We show theoretically that by combining two or more finite superlattices, i
t is possible to realize an omnidirectional acoustic mirror that prevents p
ropagation of acoustic waves over a wide range of frequencies. An appropria
te choice of the elastic parameters in the superlattices enables us to prop
ose a structure in which any incident wave launched from any type of substr
ate ( or vacuum) falls inside a minigap of the coupled SLs and therefore un
dergoes a total reflection.