You won't be able to ban the static unless you ban a subdomain/domain. As for tracing that to a person...very difficult. Most likely you would have to go through an ISP that will refuse to release it without a court order.
Require people to use identitites tied to non-anonymous emails (ie no hotmail, gmail, yahoo, etc.) and you will probably cut down a bit on your issue with people trolling while anonymous.
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