On the Ratio of Full-Resonance to Square-Root- Impedance Amplifications for Shear-Wave Velocity Profiles That Are a Continuous Function of Depth

Amplifications of seismic waves traveling upward through a continuous, interface-free velocity profile are consistently smaller when computed using the square-root-impedance (SRI) method than when computed using full-resonance (FR) calculations. This was found for a wide range of velocity profiles. For realistic profiles, for which the gradient of velocity decreases with depth, the differences are not large, with the ratio of FR/SRI amplifications ranging from about 1.05 to 1.3. Comparisons of the amplifications from a continuous veloc-ity profile with those from approximations to that profile using a stack of constant-velocity layers give some support to the hypothesis that the difference between FR and SRI ampli-fications for gradient profiles is because the former is controlled by the ratio of seismic impedances, whereas the latter is based on the square root of the seismic impedance ratios. This implies that gradient profiles will always have FR amplifications greater than SRI amplifications. A model-independent, easy-to-implement modification of the SRI amplifications is proposed that shows promise in bringing the SRI amplifications closer to the FR amplifications.