Secondary storage spaces with very complex geometries are well developed in Ordovician carbonate reservoirs in the Tarim Basin,which is taken as a study case in this paper.It is still not clear how the secondary storage space shape influences the P-& S-wave velocities (or elastic properties) in complex carbonate reservoirs.In this paper,three classical rock physics models (Wyllie timeaverage equation,Gassmann equation and the Kuster-Toks z model) are comparably analyzed for their construction principles and actual velocity prediction results,aiming at determining the most favourable rock physics model to consider the influence of secondary storage space shape.Then relationships between the P-& S-wave velocities in carbonate reservoirs and geometric shapes of secondary storage spaces are discussed from different aspects based on actual well data by employing the favourable rock physics model.To explain the influence of secondary storage space shape on V P-V S relationship,it is analyzed for the differences of S-wave velocities between derived from common empirical relationships (including Castagna’s mud rock line and Greenberg-Castagna V P-V S relationship) and predicted by the rock physics model.We advocate that V P-V S relationship for complex carbonate reservoirs should be built for different storage space types.For the carbonate reservoirs in the Tarim Basin,the V P-V S relationships for fractured,fractured-cavernous,and fractured-hole-vuggy reservoirs are respectively built on the basis of velocity prediction and secondary storage space type determination.Through the discussion above,it is expected that the velocity prediction and the V P-V S relationships for complex carbonate reservoirs should fully consider the influence of secondary storage space shape,thus providing more reasonable constraints for prestack inversion,further building a foundation for realizing carbonate reservoir prediction and fluid prediction. Secondary storage spaces with very complex geometries are well developed in Ordovician carbonate reservoirs in the Tarim Basin, which is taken as a study case in this paper. It is still not clear how the secondary storage space shape influences the P- & S-wave velocities (or elastic properties) in complex carbonate reservoirs. In this paper, three classical rock physics models (Wyllie timeaverage equation, Gassmann equation and the Kuster-Toks z model) are comparably analyzed for their construction principles and actual velocity prediction, aiming at determining the most favourable rock physics model to consider the influence of secondary storage space shape. Relationship between the P- & S-wave velocities in carbonate reservoirs and geometric shapes of secondary storage spaces are discussed from different aspects based on actual well data by employing the favourable rock physics model. To explain the influence of secondary storage space shape on V PV S relationship, it is analyzed for the differences of S-wave velocities between derived from common empirical relationships (including Castagna’s mud rock line and Greenberg-Castagna V PV S relationship) and predicted by the rock physics model. We advocate that V PV S relationship for complex carbonate reservoirs should be built for different storage space types. For the carbonate reservoirs in the Tarim Basin, the V PV S relationships for fractured, fractured-cavernous, and fractured-hole-vuggy reservoirs are respectively built on the basis of velocity prediction and secondary storage space type determination .Through the discussion above, it is expected that the velocity prediction and the V PV S relationships for complex carbonate reservoirs should fully consider the influence of secondary storage space shape, thus providing more reasonable constraints for prestack inversion, further building a foundation for realizing carbonate reservoir prediction and fluid prediction.