Full waveform inversion of a p-τ marine data set from the Gulf of Mexico provides estimates of the long-wavelength P-wave background velocity, anisotropic seismic source, and three high-frequency elastic parameter reflectivities that explain 70% of the total seismic data and 90% of the data in an interval around the gas sand target. The forward simulator is based on a plane-wave viscoelastic model for P-wave propagation and primary reflections in a layered earth. Differential semblance optimization, a variant of output least-squares inversion, successfully estimates the nonlinear P-wave background velocity and linear reflectivities. Once an accurate velocity is estimated, output least-squares inversion reestimates the reflectivities and an anisotropic seismic source simultaneously. The viscoelastic model predicts the amplitude-versus-angle trend in the data more accurately than does an elastic model. Simultaneous inversion for reflectivities and source explains substantially more of the actual data than does inversion for reflectivities with fixed source from an air-gun modeler. The best reflectivity estimates conform to widely accepted lithologic relationships and closely match the filtered well logs.