The elusive mole cricket, Gryllotalpa pluvialis, caught by one of my boys. Love these things.
Males sing at the entrances of vertical burrows specially shaped to amplify their songs. Singing characteristically commences at dusk and usually ceases within a few hours. The songs of mole crickets are deeper than those of typical crickets and many people have attributed them to frogs.
This species has a strident, rapid, chirping song that can be quite intrusive whereas the other introduced species has a slower, quieter trill. Do you have these in your garden?