This is roughly what I would identify as LA's core area for capturing transit ridership (sans La Canada and the SFV west of the 405), owing to one or a combination of: urban structure, density potential, low-income population, employment centers, and points of interest. Build high-capacity, grade-separated rail here and the riders will come. Of course there are other factors that must align with this program, but rail infrastructure is the starting point.
The first four alternatives (the fifth has already been ruled out) for the Crenshaw northern extension all have forecasted ridership densities higher than DC's Metrorail, Chicago L, and BART. The La Brea alternative has a higher forecasted ridership density than Boston's T and Philly's SEPTA.
Metro
The 12-mile-ish first phase of the Sepulveda line is forecasted to have a ridership density of 10,000+ per mile.
And these two projects having connections with the Purple Line (and Red for the Crenshaw line) will likely push the Purple Line extension's (conservative) project ridership of 72,800 to 100,000, as neither Crenshaw nor Sepulveda were factored into the original calculated figure.