Finite-difference(FD)methodsarewidelyusedinseismicforwardmodelingowingtotheircomputationalefficiencybutarenotreadilyapplicabletoirregulartopographies.Thus,severalFDmethodsbasedonthetransformationtocurvilinearcoordinatesusingbody-fittedgridshavebeenproposed,e.g.,standstaggeredgrid(SSG)withinterpolation,nonstaggeredgrid,rotatedstaggeredgrid(RSG),andfullystaggered.TheFDbasedontheRSGissomewhatsuperiortoothersbecauseitsatisfiesthespatialdistributionofthewaveequationwithoutadditionalmemoryandcomputationalrequirements;furthermore,itissimplertoimplement.WeusetheRSGFDmethodtotransformthefirstorderstress–velocityequationinthecurvilinearcoordinatessystemandintroducethehighprecisionadaptive,unilateralmimeticfinite-difference(UMFD)methodtoprocessthefreeboundaryconditionsofanirregularsurface.Thenumericalresultssuggestthattheprecisionofthesolutionishigherthanthatofthevacuumformalism.Whentheminimumwavelengthislow,UMFDavoidsthesurfacewavedispersion.WecompareFDmethodsbasedonRSG,SEM,andnonstaggeredgridandinferthatallsimulationresultsareconsistentbutthecomputationalefficiencyoftheRSGFDmethodishigherthantherest.
