Here are few examples of how the tremor plots looks like if anything important is going on in Iceland.
This is from the Grímsfjall volcano eruption in May 2011. On this tremor plot it can be clearly seen how much noise a eruption actually makes. The background noise just goes away soon as there is something going on. Copyright of this pictures belongs to Icelandic Met Office.
It is quite clear. Besides earthquakes and some harmonic tremors that are different then this signals that I have shown here. Unless you see this on Icelandic Met Office tremor plot you can be sure that it is quiet in Iceland. Volcano eruptions make a lot of noise when they are ongoing, even the small eruptions make some noise that can be detected by the SIL network in Iceland.
Note: I might update this blog post on later date and put in more examples about the difference between background noise and a eruption.