Understanding the fundamental motions of molecules, particularly vibrational motions, is essential for elucidating chemical reaction mechanisms. Time-resolved X-ray scattering (TRXS) has emerged as a powerful technique for investigating molecular vibrations, as it simultaneously provides both temporal and spatial information on vibrational modes. However, visualizing these vibrations via TRXS remains challenging due to technical limitations in achieving a high signal-to-noise ratio (SNR) and temporal resolution, making it difficult to resolve subtle oscillatory signals arising from molecular vibrations. Here, we present an integrative analysis framework developed to efficiently extract oscillatory signals from TRXS data and verify their association with molecular vibrations. The framework comprises two key steps: the extraction of oscillatory signals using singular spectrum analysis (SSA) and posterior structural analysis to assess the physical relevance of the extracted signals. By applying this scheme to simulated TRXS datasets, we demonstrate that it identifies oscillatory signals embedded in the data more effectively than conventional Fourier transform analysis, even under low SNR conditions. Furthermore, the structural analysis step effectively discriminates physically irrelevant components, such as harmonic and combination frequencies, and high-frequency artifacts from signals corresponding to the fundamental frequencies of molecular vibrations. The proposed data analysis framework is expected to advance studies of molecular vibrations and wavepacket dynamics using TRXS, ultimately providing deeper insights into the ultrafast reaction dynamics.
