Abstract Electrofacies analysis is a key component of reservoir characterization because it links well-log responses to lithological and petrophysical properties; however its effectiveness is often limited by an overreliance on macroscopic logging signals. In heterogeneous reservoirs, microscopic pore structures exert a decisive influence on fluid storage and flow, and overlooking this control can lead to ambiguous or geologically inconsistent facies classifications. To overcome this limitation, this study integrates nuclear magnetic resonance while drilling (NMR-WD) T2 spectrum features with conventional logging data, allowing pore architecture to be quantified and incorporated directly into electrofacies analysis. Multidimensional pore-structure parameters are first extracted from the T2 spectrum and subsequently reduced through principal component analysis (PCA) to retain the dominant microstructural information while minimizing redundancy. Clustering is then carried out using an improved K-means++ algorithm, which enhances stability and reduces sensitivity to initial conditions, a common issue in unsupervised classification. The resulting electrofacies are validated through correlation with core-derived lithological data, ensuring geological consistency, and Fisher discriminant analysis is further applied to establish a predictive model for uncored intervals. The results indicate that the inclusion of NMR-WD-derived microstructural parameters significantly improves electrofacies discrimination, particularly in reservoirs where lithological differences are subtle but pore-scale heterogeneity is pronounced. Overall, this pore-aware framework advances traditional electrofacies analysis by bridging macroscale logging responses and microscale reservoir characteristics, providing a reliable and transferable tool for evaluating complex reservoirs and supporting informed exploration and development decisions.
Abstract The accurate prediction for in-situ stress or pressure is highly relevant to many practical applications in hydrocarbon exploration and development such as safe production, geofluid discrimination and tectonic characterisation. The stress prediction using seismic data is currently based on the empirical (or fitting) relationship between effective stress and several estimated elastic attributes of formations, such as P-wave velocity and bulk modulus. The empirical approaches dominantly rely on the well-logging data constraints and cannot reveal the theoretical relationship between effective stress and seismic signatures. Thus, they may generate unexpected misleading interpretations in the frontier areas without sufficient prior well-logging data and in some fields with strong lateral formation discontinuity. To address this problem theoretically, we derive a PP-wave reflection coefficient equation in terms of the defined decoupled bulk and shear moduli, fluid factor, density and effective stress based on the elastic piezosensitivity model, Mavko-Jizba modified moduli model and Gassmann fluid substitution model. The new reflection coefficient equation is consistent with the exact Zoeppritz equation within the moderate incident angles. Further, a seismic amplitude-variation-with-offset (AVO) inversion method incorporating our reflection coefficient equation is developed to predict effective stress using an iterative least-squares algorithm. Two synthetic tests and a field application confirm the feasibility and robustness of the proposed method for stress prediction.
Abstract Accurate imaging of steeply dipping structures is critical for hydrocarbon reservoir identification and fault characterization in complex regions. However, conventional imaging methods based on primary reflections often fail to resolve near-vertical and overturned interfaces due to limited acquisition aperture and survey geometry. To address this limitation, we propose a dip-guided amplitude-matched fusion Fourier finite-difference (FFD) migration method for prismatic waves (PFFD). The method exploits prismatic waves, which can be observed in seismic data acquired over complex structures, especially near steep or near-vertical interfaces, and can provide complementary information for imaging steep structures. The method uses conventional migration results as the reflectivity model and constructs prismatic-wave propagation paths using an FFD operator. The flexible extrapolation range reduces computational cost. In addition, accurate separation of upgoing and downgoing wavefields suppresses non-target propagation paths. To mitigate imaging artifacts and amplitude distortion, we employ omnidirectional plane-wave destruction (OPWD) to extract dip attributes. These attributes, combined with prior spatial constraints, then guide region selection and main-lobe root-mean-square (RMS) amplitude matching for image fusion. Numerical results demonstrate that the proposed method significantly improves steep-structure imaging. It compensates for the limitations of one-way wave-equation migration (OWEM) at large dips and outperforms prismatic-wave reverse time migration (PRTM) in poorly illuminated steep-dip regions.
