Microbedded rocks have an anisotropic frequency-dependent sound speed which depends on the intrinsic sound speeds of the individual microbeds and on the O'Doherty-Anstey effect. Fractured rocks have an anisotropic frequency-dependent sound speed which depends on the intrinsic sound speed of the unfractured rock, the frequency-dependent phase shift that occurs during reflection or transmission across a fracture, and the interfracture O'Doherty-Anstey effect. These effects are neglected by the quasistatic methods presently used to generate elastic constants. Here I introduce a new method of generating elastic constants that contain all the above effects. First, a statistical description of the rock is used to generate a sample of the rock. Then an exact two-way method is used to propagate just a few plane waves, of frequency f, a distance of several wavelenghts from the source. If an equivalent homogeneous medium exists at frequency f, then the computed motions must also satisfy a one-way elastic wave equation for that equivalent medium. This one-way wave equation is used to invert for the elastic coefficients. When no equivalent medium exists, perhaps because f is too large, this is indicated by the inversion. Possible applications of the method are prediction of seismic sounds speeds from measurements of bed thicknesses in cores: analysis of laboratory data for fracture constitutive relations: and inversion of mulitoffset vertical seismic profiling data for elastic coefficients comparable with those predicted from cores. ¿ American Gophyically Uuion 1990