There　are　some　shortcomings　in　the　common　power　spectrum　models　of　ground　motion　and　in　the　corresponding　synthesis　of　artificial　ground　motion,　such　as　the　irrationality　of　the　measurement　of　the　size　of　the　power　spectrum,　the　conversion　to　the　power　spectrum　when　leading　into　the　time-domain　envelope,　and　the　ignorance　of　fluctuating　ingredient　in　power　spectrum　or　of　random　noise　part　in　autocorrelation　function.　This　article　elaborated　the　rationality　that　the　sum　of　squares　should　be　taken　as　the　measurement　of　the　size　of　power　spectrum.　The　article　discussed　that　the　sum　of　squares　had　explicit　physics　significance,　and　was　the　total　energy　parameter　of　random　stationary　signal.　A　more　accurate　mathematical　model　was　developed　in　order　to　simulate　the　random　fluctuating　ingredient　of　target　power　spectrum,　or　the　stochastic　noise　part　of　corresponding　target　autocorrelation　function,　and　proposed　the　non-stationary　ground　motion＇s　mathematical　model,　which　was　based　on　power　spectrum　and　included　three　main　controlling　physical　statistics:　the　normalized　power　spectrum　containing　random　fluctuating　ingredient,　the　sum　of　squares　and　the　time-domain　envelope　function.　Using　the　synthesis　method　of　ground　motion　developed　by　the　article,　the　total　energy　of　artificial　ground　motion　accords　with　the　target　sum　of　squares　exactly,　the　frequent　characteristics　of　the　artificial　ground　motion　are　in　accordance　with　the　normalized　target　power　spectrum　accurately,　and　the　wave-shape　of　the　artifical　ground　motion　in　time　domain　accords　with　the　target　envelope　function　approximately.　Studies　show　that　the　sum　of　squares,　the　normalized　power　spectrum,　and　the　time-domain　envelope　function　are　three　essential　physical　statistics　of　ground　motion　based　on　power　spectrum　model.