Laboratory data on dry and saturated rocks show that pore fluid has the most important effect on rock attenuation. It is known that viscous and inertial coupling between the frame of a porous rock and its pore fluid dissipates seismic energy by conversion to heat and hence cause attenuation. We show that attenuation peaks, in saturated rock have the same property as that of typical thermally activated relaxations. In the frequency domain, a plot of attenuation versus frequency shows an obvious systematic shift to higher frequencies with increasing temperatures. Similarly, the attenuation versus temperature curve moves to higher temperature with increasing frequencies. The attenuation peaks are somewhat broader than that for a Zener relaxation. A Cole-Cole distribution of relaxation times closely matches the attenuations. This behavior can be explained theoretically by local flow mechanisms.
Hysteresis such as stress‐strain loop, “X” shape of instantaneous modulus and Poisson's ratio, and effect of strain amplitude on attenuation of saturated rocks is analyzed under cyclic loading with experiments of fluid saturated sandstones and marbles. We think that the attenuation of rock is in proportion to the strain amplitude of the applied cyclic loading, and the b value of attenuation is a measurement of saturated rock's attenuation under cyclic loading. We discuss the possible micro mechanisms of attenuation and hysteresis at low frequencies by the macro behavior of saturated rocks in uniaxial stress cycling test. The flow of porous fluid might play an important role in attenuation and hysteresis of porous rock, and both the grain contact adhesion and stick‐slip friction might be the factors of porous saturated rock's hysteresis and attenuation in high stress, low frequency cycling test.
[Abstract] Low-frequency uniaxial stress cycling experiments were conducted on sandstone and marble in different saturation states to investigate the possible anisotropic and nonlinear behavior. The results indicate that under the yield point the attenuation, Young's modulus, Poisson's ratio and velocities of saturated rocks all display obvious anisotropy and rather obvious strain amplitude effect and frequency effect. As strain amplitude increases attenuation increases linearly while Young's moduli and Poisson's ratios decrease approximately linearly. In the frequency range 0.005-4 Hz attenuation shows no strong frequency dependence while Young's moduli, Poisson's ratios and velocities obviously depend on frequency. When the frequency range is enlarged to 15 Hz all the four parameters show rather strong frequency dependence. Attenuation, Yong's moduli, Poisson's ratios and velocities of saturated rocks increase as viscosity coefficient of the saturant increases.
In a semi-infinite aquifer bounded by a channel, a transient flow model is constructed for phreatic water subjected to vertical and horizontal seepage. Based on the first linearized Boussinesq equation, the analytical solution of the model is obtained by Laplace transform. Having proven the transformation between the analytical solution and some relevant classic formulas, suitable condition for each of these formulas is demonstrated. On the base of the solution, the variation of transient flow process caused by the variables, such as vertical infiltration intensity, fluctuation range of river stage, aquifer parameters such as transmissivity and specific yield, and the distance from calculating point to channel boundary, are analyzed quantitatively one by one. Lagging effect will happen to the time, when phreatic water gets its maximum fluctuation velocity, response to the varying of the variables stated above. The condition for some variables to form equivalent lagging effect is demonstrated. Corresponding to the mathematical characteristics of the analytical solution, the physical implication and the fluctuation rule of groundwater level are discussed.
We make a deep study of 3‐D resistivity inversion, and propose a practical algorithm of 3‐D inversion. Using the finite difference method to solve the 3‐D forward problem. We have properly improved the elements of roughness matrix in order to form the roughness matrix in different cases, setting up the inversion equation under the condition that the total roughness of the model is minimum. We use the least‐squares QR factorization (LSQR) algorithm, which is fast and stable, to solve inversion equations. The LSQR algorithm only requires the result of the derivative matrix and its transpose multiplying vectors. Therefore we avoid direct and complicated computations of the derivative matrix. This approach reduces the need for computer memory, and speeds the inversion calculation. Two different calculation examples show that this approach is very efficacious for solving large scale 3‐D resistivity inversion.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.