Given　the　improvements　that　have　been　made　in　the　forward　calculations　of　seismic　noise　horizontal-to-vertical　spectral　ratios　(NHVSRs)　or　earthquake　ground　motion　HVSRs　(EHVSRs),　a　number　of　HVSR　inversion　methods　have　been　proposed　to　identify　underground　velocity　structures.　Compared　with　the　studies　on　NHVSR　inversion,　the　research　on　the　EHVSR-based　inversion　methods　is　relatively　rare.　In　this　paper,　to　make　full　use　of　the　widely　available　and　constantly　accumulating　strong-motion　observation　data,　we　propose　an　S-wave　HVSR　inversion　method　based　on　diffuse-field　approximation.　Herein,　the　S-wave　components　of　earthquake　ground　motion　recordings　are　considered　as　data　source.　Improvements　to　the　objective　function　has　been　achieved　in　this　work.　An　objective　function　with　the　slope　term　is　introduced.　The　new　objective　function　can　mitigate　the　multisolution　phenomenon　encountered　when　working　with　HVSR　curves　with　multipeaks.　Then,　a　synthetic　case　is　used　to　show　the　verification　of　the　proposed　method　and　this　method　has　been　applied　to　invert　underground　velocity　structures　for　six　KiK-net　stations　based　on　earthquake　observations.　The　results　show　that　the　proposed　S-wave　EHVSR　inversion　method　is　effective　for　identifying　underground　velocity　structures.　©　2020　The　Author(s).　Published　by　Oxford　University　Press　on　behalf　of　The　Royal　Astronomical　Society.