Identifying thinly bedded reservoirs is important in exploration, appraisal, and development. The thin beds that we are referring to are of meter scale or less. Conventional seismic attributes are not able to resolve thin-bed effects. A new frequency-dependent amplitude variation with offset (FAVO) seismic attribute is developed for the prediction of thin beds. It is based on seismic wave scattering theory for vertically inhomogeneous media, in which the seismic response from a laterally homogeneous interval is represented by the Born series. The Born series characterizes the P-P and P-SV wave reflections, transmissions, and interbed multiples within the target interval with different order terms. The newly derived attribute corresponds to the second-order term of the Born series, in which P-S wave reflection and transmission energy is taken into consideration, and it is called the second-order FAVO gradient attribute. In a thinly bedded interval where sand/shale interfaces are abundant, the P-SV wave mode conversions are numerous. This leads to a strong second-order FAVO gradient attribute response compared to that of a blocky sand, silt, or shale interval under the assumption that there is no significant rock- and fluid-property differences between the intervals. Therefore, the new seismic attribute has the potential to be a thin-bed interval indicator. We have adopted a strategy to estimate the new attribute using conventional P-wave seismic data. The attribute is extracted from seismic data at the frequency range at which the second-order scattering effect is the most prominent. Synthetic and field data examples from offshore Trinidad are studied to demonstrate the second-order scattering effect and the potential usage of the second-order FAVO attribute for thin-bed reservoir characterization.