Comparison of seismic upscaling methods: From sonic to seismic

The term “upscaling” used here means a prediction of elastic-wave velocities at lower frequencies from the velocities at higher frequencies. Three different methods of upscaling are considered, including the simple averaging, Backus averaging, and pair correlation function methods. These methods are applied to upscale the elastic-wave velocities measured at sonic frequencies (⁠$2kHz$⁠, logging data) available for a well penetrating layers of gas-bearing shales and carbonates. As a result, a velocity distribution over depth for $VP$ and $VS$ is found in the frequency range of $50–500Hz$⁠. The difference in the results obtained for a particular depth by the three theoretical methods in the surface seismic frequency bandwidth $(50–100Hz)$ is $∼600m/s$ for P-wave and $∼260m/s$ for S-wave velocity. This difference is attributed to different theoretical backgrounds underlying these methods.