This　study　presents　a　rigorous　investigation　into　the　mathematical　and　physical　properties　inherent　in　the　Fourier　phase　spectrum　of　earthquake　ground　motions.　This　exploration　includes　a　detailed　examination　of　the　probability　distribution　of　phase　angles　and　differences,　elucidated　through　two　novel　numerical　experiments　utilizing　the　reduction　ad　absurdum　approach.　Moreover,　the　study　scrutinizes　the　physical　attributes　of　earthquake　ground　motion＇s　phase　spectrum,　employing　the　circular　frequency-dependent　phase　derivative　as　a　key　analytical　factor.　In　a　novel　approach,　the　research　delves　into　the　relationship　between　circular　frequency-dependent　phase　derivatives　and　Fourier　amplitudes,　shedding　light　on　essential　connections　within　earthquake　phenomena,　particularly　addressing　non-stationarity.　Expanding　the　scope,　the　study　comprehensively　examines　the　influence　of　source,　propagation　path,　and　site　on　both　the　phase　spectrum　and　accelerogram.　Employing　the　control　variate　technique　facilitates　this　analysis,　providing　valuable　insights　into　the　underlying　physical　mechanisms　governing　earthquake　wave　behavior.　The　findings　highlight　the　temporal　properties　of　the　phase　spectrum,　attributing　its　complexity　to　the　temporal　heterogeneity　in　energy　release　during　the　fault　rupture　and　dispersion　of　earthquake　waves.　This　novel　approach　not　only　enhances　the　understanding　of　earthquake　dynamics,　but　also　underscores　the　significance　of　considering　temporal　variations　in　earthquake　events.