An inverse problem for an electroseismic model describing the coupling phenomenon of electromagnetic and seismic waves

Abstract

The electroseismic model describes the coupling phenomenon of the electromagnetic waves and seismic waves in fluid immersed porous rock. Electric parameters have better contrast than elastic parameters while seismic waves provide better resolution because of the short wavelength. The combination of theses two different waves is prominent in oil exploration. Under some assumptions on the physical parameters, we derived a Hölder stability estimate to the inverse problem of recovery of the electric parameters and the coupling coefficient from the knowledge of the fields in a small open domain near the boundary. The proof is based on a Carleman estimate of the electroseismic model.

Analysis of Electroseismic Conversion in an Unbounded Rough Surface

“…Due to the coupling between Biot's poroelastic equations and Maxwell's electromagnetic equations, the seismoelectric effect can provide us with additional information about for example the porosity and permeability of the medium and information about the pore-fluid content. Therefore, the inverse problem related to the coupling of electromagnetic wave and seismic wave plays an important role in the field of geological exploration, these works on theoretical analyses and numerical experiments give us some important guidance for for researching such related practical inverse problems [8,10,11,24]. In [8], the author derived a Hölder stability estimate to the inverse problem of recovery of the electric parameters and the coupling coefficient for the electroseismic model in oil exploration.…”

“…Therefore, the inverse problem related to the coupling of electromagnetic wave and seismic wave plays an important role in the field of geological exploration, these works on theoretical analyses and numerical experiments give us some important guidance for for researching such related practical inverse problems [8,10,11,24]. In [8], the author derived a Hölder stability estimate to the inverse problem of recovery of the electric parameters and the coupling coefficient for the electroseismic model in oil exploration. The application of electroseismic and seismoelectric phenomenon plays an outstanding role in oil and gas exploration [61], in [44], the properties of glacier system are studied by seismoelectric method.…”

Bayesian inversion of joint SH seismic and seismoelectric data to infer glacier system properties

“…The authors concluded that when using noiseless data, its electric portion contains more information than the seismic one, and that the model parameters obtained via joint inversion are more accurate than the ones obtained by inverting the seismic time-series alone. It is worth to mention also the works of Guan et al (2013); Yang (2013) andBonnetier et al (2019), which deal with an electrolyte-saturated homogeneous poroelastic medium. Proposing a deterministic inversion methodology, Guan et al (2013) recovered the permeability of different fluid saturated homogeneous porous formations from seismoelectric well logs, deriving the amplitude ratio of electric signal to acoustic pressure (REP) of Stoneley waves, and obtaining the permeability from an expression involving the tangent of its phase.…”

“…the conditions under which the electric conductivity and the electrokinetic coupling coefficient can be recovered from a two-step inversion. On the other hand, Chen and Yang (2013) and Bonnetier et al (2019) carried out a stability analysis of the inverse problem for the possible recovery of the same two parameters from knowledge of the seismoelectric fields, but based on theoretical studies of electroseismic conversions stated by Pride (1994).…”

On an inverse source problem for the Biot equations in electro-seismic imaging

“…An inverse source problem for the Biot's equations was investigated in [2] in a different context by assuming access to internal measurement rather than boundary measurement. Recently, the work [3] studied the electro-seismic model ( 1)-( 6) and derived a Hölder stability estimate for recovery of the electric parameters and the coupling coefficient from internal measurement near the boundary.…”