What is Depth imbalance, depth profile?

The depth imbalance over $L$ levels is $(\sum_{i \le L}q^b_i - \sum_{i \le L}q^a_i)/(\sum_{i\le L}q^b_i + \sum_{i \le L}q^a_i)$, with $q^b_i, q^a_i$ the quantities at the $i$-th best bid and ask prices. The depth profile of a side is the vector of its quantities by distance from the touch.