Phase analysis of signals using frequency-dependent attenuation for measurements of seismic waves

Abstract

Attenuation refers to any decrease in the power of a propagated signal through a medium. Attenuation measurement techniques include ultrasonic, resonance bar, and stress-strain methods. The stress-strain method measures elastic and viscoelastic properties in the seismic frequency range. The signals received via attenuation measurement systems using the stress-strain method can be considerably weak. Moreover, the noise in these signals causes errors when estimating the signal phase-angle difference between the sample signal and probe signal, thereby reducing system precision and measurement accuracy. Accurate measurements of such phase differences are essential to the measurement of attenuation. A seismic-wave attenuation with frequency-dependent measurement based on the stress-strain method and digital signal processing techniques has been performed. The system estimates the attenuation of a rock by measuring the phase shift in the stress-strain cycle. As a preprocessing method, the finite impulse response band-pass filters are designed to eliminate the influence of noise and direct current offset while ensuring that the phase difference of the measured signal remains unchanged. Three methods for phase difference estimation, i.e., crosscorrelation, fast Fourier transform (FFT), and Hilbert transform are compared, for different signal-to-noise ratios, sampling frequencies, data sample lengths, and true phase differences. The results find that the phase difference estimation based on FFT is the best among all three methods and can effectively improve the precision of the experimental results. Simulation and measurement results further indicate that the attenuation measurement system achieves stable and reliable attenuation measurements in the range of 3–2000 Hz.