We investigated the fractal characteristics of geophysical logs in gas hydrate-bearing media to improve quantitative reservoir analyses. We implemented Detrended Fluctuation Analysis (DFA) and Multifractal Detrended Fluctuation Analysis (MFDFA) to analyze the scale-invariant features of log fluctuations, which are indicative of varying gas hydrate-saturated and gas hydrate-free zones in the Krishna-Godavari basin, India. Our findings indicate that fractal parameters such as scaling exponent (𝛼) is higher (𝛼 > 1.189) in gas hydrate zones as compared to non-hydrate zones (where, 𝛼 < 1.005). The relationship between 𝛼 and gas hydrate saturation suggests long-range correlations and self-similarity in log responses, emphasizing vertical heterogeneity. Subsequently, we performed scaling window-based DFA, which revealed clearer signatures of hydrate presence affecting the average values of resistivity and p-wave velocity for a typical window size. The associated fractal parameters, such as 𝛼 and H, showed a positive correlation with the increase in gas hydrate saturation. Furthermore, MFDFA revealed both vertical and spatial heterogeneity in these sedimentary systems, with a shift in singularity spectra towards higher scaling exponents (ℎ𝑞​) in correlation with increase in gas hydrate saturation. This study underscores the utility of statistical approaches in providing reliable insights into subsurface gas hydrate distribution patterns, setting the stage for future gas hydrate sediment investigations.