Geologic process models predict the geometry of geologic strata and their petrophysical properties, based on mathematical models of geological processes that affect the formation and evolution of geologic strata. Such processes include erosion, sediment transport, and deposition. The resulting forward model is typically nonlinear. Given observations and a misfit measure, one may attempt inversion of these models to estimate process parameters that yield compatible predictions. For seismostratigraphic inversion, seismic data are used as observations. We tested such an algorithm in a prograding-delta environment to examine the effect of using different seismic attributes as observations and, thus, different choices of misfit measures. The first measure, based on the degree of parallelism between seismic reflectors and modeled geologic strata, demonstrated a trade-off between geologic time and the sediment-influx rate used to parameterize the model. A second misfit measure used unwrapped seismic instantaneous phase as a crude proxy to relative geologic time, which regularized the model parameters. Then last, we combined the two measures to take advantage of their individual characteristics. For most of these inversion experiments, we obtained results that capture the geometry of the geologic strata as observed on the seismic data. With the exception of the depositional time-rate trade-off, where the same strata can be obtained in a shorter geologic interval when rates are increased, we found the inversion to be surprisingly stable, with a unique cluster of acceptable parameters, despite the nonlinearity of the geologic forward model.