Is there a way to calculate modulation depth after the modulation process? Suppose I have some amplitude modulated carrier wave $x$. If I have no access to the original message wave nor the unmodulated carrier, is it some how possible to calculate what is the modulation depth of $x$?

If I have understood this correctly, amplitude modulation depth is given by
$M/A$, where $M$ is peak amplitude of the message wave and $A$ is the peak amplitude of the carrier wave. From $x$ I will know that $M/A$ equals to some $\lambda$ (when I check its peak amplitude), but M and A could be anything.

Please correct me if I have understood something incorrectly.
If you look at the envelope of an AM signal then for 100% modulation the amplitude of the envelope will vary between 0 and 2 * Ac, where Ac is the amplitude of the carrier. It's a linear relationship, so for e.g. 50% modulation the amplitude will vary between 0.5 * Ac and 1.5 * Ac. So as long as you know that you have a full scale modulation signal then you can derive Ac from the max and min envelope amplitude (mean of Amax and Amin) and from there you can calculate the modulation depth (Amax / Ac).