Inversion of random heterogeneity power spectrum using the transverse coherence functions of reflected waves

Abstract:

The transverse coherence functions (TCFs) of phase and amplitude fluctuations of seismic waves are powerful tools to estimate the spatial power spectra of random heterogeneities in terms of their spatial distribution, length scales, and scattering strength. However, TCFs have been formulated using the amplitude and traveltime fluctuations of transmitted waves only, not reflected waves. Here, we propose and formulate the TCFs for reflected waves, which are useful in many scenarios. In our reflection TCF theory, we are able to calculate theoretical TCFs for random media with different power spectral density functions (PSDF), such as Gaussian, exponential, or general von Karman spectra. We validate our new reflection TCFs using 2D and 3D elastic finite-difference numerical modeling experiments. We show that we can invert for the random medium spectra using the measured reflection TCFs. The heterogeneity spectral inversion using reflected waves can be used in both exploration and global seismology.