Wang, H. and Tsvankin, I., 2018. Methodology of waveform inversion for acoustic orthorhombic media. Journal of Seismic Exploration, 27: 201-226. Three-dimensional seismic waveform inversion (WI) for anisotropic media is highly challenging due to its computational cost and trade-offs between multiple model parameters. Here, we develop a methodology of 3D WI for orthorhombic media in the acoustic approximation using two mixed-domain modeling algorithms, one of which is based on low-rank decomposition and the other on the generalized pseudospectral method. Numerical testing shows that both techniques produce kinematically accurate compressional wavefields with an acceptable computational cost. To take advantage of the superior stability and accuracy of the low-rank-decomposition-based method, it is employed to simulate both the forward and adjoint wavefields. The gradient of the data- difference objective function, however, is more convenient to obtain from the wave equations derived with the pseudospectral method. The inversion is conducted with a limited-memory version of the quasi-Newton optimization algorithm. Under the assumption that the symmetry-plane orientation is known, we invert wide-azimuth data for all six parameters of acoustic orthorhombic media. The performance of the developed wavefield-extrapolation and gradient-computation algorithms is evaluated for a medium with Gaussian anomalies in each parameter. Then we apply the method to a modified SEG/EAGE overthrust model to demonstrate the feasibility of waveform inversion and illustrate parameter trade-offs for structurally complicated orthorhombic media.