Statistical Structure in LIGO Livingston (L1) O4a Strain Residuals

This study examines the statistical structure of strain residuals recorded by the LIGO Livingston (L1) gravitational-wave detector during the O4a observing run. The analysis uses publicly available calibrated strain data obtained from the Gravitational Wave Open Science Center (GWOSC). While gravitational-wave signals themselves are rare and transient, the majority of detector output consists of residual fluctuations commonly treated as stochastic detector noise. Standard analysis frameworks often approximate this noise as Gaussian and uncorrelated over short timescales. This paper evaluates that assumption empirically. Using a continuous finite segment of O4a strain data, four complementary statistical analyses are performed: Time-series visualization of strain fluctuations Histogram analysis of strain value distributions Autocorrelation function (ACF) analysis to detect temporal correlations Power spectral density (PSD) estimation to identify frequency-dependent structure The results indicate that the Livingston detector residuals exhibit measurable temporal correlations and non-flat spectral structure. The strain distribution is broadly Gaussian but shows subtle deviations from idealized white-noise expectations. The autocorrelation analysis reveals oscillatory decay behavior at short time lags, suggesting the presence of temporal memory in the residual signal. These observations indicate that detector residuals may contain structured statistical dynamics rather than behaving as purely uncorrelated stochastic noise. While this study does not propose a specific physical mechanism responsible for these patterns, it highlights the value of empirically examining residual datasets rather than assuming idealized noise behavior. This work extends previous empirical investigations of residual structure in astrophysical datasets, including pulsar timing residual analyses from the NANOGrav collaboration. Future work may extend this analysis to additional detector datasets, including the LIGO Hanford interferometer, in order to determine whether similar statistical structures appear across multiple instruments.