Porous medium - the P-wave case

P.F. Daley


A subset of the general equations used to describe seismic wave propagation in a poroviscoelastic medium is investigated using finite difference methods. Theoretically for an isotropic medium of this type there are four modes a propagation: a compressional (P) wave, a shear (Sv) wave and a shear (Sh) wave as well as what in termed a slow compressional (Ps) whose actual existence has, until fairly recently, been questioned. The scaled down version of the full poroviscoelastic equation set is one which is viscoelastic and but does not contain any shear type propagation. It is the acoustic analogue of the elastic wave equation, being a set of two coupled equations in the fast and slow compressional (P) wave modes, which may be further downgraded to to a single equation in the fast compressional (P) wave mode as the slow compressional (P) wave mode is difficult to physically detect and as a consequence omitted, at least in this preliminary study. The relatively simple equation remaining was chosen so that a comparison with the seismic response of the acoustic wave could be done to ascertain the possible usefulness of pursuing this topic further. Apart from hydrocarbon related seismic applications, the use of this theory for near surface seismic or Ground Penetrating Radar (GPR) applications to locate toxic or hazardous waste sites and possibly be of assistance in delineating the extent of seepages either from actual dumping or deteriorating containers is a possibility.

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