenuation and motion of dislocations, which are related to solid frame of rocks and can be approximately described by the constant Q model; （2） dissipation due to pore fluid flows which may be described by a resonance model. Using the Kramer-Kr（?）nig dispersion relationship for a linear causal system, I obtain a viscoelastic model for general rocks to calculate the complex elastic modulus dispersive phase velocity and attenuation coefficients. This resonance Q model generalizes the effects due to all attenuation mechanisms we know and reduces to Futterman model when the resonance Q equals constant Q. As two examples of its application, I first introduce a method for extrapolation of Q measured in a limited frequency range to study wave attenuation and dispersion. Then I show an approach of synthesis of dispersive reflection seismic traces with computational results.