Fracture-induced anisotropy and seismic attenuation strongly influence wave propagation in fluid-saturated reservoirs but remain difficult to characterize simultaneously from conventional seismic observations. This study presents an integrated vertical seismic profiling (VSP) workflow for quantifying azimuthal velocity anisotropy and attenuation in naturally fractured carbonate reservoirs. Layer-stripping tomographic inversion of zero-offset and single-offset VSP data is first applied to estimate layer-specific anisotropic P- and S-wave velocity models. These models are subsequently combined with interval quality factors (Q) derived from the zero-offset VSP to construct a layered horizontally transverse isotropic (HTI) viscoelastic rock-physics model based on anisotropic Gassmann theory. The resulting model is used to generate synthetic multi-azimuth VSP wavefields, enabling investigation of the azimuthal dependence of seismic velocity and attenuation. The modeled azimuthal responses are interpreted alongside fracture orientations derived from formation microImager (FMI) logs. The results reveal systematic azimuthal variations in both seismic velocities and quality factors, demonstrating that fracture-induced anisotropy is the dominant control on wave propagation within the reservoir. Maximum P-wave velocities occur for propagation parallel to the dominant fracture orientation, whereas minimum velocities are observed in the fracture-normal direction. Within the reservoir interval (2800–3200 m), the modeled quality factor varies from approximately 82 in the fracture-parallel direction to approximately 100 in the fracture-normal direction, reflecting enhanced wave-induced fluid-flow attenuation and scattering associated with compliant, fluid-filled fractures. Above the reservoir, background Q values increase to approximately 125–170, indicating lower attenuation in the overlying formations. The close agreement between the modeled azimuthal Q response and the FMI-derived fracture orientations demonstrates that azimuthal attenuation provides a robust indicator of fracture geometry. The proposed framework establishes a quantitative relationship between fracture orientation and seismic attenuation, providing an effective tool for fracture characterization and reservoir evaluation in naturally fractured carbonate systems.

Fracture-induced anisotropy and seismic attenuation strongly influence wave propagation in fluid-saturated reservoirs but are challenging to quantify jointly from seismic data. We present an integrated vertical seismic profiling (VSP) framework for estimating azimuthal anisotropy and attenuation in fractured media. A layer-stripping tomographic inversion of offset VSP first arrivals is used to derive azimuthally anisotropic P - and S -wave velocity models, while quality factors ( Q ) are estimated from VSP waveforms in the time–frequency domain. The resulting elastic and attenuation parameters are incorporated into a viscoelastic rock-physics model based on anisotropic Gassmann theory to generate azimuth-dependent synthetic VSP responses. Field data analysis reveals systematic azimuthal variations in both velocities and Q factors, indicating that fractures are the dominant source of anisotropy. Maximum velocities are aligned with the principal fracture orientation, whereas minimum velocities occur in fracture-normal directions. The lowest Q values are observed along fracture-parallel azimuths due to enhanced scattering and anelastic energy loss, while higher Q values correspond to mechanically stiffer directions. These trends are consistently observed across multiple depth intervals and are well reproduced by synthetic modeling. The results demonstrate that joint analysis of azimuthal anisotropy and attenuation from VSP data provides a robust tool for fracture characterization and reservoir development in fractured carbonate systems.

