hy si cs Seismoelectric wave propagation numerical modelling in partially saturated materials

To better understand and interpret seismoelectric measurements acquired over vadose environments , both the existing theory and the wave propagation modelling programmes, available for saturated materials, should be extended to partial saturation conditions. We propose here an extension of Pride's equations aiming to take into account partially saturated materials, in the case of a water–air mixture. This new set of equations was incorporated into an existing seismoelectric wave propagation modelling code, originally designed for stratified saturated media. This extension concerns both the mechanical part, using a generalization of the Biot– Gassmann theory, and the electromagnetic part, for which dielectric permittivity and electrical conductivity were expressed against water saturation. The dynamic seismoelectric coupling was written as a function of the streaming potential coefficient, which depends on saturation, using four different relations derived from recent laboratory or theoretical studies. In a second part, this extended programme was used to synthesize the seismoelectric response for a layered medium consisting of a partially saturated sand overburden on top of a saturated sandstone half-space. Subsequent analysis of the modelled amplitudes suggests that the typically very weak interface response (IR) may be best recovered when the shallow layer exhibits low saturation. We also use our programme to compute the seismoelectric response of a capillary fringe between a vadose sand overburden and a saturated sand half-space. Our first modelling results suggest that the study of the seismoelectric IR may help to detect a sharp saturation contrast better than a smooth saturation transition. In our example, a saturation contrast of 50 per cent between a fully saturated sand half-space and a partially saturated shallow sand layer yields a stronger IR than a stepwise decrease in saturation. Over the past two decades, seismoelectric imaging has spawned new interest, due to theoretical advances In theory, the seismoelectric method could combine the sensitivity of electrical methods to hydrological properties of the subsurface, such as porosity, with a high spatial resolution comparable to that of seismic surveys (Dupuis & Butler 2006; Haines et al. 2007). In addition, it may also be sensitive to hydraulic permeability (Garambois & Dietrich 2002; Singer et al. 2005). Seismoelectric signals may have several origins, but in this work we will restrict ourselves to the study of electrokinetically induced seismoelectric conversions. When a seismic wave propagates in a fluid-containing porous medium, seismoelectric signals arise from electrokinetic conversions occurring at the microscale; these signals are measurable at the macroscale, …