Experimental verification of spherical-wave effect on the AVO response and implications for three-term inversion

Spherical-wave offset-dependent reflectivity is investigated by measuring ultrasonic reflection amplitudes from a water/Plexiglas interface. The experimental results show substantial deviation of the measured amplitudes from the plane-wave reflection coefficients at large angles. However, full-wave numerical simulations of the point source reflection response using the reflectivity algorithm show excellent agreement with the measurements, demonstrating that the deviation from the plane-wave response is caused by the wavefront curvature. To analyze the effect of wavefront curvature on elastic inversion, we simulate the spherical-wave reflectivity at different frequencies and invert for elastic parameters by least-square fitting of the plane-wave (Zoeppritz) solution. The results show that the two-parameter inversion based on the intercept and gradient is robust, although estimation of three parameters (V-P, V-S, and density) that use the curvature of the offset variation with angle (AVA) response is prone to substantial frequency-dependent errors. We propose an alternative approach to parameter estimation, one that uses critical angles estimated from AVA curves (instead of the AVA curvature). This approach shows a significant improvement in the estimation of elastic parameters, and it could be applied to class 1 AVO responses.