By utilizing SAR satellite products, one can assess the state of the ground surface prior to and following the eruption. Please refer to the following article for an illustrative example.
https://doi.org/10.1016/j.oceano.2022.03.006
Hi, I don't understand your question very well. But, If the eruption occurred in the period of activity of the satellite you can download the image from different web pages, see this article https://gisgeography.com/free-satellite-imagery-data-list/.
On the other hand you can use different type of image (e.g. SAR o visual) depending on what you want to do.
Depends on what you mean by 'past' (recent, historical, paleo) - an eruption even with in past decade might span several generations of platforms and their sensors, historical could be done by identifying with topography, mineral composition and overlaps of flows, and paleo ( 100,000s years ) by major structures and erosion pattern types. The duration of the 'eruption' might be single short violent blast (Mt. St. Helens), periodic, or continuous like in Iceland and Hawaii ("Stromboli, one of the Eolian Islands north of Sicily, is the undisputed champion. Known as the "lighthouse of the Mediterranean" by Roman and Greek sailors, Stromboli has apparently been erupting almost continuously for more than 2,400 years." - USGS). And what sort of data and associated signatures at what scales are being 'visualized' ( optical, thermal, uplift, flow velocity)? All these factor would dictate the characteristics of satellite imagery needed, and the methods and techniques for analysis, and the simple availability of a single scene or time series. And most important of all, where on the planet is the area of interest?
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