Attenuation refers to any decrease in the power of a propagated signal through a medium. Attenuation measurement techniques include ultrasonic, resonance bar, and stressstrain methods. The stressstrain method measures elastic and viscoelastic properties in the seismic frequency range. The signals received via attenuation measurement systems using the stressstrain 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. In this paper, we measure the frequency-dependent seismic wave attenuation based on the stressstrain method and digital signal processing techniques. The system estimates the attenuation of a rock by measuring the phase shift in the stressstrain cycle. As a pre-processing method, the finite impulse response bandpass 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. We compare three methods for phase difference estimation, i.e., cross-correlation, fast Fourier transform (FFT), and Hilbert transform, for different signal-to-noise ratios, sampling frequencies, data sample lengths, and true phase differences. The results show 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. Our simulation and measurement results further indicate that the attenuation measurement system achieves stable and reliable attenuation measurements in the range of 3 Hz 2,000 Hz.
Coal is a complex viscoelastic porous medium with fractal characteristics at different scales. To model the macroscale structure of coal, a fractal viscoelastic model is established, and the P-wave velocity dispersion and attenuation characteristics are discussed based on the complex modulus derived from this model. The numerical simulation results indicate that the fractional order α and relaxation time τ greatly affect the P-wave velocity dispersion and attenuation. The fractal viscoelastic model indicates a full-band velocity dispersion between 1 Hz and 104 Hz. Meanwhile, the P-wave velocity has a weaker dispersion with the fractal viscoelastic model than with the Kelvin-Voigt model and Zener model between 1 Hz and 104 Hz for the same relaxation time and elastic modulus, but the velocity at 1 Hz based on the fractal viscoelastic model is higher with the Kelvin-Voigt model and Zener model. Simultaneously, the velocities of five coal samples are tested, and the attenuation factor is calculated using a low-frequency system. The experimental results indicate a strong dispersion in coal in the range of 10–250 Hz. The classic Kelvin-Voigt model and Zener model cannot describe the dispersion characteristics of coal, but the fractal viscoelastic model can describe them well by using the appropriate fractional order and relaxation time.
Summary The key issue in the 3D seismic exploration of geothermal reservoirs is to determine how the petrophysical properties of geothermal reservoirs change with temperature. In this paper, physical experiments on six rock samples from the Yunnan Lufeng geothermal field were used to analyze the effect of temperature on the elastic moduli of dry rock. The laboratory measurements show that under formation pressure conditions, the bulk modulus and shear modulus of the studied rock decrease linearly with increasing temperature, and the rock moduli exhibit approximately linear relationships with temperature. Gassmann's equation can be used to predict the influence of pore fluid on the P- and S-wave velocities of the rocks. To include the temperature effect in Gassmann's equation, we separately considered the rock matrix and pore fluid; we combined thermoelastic theory to introduce the influence of temperature on the rock into Gassmann's equation and directly considered the influence of temperature on the pore fluid. The effects of fluid on the physical properties of rocks were evaluated based on Gassmann's equation while considering the effect of temperature. The results show that the rock shear modulus is affected by temperature more than the bulk modulus is, which implies that the S-wave information is more sensitive to temperature. When the uniform water saturation is less than 95%, temperature is the main factor influencing the rock bulk modulus. When the uniform water saturation is greater than 95%, the fluid is the main factor influencing the rock bulk modulus, and the rock shear modulus is affected by only temperature. Fluid replacement with Gassmann's equation achieves results that are more consistent with laboratory measurements when the influence of temperature is considered. Gassmann's equation considering the effect of temperature reveals crucial dependencies of the seismic wave velocities and elastic moduli on temperature and fluid content.
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