Rock Physics Model Research Articles

Rock-physics model of a gas hydrate reservoir with mixed occurrence states

Seismic interpretation of gas hydrates requires the assistance of rock physics. Changes in gas hydrate saturation can alter the elastic properties of formations, and this relationship can be considerably influenced by the occurrence state of gas hydrates. Pore-filling, load-bearing, and cementing types are three single gas hydrate occurrence states commonly considered in rock-physics investigations. However, many gas hydrate-bearing formations are observed to have mixed occurrence states, and their rock-physics properties do not fully conform to models of single occurrence states. We develop a generalized rock-physics model for gas hydrate-bearing formations with three mixed occurrence states observed in the field or laboratory experiments: coexisting pore-filling-type and matrix-forming-type gas hydrates (case 1); pore-filling type when [Formula: see text] (gas hydrate saturation) < [Formula: see text] (critical saturation) and pore-filling + matrix-forming type when [Formula: see text] (case 2); and matrix-forming type when [Formula: see text] and matrix-forming + pore-filling type when [Formula: see text] (case 3). Instead of initial porosity, the apparent porosity (the volume fraction of an effective pore filler) [Formula: see text] represents the influence of occurrence states on the pore space. These three mixed occurrence states can be modeled using a unified workflow, in which the volume fractions of various gas hydrate types are expressed in general forms in terms of the apparent porosity. In addition, the model considers the effect of a pore filler on shear modulus. The developed model is validated through calibration with real well-log data and published experimental data corresponding to five gas hydrate-bearing formations. The model effectively interprets the influences of gas hydrate saturation and occurrence state on these formations. Thus, the generalized model provides a theoretical basis for the analysis of sensitive elastic parameters and quantitative interpretation for gas hydrate reservoirs.

Rock-physics-guided machine learning for shear sonic log prediction

The S-wave velocity ([Formula: see text]) is a vital parameter for various petrophysical, geophysical, and geomechanical applications in subsurface characterization. Nevertheless, obtaining shear sonic log is frequently challenging because of its high economic, time, and operating costs. Conventional methods for predicting [Formula: see text] rely on empirical relationships and rock-physics models, which often fall short in accuracy due to their inability to account for the complex factors influencing the relationship between [Formula: see text] and other parameters. We develop a physics-guided machine learning (ML) approach to predict the shear sonic log using various physical parameters (e.g., natural gamma ray, P-wave velocity, density, and resistivity) that can be readily obtained from standard logging suites. Three types of rock-physical constraints combined with three guidance strategies form the various physics-guided models. Specifically, the three constraint models include mudrock line, empirical P- and S-wave velocity relationship, and multiparameter regression from the logging data, and the three guidance strategies involve physics-guided pseudolabels, physics-guided loss function, and transfer learning. To assess the model’s generalization ability and simulate the lack of labeled data in real-world applications, a single well is used as a training well, whereas the remaining four wells are used to blind test in a clastic reservoir. Compared with supervised ML without any constraints, all models incorporating physical constraints demonstrate a significant improvement in prediction accuracy and generalization performance. This underscores the importance of integrating the first-order physical laws into the network training for shear sonic log prediction. The most successful approach combines the multiparameter regression relationship with the physics-guided pseudolabels in this case, resulting in a remarkable 47% reduction in the average root-mean-square error during the blind test.

Rock physics and basin modeling nexus for predicting pore pressure

Improving accuracy in pre-drill pore pressure predictions is a fundamental starting point for well design including setting boundaries for casing points and mud weights. Although rock physics modeling is used routinely in pore pressure estimates, existing rock physics modeling approaches have been largely empirical and face challenges to predict pore pressure accurately, especially for deeper drilling targets where rock matrix properties deviate from normal compaction trends, due to chemical alterations of the rocks. Moreover, existing rock physics models require petrophysical inversion for porosity and volume of shale. It is well-known that petrophysical inversion has non-uniqueness issues and creates additional uncertainty and inaccuracy in pore pressure prediction. Therefore, we developed an integrated modeling approach that involves rock physics modeling and physics-based basin modeling. Through fundamental rock physics modeling and in-depth understanding of the process of clay diagenesis, we recognize that the acoustic impedance from seismic inversions and level of organic metamorphism (LOM, as a proxy for thermal stress) estimated from basin modeling are critical for pore pressure prediction in mudrocks. Based on extensive post-drill data validation, we demonstrate that our modeling approach improves accuracy in pore pressure prediction for depth zones undergoing clay-diagenesis. In addition, we demonstrate that the integrated rock physics modeling greatly reduces the number of calibration parameters as needed in existing models. Blind tests of our method on well data in two different basins with drastically different burial history demonstrates the validity and generalizability of our approach.

