On the attenuation of transient spherical waves in a four-element viscoelastic model and its implications

Summary In a four-element model, which consists of two Voigt elements in series, the impulse responses of spherical waves for particle displacement, velocity, acceleration and strain are computed numerically. These impulse responses are shown to be useful in synthesis for the desired wave response through convolution, between the input of the source function and the impulse responses. The rate of decay of peak amplitude versus distance, as waves radiate out, is examined in the region close to the source which may be nuclear or dynamite explosives and found to be linear in log-log scale. The amplitude spectra of the unit impulse response are obtained through Fourier analysis, and the model is found to behave as a low pass filter. With the properly chosen elastic constants for springs in the model and damping coefficients for dashpot, it is seen that, like the earth materials, the attenuation exponent (in neper/1000 ft) versus frequency in the model is approximately linear. One of the results observed byCollins andLee [1] is fitted by the model. The model thus simulates more nearly the wave in earth materials close to the source than the Voigt solid.