The purpose of this paper is to make clear causality of systems in seismic wave propagations by using observed data. For this purpose, methods to estimate causal transfer functions and coherence functions in the systems from observed data were developed on the basis of Wiener filtering. The estimate methods were applied to analyses of NS-components of seismic motions which had been observed for 18 earthquakes by a set of instruments placed along vertical direction and had been shown that the components of motions mainly contain vertically propagating shear-waves. The estimated results were compared with the simulated ones obtained by one dimensional multi-layered model. Following results were obtained ; 1) Coherency of wave motions is lower than that in causal systems because observed wave motions contain non-causal components in the systems of propagation. 2) In systems of shear-wave propagations, all-pass functions of causal transfer functions are near equal to phase functions which are shifted by times of wave propagation.
