In　order　to　solve　the　problem　of　inaccurate　location　of　complex　terahertz　echo　signal　caused　by　multi-layer　reflection,　material　dispersion　absorption　and　noise　of　blade　samples　with　thermal　barrier　coatings,　a　time　sliced　sparse　dispersion　model　based　on　sparse　representation　is　proposed　to　locate　the　complex　terahertz　echoes.　Considering　the　influence　of　material　dispersion　on　the　pulse　spreading　of　terahertz　time　domain　echo　signal,　the　corresponding　terahertz　sparse　dispersion　dictionary　is　established　based　on　the　convolution　model　of　terahertz　echo　signal.　The　sparse　pulse　response　function　can　be　reconstructed　by　spectral　projected　gradient　convex　optimization　algorithm　to　locate　the　delay　time　of　complex　echo　signal.　In　addition,　the　evaluation　indicators　composed　of　the　root　mean　square　error　and　sparsity　are　introduced　to　quantitatively　assess　the　performance　of　the　proposed　method　on　THz　echoes　from　the　two　dimensions　of　reconstruction　accuracy　and　sparsity.　Then,　theoretical　simulation　and　thermal　barrier　coating　experimental　results　indicate　that　the　proposed　method　has　better　reconstruction　accuracy　and　sparsity,　and　the　echo　location　performance　is　better　than　that　of　frequency　wavelet　domain　deconvolution　and　sparse　reconstruction　method　without　considering　dispersion.　It　is　more　suitable　for　precise　localization　of　complex　terahertz　echo　signal,　and　provides　a　new　way　for　the　processing　of　complex　terahertz　signal.　©　2023　Editorial　Office　of　Chinese　Journal　of　Mechanical　Engineering.　All　rights　reserved.