ON DIFFERENTIABLE MAPPINGS ACCOMPANYING KINEMATIC MODELS OF EARTHQUAKE SOURCE. 1. THE GENERAL CONSIDERATIONS
The mathematical problem of seismology is considered in connection with the simulation of the process in the earthquake focus, it is referred to the possibility to distinguish between "good" and "bad" models, the principles of the models hierarchy. The situation that is typical for the seismological practice is formalized: the kinematic model of the seismic source is described with a set of the parameters, the goal is to estimate the specific values of the parameters, knowing some "observables" measured on a digitized seismogram. It is assumed that it is possible to formulate a system of equations with regard to the parameters, in this case the integration of time displacement is proposed as the defining operator. If the analytical form of the system is known, a mapping of the set of the parameters into a set of "observables" is defined, then the mapping properties can, as claimed, serve as a characteristic of the model. In particular, the images of the regions of parameters` space ("maps of mappings") allow to visualize information on the number of possible solutions of the system as a function of the point in the space of the «observables» and about the generalized "response" of the system (the disappearance of "physical" solutions, the change in the number of solutions). At predetermined rule for the formation of "observables", the picture in the whole is determined by the model and it can be regarded as a "portrait" of the model.