I may try commenting this as a client. I see that many commercial projects use full-waveform inversion (FWI) in acoustic with options to handle Q-compensation and anisotropy internally. However, mostly we still update one parameter (velocity, epsilon, delta, Q, etc.) at a time. Options for the cost function could be based on time-lag or amplitude differences. Diving wave is mainly used for update, but I see some trends trying to use seismic reflection for updating the deeper section in addition to diving wave. Modeling could be done by finite difference in time domain, and could be either CPU- or GPU-based.

You may find more ideas from the papers or product information from leading seismic processing companies like Schlumberger, CGG, etc.

Thank you, Saeed Izadian, in arid environments, do you mean the onshore survey?

I find that multiparameter FWI from DUG is now commercialized. Then, you can use it to simultaneously estimate multiple parameters. Check this paper: https://doi.org/10.1190/tle42010034.1