The propagation of fast magnetoacoustic waves in a randomly structured solar corona is considered in the linear and cold plasma limits. The random field is assumed to be static and associated with plasma density inhomogeneities only. A transcendental dispersion relation for the fast magnetoacoustic waves which propagate perpendicularly to the magnetic field is derived in the weak random field approximation. It is shown analytically that the fast magnetosonic waves experience acceleration, attenuation, and dispersion in comparison to the homogeneous case. These analytical findings are essentially confirmed by numerical simulations for a wide-spectrum pulse, except that the waves were found decelerated. It is concluded that the coronal Moreton waves can be applied to MHD seismology of the solar corona
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