Inelastic background analysis of HAXPES spectra was recently introduced as a powerful method to get access to the elemental distribution in deeply buried layers or interfaces, at depth up to 60 nm below the surface. However the accuracy of the analysis highly relies on suitable scattering cross-sections able to describe effectively the transport of photoelectrons through overlayer structures consisting of individual layers with potentially very different scattering properties. Here, we show that within Tougaard's practical framework as implemented in the Quases-Analyze software, the photoelectron transport through thick (25-40 nm) multi-layer structures with widely different cross-sections can be reliably described with an effective cross-section in the form of a weighted sum of the individual cross-section of each layer. The high-resolution core-level analysis partly provides a guide for determining the nature of the individual cross-sections to be used. We illustrate this novel approach with the practical case of a top Al/Ti bilayer structure in an AIGaN/GaN power transistor device stack before and after sucessive annealing treatments. The analysis provides reliable insights on the Ti and Ga depth distributions up to nearly 50 nm below the surface. (C) 2017 Elsevier B.V. All rights reserved.