This paper presents a layer-stripping procedure to determine interval measurements of fracture parameters in multi-layered fractured media with vertically varying strike directions. The procedure is based on the P-wave travel time difference between two orthogonal seismic survey lines, and this difference is referred to as the P-wave azimuthal moveout response (AMR). The interval AMR of a fracture target for a fixed offset is a function of cos 2(α − _i) with respect to the line azimuth α and the fracture-strike azimuth _i. Consequently two pairs of orthogonal survey lines can be used to determine the local fracture strike _i if the interval AMR of the target is known. In the case of a weakly fractured overburden underlain by a fractured target, layer stripping can be achieved through the alignment of the top-target event by performing NMO correction separately for all survey lines. The interval AMR of the target layer may then be calculated from the residual moveout of the bottom-target event, if any. In the general case, a ray-tracing procedure, similar to that used in AVO analysis, is required to perform effective layer stripping. Full-wave modelling is used to verify and illustrate these procedures.