Inversion of low to medium frequency velocities and densities from AVO data using invertible neural networks

AVO (amplitude variation with offset) inversion and neural networks are widely used to invert elastic parameters. With more constraints from well log data, neural network-based inversion may estimate elastic parameters with greater precision and resolution than traditional AVO inversion, however, neural network approaches necessitate a massive number of reliable training samples. Furthermore, because the lack of low-frequency information in seismic gathers leads to multiple solutions of the inverse problem, both inversions rely heavily on proper low-frequency initial models. To mitigate the dependence of inversions on accurate training samples and initial models, we propose solving inverse problems with the recently developed invertible neural networks (INNs). Unlike conventional neural networks, which address the ambiguous inverse issues directly, INNs learn definite forward modeling and use additional latent variables to increase the uniqueness of solutions. Motivated by the newly developed neural networks, we propose an INN-based AVO inversion method, which can reliably invert low to medium frequency velocities and densities with randomly generated easy-to-access datasets rather than trustworthy training samples or well-prepared initial models. Tests on synthetic and field data show that our method is feasible, anti-noise capable, and practicable.

A Multi-Point Geostatistical Seismic Inversion Method Based on Local Probability Updating of Lithofacies

In order to solve the problem that elastic parameter constraints are not taken into account in local lithofacies updating in multi-point geostatistical inversion, a new multi-point geostatistical inversion method with local facies updating under seismic elastic constraints is proposed. The main improvement of the method is that the probability of multi-point facies modeling is combined with the facies probability reflected by the optimal elastic parameters retained from the previous inversion to predict and update the current lithofacies model. Constrained by the current lithofacies model, the elastic parameters were obtained via direct sampling based on the statistical relationship between the lithofacies and the elastic parameters. Forward simulation records were generated via convolution and were compared with the actual seismic records to obtain the optimal lithofacies and elastic parameters. The inversion method adopts the internal and external double cycle iteration mechanism, and the internal cycle updates and inverts the local lithofacies. The outer cycle determines whether the correlation between the entire seismic record and the actual seismic record meets the given conditions, and the cycle iterates until the given conditions are met in order to achieve seismic inversion prediction. The theoretical model of the Stanford Center for Reservoir Forecasting and the practical model of the Xinchang gas field in western China were used to test the new method. The results show that the correlation between the synthetic seismic records and the actual seismic records is the best, and the lithofacies matching degree of the inversion is the highest. The results of the conventional multi-point geostatistical inversion are the next best, and the results of the two-point geostatistical inversion are the worst. The results show that the reservoir parameters obtained using the local probability updating of lithofacies method are closer to the actual reservoir parameters. This method is worth popularizing in practical exploration and development.

Geomechanical properties of carbonate reservoir rocks and middle carbon cap rocks of the Ivinskoe oilfield

Laboratory studies of the geomechanical properties of rocks are an important and integral part in building a geomechanical model. This study resulted in a set of data on geomechanical and elastic properties of the rocks that compose the lower part of the Middle Carboniferous section of the Ivinskoye oilfield (Russia). Relationships between various elastic parameters were also established. The distribution of geomechanical properties correlates with structural/textural features of the rocks under study and their lithological type. This information can be used as a basis for geomechanical modeling and in preparation for hydraulic fracturing. Keywords: geomechanics; elastic properties; carbonate rock; laboratory core studies.

Understanding Micropolar Theory in the Earth Sciences I: The Eigenfrequency $$\omega _r$$

Even though micropolar theories are widely applied for engineering applications such as the design of metamaterials, applications in the study of the Earth’s interior still remain limited and in particular in seismology. This is due to the lack of understanding of the required elastic material parameters present in the theory as well as the eigenfrequency $$\omega _r$$ ω r which is not observed in seismic data. By showing that the general dynamic equations of the Timoshenko’s beam is a particular case of the micropolar theory we are able to connect micropolar elastic parameters to physically measurable quantities. We then present an alternative micropolar model that, based on the same physical basis as the original model, circumvents the problem of the original eigenfrequency $$\omega _r$$ ω r laking in seismological data. We finally validate our model with a seismic experiment and show it is relevant to explain observed seismic dispersion curves.

