This is a moth that we found on a curtain inside the house a couple of days ago. Unfortunately, these pictures did not come out as well as I thought before I realized it outside. But I was struck my the silver-white eyeglass-shaped spots on the wings. It also had an interestingly shaped head, but that didn't come out well. The closest I have come to identifying it is that it looks similar to a Dot Moth, but those don't seem to be native to Southern California (Los Angeles).
It was about an inch long, maybe less. It vibrated its wings after I disturbed it.