Third‐order elasticity of transversely isotropic field shales

AbstractThe formations above a producing reservoir can exhibit large mechanical changes, creating a risk of significant subsidence and loss of rock integrity. These changes can be monitored by time‐lapse seismic acquisition, which measures the corresponding velocity changes via time‐shifts. Third‐order elastic theory can be used to connect subsurface strains and stress changes to these seismic attribute changes. Existing models assume isotropic strain dependence of the dynamic stiffness in shales. It is important to re‐evaluate this isotropic assumption considering the inherent anisotropy of shales and their abundance in the overburden. Thus, we instead propose a third‐order elastic model with a transversely isotropic strain dependence of the dynamic stiffness. When calibrated, this new model satisfactorily predicted P‐wave velocity changes determined in undrained laboratory experiments conducted on overburden field shales, covering a wide range of propagation directions and stress variations. The shales exhibit anisotropic dynamic strain sensitivity, resulting in a significantly higher strain sensitivity predicted for Thomsen's anisotropy parameters epsilon and delta subjected to a uniaxial strain parallel to the horizontal bedding plane compared to the vertical direction. Geomechanical modelling, considering a depleting disk‐shaped reservoir surrounded by shales, was employed to predict the dynamic stiffness changes of the overburden using the laboratory‐calibrated third‐order elastic model. The overburden time‐shifts increased with offset angle, peaking at about 45°, suggesting a strong influence of shear strains on the time‐shifts. In contrast, a corresponding model with an isotropic third‐order elastic tensor, calibrated to the same data, exhibited a significantly lower sensitivity to the shear strains. These results underscore the importance of considering the anisotropic strain dependence of the dynamic stiffness when studying shales. Interpreting offset‐dependent trends in pre‐stack time‐lapse seismic data, along with geomechanical modelling and an appropriate strain‐dependent rock physics model, can assist in quantifying subsurface strains and stress changes.

Rock-physics modeling of deep clastic reservoirs considering the relationship between microscopic pore structure and permeability

Deep clastic reservoirs often exhibit low porosity and low permeability due to the influence of factors such as the sedimentary environment, the ground stress field, etc. The targeted seismic rock physics model can not only specify the microscopic main controlling factors that effect the macro-elastic response of rocks but also predict the shear wave velocity. Thereby, it guides reservoir prediction. Therefore, constructing a rock physics model that considers the pore-permeability relationship, pore structure, and consolidation compaction of reservoir rocks is especially crucial. However, there is the challenge of constructing direct rock-physics relationships between permeability parameters and elastic or physical property parameters. Consequently, the relationship between permeability and pore type is developed in this study using laboratory measurement data. Building upon this foundation, the calculated elastic modulus of the dry rock skeleton is further corrected by the consolidation compaction parameters and the optimization algorithm. Numerical analysis indicates that permeability parameters introduced in the modeling process can serve as guiding factors for different pore type proportions. Additionally, the compaction coefficient exerts a significant influence on the rock's elastic modulus. The applicability and effectiveness of the modeling are confirmed through the utilization of measured well data from the East China Sea.

