When you study the voice, you’ll learn about how to get resonance in your voice. One of the key ingredients to resonance is lifting the soft palate. Imagine there’s a rubber band attached to your mouth and it’s pulling from behind your head. As it pulls back your mouth is naturally going to develop a smirk or smile. This is exactly the mouth shape you need to have for your voice to carry and have vibrancy and richness, not to mention you’ll feel better when you sing.
So put on that smile and imagine that rubber band pulling from behind your head and you’ll feel a lift in the back where you’ll almost want to yawn. This is where you can develop your higher register as well as get the rich tone you want.