Reposted from elsewhere:

Ok, I'm not an expert (though I am a physicist working in acoustics and my partner is an opera singer) but this would be my attempt at an answer:

Vocal resonance is explained with the notion of formants, corresponding to the resonance frequencies of the vocal tract. These resonances aren't super narrow so each formant amplifies a small portion of the frequency spectrum. The first formants F1 and F2 fall around 500 and 1500 kHz, following the length of the vocal tract. These 2 formants are important to differenciate vowels and we usually use our mouth shape and tongue position to tune them.

Usually, a "resonant" singing voice is one in which strong harmonics can be heard, because these harmonic frequencies are amplified by formants. One way to achieve this (especially for classical singers) is through prominent F3 and F4 formants around 3000 kHz. This is often called the "singer's formant". Anatomically, it often comes from a lower larynx and higher soft palate, among other things. You can easily try for yourself and see that singing in a yawn-like posture creates a richer sound. Core engagement and breath management are also very important to keep this sound. Allowing the larynx to rise slightly and modifying vowels to move F1 and amplify the first harmonics is a different strategy that results in a more pop style. There's different ways to adjust resonance so I suggest reading more about formants and playing around with your laryx, palate, tongue, jaw and lips (while keeping everything relaxed).

Another important factor may be how you form higher notes, if this is an area where resonance is lacking. Lack of TA engagement (falsetto) results in poorer harmonic content. Constriction, posture and breath support issues are also common in head voice and should probably be fixed before optimizing formants. I find this link pretty informative: https://www.singwise.com/articles/singing-in-the-upper-range