电震转换的反问题
Inverse Problem of Electro-seismic Conversion
摘要：
当多孔岩石被电解质饱和时，电场通过电震转换与地震波耦合。Pride推导了控制模型，其中Maxwell方程通过电动迁移率参数与Biot方程耦合。线性化电-震转换的逆问题包括两个步骤，即Biot方程的反演和Maxwell方程的反演。我们分析了Maxwell方程中电导率和电动迁移率参数的内部测量重建，而内部测量由Biot方程的反演结果提供。我们表明，两个内部数据的基础上精心选择的边界条件的知识，唯一确定这两个参数。此外，一个Lipschitz型稳定性证明了基于同样的一套精心选择的边界条件。
英文摘要：
When a porous rock is saturated with an electrolyte, electrical fields are coupled with seismic waves via the electro-seismic conversion. Pride derived the governing models, in which Maxwell equations are coupled with Biot equations through the electro-kinetic mobility parameter. The inverse problem of the linearized electro-seismic conversion consists in two step, namely the inversion of Biot equations and the inversion of Maxwell equations. We analyze the reconstruction of conductivity and electro-kinetic mobility parameter in Maxwell equations with internal measurements, while the internal measurements are provided by the results of the inversion of Biot equations. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determine these two parameters. Moreover, a Lipschitz type stability is proved based on the same sets of well-chosen boundary conditions.
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