Abstract Accurate 3D seismic multi-horizon reconstruction is pivotal for structural interpretation and reservoir characterization. Existing deep learning methods predominantly rely on convolutional neural networks (CNNs) to predict relative geological time (RGT) volumes from seismic data. However, CNN-based approaches typically face challenges in capturing long-range stratigraphic relationships and often struggle to accurately resolve complex geological structures, such as faults, especially when labeled data are sparse. To address these challenges, we propose a dual-branch deep neural network (DB-Net) that synergistically integrates CNN and transformer architectures for geologically constrained RGT reconstruction. The CNN branch extracts local spatial features through hierarchical 3D convolutions, while the transformer branch models global stratigraphic dependencies via multi-head self-attention mechanisms. A spatially adaptive gated fusion module is designed to dynamically combine complementary features from both branches based on local geological complexity. Unlike purely data-driven methods, our approach incorporates explicit geological knowledge through a multi-component loss function that enforces horizon continuity in conformable regions while preserving discontinuities at fault boundaries. Sparse horizon labels and fault attributes are utilized as structural priors to guide network training. Furthermore, an auxiliary feature-level domain adaptation module mitigates the distribution gap between synthetic training data and field seismic volumes, facilitating effective knowledge transfer despite limited field annotations. Extensive experiments on both synthetic and field datasets demonstrate that DB-Net delivers state-of-the-art reconstruction accuracy, significantly improving performance in geologically complex regions.
Abstract Accurate identification of concealed geohazards around tunnel advance boreholes is crucial for refined geological prediction and risk control in tunnel construction. This study proposes an acoustic imaging method based on tunnel borehole acoustic detection to detect small anomalies around the borehole, including fractures, cavities, and fractured zones containing water. The method establishes a delay stacking imaging framework driven by traveltime calculation, in which statistical outlier removal and semblance coherence weighting are integrated to suppress incoherent noise, reduce artifacts, and enhance weak reflected signals. Numerical simulations demonstrate that the proposed method produces clearer focusing and more reliable anomaly localization than conventional diffraction stacking. Despite the inherent azimuthal ambiguity of dipole imaging based on a single borehole, the method can effectively determine the axial depth and radial distance of anomalous zones, thereby providing useful constraints for targeted drilling verification. Field application in a deeply buried tunnel shows good agreement between the imaged anomalous zones and subsequent drilling results, which revealed fractured and water rich rock masses. These results indicate that the proposed tunnel borehole acoustic detection method provides a practical high resolution tool for refined advance prediction and risk control in tunnel construction.
Abstract Predicting seismic wave velocities in fractured rocks is of great significance in geophysical exploration. However, most existing velocity models for fractured rocks have overlooked the potential contact area within fractures, as in models for penny-shaped fractures. To address this limitation, we develop a velocity model for rocks containing randomly distributed and aligned annular fractures, starting from the compliance of a single annular fracture. The impact of different fracture parameters on the velocity and anisotropy of fractured rocks is analyzed. It is found that both the inner and outer radii of the fracture exert pronounced effects on elastic wave velocities and anisotropy, for both dry and fluid-saturated rocks. In contrast, fracture thickness only influences these properties in fluid-saturated rocks. For such fluid-saturated cases, changes in the fluid bulk modulus also produce notable variations in elastic wave velocities and anisotropy. To verify the proposed model, theoretical predictions are compared against experimental measurements of P- and S-wave velocities from a Harvey sandstone under varying confining pressures. The pressure dependence of elastic wave velocities of fractured rocks is interpreted as the pressure dependence of contact area (represented by the ratio of the inner to the outer radii of annular fractures). The theoretical predictions agree well with experimental data, and the inferred contact areas are physically reasonable. The proposed model offers a more realistic representation of natural fractures, rendering it highly promising for application in the seismic characterization of fractured reservoirs.
Abstract Accurate prediction of coal seam thickness is a critical factor for enabling intelligent and efficient mining. To improve seismic-attribute-based coal seam thickness prediction under high-dimensional, redundant, and nonlinear conditions, this study develops a task-oriented Lasso-XGBoost-SVR hybrid framework. The proposed framework combines least absolute shrinkage and selection operator (Lasso) regression, extreme gradient boosting (XGBoost), and support vector regression (SVR). By integrating the complementary strengths of these three methods, the model identifies the key attributes controlling coal seam thickness. It also enables joint screening and coordinated fusion of heterogeneous data, reducing feature information loss introduced during sampling. This approach improves the accuracy of feature fusion and enhances predictive performance. On the independent test set, the proposed Lasso-XGBoost-SVR framework achieved a root mean square error (RMSE) of 0.0178, a mean absolute error (MAE) of 0.0105, and a coefficient of determination (R2) of 0.9732, demonstrating lower prediction errors and a better fit than the comparison models. Under the same data partition and evaluation protocol, the ablation study further showed that the integrated model consistently outperformed the Lasso-SVR and XGBoost-SVR variants across all three evaluation metrics. The model is also validated in a real mining area, where the predicted coal seam thickness closely matches geological observations. These results indicate that the Lasso-XGBoost hybrid approach is highly effective for optimizing seismic attributes in predicting coal seam thickness. This fusion strategy not only enhances predictive accuracy but also exhibits strong potential for practical implementation within mining panels, serving as a reliable tool for decision-making in operational mining scenarios.
