The modification of thermal relaxation mechanism for wave propagation in porous rocks
多孔岩石波传播的热弛豫模型修正

The attenuation of thermal relaxation model is much higher than BISQ model, and also higher than the attenuation of earth medium. The inversion results of imaginary modulus in low frequency (or low temperature) area and high frequency (or high temperature) area are not pleasantly satisfied with the experimental results. The inversion results coincide with the experimental results only at the nearby area of attenuation peak. The original Arrhenius relation is introduced into Biot model to substitute the used frequency-temperature relationship at attenuation peak, and some changes of the parameters have been made. Then the results of the modified model eliminate the high attenuation and the mismatch of inversion results and experimental results of imaginary modulus in the old model. 1-D P-wave and S-wave propagation characteristics are analyzed. Thermal relaxation attenuation (TA) peak and the Biot attenuation peak are obtained on both frequency and temperature spectra. Overall analysis show that the appearance of TA peak leads to a universal law, the velocity increases with the frequency. The existence of Biot peak leads to an unusual phenomenon, the velocity increases with the temperature. Comparison is made for Biot, BISQ, and thermal relaxation model. Larger dispersion and wider dispersion range are observed in thermal relaxation model. The attenuation peak frequency of thermal relaxation model is lower than that of BISQ model, and the attenuation is a little larger. These numeric results are close to experimental results, which is more realistic.