Location of Sensors for Timely Tsunami Wave Detection with Maximal Amplitude

In the paper we set and solve the optimization problem of a given number of sensors placing so as to provide earliest detection of tsunami wave with a maximal amplitude. For it two objective functions are formulated. First of the objective functions responds for minimization of time determination period for any point of a possible wave appearance. Travel time of disturbance from source to sensor in this function is determined from the long wavelength approximation. Second objective function allows to maximize amplitudes of detected disturbances. An amplitude of a wave is computed based on a theory of a shallow water model. We consider several feasible variants of amplitude function formulation and accounting of amplitude size through constrains of the optimization problem. The problem is solved by means of a genetic algorithm. Constructed computational method is verified on a number of problems which has exact solutions and then it is used for optimal sensors location in the real bathymetry of Kuril-Kamchatka area.