Prestack seismic inversion for VTI media (transversely isotropic with vertical axis of symmetry) is a technique that can be useful to obtain the properties (velocity, density, and anisotropy parameters) of shale reservoirs. Since conventional inversion with smooth constraints (e.g.,$L_{2}$-norm) is not appropriate, we propose a basis pursuit inversion (BPI) extended to VTI media, where: 1) we decompose the five elasticities into basis pursuit pairs by a dipole decomposition; 2) instead of the commonly used$L_{1}$-norm, the$L_{1}$–$L_{2}$is implemented as a regularization constraint to achieve higher resolution and stability; and 3) alternating direction method of multipliers (ADMM) is used to obtain the solutions. Since the problem is highly ill-posed, we perform the inversion using PP and PS multicomponent seismic data. The examples (synthetic and real data) verify the higher resolution and better antinoise performance of the proposed method.

Seismic exploration of unconventional hydrocarbon reservoirs (e.g., shale rocks) must take into account the transverse isotropy with a vertical axis of symmetry (VTI) characteristics. Prestack inversion for VTI media is more complex than the isotropic case, since the forward engine is highly nonlinear and more unknowns (five instead of three) are involved, which aggravate the ill-posedness of the inverse problem. Here, we propose a hierarchical inversion scheme to improve the estimation of the five parameters, where the exact reflection coefficient is used as forward engine (instead of the commonly-used approximations which lack accuracy). To handle the highly nonlinear inverse problem, we perform the prestack anisotropic inversion in two steps, namely, a preliminary linear result is used to reduce the search window and to formulate the constrain term and initial models of the subsequent nonlinear step. Specifically, for a reasonable preliminary estimation, we introduce a data-driven model building algorithm to provide reliable initial models, and employ the limited-memory Broyden–Fletcher–Goldfarb–Shanno combined with the momentum technique (LBFGS-MT) optimization to increase the convergence speed. We derive the Fréchet derivatives of the exact forward operator with respect to the parameters, i.e., the key factors of the linear part. Besides, we introduce a hybrid global optimization, the particle swarm optimization aided by very fast simulated annealing (PSO-VFSA) to enhance the accuracy and computational efficiency of the nonlinear stage. Synthetic tests demonstrate the effectiveness and accuracy of the proposed scheme. The field application shows that the method is capable to obtain reliable elastic information of shale reservoirs.

Estimation of subsurface properties by using the scattering integral equation is a method that finds increasing use in near-surface and shallow oil/gas exploration, based on seismic, low-frequency electromagnetic, and surface-radar surveys. The method can accurately simulate physical realizations induced by small-scale perturbations, but its accuracy depends on a suitable low-frequency property model. We propose a 3-D geological-structure-guided model building to provide a reliable low-frequency model and combine it with the Born–Wentzel–Kramers–Brillouin–Jeffreys (WKBJ)-approximation-based inversion algorithm. Instead of the traditional approach based on artificially interpreted horizons, we use 3-D seismic-slope attributes as lateral constraints, which contain more geological information. Plane-wave destruction (PWD) in 3-D is exploited to extract the 2-D slopes along the inline and crossline directions, which are the key factors in computing 3-D slopes. Then, by introducing the shaping regularization, we build low-frequency models by solving the inverse problem. Numerical analysis indicates that an appropriate background model is essential for seismic modeling with the Born–WKBJ approximation. The methodology is applied to synthetic and 3-D field data, and the examples show that it provides reliable background models and improves the inversion performance.

In wave propagation in rocks, the strain field affects the internal energy such that compressed regions become hotter and expanded regions cooler. This thermoelastic effect is that the lack of thermal equilibrium between various parts of the vibrating medium and energy is dissipated when irreversible heat flow driven by the temperature gradient occurs. Moreover, rocks are generally partially saturated and the interfacial tension between fluids affects the acoustic properties and induces additional slow P waves. To model these phenomena, we develop a generalized porothermoelasticity theory, including the Lord–Shulman (LS) and Green–Lindsay (GL) theories, for wave propagation in partially saturated nonisothermal media. The dynamical equations have as solutions the classical P1 and S waves and three slow waves modes, namely, the slow P2, slow P3, and the thermal (T) waves, which present diffusive behavior depending on the viscosity, frequency, and thermal properties. We compute the wavefields with a direct meshing algorithm by using an optimized finite-difference (FD) method to obtain the spatial derivatives and a first-order explicit Crank–Nicolson method for temporal extrapolation. The simulated snapshots and waveforms for the homogeneous and heterogeneous models with two different sets of thermal properties illustrate the characteristics of propagation as a function of frequency and saturation, which are consistent with the plane-wave analyses. The GL model can predict a higher thermal attenuation of the P1 wave and, consequently, a larger velocity dispersion than the LS theory. The thermal relaxation peak moves to low frequencies as the conductivity increases. This study is relevant to understand wave propagation in porous rocks and high temperature and pressure fields.

Regularization is effective in mitigating the ill-condition existing in inverse problems. With respect to the ill-conditioned prestack seismic inversion, regularization aims to stabilize the multiple inverted results and, essentially, reconstruct structural features of subsurface parameter (model) as realistic as possible. Among variants of regularization method, Markov random field (MRF) is an effective approach in formulating prior constraint. However, standard MRF-based or other methods often require prior knowledge of the structural features of desired models, e.g., smoothness, blockiness, and sparsity, after which the prior constraint is formulated. Therefore, such a model-driven regularization method lacks applicability to the cases with geological complexity or limited prior knowledge. In this article, we propose a data-driven regularization scheme for prestack seismic inversion. The MRF-based constraints formulated by multiple orders are quantitatively integrated into the inversion procedure driven by seismic data. In order to endow the method with high adaptation to geological complexity, we iteratively adjust the regularization parameters of multiple orders via the maximum likelihood estimator. Besides, we incorporate the multivariate Gaussian distribution among elastic parameters into the model update/perturbation in fast simulated annealing, by which the objective function is optimized while the multiple results are correlated and stabilized. Synthetic tests indicate that the proposed method is capable of revealing structural details and achieving multiple results with less uncertainty. Field application provides further validation, wherein the results distinctly reveal structural details within the target formation.

For seismically thin-reservoir layers, variations in rock properties may not be directly linked to seismic amplitude due to the wave interference of layer top and base reflections. In addition, thin-layer reflection signal locally has a different phase from that of the signal wavelet. Signal even and odd components can be considered as amplitudes at different signal phases, which may have a different sensitivity to the variations in thin layer and surrounding layer properties. A novel extension of the spectral decomposition concept is proposed that decomposes seismic signal into its even and odd components via the short-time Fourier transform. Amplitude attributes for the original signal and even and odd part components are compared for their ability to restore the correct “amplitude-layer property” correlation without resolving the thin layer. Numerical modeling analysis shows that amplitude at peak frequency (APF) of the seismic data odd component APF (OAPF) is more sensitive to thin-reservoir property change compared to the conventional APF and even component APF attributes. When applied in analyzing real seismic data in a tight-dolomite reservoir, conventional APF and conventional acoustic impedance inversion did not provide a correct relationship to porosity variations. Meanwhile, the OAPF attribute responds well to porosity measured in boreholes. This suggests that the interpretability of amplitude attributes in thin layers can be improved by signal even and odd decomposition.