Thus, as a result of the experimental discovery of previously unknown pendulum waves, the elementary carriers of which are geoblocks differing in hierarchic level, with dynamic-kinematic characteristics that depend on the stress-strain state of the rock masses and the dimensions of the focal zones of rock bursts and explosions, we are able to propose a new approach to the prediction of catastrophic events. Here, as diagnostic indexes with respect to the critical stages of stress concentration for focal zones of rock bursts that are being formed, we can use the angular characteristic θ of the conical envelope of the μ-wave packets and their energy characteristics Ψ1 and Ψ2. With such an approach, seismograms from technological explosions can be used as integral information in a new system of geomechanical monitoring.