Modeling of Signature Waves Based on Fourier Series for Blast Vibration Prediction

"The original signature hole technique to predict vibration levels from blasting, is based on theassumption that each hole in a production blast, generates an identical vibration waveformarriving to the point of interest. When the same waveform is used to represent the vibrationproduced by each hole, the complete waveform for the whole blast is the convolution betweenthe waveform and the impulse sequence that represents the initiation timing of the blast. In thisresearch, several field tests were developed to establish the validity of the invariability of thewaveform hole-to-hole in a mining production blast. The results of the tests showed that thereare variations in amplitude and frequency content for the hole-to-hole waveforms. Thevariations can be explained due to the character of the parameters involved in a production blastbetween them: different vibration path for each hole, differences in the geometry of each hole,differences in the explosive charge for each hole (chemical and quantity), etc. This paperdescribes a methodology based on the main characteristics in both; time and frequency domainof any recorded signature waveform and uses Fourier series to approach one equation to generatedifferent random waveforms for each hole that can be used in the prediction of the completevibration record of the blast. The methodology is the base for signature hole analysis using aMonte Carlo scheme."