  We prove, with an unconditional effective error bound, the Sato-Tate
distributions for two families of surfaces arising from products of elliptic
curves, namely a one-parameter family of K3 surfaces and double quadric
surfaces. To prove these effective Sato-Tate distributions, we prove an
effective form of the joint Sato-Tate distribution for two twist-inequivalent
elliptic curves, along with an effective form of the Sato-Tate distribution for
an elliptic curve for primes in arithmetic progressions. The former completes
the previous work of Thorner by including the cases in which one of the
elliptic curves has CM.
