Poroelastic near-field inverse scattering
Poroelastic near-field inverse scattering
复制标题
多孔弹性近场逆散射
DOI：
10.1016/j.jcp.2022.111005
复制
发表时间：
2022
影响因子：
4.1
通讯作者：
Napal, Kevish
中科院分区：
文献类型：
--
作者：
Pourahmadian, Fatemeh;Napal, Kevish
建立了多物理场数据分析平台，用于根据弹性波形和/或声学孔隙压力测量对有限渗透率（例如水力裂缝）的孔隙弹性界面进行成像。这是通过逆散射非迭代采样方法设计的最新进展来实现的。直接问题是通过频域中的毕奥方程来表述的，其中不连续性网络由一组总体力和流体体积源照亮，同时监测任意近场配置中的感应（声学和弹性）散射波。采用薄层近似来捕获界面的粗糙和多相性质，其空间变化的流体力学特性是先验未知的。在这种情况下，前向问题的适定性分析产生了接触参数的可接受条件。据此，介绍了多孔弹性散射算子及其第一和第二因式分解，并仔细研究了它们的数学性质。结果表明，Biot 系统的非自共轭性质导致散射算子本质上不对称因式分解，该算子在某些限制下可能是对称的。这些结果为正则化和凸成本函数的系统设计提供了一个强大的框架，其最小化器支撑了多物理场成像指标。所提出的解决方案通过深井测量综合应用于水力裂缝网络的时空重建。
A multiphysics data analytic platform is established for imaging poroelastic interfaces of finite permeability (e.g., hydraulic fractures) from elastic waveforms and/or acoustic pore pressure measurements. This is accomplished through recent advances in design of non-iterative sampling methods to inverse scattering. The direct problem is formulated via the Biot equations in the frequency domain where a network of discontinuities is illuminated by a set of total body forces and fluid volumetric sources, while monitoring the induced (acoustic and elastic) scattered waves in an arbitrary near-field configuration. A thin-layer approximation is deployed to capture the rough and multiphase nature of interfaces whose spatially varying hydro-mechanical properties are a priori unknown. In this setting, the well-posedness analysis of the forward problem yields the admissibility conditions for the contact parameters. In light of which, the poroelastic scattering operator and its first and second factorizations are introduced and their mathematical properties are carefully examined. It is shown that the non-selfadjoint nature of the Biot system leads to an intrinsically asymmetric factorization of the scattering operator which may be symmetrized at certain limits. These results furnish a robust framework for systematic design of regularized and convex cost functionals whose minimizers underpin the multiphysics imaging indicators. The proposed solution is synthetically implemented with application to spatiotemporal reconstruction of hydraulic fracture networks via deep-well measurements.
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