Earthquake waves propagate mainly in rock mass from hypocenter to the bedrock directly underneath a monitoring station. Then, it propagates as shear waves from the bedrock to a geophone, where the surface motion is measured. For a deposit with uniform soil layers of horizontal interfaces, one-dimensional finite element analysis can be performed to analyze the dynamic responses of a horizontal soil deposit. In an ideal dynamic soil-structure interaction analysis, seismic waves are propagated from the bedrock through soils and foundations, and then to structure. Thus, it is necessary to obtain the bedrock motion from a measured surface motion registered in geophone. Conventionally the process is called de-convolution. The de-convolution is treated as wave propagation in a frequency domain involving damping factor independent of motion velocity. The time-domain analysis is usually used in assessing the effects of soil-structure interaction. The time domain analysis requires the use of viscous damping proportional to motion velocity. Thus, it is necessary to device a method for the evaluation of viscous damping that, when used in the time domain analysis for the upward wave propagation from the bedrock back to ground surface, produces a surface motion in close agreement to the measured surface motion. This paper presents a procedure for evaluation of viscous damping from a given damping factors. This viscous damping successfully produces a surface motion in close agreement with the measured surface motion in a time domain analysis of upward wave propagation.