Abstract The Paraná Basin in Brazil contains enormous reserves of unconventional shale oil and gas. However, the rock physical research on these shales remains relatively scarce, constraining the comprehensive understanding of intrinsic elastic properties. We investigated the elastic and anisotropic properties of shale from the Paraná Basin by combining laboratory measurements and rock physical modeling. We collected four shale samples from Irati Formation and measured the P- (Vp) and S-wave (Vs) velocities in different directions under changing pressure conditions. The velocities were quantitatively compared and analyzed to reveal the influence of kerogen fraction, crack, and pressure. Afterwards, we performed rock physics modeling to investigate the elastic moduli theoretically. The results showed that the velocities increase with pressure, which could be up to 50% for pressure rising from 500 to 2500 psi, while Vp/Vs ratio shows 8% decrease. Under dry conditions, the Vp ranges from 1.5 to 3.75 km/s and Vs ranges from 0.8 to 2.0 km/s, while fluid saturation modifies these bounds to a Vp interval of 2.4–3.8 km/s and Vs interval of 1.2–1.8 km/s. Besides, the kerogen content and cracks have negative influence on velocities. The modeling results with pore aspect ratios of 0.006 and 0.008 exhibited well agreement with the measurements. Overall, this study provides a quantitative rock physical characterization of the Irati shales, highlighting the effects of pressure, kerogen content, and cracks on the elastic properties of the samples, which can facilitate better understanding of the elastic and anisotropic properties of Irati shales.
Full-waveform inversion (FWI) provides high-resolution subsurface characterization but remains vulnerable to ill-posedness, cycle skipping, and local minima when the starting model is inaccurate or low-frequency information is missing. We introduce a physics-informed reparameterized FWI framework that leverages a hybrid architecture combining convolutional neural network (CNN) and a vision transformer (ViT) enhanced with spatial-reduction attention, which reduces the computational cost while preserving global dependencies, to enhance robustness under challenging acquisition conditions. In the proposed scheme, the CNN extracts multi-shot local seismic attributes, whereas the ViT models long-range correlations and enforces structural coherence. The untrained nature of the hybrid network acts as an implicit regularization, enabling smooth and geologically plausible model updates while reducing the non-uniqueness of the inversion. Numerical tests on representative synthetic models demonstrate that the method reliably reconstructs velocity structures from low-quality initial models and outperforms conventional FWI and CNN-based FWI approaches, particularly under noise contamination and low-frequency-deficient data. The field data example further demonstrates that the recovered velocity models lead to improved seismic imaging quality and provide a more reliable foundation for subsequent imaging workflows.
Abstract Short-offset transient electromagnetic (SOTEM) surveys with grounded sources have recently emerged as a promising method for mineral exploration. However, two fundamental scientific challenges persist in near-source observations: the significant increase in signal bandwidth and the pronounced near-field source effects. While the problem of bandwidth broadening has been widely investigated, a comprehensive understanding of the near-source stratified-wavefield source effect remains lacking. When an anomalous body lies between the transmitter and receiver, the stratified wavefield generated by the source illuminates the anomaly and casts a shadow zone on its far side, producing false anomalies in the recorded data and obscuring the true location of the target. In this review, we systematically summarize the research progress of multi-source transmission techniques for SOTEM, compare the excitation characteristics of different numbers of transmitters, examine recent advances in defining full-time and full-space multi-component apparent resistivity, and analyze multi-line-source observation strategies. These approaches help suppress the transverse electric (TE) component generated by the transmitter and enhance the contribution of the transverse magnetic (TM) component in field measurements, thereby enabling a predominantly TM-mode transient electromagnetic response. We further provide a critical evaluation of the advantages and limitations of existing multi-source techniques, and propose that the “shadow-free illumination” observation mode and cascaded multi-transmitter systems will form key directions for future development, with detailed operational definitions and implementation paths provided.
