Radiation of seismic body waves from a finite moving source in the Earth

Body waves from a finite moving source are investigated. Ray theory is used to obtain a long-range approximation for the surface displacements from a buried horizontal force. A weak velocity gradient in the medium is assumed, and the curvature of the earth is replaced by an equivalent additional velocity gradient. The displacements are then integrated over a finite line to simulate a disturbance moving with constant speed. Results indicate that the finiteness of the source is manifested in a factor of the form e-iXsinX/X and that the derivation of the fault length and the velocity of rupture of earthquakes from the spectra of body waves is possible. The results are similar to those obtained earlier for seismic surface waves, except that for body waves X depends on both polar coordinates of the station with respect to the source. The method can be extended to other types of common faulting.