Interferometric seismoelectric Green's function representations

Abstract

S U M M A R YInterferometric Green's function representations can be used to retrieve a Green's function between two receiver stations, effectively turning one receiver into a source. Through reciprocity theorems of the convolution and correlation types, we derive interferometric Green's function representations for coupled electromagnetic and seismic wave propagation in 1-D. These representations express a symmetrized Green's function in terms of correlations of sources distributed throughout the domain of reciprocity and on its boundary. The main challenge for practical implementation is the necessity of sources throughout a domain. Numerical examples show how this constraint can be relaxed for different configurations. In a configuration of two layers bounded by a vacuum, seismic noise sources behind the interface can be used to recover seismoelectric reflection responses that suffer from small amplitude losses, but are not corrupted by spurious events.

Experimental Validation of the Electrokinetic Theory and Development of Seismoelectric Interferometry by Cross-Correlation

“…We take the principle to the next level by numerically simulating seismoelectric interferometry by cross-correlation. de Ridder et al [46] have already shown, with three numerical examples, that it is indeed possible (under certain conditions) to obtain accurate Green's functions from boundary sources only. Here, we will increase the complexity of the numerical configuration by adding an extra layer to the system, to investigate the Green's function retrieval for a 1D, three-layered system bounded by a free-surface.…”

“…This is not always possible and therefore it is beneficial to be able to replace those strong sources by receivers: the principle of interferometry. In addition, by doing interferometry, stacking inherently takes place with a possible improvement of the signal-to-noise ratio as a result [46]. From an imaging point of view, the principle of interferometry has already been proven useful for a wide class of phenomena, for example in seismic and electromagnetic systems (e.g., Wapenaar et al [47], Slob et al [48]).…”

Virtual electrode current injection using seismic focusing and seismoelectric conversion

“…Finally we note that focusing of seismic energy could be simulated computationally through techniques like, for example, seismic interferometry (Thorbecke & Wapenaar 2007). This approach can also be used for interferometric Green's function representations of coupled electromagnetic and seismic wave propagation (De Ridder et al 2009). Here we take a different approach and discuss about physical focusing achieved in a medium of known acoustic properties to evaluate the electric properties in its vicinity.…”

Experimental quantification of the seismoelectric transfer function and its dependence on conductivity and saturation in loose sand

“…; De Ridder et al . ) and coseismic (Schoemaker et al . ) seismoelectric before being extended by Gao and Hu () to the seismomagnetic aspects.…”

“…Lately, seismic interferometry methods using Green's function Wapenaar and Fokkema 2006;Slob and Wapenaar 2007) have been adapted to provide the impulsive seismoelectric response of the porous medium equivalent to the usual transfer functions. This method was first implemented for interfacial (Wapenaar et al 2008;De Ridder et al 2009) and coseismic (Schoemaker et al 2012) seismoelectric before being extended by Gao and Hu (2010) to the seismomagnetic aspects.…”