基于黏弹波动方程解析解的频变AVO分析

Frequency-dependent AVO analysis based on analytical solution of viscoelastic wave equation

介观尺度(mesoscale)波致流体流动(wave-induced fluid flow)是导致孔隙介质中地震波本征衰减的主要原因,因此正确地表征其衰减特性尤为重要.受限于模拟方法的稳定性与岩石物理参数复杂关系式带来的计算成本,本文提出利用复合矩阵法推导一维黏弹波动方程频率域解析表达式,从而定量表征孔隙介质中地震波的衰减以及速度频散特征.针对常规方法仅讨论传播界面对反射系数随频率变化的影响情况,基于斑块饱和模型,本文利用新方法对比传播过程和传播界面的对其影响.在考虑传播过程的影响下,重新建立孔隙度、含气饱和度、渗透率与地震响应的联系.最后,基于黏弹介质理论,提出利用Kolsky-Futterman衰减模型定量表征斑块饱和模型的黏弹特性,并进一步通过新方法验证等效表征结果,从而扩展频变AVO技术的适用范围.研究结果表明:反射系数频率依赖影响中,传播过程远远大于传播界面;储层物性参数中,地震波对孔隙度变化的敏感度最高;在地震响应上,黏弹介质模型与斑块饱和模型的衰减特征具有良好的一致性,为后续频变AVO反演提供坚实的理论依据.

The mechanism of wave-induced fluid flow causes significant attenuation and dispersion of seismic waves in heterogeneous porous media, so it is especially important to correctly characterize its attenuation characteristics. In theory, based on the mesoscopic petrophysical model the wave equation can accurately characterize the attenuation and dispersion characteristics, but is limited by the stability of the simulation method and the calculation cost brought the complex relationship between the petrophysical parameters. Based on this, in this paper, the compound matrix method combined with complex elastic parameters is used to obtain the analytical solution of one-dimensional wave equation, so as to quantitatively characterize the attenuation and velocity dispersion characteristics of seismic waves in porous media. The conventional method only considers the reflection coefficient changes with frequency in the case of propagation interface. Therefore based on the patchy-saturation model, we analyze the influence of propagation and propagation interface on the reflection coefficient with frequency, and further re-establish the relationship between porosity, permeability, gas saturation and seismic response. Finally, we use the Kolsky-Futterman attenuation model to quantitatively characterize the viscoelastic properties of the patchy-saturation model based on the viscoelastic medium theory and confirm the consistency of the two in seismic response, thereby stretching the scope of application of frequency-dependent AVO technology. The results show that the influence of the propagation on the reflection coefficient with frequency is much larger than that of the propagation interface;the seismic wave has the highest sensitivity to the change of porosity;the attenuation and velocity dispersion characteristics between the patchy-saturation model and the viscoelastic model have good consistency in seismic response.