Reflection of Inhomogeneous Seismic Waves at the Free Surface of an Effective Biot Solid

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Summary Seismic waves propagating in lossy materials are generally inhomogenous waves having different directions of propagation and attenuation. Unlike the homogenous waves, the inhomogeneity parameters, dissipation factors and phase velocities (denoted as the three wave quantities) of reflected/transmitted inhomogeneous waves can depend on the incidence angle. To estimate the three wave quantities of the reflected inhomogeneous waves, two new methods are introdueced and demonstrated by investigating the free surface reflection behaviour of P and S waves in an effective Biot solid which can explain the high level of attenuation observed in a reservoir. We prove that the three wave quantities of the pure-mode reflected waves PP and SS are exactly equal to those of the incident wave and independent of the incidence angle. Two sets of the dissipation factor expressions are derived as the functions of the material parameters and (1) the wave complex amplitudes, and (2) the inhomogeneity parameters of the waves. We also derived a new equation relating the inhomogeneity parameter to the complex slowness vector, called the D-p equation. The dissipation factors functions and the D-p equation are applied to the three wave quantities of the mode-converted waves PS and SP.