  We study the spherical mean transform on $\rN^n$. The transform is
characterized by the Euler-Poisson-Darboux equation. By looking at the
spherical harmonic expansions, we obtain a system of 1+1-dimension hyperbolic
equations, which provide a good machinery to attack problems of spherical mean
transform.
  As showcases, we discuss two known problems. The first one is a local
uniqueness problem investigated by M. Agranovsky and P. Kuchment, [{\em Memoirs
on Differential Equations and Mathematical Physics}, 52:1--16, 2011]. We
present a simple proof which works even under a weaker condition. The second
problem is to characterize the kernel of spherical mean transform on annular
regions, which was studied by C. Epstein and B. Kleiner [{\em Comm. Pure Appl.
Math.}, 46(3):441--451, 1993]. We present a short proof that simultaneously
obtains the necessity and sufficiency for the characterization. As a
consequence, we derive a reconstruction procedure for the transform with
additional interior (or exterior) information.
  We also discuss how the approach works for the hyperbolic and spherical
spaces.
