My firewall (zonealarm) keeps blocking attempts to scan my ports. It
shows an IP address of the source and can trace the general area it
came from.
Is it possible to send an anonumous message to that address telling
them to stop it?

gooser-ga,

Thanks for the opportunity to answer this question.

It's not possible to send an anonymous message to that address telling
them to stop scanning your ports.  You have several alternatives.

1) Ignore the attempt.
2) Contact the originating service provider and ask them for
assistance.

  Generally, option #2 is done by doing what's called a WHOIS query on
the source range or address and sending them an electronic mail
message (email) informing them of the attempt.  They will often either
contact the user for you and tell them to cease and desist, or
disconnect the user's service if the action is against that company's
acceptable use policy.  (Generally these emails go to abuse@(their
company).com).

3) Contact your service provider and ask them to block the attempts.

  Some service providers will block these sorts of requests at their
"borders".  Contact your provider's customer support department for
information.

It is my pleasure to answer this question for you.  If I can provide
any more help, please request a clarification to my answer.

Best regards,
arimathea-ga

Thankyou for a rapid and clear answer.