Structural interpretation of seismic images can be highly subjective, especially in complex geologic settings. A single seismic image will often support multiple geologically valid interpretations. However, it is usually difficult to determine which of those interpretations are more likely than others. We have referred to this problem as structural model appraisal. We have developed the use of misfit functions to rank and appraise multiple interpretations of a given seismic image. Given a set of possible interpretations, we compute synthetic data for each structural interpretation, and then we compare these synthetic data against observed seismic data; this allows us to assign a data-misfit value to each structural interpretation. Our aim is to find data-misfit functions that enable a ranking of interpretations. To do so, we formalize the problem of appraising structural interpretations using seismic data and we derive a set of conditions to be satisfied by the data-misfit function for a successful appraisal. We investigate vertical seismic profiling (VSP) and surface seismic configurations. An application of the proposed method to a realistic synthetic model shows promising results for appraising structural interpretations using VSP data, provided that the target region is well-illuminated. However, we find appraising structural interpretations using surface seismic data to be more challenging, mainly due to the difficulty of computing phase-shift data misfits.