The main dirt circuit uses a single op amp (usually a TL070, that is very similar to a LM308) in a topology similar to a RAT. The Texture control allows to mis-bias the chip and introduce gated sounds and texture. This imbalance of headroom also allows to clean up the dirt with the guitars volume control pretty good, even with buffered pedals before it.
When engaging the Octave footswitch the octave up/down signal gets mixed to the clean signal and runs through the main dirt section. The individual volume controls for the octaves define how much (if any) of each gets mixed in.