Application　of　local　artificial　boundary　conditions　in　high-efficient　spectral　element　method　(SEM)　is　a　problem　that　needs　further　study,　where　difficulties　focus　on　how　to　design　an　appropriate　numerical　scheme　of　artificial　boundaries　that　is　in　good　accordance　with　the　unequally-spaced　grid　nodes　and　high-order　property　of　the　element.　Liao＇s　local　artificial　boundary,　i.e.　multi-transmitting　formula　(MTF),　provides　a　convenient　way　of　implementing　arbitrary-order　displacement-type　boundaries　because　it　is　defined　directly　in　discrete　form　and　can　be　transformed　into　numerical　schemes　by　using　merely　some　interpolation　approaches.　A　new　set　of　numerical　schemes　of　MTF　is　developed　and　its　accuracy　and　stability　are　thoroughly　discussed　in　the　application　of　spectral-element　simulation　of　1D　and　2D　seismic　wave　propagation.　The　new　MTF　scheme　cannot　be　written　into　a　binomial　form　like　the　traditional　one　does.　This　fact　has　a　significant　influence　on　numerical　properties　of　high-order　boundary,　but　merely　slightly　affects　the　performance　of　lower-order　boundaries　which　are　daily　used　in　practical　simulations.　Numerical　examples　compared　with　viscous-spring　or　perfectly　matched　layer　(PML)　boundary　exhibits　that　stable　and　quite　good　accuracy　can　be　achieved　by　using　the　proposed　method.　©　2020　Elsevier　Ltd