Re: Modeling sonic log from resistivity log
I am joining this discussion at quite a late stage and not even sure if it is still active.
I have not done much work on deriving compressional sonic log from resistivity logs.
However, in your case, it looks like a combination effect of mud filtrate invasion and shale alternation when using the Faust equation to derive compressional sonic log from induction resistivity logs.
In the case of sandy intervals, the medium induction is more affected by mud filtrate invasion, which I presume to be water base mud. Therefore, the medium induction gives you the best match, since the flushed zone is now water bearing.
In the shaly intervals, there may be shale alteration due to drilling process in the near wellbore area. That my be the reason the deep induction is giving you a better match, since the medium induction is now more affected by near wellbore shale alteration.
Please note that I am just speculating and that I may be wrong.
As you have done, you can back calculate the sonic log using a porosity from suitable resistivity logs. However, here you are assuming that the invaded zone is fully flushed with mud filtrate, which is water. Therefore, the invaded zone is 100% water bearing.
This may not be true in the case of hydrocarbon bearing zones, especially gas bearing intervals.
Although water and oil have densities which are relatively similar, gas has a very low density and if the invaded zone is not fully flushed with mud filtrate, you computed sonic log may not be very accurate due to the lower gas density still present in the invaded zone.
Another thing is that when you are deriving a porosity log from a laterolog curve (I believe it would be the deep laterolog), you need to know the formation water resistivity Rw and the cementation factor m. If you already know these values, it should be alright.
Again, if you are using Archie's equation, you may end up with less accurate sonic log values in shaly sands, because of the conductive clay present in the sands.
There is another equation to compute sonic log from a resistivity log, but I cannot remember it offhand. I will have to dig up my reference materials and get back to you later, if you are still interested.
Ko Ko Kyi