# Compressional Wave Theory

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When a compressional wave travels through a fluid-saturated porous material, a fluid pressure gradient and an acceleration of the solid matrix are created. This leads to the flow of the pore fluid. The mobile ions in the electric double layer move with the flow, while those ions which are attached to the surface of the grains, remain fixed. The net flow of charge relative to the grains is called streaming current and the associated electric field is known as the coseismic field, see Figure \ref{fig:coseismic}(a). The coseismic field travels with the seismic wave. The second seismoelectric phenomenon occurs when the compressional wave hits an interface in the material. This interface can be a heterogeneity in elastic properties of the medium…show more content…
The Biot theory is a set of differential equations that predict the average displacement $\mathbf{u}$ of the grains and the average fluid filtration displacement $\mathbf{w}$ (time derivative of the filtration displacement gives the Darcy velocity) \cite{biot1956a,biot1956b}. \par This theory predicts the existence of two longitudinal waves (P waves) and one shear wave (S wave). The two compressional waves are the fast P wave and the slow P wave. The fast P wave arises when the fluid and the skeleton move in phase with respect to each other. while in the case of slow P wave, the fluid and the skeleton move out-of-phase. The fast P wave and the shear wave propagate with little dispersion. The slow P wave moves with a lower speed and is highly attenuative. Pride's theory is based on a number of assumptions. Only linear disturbances are considered. The fluid is assumed to be an ideal