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Pore pressure prediction is critical for shale gas reservoir characterization and simulation. The Wufeng–Longmaxi shale, in the southeastern margin of the Sichuan Basin, is identified as a complex reservoir affected by overpressure generation mechanisms and variability in lithification. Thus, standard methods need to be adapted to consistently evaluate pore pressure in this basin. Based on wireline logs, formation pressure tests, and geological data, this study applied the Eaton–Yale approach, which extends the theoretical basis of Eaton and Bowers methods to reservoir geological conditions and basin history. The method was developed by integrating petrophysical properties, rock physics interpretations, and geology information. The essential steps include (1) a multi-mineral analysis to determine mineral and fluid volumes; (2) a determination of the normal pressure trend line and extending it to overpressured sections; (3) predicting pore pressure using the basic Eaton approach and identifying overpressured zones; (4) correcting compressional velocity using lithology logs and a rock physics model; (5) determining the Biot Alpha coefficient and vertical-effective stress and estimating the new pore pressure values using the Eaton–Yale method. Overpressure zones were corrected, and reservoir pore pressure varied between 30.354 and 34.959 MPa in the wells. These research results can provide a basis for building reservoir simulation models, identifying reservoir boundaries, and predicting relative permeability.

Tectonically deformed coal (TDC) is closely related to gas outbursts. Since TDC exploration is an essential objective for coalfield exploration, it is of great significance to study the petrophysical properties of TDCs and explore their differences. This study collected 17 TDCs and undeformed coal samples from the Huaibei coalfield and ultrasonically tested their petrophysical parameters, including densities, P- and S-wave velocities, and their derived petrophysical parameters (VP/VS ratio, P- and S-wave impedances). Undeformed coal and TDCs with different deformation types (brittle, shear, and plastic deformations) show significant differences in their petrophysical parameters, and cross-plot analysis can directly differentiate them. As with traditional geological methods, acoustically measured petrophysical parameters are good indicators to determine the type of coal deformation. However, the TDCs with the same deformation type have similar petrophysical parameters; it is not easy to distinguish them directly. Instead, the proposed method incorporating principal component analysis and clustering can accurately distinguish up to five classes of TDCs. Different types of tectonic deformation environments and their intensities are highly correlated with the clustering results. This paper also provides essential petrophysical parameters for undeformed coal and TDCs in the Huaibei coalfield, and these parameters can help interpret undeformed coal and TDCs using wireline logs and seismic data.

Although Mercury Intrusion Porosimetry (MIP) and Nuclear Magnetic Resonance (NMR) are widely used for pore characterization, their effectiveness is fundamentally constrained by theoretical limitations. This study investigated the pore structure characteristics of coal-bearing sandstones from the northeastern Ordos Basin using an integrated approach combining experimental measurements and model-based inversion. The experimental measurements comprised a stress-dependent acoustic velocity test (P- and S-wave velocities), X-ray diffraction (XRD) mineralogical analysis, and NMR relaxation T2 spectra characterization. For model-based inversion, we developed an improved Mori-Tanaka (M-T) theoretical framework incorporating stress-sensitive pore geometry parameters and dual-porosity (stiff/soft) microstructure representation. Systematic analysis revealed four key findings: (1) excellent agreement between model-inverted and NMR-derived total porosity, with a maximum absolute error of 1.09%; (2) strong correlation between soft porosity and the third peak of T2 relaxation spectra; (3) stiff porosity governed by brittle mineral content (quartz and calcite), while soft porosity showing significant correlation with clay mineral abundance and Poisson’s ratio; and (4) markedly lower elastic moduli (28.78%–51.85%) in Zhiluo Formation sandstone compared to Yan’an Formation equivalents, resulting from differential diagenetic alteration despite comparable depositional settings. The proposed methodology advances conventional NMR analysis by simultaneously quantifying both pore geometry parameters (e.g., aspect ratios) and the stiff-to-soft pore distribution spectra. This established framework provides a robust characterization of the pore architecture in Jurassic sandstones, yielding deeper insights into sandstone pore evolution within the Ordos Basin. These findings provide actionable insights for water hazard mitigation and geological CO2 storage practices.

Thickness of tectonically deformed coal (TDC) has positive correlations with the susceptible gas outbursts in coal mines. To predict the TDC thickness of the coalbed, we proposed a prediction method using seismic attributes based on the deep belief network (DBN) and dimensionality reduction. Firstly, we built a DBN prediction model using the extracted attributes from a synthetic seismic section. Next, we transformed the possibly correlated seismic attributes into principal components through principal components analysis. Then, we compared the true TDC thickness with the predicted TDC thicknesses to evaluate the prediction accuracy of different models, i.e., a DBN model, a support vector machine model, and an extreme learning machine model. Finally, we used the DBN model to predict the TDC thickness of coalbed No. 8 in an operational coal mine based on synthetic experiments. Our studies showed that the predicted distribution of TDC thickness followed the regional characteristics of TDC development well and was positively correlated with the burial depth, coalbed thickness, and tectonic development. In summary, the proposed DBN model provided a reliable method for predicting TDC thickness and reducing gas outbursts in coal mine operations.

