Modeling the elastic properties of organic shale has been of long-standing interest for source rocks and unconventional reservoir characterization. Organic shales exhibit significant variabilities in rock texture and reservoir properties at different maturity stages, subsequently affecting their elastic responses. We have developed a new rock-physics modeling scheme honoring the maturity levels (immature, mature, and overmature), which are constrained by the evolution of the physical properties of organic shale upon kerogen maturation. In particular, at different maturity stages, the manners in which the compliant organic materials interact with the inorganic mineral matrix are characterized by different effective medium theories. On the basis of the developed rock-physics templates, organic shales have different elastic behaviors at different maturity stages. Ignoring the impact of kerogen maturation is insufficient to adequately characterize the elasticity of the whole organic shale system. Modeling results suggest that the elastic responses of organic shale are sensitive to two dominant factors — organic matter content and mineralogical composition. The elastic anisotropy characteristics are not only affected by the kerogen content and clay alignment but also depend on the morphology of kerogen distribution. Our results compare satisfactorily with data from ultrasonic velocity and log measurements, confirming validity and applicability of our modeling framework.

Obtaining accurate subsurface Q (quality factor) models using full-waveform inversion (FWI) methods remains a challenging task. The forward modeling problem of viscoelastic wave propagation can be solved by superimposing N rheological bodies of Maxwell or Zener type with generalized standard linear solid rheology. However, different approaches were proposed to calculate the attenuation sensitivity kernels in viscoelastic FWI. This study reviews and compares previous theories for constructing the viscoelastic sensitivity kernels. Furthermore, we derive the viscoelastic sensitivity kernels directly following the adjoint-state (or Lagrangian multiplier) method. Compared to previous approaches, we reveal that the Q sensitivity kernels can be calculated with adjoint memory strain variables. In the numerical experiments, different methods are used to calculate the viscoelastic sensitivity kernels for comparison. We have found that when simultaneously inverting for velocity and Q models, these methods can provide inversion results of comparable quality. However, in the event of inaccurate velocity structures, the Q sensitivity kernels calculated with memory strain variables can resolve the Q anomalies more clearly, while suffering from fewer parameter trade-offs.

In oil and gas exploration, formation water (or hydrocarbon) content estimation is essential for reservoir evaluation, development and production. Archie’s law, which associates the formation resistivity and the water saturation, has been widely adopted for reservoir assessment. However, the accuracy of the scalar-based Archie’s law falls when the formation exhibits strong heterogeneity (e.g. fractured shales), as the electrical anisotropy are neglected in the scalar model. In this paper, we propose a tensorial Archie’s law based on the effective resistivity tensor of the formation. We construct numerical experiments of idealized three-phase formation geometries that contain ellipsoidal inclusions. The resistivity tensor is calculated from the simulation results and used in the newly proposed Archie’s law to calculate the water saturation of the formation, and the model is validated by comparing the predicted saturation with the calculated value from the known geometries. The results show that the tensorial Archie’s law captures the anisotropy of the formation by including all tensor elements of the resistivity in, thus improves the predictability.

Seismic deconvolution is a useful tool in seismic data processing. Classical non-machine learning deconvolution methods usually apply quite a few constraints to both wavelet inversion and reflectivity inversion. Supervised machine learning deconvolution methods often require appropriate training labels. The existing self-supervised machine learning deconvolution methods need a given wavelet, which is a non-blind process. To overcome these issues, we propose a blind deconvolution method based on self-supervised machine learning. This method first estimates an initial zero-phase wavelet by smoothing the amplitude spectrum of averaged seismic data. Then, the loss function of self-supervised machine learning is taken as the error between the observed seismic data and the reconstructed seismic data that come from the convolution of phase-rotated wavelet and reflectivity generated by the network. We utilize a residual neural network with long skip connections as the reflectivity inversion network and a fully connected convolutional neural network as the wavelet phase inversion network. Numerical experiments on synthetic data and field data show that the proposed method can obtain reflectivity inversion results with higher resolution than the existing self-supervised machine learning method without given wavelet.

Geofluid identification from seismic data are crucial for understanding reservoir characteristics. However, fluid indicators based on elastic parameter combinations show strong ambiguity in terms of geofluid identification. Although the effective pore-fluid bulk modulus proves to be the superior fluid indicator in geofluid discrimination, it is limited to empirical models such as the critical porosity model. The consolidation parameter model can evaluate the consolidation and compaction of sediments and is widely used due to its better applicability. Therefore, a novel fluid indicator considering consolidation parameter is proposed and a boundary-constrained inversion strategy for geofluid identification is developed. First, the novel fluid indicator is defined based on the poroelasticity theory. Then, the linearized AVA (amplitude variation with angle) approximation equation related to the new fluid indicator is derived to directly link seismic data and properties of pore-filling materials. The model analysis verifies the accuracy of the derived approximation equation at moderate incident angles, which can be used for parameter prediction by pre-stack seismic inversion. Furthermore, the contribution of each attribute of the novel equation to the reflectivity is analyzed to validate the feasibility of new fluid indicator inversion. Finally, a boundary-constrained AVA pre-stack inversion method is presented to enhance the robustness of the inversion results of the model parameter. The reliability of the improved method is proved by accurate inversion results of synthetic seismic records. After determining the consolidation parameter using well-log data combined with BGT (Biot–Gassmann Theory), the field data further demonstrated that the proposed approach is accurate and effective.

The prediction of physical properties for porous medium plays an essential role in geological resource exploration and subsurface exploitation. Deterministic methods based on computational or numerical experiment provide an efficient way to estimate the physical properties of porous medium. However, uncertainty and randomness are common characteristics in the geological system. The variability of physical property in porous medium cannot be explicitly explained by a limited number of models. In this article, we propose an interval estimator-based Bayesian evidential learning (IE-BEL) framework to quantify the uncertainty while predicting physical properties of porous medium at the same time. First, we utilize a stochastic simulation to generate a number of high-quality 3-D models. Second, the morphological characteristics and physical properties are numerically computed as the training data. Third, a combination of machine learning techniques, including eXtreme gradient boosting (XGBoost) and model agnostic prediction interval estimator (MAPIE), is employed to obtain reliable interval predictions with uncertainty quantification. Fourth, a model calibration process is conducted to regulate the physical property predictions. We validate the proposed method by three practical examples, including both artificial and natural porous materials. Compared with the previous method, the IE-BEL framework shows competitive performance in predicting the physical properties of porous medium. The experiment result indicates that the proposed method can address the uncertainty quantification problem associated with physical properties prediction.