AUTHOR=Villante U. , Recchiuti D. , Di Matteo S. TITLE=The Transmission of ULF Waves From the Solar Wind to the Magnetosphere: An Analysis of Some Critical Aspects JOURNAL=Frontiers in Astronomy and Space Sciences VOLUME=Volume 9 - 2022 YEAR=2022 URL=https://www.frontiersin.org/journals/astronomy-and-space-sciences/articles/10.3389/fspas.2022.835539 DOI=10.3389/fspas.2022.835539 ISSN=2296-987X ABSTRACT=Several critical aspects may influence the analysis of the relationship between the solar wind (SW) and the magnetospheric fluctuations: for example, the characteristics and the frequency of the SW fluctuations that are expected to impinge the magnetosphere may be not the same when they are observed by spacecraft located at different places in front of the magnetosphere; similarly, the choice of the analytical methods adopted for the spectral analysis might influence the frequency estimate (as well as the wave identification itself) both in the SW and in the magnetosphere (Di Matteo and Villante, 2017, 2018). Focusing attention on these aspects, we present an analysis of the SW compressional fluctuations (f ≈ 1 – 5 mHz), following two interplanetary shocks as observed by two interplanetary spacecraft, considering two different situations in terms of the spacecraft separation and distance from the magnetosphere. Our results show that some differences in the characteristics of the SW fluctuations emerge when the same stream is observed at different places and confirm the critical role of the analytical methods in determining the fluctuation characteristics. We then compared the aspects of the SW fluctuations with those of the magnetospheric fluctuations following the sudden impulses due to the impact of the interplanetary shocks. For this scope we examine the observations by two satellites at geostationary orbit and at several ground-based stations. We found that the magnetospheric fluctuations were related to compressional SW fluctuations approximately at the same frequencies, with no evidence for wave activity of internal origin, or directly driven by the shock impact.