A seismic physical model experiment has been conducted to acquire multi-offset multi-azimuth P-wave 3D seismic data, and to verify the suitability of physically-modeled data for AVAZ (amplitude variation with azimuth) analysis. Our model consisted of an azimuthally anisotropic layer, phenolic layer simulating a vertically fractured medium, overlain by two isotropic layers with the top most layer being water. The amplitudes reflected from the top of the fractured layer have been picked from the primary reflection; acquisition was designed to avoid the overlapping of the primary and ghost events. The picked reflection amplitudes required corrections to make them suitable for an AVAZ study. In addition to amplitude corrections used for seismic field data, a directivity correction specific to the physical model transducers was needed. The corrected amplitudes from different azimuths showed a clear azimuthal variation caused by the fractured layer, and agreed with amplitudes predicted theoretically.

We evaluated a quantitative amplitude analysis of 3D physical model reflection data acquired over an experimental phenolic layer that modeled a fractured medium with one set of vertical fractures. The phenolic layer was overlain by two isotropic layers, the uppermost being water, and the data acquisition was designed to avoid the interference of the primary and ghost events. The elastic stiffness coefficients and hence the anisotropy of the phenolic layer were known in advance from a previous traveltime analysis. The reflection amplitudes from the top of the phenolic layer required corrections to make them suitable for an amplitude study. In addition to the usual amplitude corrections applied to seismic field data, a directivity correction specific to the physical model transducers was applied. The corrected amplitudes along different azimuths showed a clear azimuthal variation caused by the phenolic layer and agreed with amplitudes predicted theoretically. An amplitude variation with angle and azimuth inversion was performed for horizontal transverse isotropy (HTI) parameters of the phenolic layer. We determined from the inversion results that from the azimuthally varying P-wave reflectivity response, it was possible to estimate HTI parameters that compared favorably to those obtained previously by a traveltime analysis. This result made it possible to compute the S-wave splitting parameter [Formula: see text] (historically determined from S-wave data and directly related to fracture density) from a quantitative analysis of the PP data.

We acquired 3C ultrasonic transmission seismograms, measured group velocities associated with the three quasi-body wave types, and determined density-normalized stiffness coefficients ([Formula: see text]) over an orthorhombic physical (laboratory) model. The estimation of [Formula: see text] is based on an approximate relationship between the nine orthorhombic [Formula: see text] and group velocities. Estimation of the anisotropic [Formula: see text] is usually done using phase velocities with well-known formulas expressing their theoretical dependence on [Formula: see text]. However, on time-domain seismograms, arrivals are observed traveling with group velocities. Group velocity measurements are found to be straightforward, reasonably accurate, and independent of the size of the transducers used. In contrast, the accuracy of phase velocities derived from the [Formula: see text] transform analysis was found to be very sensitive to small differences in picked arrival times and to transducer size. Theoretical phase and group velocities, calculated in a forward manner from the [Formula: see text] estimates, agreed with the originally measured phase and group velocities, respectively. This agreement confirms that it is valid to use easily measured group velocities with their approximate theoretical relationship to the [Formula: see text] to determine the full stiffness matrix. Compared to the phase-velocity procedure, the technique involving group velocities is much less prone to error due to time-picking uncertainties, and therefore is more suitable for analyzing physical model seismic data.

The nonlinearity of the seismic amplitude‐variation‐with‐offset response is investigated with physical modelling data. Nonlinearity in amplitude‐variation‐with‐offset becomes important in the presence of large relative changes in acoustic and elastic medium properties. A procedure for pre‐processing physical modelling reflection data is enacted on the reflection from a water‐plexiglas boundary. The resulting picked and processed amplitudes are compared with the exact solutions of the plane‐wave Zoeppritz equations, as well as RPP(θ) approximations that are first, second, and third order in ΔVP/VP, ΔVS/VS, and Δρ/ρ. In the low angle range of 0°–20°, the third‐order plane‐wave approximation is sufficient to capture the nonlinearity of the amplitude‐variation‐with‐offset response of a liquid‐solid boundary with VP, VS, and ρ contrasts of 1485–2745 m/s, 0–1380 m/s, and 1.00–1.19 gm/cc respectively, to an accuracy value of roughly 1%. This is in contrast to the linear Aki–Richards approximation, which is in error by as much as 25% in the same angle range. Even‐order nonlinear corrective terms are observed to be primarily involved in correcting the angle dependence of RPP, whereas the odd‐order nonlinear terms are involved in determining the absolute amplitude‐variation‐with‐offset magnitudes.