Understanding Parameter Influence in Gravitational Waveforms: A Dual-Method Sensitivity Analysis

Gravitational waveforms from binary black hole mergers are governed by several physical parameters, including mass, spin, distance, and inclination. Understanding how these parameters affect waveform structure is critical for accurate modeling and parameter estimation. In this study, we develop a general sensitivity analysis framework for gravitational waveforms and apply it to two representative waveform models. Two complementary methods are used: Sobol variance decomposition, which captures nonlinear and interaction effects, and ANOVA, which offers interpretable linear attribution of variance across waveform features. We focus on four key parameters—chirp mass (ℳ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf>), aligned or effective spin (e.g., χ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1z</inf> or s<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1,mag</inf>), luminosity distance (d<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf>), and inclination angle (ι)—and evaluate their influence on both global waveform mismatch (measured by time-domain mean squared error) and specific waveform features such as peak amplitude, peak time, and signal energy.Our results show that spin-related parameters consistently dominate waveform variability across models, contributing over 50% to the variance of waveform mismatch and nearly all the variance in peak timing. In contrast, distance and inclination primarily affect amplitude and energy but have little impact on timing or overall shape. Chirp mass exhibits negligible direct effect but plays a significant role through interaction with spin. We further visualize how the impact of spin varies with different values of inclination, confirming strong second-order interactions. These findings demonstrate the effectiveness and flexibility of our framework, and offer practical guidance for waveform modeling, including parameter prioritization, reduced-order modeling, and surrogate optimization.