Elder (1-1) was hit with the loss against the Dodgers on Saturday, allowing seven runs on seven hits and four walks while striking out four over 3.1 innings.
Murphy (oblique) began hitting off the tee during Atlanta's most recent series against Seattle earlier this week, Justin Toscano of The Atlanta Journal-Constitution reports.
Herget was traded from the Angels to Atlanta on Thursday in return for cash considerations, Justin Toscano of The Atlanta Journal-Constitution reports.
Sale (4-1) picked up the win Wednesday in a 5-2 victory over the Mariners, allowing one run on six hits over five innings. He struck out nine without walking a batter.