Accurate three-dimensional acoustic impedance modeling in offshore clastic reservoirs remains a significant challenge due to sparse well control and the highly nonlinear relationship between seismic attributes and subsurface elastic properties. This study introduces an integrated, physics-guided machine learning (ML) workflow that combines rock-physics-driven pseudo-well generation with neural networks to directly map seismic attributes to acoustic impedance under data-limited conditions. A soft-sand rock physics workflow was applied, in which grain moduli were determined using the Voigt–Reuss–Hill average. The dry rock frame was modeled at critical porosity by Hertz–Mindlin contact theory and then interpolated toward zero porosity using the Modified Hashin–Shtrikman lower bound. Gassmann fluid substitution was subsequently performed. Using this approach, 45 pseudo-wells were generated and conditioned through lithofacies classification and spatial statistics, mitigating the risk of overfitting associated with the three available real wells. Six seismic attributes—envelope, RMS amplitude, instantaneous phase, instantaneous frequency, quadrature trace, and sweetness—were selected as predictors. Two neural architectures, a multi-layer feedforward network (MLFN) and a radial basis function network (RBFN), were trained and benchmarked using a leave-one-well-out cross-validation scheme. The MLFN achieved higher predictive accuracy (CC = 0.87, NRMSE = 0.493) compared to the RBFN (CC = 0.79, NRMSE = 0.613), which may reflect its greater capacity to model broader hierarchical relationships between seismic attributes and acoustic impedance. The resulting impedance volume delineates laterally coherent high-impedance sandstone units and low-impedance porous intervals consistent with geological interpretation. These results suggest that integrating physics-guided pseudo-well augmentation with feed-forward neural networks offers a practical and computationally efficient approach for acoustic impedance inversion in data-limited offshore settings. Future work may explore validation across diverse geological settings to assess the robustness and transferability of the proposed methodology. This study provides a basis for hybrid and uncertainty-aware inversion frameworks that may help address complexities in heterogeneous reservoir systems, highlighting the importance of reproducible and widely applicable data-driven seismic inversion methods under sparse well control.

This study presents a hybrid seismic inversion framework to estimate 3D acoustic impedance volumes in a geologically complex and data-limited environment. The approach integrates physics-informed pseudo-well generation, based on calibrated rock physics modeling and variogram statistics, with a deep feedforward neural network (DFNN) that maps multi-attribute seismic data to acoustic impedance while substantially reducing dependence on low-frequency background models and dense well calibration. The compact DFNN serves as a high-dimensional nonlinear mapper that learns the relationship between seismic attributes and impedance logs, a task for which it is well suited, leading to accurate predictions. We generated synthetic elastic logs (compressional and shear velocities, and bulk density) using calibrated rock physics modeling and variogram-constrained stochastic simulation to supplement real well logs. We produced a lithologically diverse and statistically coherent training dataset. This process, applied to only 3 real wells, generated a robust ensemble of 36 synthetic pseudo-wells, effectively addressing the severe data scarcity and providing sufficient training data. Seismic attributes representing amplitude, phase, and frequency characteristics are selected to facilitate the model’s ability to resolve subtle geological heterogeneity. The trained DFNN is validated through a leave-one-well-out strategy yielding a cross-correlation coefficient of up to 95.4% and a normalized relative error below 1% when tested on the blind wells. Combining physical modeling with data-driven learning reduces reliance on low-frequency background models and dense calibration. Rather than replacing conventional inversion, it provides a complementary, geologically consistent, and computationally efficient approach for reliable reservoir characterization in offshore environments. Future work may focus on incorporate uncertainty quantification and volumetric convolutional networks to further improve spatial resolution and model reliability in complex subsurface settings.

Characterizing pore types in carbonate rocks is essential for understanding their reservoir properties, such as water saturation, porosity, and permeability, as well as their reservoir quality and dynamic behavior. The aim and objective of this study are primarily to identify the pore types and then, as an innovative approach, to specify whether the fluid within the pores in the reservoir is producible or remains immobile. To achieve this goal, bound and free fluid pore types are defined using nuclear magnetic resonance logs and post-stack 3D seismic data from an Iranian oil reservoir for the Main Ilam carbonate Formation. Initially, the fullset of logs for two wells (A and B) were used to determine porosity, lithology, and fluid content, followed by the nuclear magnetic resonance log to identify macro, meso, micro, and clay pore types. Subsequently, in well A, the results were validated through pore-size distribution analysis of the available core samples. Afterward, a rock physics model for carbonated rocks was used to estimate compressional velocity and density based on petrophysical evaluation and pore-type calculation. The correlation coefficients for compressional velocity in wells A and B of the Main Ilam Formation were 92

