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arXiv 0801.2442physics.geo-ph
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流体饱和深度相关孔隙弹性介质地震反射率的扰动

Perturbations of the seismic reflectivity of a fluid-saturated depth-dependent poro-elastic medium

Louis De Barros, M. Dietrich

摘要:

本文推导了充液层状多孔介质中平面不均匀性对点源地震响应的一阶影响的解析计算公式。推导是通过在平面波域中使用玻恩近似的孔隙弹性波动方程式的扰动分析来实现的。这种方法产生的P - SV -和SH-波响应的未扰动介质的格林函数的Fréchet导数。导出的运营商的准确性和稳定性进行检查,通过比较,在时间-距离域,从这些解析表达式与完整的解决方案,通过引入离散扰动模型的属性计算的微分地震图。对于垂直和水平的点力,它被发现,Fréchet导数的方法是非常准确的小和局部扰动的介质属性是一致的玻恩近似的要求。此外,一阶公式似乎是稳定的,在所有源-接收器偏移。孔隙度、固结参数、固体密度和矿物剪切模量是正反演问题中最敏感的参数。最后,薄层的振幅-角度响应显示了几个模型参数之间的强耦合效应。

英文摘要:

Analytical formulas are derived to compute the first-order effects produced by plane inhomogeneities on the point source seismic response of a fluid-filled stratified porous medium. The derivation is achieved by a perturbation analysis of the poro-elastic wave equations in the plane-wave domain using the Born approximation. This approach yields the Fréchet derivatives of the P -- SV - and SH-wave responses in terms of the Green's functions of the unperturbed medium. The accuracy and stability of the derived operators are checked by comparing, in the time-distance domain, differential seismograms computed from these analytical expressions with complete solutions obtained by introducing discrete perturbations into the model properties. For vertical and horizontal point forces, it is found that the Fréchet derivative approach is remarkably accurate for small and localized perturbations of the medium properties which are consistent with the Born approximation requirements. Furthermore, the first-order formulation appears to be stable at all source-receiver offsets. The porosity, consolidation parameter, solid density and mineral shear modulus emerge as the most sensitive parameters in forward and inverse modeling problems. Finally, the Amplitude-Versus-Angle response of a thin layer shows strong coupling effects between several model parameters.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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