The effect of the earth's surface on the S wave particle motion

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Abstract
This paper is concerned with the determination of the particle motion of the earth's surface due to the incidence of a plane S wave of arbitrary polarization and incidence angles. It is assumed that the earth's surface may be represented by a plane surface. For angles of incidence less than sin-1(b0/a0, where a0 and b0 are the P and S wave velocities at the earth's surface, all three components of ground motion will be in phase, and the resultant motion is linear. For angles of incidence greater than sin-1(b0/a0), all three components of ground motion will in general be out of phase, with the resultant motion describing some three-dimensional figure. The epicentral distance at which the motion changes from linear to non-linear depends upon the wave length of the S wave and the slope of the travel time curve at that distance.

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