The one-dimensional convolution model or synthetic seismogram provides more information about the seismic waveform expression of hydrocarbon reservoirs when petrophysical data (porosity, shale volume, water saturation, etc.) are systematically integrated into the seismogram generation process. Use of this modeling technique, herein called Incremental Pay Thickness (IPT) modeling, has provided valuable insights concerning the seismic response of several offshore Gulf of Mexico amplitude anomalies. Through integration of the petrophysical data, comparisons between seismic waveform response and expected reservoir pay thickness are extended to include estimates of gross pay thickness, net pay thickness, net porosity feet of pay, and hydrocarbons in place.These 1-D synthetic data easily convert to 2-D displays that often show exceptional waveform correlations between the synthetic and actual seismic data. Anomalous observed waveform responses include complex tuning curves; diagnostic isochron measurements even in unresolved thin-bed reservoirs; and extreme variations in the seismic expression of hydrocarbon-fluid contacts. While IPT modeling examples illustrate both the variability and nonuniqueness of seismic responses to hydrocarbon reservoirs, they often show good seismic predictability of pay thickness if the appropriate choice of amplitude-isochron versus pay thickness is made (i.e., peak amplitude, trough amplitude, or average amplitude versus gross pay thickness, net pay thickness, net porosity feet of pay, or hydrocarbons in place).