We investigated the frequency dependence of Poisson’s ratio ν in partially/fully fluid-saturated rocks. Based on one dominant fluid flow mechanism at each condition, we theoretically summarized that (1) when a rock is partially saturated or transits from drained state to undrained state at full saturation, ν increases monotonously with frequency, and the associated attenuation 1/Qν is positive with one peak. (2) When the rock transits from undrained state to unrelaxed state at full saturation, there are three cases: 1) ν increases monotonously with frequency and has positive 1/Qν with one peak, 2) ν keeps constant with frequency and has no attenuation, 3) and ν decreases monotonously with frequency and has negative 1/Qν with one peak. In this condition, the dependence is influenced by the concentrations of stiff and soft pores, the aspect ratio of soft pores, and the pore fluid bulk modulus. (3) When it comes to the transition from drained state to unrelaxed state at full saturation, ν can exhibit two shapes with frequency: 1) step shape with two positive attenuation peaks and 2) bell shape with one positive attenuation peak and one negative attenuation peak. Then, we conducted a numerical example to indicate the effect of influence factors (the concentrations of stiff and soft pores, the aspect ratio of soft pores, and the pore fluid bulk modulus) on Poisson’s ratio from undrained state to unrelaxed state, and validated the theoretical analysis by the published experimental data. In addition, based on 1/Qν, we reanalyzed and validated the relationship between different attenuation modes (i.e., bulk attenuation 1/QK, P-wave attenuation 1/QP, extensional attenuation 1/QE, and S-wave attenuation 1/QS): (1) when 1/Qν is positive, the relationship between them is 1/QK>1/QP>1/QE>1/QS; when 1/Qν is 0, the relationship between them is 1/QK=1/QP=1/QE=1/QS; and when 1/Qν is negative, the relationship between them is 1/QK<1/QP<1/QE<1/QS. The relationship between different attenuation modes does not depend on saturation state (partial or full saturation) or ν but on 1/Qν. This research provides the frequency dependence of Poisson’s ratio in partially/fully saturated rocks, which helps better understand Poisson’s ratio at different frequencies and saturation states and can be used to improve the accuracy of geophysical data interpretation, such as lithology identification, hydrocarbon characterization in conventional reservoir, and brittleness evaluation of shale/tight sandstones in unconventional reservoir.

Wireline logging plays a critical role in coalbed methane exploration. However, the lack of crucial log data, such as neutron and sonic logs, makes coalbed methane exploration difficult. In this paper, we propose a principal component regression model incorporating a multiscale wavelet analysis, a histogram calibration, a principal component analysis, and a multivariate regression to reconstruct essential neutron and sonic logs from conventional logs (i.e., density, resistivity, gamma ray, spontaneous potential, and caliper logs). Our proposed model does not need core-related correlation, and there is no local optimization. We have applied the model to evaluate coalbed methane content in a real case. Firstly, we use the multiscale wavelet analysis and histogram calibration to improve logs’ reliability and lateral comparability. Then, we apply principal component analysis to transform the well-correlated wireline logs into linearly independent components and regress reconstruction functions for neutron and sonic logs with multivariate regression. The reconstructed logs are like the measured logs in trend, mean, and scale. Finally, we apply the reconstructed neutron logs to predict the coalbed methane-content distribution. The predicted distribution is not only following the regional distribution characteristics of coalbed methane enrichment zones but also validated by the coalbed methane production data. In summary, the successful applications of wireline-log reconstruction and regional coalbed methane-content prediction have demonstrated the reliability of the proposed principal component regression model.

Coal-hosted gallium-rich ores are mainly explored with geochemical analyses, and their elasticities lack research. This paper incorporated core testing, rock-physics modeling, and Monte Carlo simulations to characterize the elastic parameters of gallium-rich cores and discuss whether coal-hosted gallium-rich ores are elastically detectable. The measured cores from No. 6 coal in the Heidaigou mine showed that the gallium contents strongly correlate to the boehmite contents with a 0.96 correlation coefficient. The rock-physics modeling results showed that mineral compositions and contents are critical factors influencing elastic parameters, and elastic parameters in No. 6 coal showed profound heterogeneities as mineral compositions and contents. The preferred parameters for classifying and grouping different mineral-rich cores are the bulk modulus and moduli ratio. Cross-plotting bulk modulus vs. moduli ratio can qualitatively group measured cores and Monte-Carlo simulated realizations into different mineral-rich and saturation states properly. Concerning the factors of boehmite content, porosity, and saturation state, an interpretation template for boehmite-rich coal was proposed and used. As the template interpreted readings close to the measured contents, the built templates can quantitatively interpret boehmite and gallium contents in coal-hosted ores with high precision. In summary, the coal-hosted gallium-rich ores are elastically detectable.