Abstract Fluid infiltration into porous sandstone relics induces micro-fractures that serve as critical early damage indicators. However, detecting these incipient micro-fractures exceeds the resolution limits of conventional non-destructive testing techniques, thereby posing significant challenges for precise identification and risk assessment. Full-polarimetric ground penetrating radar (FP-GPR) facilitates high-resolution, non-destructive detection of micro-fractures by acquiring and analyzing multi-polarimetric data. This study proposes an FP-GPR method for fracture detection in cave temple relics, leveraging the volumetric effect of seepage within rock fractures. The method is applied to detect micro-fractures in the Beishan Rock Carvings, Chongqing, China. First, numerical models of sandstone containing fractures with varying dip angles were constructed. Hydrological simulations were then performed to obtain time-lapse fluid infiltration states. Subsequently, FP-GPR simulations were conducted on the resulting time-lapse dielectric models. Freeman and H-Alpha decompositions were then employed to quantitatively analyze the polarization responses under different infiltration durations and fracture dip angles. Finally, field measurements were conducted to validate the numerical simulations. The results reveal a high correlation between moisture variation and key polarimetric parameters, including surface scattering power, double-bounce scattering power, and entropy. This study demonstrates the capability of FP-GPR for micro-fracture detection, offering valuable insights for the conservation of cave temple relics.
Abstract Accurate estimation of crude oil viscosity is crucial for formulating optimal hydrocarbon recovery strategies. Nuclear magnetic resonance (NMR) is a non-destructive technique for viscosity characterization with a longitudinal and transverse relaxation times (T₁ and T₂), diffusion coefficient, or apparent hydrogen index derived from ¹H signals. In this review, the theoretical methods for crude oil viscosity characterization with NMR are systematically sorted, which is crucial for novices and petroleum engineers. First, the basic principles of NMR are introduced, and the theoretical basis of NMR-based crude oil viscosity characterization is described in terms of relaxation times, diffusion coefficient, and apparent hydrogen index. Then, a systematic review is conducted for NMR-based crude oil viscosity characterization method developed over the past three decades. Finally, four kinds of influence factor—instrument parameters, temperature, crude oil type, and gas oil ratio—are analyzed. The results emphasize the importance of selecting a suitable viscosity model based on reservoir type and formation conditions. Two-dimensional NMR T1−T2 techniques demonstrate potential for addressing crude oil viscosity characterization challenges. In general, the key to crude oil viscosity characterization with NMR is selecting the appropriate NMR method rationally based on clear reservoir characteristics. This study aims to assess the existing methods and their limitations critically while providing guidance toward more robust viscosity quantification protocols.
Abstract Seismic impedance inversion is a key technology for oil and gas reservoir prediction. However, linear inversion is inherently limited in accuracy, while nonlinear approaches remain computationally intensive; furthermore, neither effectively resolves geological boundaries without sufficient prior constraints. Therefore, we propose an inversion method termed spatio-temporally coupled adaptive delayed-rejection relativity-of-Gaussian Markov chain Monte Carlo (MCMC). The method relies on a hidden Markov model (HMM) to capture the spatio-temporal evolution of impedance. By facilitating appropriate state transitions, this HMM provides essential prior-informed constraints for the posterior distribution within the MCMC framework. Furthermore, a two-stage delayed rejection algorithm incorporating adaptive covariance updating is utilized to enhance computational efficiency. Subsequently, the inversion results are processed using the relativity-of-Gaussian method, which effectively preserves strata boundaries and structural features while significantly enhancing the sharpness of the inverted results. Numerical experiments and field applications validate the effectiveness of the proposed method, showing enhanced robustness and better-defined spatial features over conventional MCMC inversions.