Investigating the analytical relationship between pore geometry and other pore space properties in carbonate rocks

Although pore geometry plays an important role in carbonate rock physics modelling, few studies have been carried out on its analytic relationship with other pore space properties such as pore space stiffness. We propose an analytical workflow based on the differential effective medium (DEM) to estimate the elastic properties of carbonate rocks. The validity of our results is then cross-checked with the Xu and Payne model on a real carbonate dataset. This workflow establishes a direct and quantitative link between the pore geometry of carbonate rock and its other pore space properties such as the Biot coefficient and pore space stiffness. This relationship can, furthermore, be utilized in defining rock physics templates (RPTs) to investigate the role of pore geometry on the rock elastic properties. Furthermore, we extended the Biot–Gassmann–Krief (BGK) model through our proposed workflow by establishing a theoretical framework to relate the main components of the BGK model to the pore geometry usually estimated in the laboratory or empirically. This can help to investigate the impact of fluid substitution on each of these main components. Our investigation suggests that the higher the Biot and Gassmann coefficients, the more sensitive the rock is to fluid substitution. Moreover, this analytical workflow has been employed to examine the role of selecting different rotational spheroids (i.e. oblate and prolate) on the modelled velocities. Our results show that the modelled velocities depend on this selection in such a way that prolate pores are less sensitive to the variations in their pore aspect ratio compared with oblate pores.

Constrained nonlinear amplitude-variation-with-offset inversion for reservoir dynamic changes estimation from time-lapse seismic data

We develop a novel elastic amplitude-variation-with-offset (AVO) inversion process to estimate the fluid saturation and effective pressure or variations in these properties from time-lapse seismic data sets. These changes occur in oil and gas reservoirs caused by fluid injection or hydrocarbon production that leads to changes in the elastic wave properties, reflectivity, and seismic response. Our method is based on a seismic forward model that consists of a linearized AVO equation and a rock-physics model. The AVO equation links the elastic wave properties to seismic reflection amplitudes, whereas the rock-physics model maps the saturation and pressure into seismic velocities and density. The inversion approach relies on the gradient descent technique to estimate the unknown variables by searching for the minimum of the least-squares misfit between the observed and modeled data. The first-order gradient equations of the least-squares data misfit function with respect to effective pressure and water saturation are derived by using the adjoint-state method and the chain rule. The optimization method used to minimize the misfit function and obtain the best optimal solution is a limited-memory quasi-Newton algorithm. This inversion process allows us to incorporate prior constraints by using the logistic function to map the model variables to a bounded range. To achieve a stable solution to ill-posed inversion problems, optimal regularization weights are applied. The application of the developed workflow on 1D synthetic and real well-log data from the Edvard Grieg oil field simulating various saturation-pressure conditions during production demonstrates the validity of the approach with different noise levels. The inversion is then applied to a 2D synthetic data set modeled from the reservoir model of the Smeaheia field, a potential site for a large-scale offshore CO2 storage field located in the North Sea. Our results illustrate that our inversion method efficiently and accurately estimates reservoir saturation and pressure variations.

Curved Pseudo Elastic Impedance based on Elastic Attribute Rotation Scheme for Reservoir Petrophysical Property Prediction

Seismic based reservoir characterization commonly attempts to estimate petrophysical properties of a reservoir from a combination of elastic attributes resulted from seismic inversion. Two most wanted main reservoir properties to be estimated are porosity variation and hydrocarbon saturation across the reservoir. A combination of acoustic impedance (AI) and the ratio between P- and S-wave velocities (Vp/Vs ratio) based on rock physics models had been used in the earlier study to form Curved Pseudo Elastic Impedance (CPEI) attribute. However, the approach involved a fourth order polynomial in the logarithmic domain of AI and Vp/Vs ratio. A much simpler approach of combining these elastic properties to form CPEI attributes which is based on attribute rotation scheme is proposed in this study. To illustrate the methodology, we applied to well and seismic data located in the Natuna Basin, Indonesia. Results show that better attributes correlation to porosity and hydrocarbon saturation variation is achieved.

