In this paper, a method for simultaneously reconstructing the two‐dimensional shear modulus and density configurations fromSHdata is presented. The method requires a complete suite of surface receivers for each oftwosource locations. This is in contrast to previous multiparameter, multidimensional inversion methods, which require complete source coverage for each one of a continuous set of surface receiver locations. The method presented here is a multiparameter extension of the recent single source, single parameter, multidimensional acoustic velocity inversion procedure of Esmersoy, Oristaglio, and Levy [J. Acoust. Soc. Am.78, 1052–1057 (1985)]. A simple change of variables allows the multiparameter procedure to be directly applied to the acoustic inversion problem, i.e., to identify the multidimensional acoustic velocity and density configurations.