Abstract Accurate and intelligent identification of subsurface cavities in carbonate reservoirs remains challenging due to the absence of reliable labeled data and sensitive seismic attributes (SAs). To overcome these limitations, this paper proposes an intelligent framework that integrates multi-attribute label generation, vector quantized variational autoencoder (VQ-VAE) based feature enhancement, and TransUNet for carbonate cavity identification. Multiple SAs, including root mean square amplitude, envelope, sweetness, and reflection intensity, are combined with geometric constraints to construct weakly supervised labels with confidence masks, which effectively reduce annotation dependence and constrain uncertain regions. The VQ-VAE further generates a new class of data-driven sensitive attributes by mapping seismic data into a latent codebook space, where typical local reflection patterns of cavities are adaptively learned. Guided by soft labels, the enhanced feature volumes and the original seismic data, are then fed into a TransUNet network for cavity prediction. We apply the proposed method to both a 3D physical simulation model and a field carbonate reservoir dataset. Comparative tests demonstrate that the selected VQ-VAE features enhance the expression of cavity reflections, suppress strong reflection interference, thereby improve the depiction accuracy of cavity structures. Furthermore, the identified cavities from field data show high consistency with impedance inversion results, as well as drilling leakage and overflow evidence, confirming the geological reliability and robustness of the approach.
Abstract The fictitious wave domain (FWD) method establishes an efficient computational framework for independently characterizing the lossless propagation and energy attenuation of low-frequency marine controlled-source electromagnetic (CSEM) fields, while also providing a novel perspective for interpreting diffusive EM wave propagation. It simplifies traditional diffusive-domain modeling by avoiding complex grid discretization. However, the traditional explicit finite-difference time-domain (FDTD) method used to compute fictitious electromagnetic wave time series in the FWD is limited by the Courant–Friedrichs–Lewy stability condition, which restricts the maximum allowable time step. To overcome this, a high-order spatiotemporal FDTD (HAIT-FDTD) scheme is proposed, incorporating an optimized stability framework based on Taylor polynomial expansions of electromagnetic fields. This method allows time steps up to 6.5 times larger than conventional FDTD while maintaining numerical stability. For further optimization in complex marine environments with heterogeneous conductivity, an adaptive HAIT-FDTD (AHAIT-FDTD) algorithm is proposed. It dynamically selects the optimal time step according to the conductivity range of the model and assigns tailored Taylor polynomial orders to different media, thereby effectively resolving the conflict between large grid sizes permissible in conductive regions and the small time steps required in resistive areas. Moreover, as a versatile computational framework, AHAIT-FDTD seamlessly integrates with existing mesh generation strategies and spatial discretization algorithms, without requiring any modifications to the underlying parallelization scheme, meshing, or difference operators. In models characterized by a sparse distribution of high-resistivity bodies, this framework achieves up to a 2-fold increase in computational efficiency.
Abstract Least-squares reverse time migration (LSRTM) involves three essential components: objective function, gradient computation, and update strategy. Typically, the L2-norm misfit is used with gradients computed via adjoint-state method. However, the L2-norm misfit only emphasizes pointwise amplitude differences, ignoring structural information of seismic signals and lacking the ability to capture global waveform similarities. Moreover, it also tends to overemphasize data points with large residuals, which inadvertently diminishes the influence of small misfit data during inversion, thereby potentially degrading the overall imaging quality. To alleviate these issues, based on optimal transport (OT) theory, we propose novel adaptive Wasserstein distance-driven LSRTM inversion methods with Mini-batch strategy. Specifically, we integrate the Wasserstein1 distance and its coupled form into the objective function. Then, the Wasserstein gradient flow is computed by novel automatic differentiation (AD) framework instead of adjoint-state method, thus avoiding heuristic approximations. For gradient updates, we perform batch sampling to original shots, forming small batches to enable Mini-batch optimization. This strategy reduces memory consumption and enhances the exploration capability for imaging in localized regions. In optimization process, we replace the computationally expensive line-search iteration method with an adaptive moment estimation (Adam) algorithm, which approximates adaptive step correction through momentum and bias correction, thereby ultimately establishing adaptive LSRTM inversion framework. Numerical experiments demonstrate that Wasserstein distance-driven LSRTM methods, including Wasserstein1-LSRTM and Coupled-LSRTM, significantly outperform L2-LSRTM in recovering deep structures. Overall, it shows notable advantages in edge preservation, convergence speed, and improved imaging quality, offering a promising alternative for geophysical imaging.
