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

Figure 17

Comparison between the exact Green’s function 𝐺^𝐸,𝑓(𝑥_𝐵,𝑥_𝐴,𝑡)+𝐺^{𝑣𝑠,𝐽𝑒}(𝑥_𝐴,𝑥_𝐵,−𝑡) and the Green’s function retrieved by considering only electromagnetic boundary source contributions (𝐽^𝑒 and 𝐽^𝑚) in the right-hand side of (52). In other words, the contributions of the domain sources and seismic boundary sources are neglected. As is visible, the electromagnetic boundary sources have a negligible contribution to the retrieved Green’s function in the positive time window 𝐺^𝐸,𝑓(𝑥_𝐵,𝑥_𝐴,𝑡). However, the electromagnetic boundary sources do contribute to the Green’s function retrieval in the negative time window, that is, 𝐺^{𝑣𝑠,𝐽𝑒}(𝑥_𝐴,𝑥_𝐵,−𝑡). The two red-dashed peaks at roughly 𝑡=−0.28 s and 𝑡=−0.38 s correspond to the spurious events 𝐵1 and 𝐵2, respectively. It is visible that the spurious events are not present in the exact case. The contribution of the electromagnetic boundary sources in cancelling out the spurious events in the negative time window is clearly illustrated.