Transfer equations applying to layered media sounding problems

Abstract

SUMMARY The sounding problem of 1‐D layered media has been solved with wave energy transfer equations. Forward and backward wave propagation at any trajectory point are calculated. Analytical solutions for simple trajectories are derived. In the general case the solutions can be determined numerically. For certain active seismic sounding problem having good data coverage, this algorithm can be used to invert for characteristics of the layered media.

Modified Kubelka-Munk equations for localized waves inside a layered medium

“…This behavior is in stark contrast to T (L) ≈ z e /L [30] obtained when interference is neglected (ℓ loc → ∞). The fact that the length scale controlling the exponential decay with L in equation (A14) is ℓ loc supports the use of this term in equation (19) and, as a consequence, the expression for ℓ loc in equation (18).…”

“…Here, we give credence to our use of the term localization length ℓ loc as it appears in equation (19). By doing so, we justify the expression for ℓ loc in equation (18).…”

“…Thus, our definition for ℓ s in equation (22) is consistent with the usual definition of ℓ s in the weak scattering limit. Appendix A demonstrates the consistency of the definition for ℓ loc as it appears in equation (19) based on the relation in equation (18). We have just shown how to apply the limiting procedure to equation (14).…”

“…Building upon the work of Wu and Xie [15], which centered on stationary RT in layered media, the time dependent case has been recently considered [18]. Bakut et al [19] have generalized the Green's function of 1D RT in homogeneous media to the case of a medium composed of piecewise homogeneous layers. Though 1D RT has been thoroughly understood in the course of these studies, how wave interference changes the picture -from the point of view of RT -has so far not been covered.…”