This paper makes a proposal of prediction formula showing distance reduction in vibration propagation that imported a new thinking of "vibration source power level" on the vibration propagation along the ground surface causing by the industrical machines that is established a forging factory, a metal press factory, a foundary, and so on. Next, it was evident that the theory of "noise source power level "used in the field of noise control engineering could apply to this prediction process, and an appropriateness as the prediction formula at distance reduction could confirm from an examination result of double-sides of the theory and the field measurement. It showed these conclusions as follows. (1)Getting vibration velocity at vibration source, vibration power at vibration source can calculate from it. (2)Wave impedance in the ground is a foctor to determine the reference of vibration power. In case of using wave impedance in the ground (the first kind of groud soil-rock)showing this paper, the reference of vibration power W_0(W_0=1. 2*10^<-7> watt)is determined by the above. Consequently, vibration source power level L_<vw>(L_<vw>=10log_<10>W/W_0 dB)can be calculated, the prediction concerned with vibration propagation with L_<vw>(dB)might be possible. (3)There are correlation between vibration source power level in theory. Similarly, there are correlation between vibration source assumed power level and vibration source assumed power level and vibration source power level in prediction as well. Therefore, it is a good reason in the thinking of "vibration source power level. "(4)The most suitable prediction formula(L_<vr>=L_<vw>-15log_<10>γ-8. 68α・γ-k_γdB. Here, L_<vr>:vertical vibration level, γ:the distance from receive vibration point to vibration source, α:soil nature damping constant, k_γ:the coefficient depending to distance) could find from an examination result in the field measurement, and it becomes the prediction formula in the field measurement, and it becomes the prediction formula in hte field measurement. (5)The field measurement values are more appreximate to values according to the prediction formula than according to theoretical formula
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