age, Z => (alog10(age) + Z)/sqrt(2), (alog10(age) - Z)/sqrt(2) : v1, v2

limits (v1) = [alog10(min(age))+min(Z), alog20(max(age))+max(Z)]/sqrt(2)
limits (v2) = [alog10(min(age))+max(Z), alog20(max(age))+min(Z)]/sqrt(2)

(age, Z) = ((v1+v2)/sqrt(2), (v1-v2)/sqrt(2))
age_min = alog10(min(age))+min(Z)+max(Z)