Nondimensionalization and Perturbation Analysis of Seismo-electromagnetic Governing Equations

TitleNondimensionalization and Perturbation Analysis of Seismo-electromagnetic Governing Equations
Publication TypeConference Paper
Year of Publication2018
AuthorsFournier, A, Grobbe, N, Demanet, L
Conference NameAGU Fall Meeting
Date Published12/2018
PublisherAmerican Geophysical Union
Conference LocationWashington, DC

Coupled seismo-electromagnetism describes phenomena in (partially) fluid-saturated, porous media, in which elastic mechanical fields and electromagnetic fields are comparably strong, and coupled to each other. It provides a very complete picture that potentially significantly augments subterranean science and technology applications such as: fossil-fuel or geothermal exploration and production; near-surface characterization; groundwater study; and seismic electromagnetism. Notwithstanding this promising potential, there are formidable challenges, including: uncertainty of many material parameters and of initial and boundary conditions; and an enormous range of signal amplitudes in observations or realistic simulations. The governing equations comprise essentially: the Biot poroelastic wave equations for a solid-fluid composite; the Maxwell equations of electromagnetism; and terms representing the physical coupling of the former to the latter. Given the wide variety of behavior of the solutions of the equations, and wide range of spatiotemporal scales displayed by them, an analytical imperative is to nondimensionalize the equations e.g., by applying the Buckingham π theorem. Nondimensionalization will: remove spurious dependencies on, and incommensurabilities due to physical units; and identify candidate dimensionless parameters whose values may delineate solution-behavior regimes (analogously as the Reynolds number does in fluid dynamics), including spatial-scale regimes from lab up to global. A nondimensionalization cannot be unique; but to the best of our knowledge, none has been reported in the literature before for the coupled seismo-electromagnetic equations, so we will present one. We will define dimensionless parameters with meaningful physical interpretations and value ranges e.g., ratios of typical magnitudes of equation terms. We will also apply perturbation with respect to a selected small dimensionless parameter, in order to obtain reflection coefficients for coupled wave-medium interactions at surfaces of material spatial discontinuity. These coefficients provide the most straightforward description of such interactions, but explicit formulas for them tend to be impractically long and obscure, without a perturbation analysis such as we will derive.