Abstract Ultra-deep clastic reservoirs in the NY block of the Junggar Basin, China, are generally characterized by ultra-low porosity, extremely low permeability, the development of micro-fractures, and weak fluid-response signals. In addition, the lack of prior information such as rock-physics data limits the applicability of traditional reservoir classification methods based on logging-derived petrophysical parameters. To address these challenges, this study proposes a reservoir classification method for ultra-deep formations based on multidimensional well-logging feature fusion and multivariate statistical analysis. First, multiple identification factors are constructed using conventional logs, array acoustic logs, and nuclear magnetic resonance (NMR) logs. Second, principal component analysis is applied to reduce the dimensionality of the identification factors and extract principal components that reflect overall reservoir characteristics, fluid properties, and invasion features. Finally, linear discriminant analysis is employed to establish a reservoir classification function using well-testing results as labels. Field application demonstrates that the proposed method can effectively classify ultra-deep reservoirs. Reservoir classification was conducted for 10 wells in the study block, covering a total of 16 tested intervals, achieving an identification accuracy of 81%, which indicates that the method has strong practical applicability and good potential for wider application.
Abstract Managed Pressure Drilling (MPD) utilizes a sophisticated network of sensors, control systems, and specialized drilling equipment to continuously monitor pressure at various depths and adjust parameters to maintain a desired pressure profile. The primary objective of MPD is to achieve an optimal pressure balance within the wellbore, enabling safe and effective drilling operations without compromising the integrity of the formation. In this study, a MATLAB Simulink-based MPD model was developed and compared to the VICTUS software for validation. Mathematical connections between system components in the Simulink Editor were made by connecting blocks with signal lines. Subsystems were created in the model by grouping several blocks into single components. The model was based on data from a high-pressure-high-temperature onshore well located in River State, Nigeria, with a pressure of 15 000 psi at the top of the formation and a formation temperature of 150°C. Early kick detection was accomplished via Kick Influx Volume analysis in the MPD model. The critical gas level indicators from the Simulink MPD model indicate effective well control during the MPD operations. The results showed that the average surface backpressure (SBP) recorded by the VICTUS software and the MATLAB Simulink MPD model were in agreement. The Simulink model SBP predictions for coefficient of determination (R2), correlation coefficient (R), and Root Mean Square Error (RMSE) were 0.9928, 0.9964, and 0.4705, respectively. Additionally, a Physics Informed Neural Network (PINN) was used to predict SBP, with a testing R2of 0.9815. These findings indicate a significant and positive correlation between the VICTUS software, MATLAB Simulink MPD, and PINN models, developed as a cost-effective tool.
Abstract Seismic inversion plays an important role in seismic exploration by enhancing the accurate characterization of subsurface structures and lithologic parameters. However, conventional inversion methods often neglect the intrinsic spatial correlation of stratigraphic architectures formed by sedimentary processes, thereby reducing inversion accuracy and structural continuity. To address this limitation, we construct a spatial correlation function by integrating empirical geological information with theoretical formulations and propose a spatially correlation constrained Bayesian sparse inversion (SCCBSI) method, which uses the function as a spatial constraint and incorporates sparse inversion within a Bayesian framework. This method addresses two major issues: the insufficient spatial autocorrelation within individual parameters (both laterally and longitudinally), and the spurious linear correlations between different parameters induced by background trends and other factors. The approach enhances inversion accuracy and improves lateral continuity in the inversion results. Synthetic model tests and field data applications demonstrate that the proposed method provides stable and reliable estimations of P-velocity, S-wave velocity, and density. The inversion results are consistent with geological prior information, validating the robustness and effectiveness of the proposed method.
Abstract A novel dual-porosity strain energy function model based on the dual-porosity framework was proposed and applied to delineate the rock into stiff (the rock matrix and stiff pores) and compliant (predominantly penny-shaped cracks) components. By deriving each component’s contribution to strain energy, a nonlinear seismic wave equation that evolves with porosity was formulated by integrating the kinetic energy equation with Lagrangian equations. Furthermore, it was analyzed how the stiff rock frame and compliant pores, separately and coupled, influence the seismic wave velocity, revealing a nonlinear relationship with pore compressibility. Unlike conventional effective medium approaches that solely account for the stiff rock frame, the proposed coupled dual-component model overcomes the limitations of univariate analyses, shedding light on the microstructural mechanisms by which crack closure enhances the effective rock frame’s stiffness, thereby providing a more comprehensive interpretation of the pressure-dependent behavior of elastic seismic wave velocities.
