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Finding landslide initiation points

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I would like to know if there is a simple geoprocessing sequence to get landslide initiation points from these layers:
  • SRTM DEM (90m)
  • Landslide polygons (many different sizes and shapes)
(Initiation points are typically near the top of the slope portrayed by these polygons.)
I think that there might be a creative solution (like reversing the elevation and then using raster hydrology tools), but I am not familiar enough with ArcHydro to see what it is.

I have already considered these methods:

A geologist examines each of over 24k polygons and digitizes the initiation points individually.
This is the right way to do it, but too expensive.

Write a python script from scratch that does this.
Sounds like fun, but I don't have the time.

Use zonal statistics.
This seems like it would be the right answer, but it has 2 problems:
The raster resolution is so coarse that some small landslides may be lumped with big ones.
Attachment 29723
Some polygons have multiple initiation points.
Attachment 29724
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