Estimation of elastic stiffness coefficients of an orthorhombic physical model using group velocity analysis on transmission data

摘要

We acquired 3C ultrasonic transmission seismograms, measured group velocities associated with the three quasi-body wave types, and determined density-normalized stiffness coefficients (A_ij = C_ij∕ρ) over an orthorhombic physical (laboratory) model. The estimation of A_ij is based on an approximate relationship between the nine orthorhombic A_ij and group velocities. Estimation of the anisotropic A_ij is usually done using phase velocities with well-known formulas expressing their theoretical dependence on A_ij. 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 eτ; pT 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 A_ij 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 A_ij 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.