Three perturbative inverse methods for obtaining bottom geoacoustic parameters as a function of depth in shallow water are described. The required input data are the trapped mode eigenvalues for one or more frequencies, the group velocity dispersion curves for one or more modes, or the cw pressure field versus range. In each case, a Fredholm integral equation arises that can be solved using linear inverse theory, and for which resolution and variance estimates of the solution can be readily made. Attention is focused primarily on the modal eigenvalue inverse problem for which the theory for determining the compressional wave speed, compressional wave attenuation, and density is developed in detail. Properties of this technique are studied using synthetic data and include investigations of the dependence of the results on acoustic frequency, number of modes excited, and partialaprioriknowledge of the bottom. The method is demonstrated on experimental data obtained in Nantucket Sound at 140 and 220 Hz. Directions of future research on these techniques are indicated.