Sum polygons within polygons

Hello,

I am trying to sum small polygons (land disturbance) that are within larger ones (counties). Some polygons are completely within a county; others cross county boundaries. I would like to say, at the end of the day, "County X has 2,000 acres of disturbed land while County Y has 5 acres." (This is somewhat similar to this, except I am attempting to sum thousands of polygons within dozens of larger ones ).

Attachment 19157

Here is what I have done:
-Add county layer to ArcGIS
-Add land disturbance layer
-Spatially join them (Analysis Tools > Overlay > Spatial Join)
Target features: counties
Join features: land disturbance layer
Join operation: one to many
Join type: Intersects

I get a spreadsheet with a list of all of the polygons and their areas for each county. Some counties have 0, which is accurate. Other counties have several thousand entries, which is also accurate. The problem: The total area I come up with for land disturbance (if I sum everything by county) is greater than the total area of land disturbance in the original land-disturbance .dbf file.

If "intersect" over-counts, I figured using "contains" for the join type might be accurate. However, this undercounts the amount of total land disturbance. How do I get the right amount of land disturbance per county?

I would appreciate any help or advice. Thank you so much!

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