Procedure of processing groud-based and space measurements of geophysical fields for the purpose of predicting earthquakes is considered. Much attention is gives to the processing and analysis of those fields forerunners of seismic events were detected earlier. A mathematical model of earthquake prediction is suggested. Detection of forerunners is regarded as a problem of detecting a forerunner signal on the background of a multidimensional stochastic process which is represented by measurements of geophysical fields in the ionosphere and on the Earth's surface.