Thescatteringprobleminvolvingwaterwavesbysmallundulationontheporousocean-bedinatwo-layerfluid,isinvestigatedwithintheframeworkofthetwo-dimensionallinearwaterwavetheorywheretheupperlayeriscoveredbyathinuniformsheetoficemodeledasathinelasticplate.Insuchatwo-layerfluidthereexistwaveswithtwodifferentmodes,onewithalowerwavenumberpropagatealongtheice-coverwhilstthosewithahigherwavenumberpropagatealongtheinterface.Anincidentwaveofaparticularwavenumbergetsreflectedandtransmittedoverthebottomundulationintowavesofbothmodes.PerturbationanalysisinconjunctionwiththeFouriertransformtechniqueisusedtoderivethefirst-ordercorrectionsofreflectionandtransmissioncoefficientsforboththemodesduetoincidentwavesoftwodifferentmodes.Onespecialtypeofbottomtopographyisconsideredasanexampletoevaluatetherelatedcoefficientsindetail.Thesecoefficientsaredepictedingraphicalformstodemonstratethetransformationofwaveenergybetweenthetwomodesandalsotoillustratetheeffectsoftheicesheetandtheporosityoftheundulatingbed.
