Abstract
The far-field body waves generated by a slip dislocation with an elliptically expanding rupture are analysed in the time domain. It is assumed that the ratio of the lengths of the axes of an expanding ellipse is an arbitrary constant α. The radiated body waves are described by the product of two factors. The first one due to the double couple without moment is excluded from the consideration. The second factor Tj (j stands for the P- and S- motions), which includes the time dependence of the seismic impulse and which reflects the character of the rupture propagation, is analysed for three models with different values of the parameter α. The graphic representation of the Tj pattern consists of three components: 1) the spatial distribution of the slope of the initial part of the impulse Tj, 2) the graphs of the impulse Tj as a function of time for the chosen directions, 3) the spatial distribution of the maximum amplitude of the impulse Tj. The slope of the initial part of the displacement Tj is the greatest in the rupture plane and the smallest in the direction perpendicular to the fault. If the angle between the rupture plane and the observer is kept constant, then the slope is the greatest for the direction whose projection on the rupture plane lies along the direction of maximum velocity of the rupture propagation. If the boundary of the faulting area is rectilinear or concave, then some impulses can exhibit two displacement maxima, at the times of the first and the second stopping phases, respectively. The maximum amplitude of the displacement Tj depends to a high degree on the ultimate boundary of faulting in relation to the initial point of rupture, as well as on the form of the rupture propagation. It is found that if the fault surface is not elongated and the starting point of the rupture is approximately in the center of the fault, then the maximum amplitude of the displacement Tj should be the greatest, in general, for the directions whose projection on the rupture plane lies along the direction of minimum and not of maximum velocity of the rupture propagation.
