The problem of seafloor electromagnetic sounding is defined in terms of recovering the electrical conductivity profile beneath the seafloor from measurements of the electromagnetic field. From this viewpoint, electromagnetic sounding can be regarded as an inverse problem that infers parameters characterizing the environment. The propagation of the electromagnetic field in a multilayered marine environment is modeled by solving the Maxwell's equations and the boundary conditions for a horizontal electric dipole placed in seawater. Electromagnetic inversion represents a strongly nonlinear problem for which a direct solution is not available. A matched-field approach to this problem can be formulated based on Bayesian inversion theory, which provides environmental parameter estimates and their uncertainties. The goal of this paper is to investigate the matched-field inversion capability to recover the conductivity profile from measurements of the electromagnetic field.