That is, on an absolute time scale, the acceleration, velocity and displacement time histories of two points along the propagation path are assumed to differ only by a time lag, which is a function of the separation distance between the two points and the speed of the seismic wave. C is the propagation velocity of the seismic wave. These two relations for ground strain and curvature along the direction of wave propagation are relatively straightforward. The ground motion parameters V m and A m , the maximum particle velocity and acceleration, can be obtained from attenuation relations. These relations for ground strain and curvature need to be modified if the direction of interest is not parallel to the direction of wave propagation.
Body waves propagate through earth, while surface waves travel along the ground surface.
For vertically incident S-waves, the apparent propagation velocity is infinity. However, there is typically a small angle of incidence in the vertical plane leading to non-zero horizontal ground strain. O'Rourke et al. C s is the shear wave velocity of the surface soils. R-waves cause the ground particles to move in a retrograde ellipse within a vertical plane.