The standard sweep is used for normal patrol. The standard sweep can also be used as a pursuit pattern.
The enclosure pattern is useful when you don't know the exact location of your target, but you do have a perimeter. The only limitation is how many personel are at your disposal to create the search perimeter.
The pursuit pattern is most useful when the target is being chased to an unsurmountable obstacle such as a gorge, canyon, mountains, etc. This pattern is most commonly used when the target gets an advantage over security forces or there aren't enough men to deploy for a herd formation.
The herd pattern is very useful and is especially effective with large numbers of security forces. The target is forced to go toward the waiting security guards. If the target moves for the hole in the middle of the arms they swing closed cutting of the target's only escape.