Stress-induced progressive deformations in fractured rocks with increasing effective pressure generally undergo nonlinear elastic (due to the closure of compliant pores), hyperelastic (due to residual stress), and inelastic (due to fracture growth) deformations prior to mechanical failure. Wave propagation in such rocks involves the complex interaction of fracture-and stress-induced changes in both velocity and anisotropy. With attention to nonlinear elastic and hyperelastic deformations, we incorporate acoustoelasticity into the traditional Hudson/Cheng models to describe the coupling of fracture-induced and stress-induced anisotropies. The resulting acoustoelastic Hudson model (AHM) is valid for the crack density smaller than 0.1 whereas the Padé AHM could handle higher crack densities. We extend the Padé AHM to consider the stress-induced crack closure with nonlinear elastic deformations by incorporating the dual-porosity model. These models approach the coupled anisotropies with different accuracies and computational complexities. The plane-wave analyses and effective-moduli calculations of stressed fractured rocks with varying crack densities determine the accuracy of these models under the isotropic (confining) and anisotropic (uniaxial and pure shear) prestress conditions. The relevant Thomsen parameters are applied to experimental data to validate the applicability. Finite-difference simulations are implemented to identify the contribution of different anisotropies through the variety of wavefronts, depending on fracture orientation, crack density, prestress mode and magnitude, and loading direction. Particular attention is paid to the anisotropic prestress, where the coupled anisotropies are constructive or destructive interference, strongly related to the relativity between fracture strike and loading direction. The stress-induced crack closure will reduce the fracture anisotropy so that the stress-induced background anisotropy dominates the shape of wavefronts with increasing prestress.

In this paper, we extend the velocity-stress acoustoporoelastic formulation from 2D to 3D, and Padé acoustoelasticity to Padé acoustoporoelasticity. Applications to experimental data with porous rocks differentiate the acoustoelasticity, acoustoporoelasticity, and Padé acoustoporoelasticity in accuracy. The SSG-FD numerical method was used to simulate the propagation of elastic waves in both 3D acoustoporoelastic and Padé acoustoporoelastic media. By comparing the theoretical and calculated wave velocities, the presented numerical scheme is verified using plane-wave theoretical solutions.Â

Seismic AVO has a significant potential for fluid identification in time-lapse monitoring of the cyclic recovery of geothermal reservoirs. With this goal, we develop an AVO method based on the reflection and transmission (R/T) of elastic waves at an interface between two fluid-saturated thermo-poroelastic media. The method is applied to the Olkaria geothermal reservoirs in Kenya. This system is characteristic of a natural cyclic recovery, where cyclic meteoric water undergoes complex phase transition and thermo-hydro-mechanical coupling process. Conceptual models are built based on petrophysical and thermophysical properties of trachyte thermal reservoirs in the eastern field, with an attempt to model the shallow steam and deep boiling water zones. A plane-wave analysis illustrates the effects of thermal conductivity, specific heat, and porosity on velocity dispersion and attenuation of the fast-P, Biot slow-P, and thermal slow-P waves. AVO modeling by P-wave incidence is conducted to investigate the effects of temperature, porosity, specific heat, and fluid type on the R/T coefficients. For trachyte reservoirs with a temperature less than 400°C, limited changes in the thermophysical properties (e.g., thermal conductivity and specific heat) have negligible effects on wave propagation, whereas significant effects are due to temperature, porosity, and fluid type. Particularly, comparisons of cyclic recovery using water, supercritical CO2, and gas (dry case) as the heat transfer fluid, demonstrate that the crossplot of fluid factors and intercept gradient (PG) can be used as a precursor to hydrofracturing-induced permeability, fluid leakage or short circuits.

Temperature is an important factor for evaluating the seismic response of deep reservoirs. We develop an amplitude variation with offset (AVO) approximation based on the Lord-Shulman (LS) thermoelasticity theory. The model predicts two compressional (P and T) waves (the second is a thermal mode) and a shear (S) wave. The T mode is due to the coupling between the elastic and heat equations. In the thermoelastic case, the approximation is more accurate than in the elastic case. Its accuracy is veried by comparison with the exact equations calculated in terms of potential functions. We examine two reservoir models with high temperatures and compute synthetic seismograms that illustrate the reliability of the approximation. Moreover, we consider real data to build a model, and show that the approximate equation not only simplies the calculations, but is accurate enough and can be used to evaluate the temperature-dependent elastic properties, providing a basis for further application of the thermoelasticity theory, such as geothermal exploration, thermal enhanced oil recovery, and ultra-deep oil and gas resources subject to high temperatures. Temperature is an important factor for evaluating the seismic response of deep reservoirs. We develop an amplitude variation with offset (AVO) approximation based on the Lord-Shulman (LS) thermoelasticity theory. The model predicts two compressional (P and T) waves (the second is a thermal mode) and a shear (S) wave. The T mode is due to the coupling between the elastic and heat equations. In the thermoelastic case, the approximation is more accurate than in the elastic case. Its accuracy is veried by comparison with the exact equations calculated in terms of potential functions. We examine two reservoir models with high temperatures and compute synthetic seismograms that illustrate the reliability of the approximation. Moreover, we consider real data to build a model, and show that the approximate equation not only simplies the calculations, but is accurate enough and can be used to evaluate the temperature-dependent elastic properties, providing a basis for further application of the thermoelasticity theory, such as geothermal exploration, thermal enhanced oil recovery, and ultra-deep oil and gas resources subject to high temperatures.

How to represent spatiotemporal information in an artificial neuron model has been a problem of longstanding interest in artificial intelligence. After a brief review of recent advances, Caianiello's neuronic convolutional model is extended in this paper for spatiotemporal information representation. The kernel functions that correspond to the convolutional neuron's receptive field profile can be described by neural wavelets. The convolutional neuron-based multilayer network and its back propagation algorithm are developed to perform spatiotemporal pattern processing. The results provide a natural framework for the discussion of spatiotemporal information representation in an artificial neural network

Natural rocks belong to the polymineral composite material with complex microstructures. Such a strong heterogeneity of rocks makes it difficult to estimate the effective moduli by traditional models in theory. In the present study, a Mori-Tanaka (MT) model considering the shape and orientation of inclusion minerals obtained by the micro-CT is established, and then it is applied to evaluate the anisotropic parameters of shales. In the MT model, the principal radii and Eulerian angles of the ellipsoidal inclusion are obtained by solving its inertia matrix through the micro-CT. According to these inclusion information, we make statistics on the ratio of average principal radii and the distribution of Eulerian angles of inclusions with different minerals. In what follows, the effective elastic stiffness matrix of shale samples is predicted by the MT model, and the corresponding digital core is input for finite element method (FEM) analysis to verify the accuracy of the theoretical results. It is shown that the anisotropy of the elastic stiffness matrix predicted by the MT model and FEM is consistent under two sizes of representative volume elements. These findings are potential for applications in rock mechanics, civil engineering and oil exploitation, etc.