Transfer distortions of acoustic emission signals - power relations between the signal parameters and normalized temporal shapes of avalanches

Abstract Power law correlation between the rising time, \(\:R\), and amplitude,\(\:\:A\), of the detected acoustic emission, AE, signals of crackling noises is investigated in the framework of a driven damped harmonic oscillator model. It is shown that the \(\:R~{A}1-φ\:\) relation holds, similar to the well-known enigma for acoustic emission between the detected energy, \(\:E\) and amplitude, \(\:A\), as well as area, \(\:S\), and amplitude (\(\:E~{A}3-φ\:\:\)as well as \(\:S~{A}2-φ\:\), where 3 and 2 are the expected exponents from the mean field theory, MFT), with the same value of \(\:φ\:\). For the experimental value \(\:{φ\:}ₑₓₚ={φ\:}AE+{φ\:}ₒ\) fulfils, where \(\:{φ\:}AE\) results from transfer distortions of AE signals and \(\:{φ\:}ₒ\) is the exponent in the power relation between the amplitude and the rising time of the source function (\(\:{φ\:}ₒ=-0.32\) beyond the MFT and \(\:{φ\:}ₒ=0\:\)in MFT). The calculated value of \(\:{φ\:}AE=1\) is in good agreement with experimental data obtained for different jerky structural changes: \(\:{φ\:}ₑₓₚ\:0.8±\:0.2\). Well scaled together universal functions can be obtained for the temporal avalanche shapes at fixed area normalizing the voltage by \(\:A\) and the time by \(\:R~{A}1-φ\:\). The first part (around the peak) of it is not sensitive to transfer distortions, while the tail region can be heavily distorted.