Data　backup　is　a　pervasive　strategy　adopted　by　cloud　service　providers　(CSPs)　to　avoid　potential　risks　of　data　loss.　As　a　result,　a　CSP　normally　maintains　multiple　replicas　for　each　piece　of　data　on　geographically　distributed　servers　to　improve　reliability.　A　key　problem　of　this　replication　technique　is　that　users　will　be　charged　more　when　more　replicas　are　stored.　Therefore,　an　auditing　service　is　desired　to　help　users　verify　whether　an　untrusted　CSP　stores　all　their　replicas　in　different　geographic　locations　or　not.　In　this　paper,　we　propose　a　dynamic　multi-replica　auditing　scheme　that　has　the　following　features:　(1)　it　can　verify　both　the　integrity　and　geographic　locations　of　a　cloud　user＇s　data　replicas;　(2)　the　proposed　scheme　can　identify　different　copies　with　geographic　locations,　which　reduces　the　complexity　in　data　preprocessing,　dynamic　operations　and　backup　recovery;　(3)　by　introducing　an　Indexed　Merkle　Hash　Tree　(IMHT),　we　can　reduce　overall　costs　of　existing　Merkle　Hash　Trees.　We　prove　the　security　of　the　proposed　scheme　under　the　random　oracle　model,　and　further　provide　a　comprehensive　comparison　between　the　proposed　scheme　and　existing　schemes.　The　theoretical　analysis　and　experiment　evaluation　show　that　our　scheme　reduces　both　the　communication　and　computation　costs　compared　with　existing　schemes.　The　analysis　also　shows　that　the　proposed　scheme　can　achieve　99%　verification　probability　by　challenging　only　90　data　blocks.　(C)　2021　Elsevier　B.V.　All　rights　reserved.