Relationships among elastic-wave values (R^pp, R^ps, R^ss, Vp, Vs, ρ, σ, κ)

Robert R. Stewart, Qi Zhang, Felix Guthoff

The average Vp/Vs value of a set of layers is a weighted sum of the interval velocity ratios. The average value is also bounded by the maximum and minimum interval values. The average value will change according to changes in the target layer. The thicker the layer, the greater its influence on the average value.

The approximate equations for converted-wave reflectivity Rps and pure-shear reflectivity Rss can be combined to give a simple relationship between the two: Rps ~ 4sin()Rss, where is the reflection angle of the shear wave.

The normalized elastic parameters (/, /, /) are estimated from summed P-P and P-S reflection coefficients using a linear inversion method. Normalized Poisson's ratio (/) and Lam parameters (/, /) can then be computed from the estimated velocity and density changes.