Seismic characterisation of multiple BSRs in the Eastern Black Sea Basin

Long offset seismic reflection data reveal the presence of four Bottom Simulating Reflectors (BSR0-3) within folded sediments of the Tuapse Trough, along the NE margin of the Eastern Black Sea Basin (EBSB). Multiple BSRs are observed in other sites worldwide, however, their origin and formation mechanisms are still debated. Here, we investigate the formation mechanisms of the EBSB multiple BSRs based on their seismic character and on their physical properties derived from reflected and refracted arrival seismic velocities. Seismic reflection data are downward continued to enhance refracted arrivals. A 2D travel-time velocity model of the sub-seabed, using combined travel-times from non-downward-continued reflected and downward-continued refracted signals, shows variations in the physical properties at the BSRs and nearby sediments. The P-wave velocity (VP) increase of 1.55–1.72 km/s between the seafloor and BSR0 (258 mbsf) reflects normal compaction trends in sediments, whereas the VP of 1.75–1.83 km/s between BSR0 and BSR1 (360 mbsf) is higher than that expected for sediments at that depth. Beneath BSR1, a VP decrease from 1.83 km/s to 1.61 km/s occurs within a 70-80 m-thick layer including BSR2 (395 mbsf) and extending to BSR3 (438 mbsf). Beneath BSR3, VP increases. Based on an analytical model linking seismic velocity to physical properties, these VP trends can be explained by a gas hydrate saturation from 0 to 2% between the seafloor and BSR0, reaching 4 ± 2% just above BSR1. A free gas saturation of up to 20–25% is estimated within the low-velocity zone between BSR1 and BSR3. BSR1 likely represents the present-day base of the gas hydrate stability zone (BGHSZ), which aligns with the theoretical BGHSZ assuming a geothermal gradient of 26–30 °C/km. Based on seismic polarities and results from travel-time analysis and rock physics modelling, we suggest that hydrate dissociation and recycling processes may explain the negative polarity of BSR2 and BSR3, which are still visible due to the presence of relict gas, and inferred higher gas hydrate saturations close to the present-day base of the stability zone at BSR1. Also, structural and stratigraphic controls seem to have favoured focused free gas flow and hydrate formation at the top of an anticlinal structure, thus likely controlling multiple BSR generation in the EBSB.

Stochastic seismic inversion and Bayesian facies classification applied to porosity modeling and igneous rock identification

We apply stochastic seismic inversion and Bayesian facies classification for porosity modeling and igneous rock identification in the presalt interval of the Santos Basin. This integration of seismic and well-derived information enhances reservoir characterization. Stochastic inversion and Bayesian classification are powerful tools because they permit addressing the uncertainties in the model. We used the ES-MDA algorithm to achieve the realizations equivalent to the percentiles P10, P50, and P90 of acoustic impedance, a novel method for acoustic inversion in presalt. The facies were divided into five: reservoir 1, reservoir 2, tight carbonates, clayey rocks, and igneous rocks. To deal with the overlaps in acoustic impedance values of facies, we included geological information using a priori probability, indicating that structural highs are reservoir-dominated. To illustrate our approach, we conducted porosity modeling using facies-related rock-physics models for rock-physics inversion in an area with a well drilled in a coquina bank and evaluated the thickness and extension of an igneous intrusion near the carbonate-salt interface. The modeled porosity and the classified seismic facies are in good agreement with the ones observed in the wells. Notably, the coquinas bank presents an improvement in the porosity towards the top. The a priori probability model was crucial for limiting the clayey rocks to the structural lows. In Well B, the hit rate of the igneous rock in the three scenarios is higher than 60%, showing an excellent thickness-prediction capability.

Joint inversion for facies and petrophysical properties based on a bi‐level optimization model

AbstractIn many subsurface studies, facies and petrophysical properties are two important reservoir parameters that are closely correlated. They are routinely used in well interpretation, hydrocarbon reserve calculation and production profile prediction. These two parameters have commonly been determined in two separate tasks because of their mathematical differences (facies are discrete, and petrophysical properties are continuous). However, this is incorrect because facies and petrophysical properties are often strongly correlated. Therefore, we propose a new joint inversion method of facies and petrophysical properties based on a bi‐level optimization model. In the bi‐level optimization model, the upper‐level problem is the petrophysical property inversion while the lower‐level problem can identify the facies and add a facies‐related constraint for the upper‐level optimization. We also develop a new genetic algorithm for the discrete‐continuous inversion problem based on the bi‐level optimization model because the inversion problem usually has multiple local solutions. In addition, rock physics and statistics are combined in the inversion process. A rock physics model is used to establish the basic relationships between the petrophysical and elastic parameters, and the statistical approach is used to describe the intrinsic connection among the multiple reservoir parameters based on well log data. The numerical experiments indicate that the traditional separate prediction method and the new joint inversion method can quickly obtain more accurate results. In the application examples of real data, the inversion results can be matched to the well log data within the limits of the input data resolution, which further verifies the reliability and application potential of this new method.

