Similarly, fc and fOld are the current and previous objective function evaluations(respectively), xc and x_last are current and previous models, x0 is the initial model and |proj(x-g) -x| is a global estimate of how much change will take place in the model. This has to do with the stopping criteria of the inversion and depends on the type of inversion. I personally don't find this information all that informative or helpful to detemain the reason for the termination of the inversion.
When I run inversion, I do look at the progress of the objective functions ( phi_m, phi_d and f) at each iteration to make sure that they are converging. After completion, I plot the curves based on the data in the .npz files that are generated. I will try to put some better example together in the next couple of weeks on how I do this.
I hope this was helpful (though late). If you have more question, post them and I will try to be better on top of them this time around.
Have a good day.
Gudni