If you were going to do it more properly, the first choice would probably be Riemann, which has already seen some adoption in this role. There are already plugins on both sides to forward events to the other:
https://www.elastic.co/guide/en/logstash/current/plugins-out...
ElasticSearch is a great search engine. It's not a CEP or SEP. I don't mean to discourage its use, but for this purpose it's not a good fit. It does make sense to tee incoming logs to both as they suit different purposes, but I'd delegate pattern analysis to the latter.
If anyone runs a team of 25 or more SREs and effectively uses Riemann (and there's more than 3 domain experts), and is not otherwise a Clojure shop, I'd love to hear from you.
And yet, it's the most widely used option in this role. Crazy days.