Characterization of Tight Gas Sandstone Properties Based on Rock Physical Modeling and Seismic Inversion Methods

Tight sandstones produce an increasing amount of natural gas worldwide. Apart from identifying the gas enrichment, the predictions of lithology and permeable zones are crucial for the prediction of tight gas sandstones. In the present study, a seismic inversion method is developed based on rock physical modeling, by which it is possible to directly predict the lithology and pore structure in tight formations. The double-porosity model is used as a modeling tool in considering complex pore structures. Based on the model, the microfracture porosity is then predicted using logging data, which are used as a factor to estimate microfractures. Parameters representing the lithology and pore structure are proposed and estimated using logging data analyses and rock physical modeling based on the framework of the Poisson impedance. Thereafter, a new AVO equation is established and extended to the form of an elastic impedance for a direct prediction of the lithology and pore structure parameters. Real data applications show that the indicators of lithology and permeable zones are consistent with the production status. They agree with the petrophysical properties measured in wellbores, thereby proving the applicability of the proposed method for the effective characterization of tight gas sandstones.

Extracting crucial microstructures to characterize the elastic wave velocity and resistivity of Berea sandstone using convolutional neural networks

To reveal the internal structure of the earth, rock physical models are insightful for interpreting geophysical observation data and are often used for estimating subsurface structures. However, as the estimated value of each model significantly depends on the assumed microstructure, the obtained subsurface structure may be biased. Despite the innovations of high-resolution imaging technologies and their application to digital rock physics (DRP) and machine learning (ML), the characteristic microstructure controlling rock physical properties remains unclear. We apply ML and extraction of regression activation mapping (RAM) and learned filters to visualize the characteristic microstructure underlying the elastic and electrical properties of rock (P-wave velocity [Formula: see text], S-wave velocity [Formula: see text], [Formula: see text]/[Formula: see text] ratio, and electrical resistivity). This regression task is implemented using convolutional neural networks (CNNs) that are trained on these properties and calculated with the DRP approach using Berea sandstone images as samples. Although the calculated geophysical properties show perturbations even among digital rocks that have the same porosity, the results predicted using the best-performing CNN model exhibit a relative error of 2%–7% with respect to elastic properties. The visualized RAM revealed that the machine focuses on larger grains for predicting P-wave and S-wave velocities, whereas their ratio ([Formula: see text]/[Formula: see text]) takes into account the pore space. In contrast, electrical properties consider grain edges and surrounding pores, which may be related to the tortuosity of the pore space. Moreover, filter visualizations demonstrated that the geometric characteristics of Berea sandstone could be representative of circular or elliptical shapes for determining elastic properties, whereas tube-like shapes were extracted for electrical resistivity. These findings shed new light on the crucial internal structures used for defining each rock property.

Elastic properties of unconsolidated sandstones of interest for carbon storage

AbstractUnconsolidated sandstones are attractive targets for underground storage of carbon due to their high porosity and permeability. Monitoring of injection and movement of CO2 in such formations using elastic waves requires an understanding of the acoustic properties of the sandstone. Current approaches often use the so‐called soft‐sand model in which a Hertz–Mindlin model of the acoustic properties at high porosity is mixed with the acoustic properties of the mineral phase to predict the acoustic properties over the entire porosity range. Using well‐log data from two unconsolidated sand formations of interest for CO2 storage, we discuss the limitations of this model and provide an alternative approach in which the mechanical properties of grain contacts are obtained by inversion, and the properties of infill material lying within the pore space are estimated. The formations considered are the Paluxy Formation in Kemper County, Mississippi, and the Frio Formation near Houston, Texas. The ratio of the normal to shear compliance of the grain contacts is found to be significantly less than unity for both formations. This implies that the grain contacts are more compliant in shear than in compression. However, the grain contact compliance is higher and the ratio of the normal to shear compliance is lower for the Frio example than for the Paluxy case, and this may lead to sliding at grain contacts with low shear compliance and transport of grains during fluid flow, particularly if CO2 acts to weaken any cement that may be present at the grain contacts. Such transport was suggested by Al Hosni et al. in explaining why the magnitude of the time‐lapse effect due to the injection of CO2 at the Frio CO2 injection site is greater than predicted using conventional rock physics models. A simple model of the mechanical properties of infill material lying within the pore space suggests that the bulk and shear moduli of infill material in the Paluxy case are significantly higher than the Frio case, consistent with the lower grain contact compliance in the Paluxy case.