The absorption (anelastic attenuation) and anisotropy properties of subsurface media jointly affect the seismic wave propagation and the quality of migration imaging. Anisotropic viscoelastic model can effectively describe seismic velocity and attenuation anisotropy effects. To reduce the computational cost and complexity of elastic wave modes decoupling for seismic imaging in anisotropic attenuating media, we have developed a pure-viscoacoustic transversely isotropic (TI) wave equation starting from the complex-valued velocity dispersion relation of quasi-compressional (qP) wave. The wave equation involving fractional Laplacians has advantages of being able to describe the constant-Q (frequency-independent quality factor) attenuation, arbitrary TI velocity and attenuation, decoupled amplitude loss and velocity dispersion effects. Numerical analyses showed that the simplified equation can accurately hold the velocity and attenuation anisotropy of qP-wave in viscoelastic anisotropic media in the range of moderate anisotropy. Compared to previous pseudo-viscoacoustic equations, the pure-viscoacoustic equation can be completely free from undesirable S-wave artifacts and behaves good numerical stability in tilted transversely isotropic (TTI) attenuating media. There are obvious wavefield differences between isotropic attenuation and anisotropic attenuation cases especially in the direction perpendicular to the axis of symmetry. Furthermore, to mitigate the influences of velocity and attenuation anisotropy on migrated seismic images, we have developed an anisotropic attenuation (Q) compensated reverse time migration (AQ-RTM) approach based on the new propagator. The compensation can be implemented by reversing the sign of the dissipation terms and keeping the dispersion terms unchanged during wavefields extrapolation. Synthetic example from a Graben model illustrated that the anisotropic Q-compensated RTM scheme can produce images with more balanced amplitude and accurate position of reflecters compared with conventional RTM methods under assumptions of acoustic anisotropic (uncompensated) and isotropic attenuating media. Results from a Marmousi-II model demonstrated that the new methodology is applicable for complicated geological model to significantly improve imaging resolution of the target area and deep layers.

This paper presents the zonal geochemistry and elasticity characteristics of gallium- and lithium-rich No. 6 coalbed in the Haerwusu mine and discusses interpretation methodologies of coal-hosted gallium and lithium resources using lab-measured samples and field-measured wireline logs. The results demonstrate that both coal-composition-based and elastic-parameter-based classifications yield similar results, categorizing the coalbed into subzones related to coal quality. Material compositions, elastic properties, critical metals, and host minerals exhibit zonal distribution characteristics within the ultrathick No. 6 coalbed. Three-class classifications significantly enhance correlations among host minerals, elastic parameters, and critical metals, albeit with differing trends among classes. In classes II and III (ultralow- and low-ash-yield coals), boehmite and kaolinite primarily host gallium and lithium, respectively. In class I (medium-ash-yield coal), gallium is associated with kaolinite, while lithium lacks specific mineral associations. Constrained by wireline logs, a rock physics modeling strategy is proposed to link mesoscale coal compositions to macroscale elastic responses. Moreover, explicit correlations between host minerals and critical metals are established, connecting macroscale elastic responses to microscale gallium and lithium enrichments and exploring interpretation methods of coal-hosted critical metals. Preferred lithium interpretation methods include compositional ternary plots and elastic parameter cross plots, while preferred gallium interpretation methods involve boehmite-gallium and elastic parameter-gallium fitting. These findings may contribute to understanding the enrichment mechanisms and interpretation technologies of coal-hosted critical metals in ultrathick low-rank coalbeds.

The acoustic behavior in fluid attenuating media can be effectively simulated using a fractional Zener model (FZM). Because of the fractional time derivatives of both stress and strain in the constitutive relationship, this mechanism is very realistic and flexible in describing seismic attenuation. However, using conventional FZM wave equations to propagate seismic waves requires storing large amounts of previous wavefield information to calculate the fractional time derivatives, which is unacceptable in practice. In this paper, we derive a new time-domain viscoacoustic wave equation in the framework of the FZM. This new equation does not contain any fractional time derivatives; thus, it is more economical in computational costs. Furthermore, the amplitude attenuation and phase dispersion effects are separated in the newly proposed equation, which is very favorable to compensate for energy loss and correct phase dispersion in reverse-time migration. To improve the accuracy, we incorporate a wave number (k)-space operator into the decoupled FZM wave equation to compensate for temporal dispersion errors caused by the second-order finite-difference discretization. Therefore, a high-temporal-accuracy viscoacoustic wave equation is derived to simulate nearly constant-Q wavefields in attenuating media. In the implementation, a low-rank decomposition method is introduced to solve the mixed-domain operators. Numerical analysis and modeling results demonstrate the effectiveness and applicability of the proposed method for simulating the decoupled viscoacoustic wavefield with high accuracy.