On the Cauchy problem for the wave equation with data on the boundary

We consider the Cauchy problem for the wave equation in $\Omega\times\mathbb R$ with data given on some part of the boundary $\partial\Omega\times\mathbb R$. We provide a reconstruction algorithm for this problem based on analytic expressions. Our result is applicable to the problem of determining nonstationary wave field arising in geophysics, photoacoustic tomography, tsunami wave source recovery.