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The only way to get close approximations of your PPC traffic is to put marker parameters in the destination URL that's programmed into the PPC ad. At the simplest level it would be something like "source=PPC_ad" although most people try to get a lot more information than that, like which PPC program, what keyword was paid for, and so on.
Then, if you have a good idea of all search engine traffic, you subtract this activity from the total SE traffic and you have an estimate of organic SE traffic. This, however, requires 1) that the referrer field be populated, which it often isn't, and 2) that you have an accurate lookup table that contains a complete list of referrer strings that belong to search engines as opposed to non-search engines.
Hope this helps.
The final stage of the program will be to track the customer from a search engine to the website and on to filling out a form on the site.
Any additional thoughts on distinguishing PPC refers from organic?
Using the referrer field to distinguish between them is very unreliable.
I would advise my clients to use a specific parameter in the destination url and track it as a unique channel in the software. This simple solution works for PPC, email, and other offline advertising.