Geophysical Journal International

SummaryThe amplitude of the ${{P}_s}$ phase relative to the direct P wave (i.e., the ${{P}_s}/P$ ratio) provides valuable information about the contrasts across the crust-mantle boundary. Understanding how these amplitudes respond to variations in subsurface parameters improve interpretation of lithospheric structures. We examined the sensitivity of eight key parameters, including compressional and shear wave velocities, lower crustal and upper mantle densities, ray parameter, and Moho depth, to receiver function (RF) amplitudes and ${{P}_s}/P$ ratios. Using the synthetic RF (synRF) code of Ammon et al. (1990), we applied a Monte Carlo approach to generate randomized parameter sets, incorporated random noise, and tested both sharp and gradational Moho structures. The results show that lower crustal shear velocity has the strongest influence on all RF amplitudes and ${{P}_s}/P$ ratios, while lower crustal ${{V}_p}$, density, and upper mantle ${{V}_s}$ have moderate effects, and upper mantel ${{V}_p}$ and density show weaker sensitivity. In both sharp and gradational models, lower crustal and upper mantle shear velocities largely control the ${{P}_s}/P$ ratio. Theoretical ${{P}_s}/P$ ratios exhibit higher correlation with observed RFs than synthetic ones. Compared with the Shen & Ritzwoller (2016) model, our analysis yields ∼10% lower uncertainties in lower crustal ${{V}_s}$ and smaller uncertainties in lower crustal density derived from ${{P}_s}/P$ ratios, with consistent results in complex regions such as the northern Rocky Mountains. This study establishes the first quantitative framework linking ${{P}_s}/P$ ratio variability to lower crustal velocity and density while explicitly quantifying parameter sensitivity and uncertainties, clarifying how Moho sharpness and noise affect amplitude stability.

SummaryMacnae (2025) presented a physical interpretation of the Cole Cole Complex Conductivity model in the case of porous materials with sulphides. According to his paper, the Cole Cole parameters determined from such model can be easily interpreted in terms of underlying physics. His model is partly based on the electrochemical polarization model of Wong (1979) to explain the relationship between the chargeability and the volumetric content of sulfide. None of the statements made by Macnae (2025) are however novel. That said, we agree with Macnae (2025) that the Cole Cole complex resistivity relaxation time is quite useless in deciphering the underlying physics of the induced polarization problem.