Deriving mineral moduli of the noncarbonate fraction in a marly chalk reservoir using petrophysical logging data and an isoframe model

Knowledge of the elastic properties of clays and clay-rich sediments is essential when performing quantitative seismic interpretation and geomechanical modeling of reservoirs where they are present. Such is the case for the marly chalk reservoirs of Lower Cretaceous age in the Danish North Sea. We develop a new method to derive the elastic properties of the clay-rich insoluble residue (IR) fraction in marly chalks, using petrophysical logs and rock physical modeling. We calculate compressional ( M), shear ( G), and bulk ( K) moduli of the formation along the borehole using the density and sonic (shear and compressional) logs and model the elastic properties of minerals using the isoframe (IF) rock-physics model. In our model, the marly chalk is composed of two materials: calcite, with well-known elastic properties, and the IR fraction, whose elastic properties are the sought variable. We systematically vary the assumed elastic properties of the IR fraction, each time achieving equality between the measured and modeled elastic moduli solving for the IF values of calcite ([Formula: see text]) and IR fraction ([Formula: see text]) for each of the three elastic parameters one at a time, deriving the modeled values for the other two. We add up the error between the modeled and logged values for each set of assumed elastic properties of the IR fraction. We adopt the values of [Formula: see text] and [Formula: see text] that minimize the compound error as the actual elastic properties of the IR fraction. We run the algorithm in the Boje-2C and Valdemar-2H wells in different stratigraphic units of the Lower Cretaceous: the Fanø Formation and the marly chalk of the Tuxen and Sola formations. Elastic properties derived for the IR fraction compare well to data for wet clays from ultrasonic velocity laboratory tests. In a clean chalk section (almost 100% calcite), the model outputs values similar to calcite.

Empirical determination of the effective solid modulus in organic-rich shales

Calculating the change in the saturated bulk modulus of a saturated rock with new fluid properties requires a priori selection of an effective bulk modulus of the solid constituents. When the rock constituents have similar mineral moduli, the theoretical bounds on the solid modulus are close to each other. However, when solid properties vary greatly, as in organic-rich shales, the actual effective solid modulus of a physical rock may vary significantly between the bounds which results in uncertainty in the predicted change in the saturated bulk modulus of the rock. We use a semi-empirical rock physics model utilizing the Brown–Korringa equation for mineralogically heterogenous rocks and introduce three parameters to estimate the pore space compressibility, the dry frame compressibility, and the fractional position of the effective solid modulus relative to the Reuss and Voigt bounds. We optimize for these three parameters in seven organic shale formations and find that the Reuss bound for the effective solid material modulus best fits the data when organic content is high. Furthermore, we use this model to fluid substitute to 100% brine saturation and find Gassmann’s equation using the Hill average predicts similar saturated moduli to the semi-empirical Brown–Korringa rock physics model when volume fraction of solid organic matter is less than 5%. However, at higher organic contents, we find that the error using the Gassmann–Hill approach increases, and the semi-empirical Brown–Korringa model better fits the data.

Shale Gas Reservoir Pore Pressure Prediction: A Case Study of the Wufeng–Longmaxi Formations in Sichuan Basin, Southwest China

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.

