Displays of complex trace attributes can help to define thin beds in seismic sections. If the wavelet in a section is zero phase, low impedance strata whose thicknesses are of the order of half the peak-to-peak period of the dominant seismic energy show up as anomalously high-amplitude zones on instantaneous amplitude sections. These anomalies result from the well-known amplitude tuning effect which occurs when reflection coefficients of opposite polarity a half period apart are convolved with a seismic wavelet. As the layers thin to a quarter period of the dominant seismic energy, thinning is revealed by an anomalous increase in instantaneous frquency. This results from the less well-known but equally important phenomenon of frequency tuning by beds which thin laterally. Instantaneous frequency reaches an anomalously high value when bed thickness is about a quarter period and remains high as the bed continues to thin. In this paper, complex trace analysis is applied to a synthetic model of a wedge and to a set of broadband field data acquired to delineate thin lenses of porous sandstone. The two case studies illustrate that sets of attribute displays can be used to verify the presence and dimensions of thin beds when definition of the beds is not obvious on conventional seismic sections.--Modified journal abstract.