Prestack Seismic Inversion via Nonconvex L1-2 Regularization

Using seismic data, logging information, geological interpretation data, and petrophysical data, it is possible to estimate the stratigraphic texture and elastic parameters of a study area via a seismic inversion. As such, a seismic inversion is an indispensable tool in the field of oil and gas exploration and development. However, due to unknown natural factors, seismic inversions are often ill-conditioned problems. One way to work around this unknowable information is to determine the solution to the seismic inversion using regularization methods after adding further a priori constraints. In this study, the nonconvex L1−2 regularization method is innovatively applied to the three-parameter prestack amplitude variation angle (AVA) inversion. A forward model is first derived based on the Fatti approximate formula and then low-frequency models for P impedance, S impedance, and density are established using logging and horizon data. In the Bayesian inversion framework, we derive the objective function of the prestack AVA inversion. To further improve the accuracy and stability of the inversion results, we remove the correlations between the elastic parameters that act as initial constraints in the inversion. Then, the objective function is solved by the nonconvex L1−2 regularization method. Finally, we validate our inversion method by applying it to synthetic and observational data sets. The results show that our nonconvex L1−2 regularization seismic inversion method yields results that are highly accurate, laterally continuous, and can be used to identify and locate reservoir formation boundaries. Overall, our method will be a useful tool in future work focused on predicting the location of reservoirs.

Leveraging active-source seismic data in mining tailings: Refraction and MASW analysis, elastic parameters, and hydrogeological conditions

We applied active-source seismic method for the interpretation of elastic parameters in tailings facilities which is essential for evaluating stability and seismic response. The methodology uses different analysis methods on the same dataset, i.e., conventional seismic refraction (SR) to determine compressional-wave velocity (Vp) and multichannel analysis of surface wave (MASW) to estimate shear-wave velocity (Vs). Seismic velocities in conjunction with tailings physics approach revealed interpretable data in terms of elastic parameters and hydrogeological conditions. The results determined the empirical linear relationships between Vp and Vs that are particular to an unconsolidated media such as tailings and showed that variability of hydrogeological conditions influences the elastic seismic response (Vp and Vs) and the elastic parameters. The analysis of the elastic parameters identified the state condition of the tailings at the time of the survey. The Bulk modulus K that relates the change in hydrostatic stress to the volumetric strain was predominant between 1.0−2.0 GPa. The Young’s modulus E in the tailings media was in the low range of 0.15−0.23 GPa. Poisson’s ratio values in all sections were in the upper limit in the range of 0.37−0.49, meaning that the tailings media is highly susceptible to transverse deformation under axial compression.

A Machine-Learning Based Workflow for Predicting Overpressure in a Stiff Dolomitic Formation

Overpressure refers to the abnormally high subsurface pressure that may exceed hydrostatic pressure at a given depth. Its characterization is an important part of subsurface characterization as it allows to complete drilling operations in a safe and optimal way. In dolomitic formations, however, the prediction of such overpressure is especially challenging because of (1) the high degree of lateral variability of the formations, (2) the limited effect of overpressure on tight rocks elastic parameters, and (3) the complexity of physical processes involved to form overpressure. In addition to these factors, existing experimental models generally used to relate elastic parameters to pressure are often not well calibrated to carbonate rocks. The alternative to existing purely physical approaches is a data-driven model that leverages data from offset wells. We show that due to the complexity of the characterization question to be solved, an end-to-end machine learning based approach is deemed to fail. Instead of a fully automated approach, we show a semi-supervised workflow that integrates seismic, geological data, and overpressure observations from previously drilled wells to map overpressure regions. Attribute maps are first extracted from a 3D seismic data set in an overpressured geological formation of interest. An auto-encoder is then used to learn a more compact representation of data, resulting in a reduced number of latent attributes. Then, a hand-tailored semi-supervised approach is applied, which is a combination of clustering method (here based on DBSCAN algorithm) and Bayesian classification to determine overpressure risk degree (no risk, mild, or high risk). The approach described in this study is compared to direct end-to-end models and significantly outperforms them with an error on a blind well prediction of around 25%. The overpressure probability maps resulting from the models can be used later for the optimization of drilling processes and to reduce drilling hazards.