A "shallow invasion" of a framework is something between an invasion and a reduction. It is not as severe as an invasion, which intends to live inside the framework and even dislodge the surrounding groups, but it's not as mild as a reduction on the sector line which intends to force the framework into a smaller territory than its original ambition.
As an example:
In this diagram, if we factor in the exchange of a for b, the sector line between the high end points of Black's position has been marked.
A good reduction looks like this. Not only does it take the sector line into account but it also takes the marked stone into account, which has some aji towards the black group below. After , Black turns to a reduction of his own with the shoulder hit of .
A shallow invasion looks like this. stays on the 4th line. If caps then White has a relatively easy time by either pressuring qt a or connect out at b.