  We suggest a new asymptotic representation for the solutions to the 2-D wave
equation with variable velocity with localized initial data. This
representation is a generalization of the Maslov canonical operator and gives
the formulas for the relationship between initial localized perturbations and
wave profiles near the wave fronts including the neighborhood of backtracking
(focal or turning) and selfintersection points. We apply these formulas to the
problem of a propagation of tsunami waves in the frame of so-called piston
model. Finally we suggest the fast asymptotically-numerical algorithm for
simulation of tsunami wave over nonuniform bottom. In this first part we
present the final formulas and some geometrical construction. The proofs
concerning analytical calculations will be done in the second part.
