Seismic radiation released during the planar rupture of a glass plate is studied. It is found that this process is complicated: the rupture plane is formed from a sequence of quasilinear cracks running parallel to the initial groove cut in the plate. A quasilinear crack forms with high (seismic) velocity (10$^4$--10$^5$ cm/s); the rupture plane, which is built up from a sequence of linear cracks, grows with a low velocity of the order of 10$^2$--10$^3$ cm/s. Signals corresponding to the formation of a planar rupture built up from a sequence of linear cracks were found in the spatial and temporal structure of the aftershocks of an Alaskan earthquake. After the signals are interpreted, the earthquake process can be represented as the stagewise formation of several planar ruptures. Each rupture is formed in two phases: During the first phase (lasting 15 min) a leader crack is formed and during the second phase (lasting about one hour) a planar rupture is formed with the leader crack acting as the generatrix. The relationship between the characteristics of the process of successive formation of rupture planes and the parameters of tsunamis generated by the earthquake is analyzed. The relationship between the tsunami focus and the parameters--the coordinates and propagating velocity of the leader crack at the first phase--is established. It is found that the generation time of the high-frequency component is related with the formation of the rupture plane while the generation time of the low-frequency component is related with the successive stages during which successive rupture planes are formed. The possibilities for improving tsunami and earthquake warnings on the basis of the new possibilities for interpretation of seismic signals are discussed.