Chang, H. and McMechan, G.A., 2009. Synthetic data tests of 3D full-wavefield inversion for P-wave anisotropic parameter estimation in flat layered VTI, HTI and orthorhombic media. Journal of Seismic Exploration, 18: 249-270. Full-wavefield inversion is developed to estimate the P-wave anisotropic parameters for VTI, HTI and orthorhombic media. With full-wavefield inversion, both the traveltime and amplitude information are utilized simultaneously. The unknowns are velocities in three orthogonal directions, the azimuth of the fast horizontal velocity, and the thickness of each anisotropic layer. This parameterization assumes elliptical anisotropy, and hence limits the inversion to near offset data. A linearized (conjugate gradient) inversion is performed, in layer stripping mode, for parameters of overlapping pairs of layers; conventional isotropic NMO provides adequate starting models. All layers are inverted as if they were orthorhombic; the inversion results reveal the actual anisotropic symmetry that is present in each layer. The inversion is illustrated by application to synthetic data for a four-layer model containing three anisotropic symmetries (VTI, HTI and orthorhombic). Unlike traveltime-based estimations, full-wavefield inversion can recover anisotropic parameters using only surface survey P-wave data; most of the inverted parameters have errors less than two percent for noise-free data. Noise contamination leads to increasing errors with increasing depth. The standard deviations of the parameter estimates are reduced, and the azimuthal coverage is improved as the number of sources increases. The inversion results for a layer are most satisfactory when constraints provided by reflections from both upper and lower interfaces are available. Correlation analysis between the parameters reveals a strong positive correlation between depth and vertical velocity in all media, and a strong correlations between fracture orientation and horizontal velocities in HTI and orthorhombic media. This approach provides an alternative to the usual use of traveltimes only for anisotropic parameter estimation. It sets the stage for extending full waveform inversion to elastic, non-elliptical, anisotropic models with more complicated geometries and symmetries.