  Given near or far field wave measurements generated by some unknown time- and
space-dependent acoustic source, we seek to rapidly determine a domain in
space-time, as small as possible, that contains the support of a source
radiating these measurements. As for any inverse source problem, this task is
challenging without further restrictions on the source, particularly due to the
infinite-dimensional space of silent sources radiating zero measurements. This
first causes non-uniqueness, that is, the source in general cannot be
determined uniquely, and second prevents the computation of, e. g., a largest
set that must contain the support of the source. To determine small domains
containing the support of some source that radiates given measurements, we
exploit that solutions to the wave equation propagate along characteristics. We
further indicate restrictions on the support of a source that allow to
theoretically characterize this support uniquely from near or far field
measurements.
