In the earth’s crust, an electromagnetic (EM) field may be generated spontaneously by a seismic wave through a variety of mechanoelectromagnetic transducer mechanisms, such as the piezomagnetic effect, the piezoelectric effect, the electrokinetic effect, and the EM induction (the movement of an electrically conducting crust through a geomagnetic field). The coseismic EM field contains information about the structure and physical parameters of the crust, which complements that which can be obtained by purely seismic or purely EM methods. The magnitude, direction, and polarization of this field depend on the origin of the source, the type of seismic wave, and the geometry of the crust. Of the possible mechanisms mentioned above, the electrokinetic effect produces the largest magnitude of coseismic EM field. Detailed theoretical and computational calculations of the electric and magnetic fields, thus induced by a Rayleigh wave, were obtained. Several typical models of heterogeneity were considered, including horizontally stratified layers and fault like heterogeneities. We determined that the polarization and spatial distribution of the electric and magnetic fields arising from the electrokinetic effect are very specific and distinguishable from the fields generated by other sources. The expected magnitudes of electric and magnetic fields were large enough to be detected by conventional sensors and specific enough to be separated from the noise. The results obtained can be used for the interpretation of electric and magnetic disturbances observed during an earthquake and for prospecting the earth’s upper crust from depths of a few meters to a few kilometers.