A new data assimilation algorithm for joint litho-petroelastic (LPE) inversion using nonlinear anisotropic Zoeppritz reflectivity operators, together with iterative sequential filtering, is used to provide joint elastic, lithology, and petrophysical estimates. The sequential filtering approach is an attractive choice because integration of petroelastic rock models with seismic data for multiparameter estimation can become quickly ill posed. Data assimilation techniques integrate the data and model in a manner that tracks uncertainties and manages the flow of data, which helps control this difficult, ill-posed estimation problem. For anisotropic formations, joint LPE inversion makes it possible to use anisotropy information associated with the lithology units or petrophysical parameters, either as fixed lithology-dependent trends by means of prior averages or as a direct function of the petrophysical parameters. This proves beneficial for amplitude variation with angle/amplitude variation with azimuth inversion where the azimuthal invariant anisotropic parameter space, containing the vertical transverse isotropy (VTI) components of the reflectivity operators, is not resolvable independently from shear and density information. In many cases, neglecting to account for anisotropy will lead to inferior characterization of anisotropic plays. Anisotropic LPE inversion enables anisotropic characterization by identifying the anisotropic formation as part of the inversion process. LPE inversion also provides estimates of the petrophysical parameter space and, therefore, honors the relation between the anisotropic elasticity, lithology, and petrophysical parameters. This study reviews the LPE inversion workflow and shows how anisotropic LPE inversion in VTI media is used to derive jointly elastic properties, lithology, and petrophysical parameters of the Wolfcamp Permian Basin shale play in Texas. We also demonstrate the importance of including anisotropy in the inversion and show that isotropic inversion poorly delineated the lithology of the play.