Detection and picking of shear wave arrival for stiffness evaluation of highly porous chalk

AbstractElastic wave velocities of compressional and shear waves propagating through sedimentary rocks are often coupled with information of bulk density to derive the rock stiffness. Acquiring the transit time of compressional and shear waves often involves manual picking of wave arrival times from wave trains recorded in the laboratory or by well‐logging tools. Picking the compressional wave arrival time is commonly accepted as straightforward. Oppositely, detecting the shear wave arrival and picking its arrival time is often troublesome because the transmitted shear wave partly converts to compressional waves and back to a secondary shear wave, concealing the transmitted shear wave arrival in the wave train. In laboratory settings, we illustrate the difficulty of shear wave detection in wave trains recorded on highly porous chalk plug samples from the Danish North Sea Basin. Wave trains were recorded on plugs dry, Tap‐water or Isopar‐L saturated during uniaxial strain compaction. The recorded shear wave trains showed two distinct features, which could be interpreted as the transmitted shear wave first arrival; we denoted them as early and late arrivals. However, as only one feature can mark the arrival of the transmitted shear wave, we propose a semi‐empirical disclosure strategy combining a graphical representation of stacked wave trains with rock physical modelling. By stacking recorded wave trains in a graphical strain–time–amplitude domain, we demonstrate that an early shear wave feature marks a converted shear to compressional to shear wave and not the transmitted shear wave. We used physical modelling to identify early shear wave features and illustrate the consequences of adopting a falsely interpreted shear wave on stiffness properties.

Biot's theory-based dynamic equation modeling using a machine learning auxiliary approach

Abstract Characterizing seismic wave propagation in a fluid-saturated porous media well enhances the precision of interpreting seismic data, bringing benefits to understanding reservoir properties better. Some important indicators, including wave dispersion and attenuation, along with the wavefield, are widely used for interpreting the reservoir, and they can be obtained from a rock physics model. In existing models, some of them are limited in scope due to their complexity, for example, numerical solutions are difficult or costly. In view of this, this study proposes an approach of establishing equivalent dynamic equations of existing models. First, the framework of the equivalent model is derived based on Biot's theory, while the elastic coefficients are set as unknown factors. The next step is to use deep neural networks (DNNs) to predict these coefficients, and surrogate models of unknowns are established after training DNNs. The training data is naturally generated from the original model. The simplicity of the equation forms, compared to the original complex model and some other equivalents such as the viscoelastic model, enables the framework to perform wavefield simulation easier. Numerical examples show that the established equivalent model can not only predict similar dispersion and attenuation, but also obtain wavefields with small differences. This also indicates that it may be sufficient to establish an equivalent model only according to dispersion and attenuation, and the cost of generating such data is very small compared to simulating the wavefield. Therefore, the proposed approach is expected to effectively improve the computational difficulty of some existing models.

Interpretable machine learning model for shear wave estimation in a carbonate reservoir using LightGBM and SHAP: a case study in the Amu Darya right bank

The shear wave velocity (Vs) is significant for quantitative seismic interpretation. Although numerous studies have proved the effectiveness of the machine learning method in estimating the Vs using well-logging parameters, the real-world application is still hindered because of the black-box nature of machine learning models. With the rapid development of the interpretable machine learning (ML) technique, the drawback of ML can be overcome by various interpretation methods. This study applies the Light Gradient Boosting Machine (LightGBM) to predict the Vs of a carbonate reservoir and uses the Shapley Additive Explanations (SHAP) to interpret the model. The application of ML in Vs estimation normally involves using conventional well-log data that are highly correlated with Vs to train the model. To expand the model’s applicability in wells that lack essential logs, such as the density and neutron logs, we introduce three geologically important features, temperature, pressure, and formation, into the model. The LightGBM model is tuned by the automatic hyperparameter optimization framework; the result is compared with the Xu-Payne rock physics model and four machine learning models tuned with the same process. The results show that the LightGBM model can fit the training data and provide accurate predictions in the test well. The model outperforms the rock physics model and other ML models in both accuracy and training time. The SHAP analysis provides a detailed explanation of the contribution of each input variable to the model and demonstrates the variation of feature contribution in different reservoir conditions. Moreover, the validity of the LightGBM model is further proved by the consistency of the deduced information from feature dependency with the geological understanding of the carbonate formation. The study demonstrates that the newly added features can effectively improve model performance, and the importance of the input feature is not necessarily related to its correlation with Vs