The reflection response of a seismic target is significantly affected by a thinly layered overburden, which creates velocity anisotropy and a transmission loss by scattering attenuation. These effects must be taken into account when imaging a target reflector and when inverting reflection coefficients. Describing scalar wave (i.e., acoustic wave or SH-wave) propagation through a stack of thin layers by equivalent-medium theory provides a simple generalized O'Doherty-Anstey formula. This formulation is defined by a few statistical parameters that depend on the 1-D random fluctuations of the reflector overburden. The formula has been combined with well-known target-oriented and amplitude-preserving migration/inversion algorithms and amplitude variation with offset (AVO) analysis procedures. The application of these combined procedures is demonstrated for SH-waves in an elastic thinly-layered medium. These techniques offer a suitable tool to compensate for the thin-layer influence on traveltimes and amplitudes of seismic reflection data. The thin-layer sensitive AVO parameters (zero-offset amplitude and AVO gradient) of a target reflector can thus be better recovered.