Accurate three-dimensional acoustic impedance modeling in offshore clastic reservoirs remains a significant challenge due to sparse well control and the highly nonlinear relationship between seismic attributes and subsurface elastic properties. This study introduces an integrated, physics-guided machine learning (ML) workflow that combines rock-physics-driven pseudo-well generation with neural networks to directly map seismic attributes to acoustic impedance under data-limited conditions. A soft-sand rock physics workflow was applied, in which grain moduli were determined using the Voigt–Reuss–Hill average. The dry rock frame was modeled at critical porosity by Hertz–Mindlin contact theory and then interpolated toward zero porosity using the Modified Hashin–Shtrikman lower bound. Gassmann fluid substitution was subsequently performed. Using this approach, 45 pseudo-wells were generated and conditioned through lithofacies classification and spatial statistics, mitigating the risk of overfitting associated with the three available real wells. Six seismic attributes—envelope, RMS amplitude, instantaneous phase, instantaneous frequency, quadrature trace, and sweetness—were selected as predictors. Two neural architectures, a multi-layer feedforward network (MLFN) and a radial basis function network (RBFN), were trained and benchmarked using a leave-one-well-out cross-validation scheme. The MLFN achieved higher predictive accuracy (CC = 0.87, NRMSE = 0.493) compared to the RBFN (CC = 0.79, NRMSE = 0.613), which may reflect its greater capacity to model broader hierarchical relationships between seismic attributes and acoustic impedance. The resulting impedance volume delineates laterally coherent high-impedance sandstone units and low-impedance porous intervals consistent with geological interpretation. These results suggest that integrating physics-guided pseudo-well augmentation with feed-forward neural networks offers a practical and computationally efficient approach for acoustic impedance inversion in data-limited offshore settings. Future work may explore validation across diverse geological settings to assess the robustness and transferability of the proposed methodology. This study provides a basis for hybrid and uncertainty-aware inversion frameworks that may help address complexities in heterogeneous reservoir systems, highlighting the importance of reproducible and widely applicable data-driven seismic inversion methods under sparse well control.

Carbonate formations, known for their complex characteristics, require detailed internal heterogeneity knowledge for effective exploration and production. This study presents an integrated workflow to investigate heterogeneity at different scales, from microscopic to log level, in southwest Iran wells. Geological settings were studied, including depositional systems, structural elements, field stresses, diagenesis, and facies variations. Conventional petrophysical evaluation determined lithologies, porosity, and fluid types/content. Statistical methods such as Lorenz curves, semivariance analysis, and the coefficient of variation were used to analyze porosity heterogeneity. Image processing (segmentation) analyzed petrographic images to identify rock matrix and pore spaces. Image logs from oil-based microimagers and ultrasonic borehole imagers showed variations in porosity, fracture networks, zonation, and stress directions. Nuclear magnetic resonance log provided porosity types and sizes. We evaluated vertical and lateral heterogeneities across different zones and wells. This study’s results show that a multi-scale workflow is essential for accurately characterizing reservoir heterogeneity in carbonate fields. The analysis effectively identifies sedimentological and structural influences, quantifies heterogeneity, and ranks zones based on their heterogeneity. The models developed through this workflow enhance decision-making in reservoir characterization and offer practical applications for field studies. Despite limitations like imaging resolution and data availability, this approach remains integral to advancing the understanding of heterogeneity and guiding further improvements.

Acoustic wave anisotropy in fractured carbonate reservoirs remains a key challenge for accurate reservoir evaluation and well placement. The Asmari Formation, one of Iran’s most productive reservoirs, is strongly affected by complex fracture networks and heterogeneity, significantly distorting its acoustic log responses. This study applies an integrated workflow combining facies analysis, borehole image interpretation, borehole geometry assessment, and advanced dipole sonic processing across five reservoir zones in a well in a Southwest Iranian oilfield. Geological controls were constrained through petrography and facies descriptions, while textural and structural features, fracture sets, and in-situ stresses were identified from borehole image logs. Dipole sonic data were processed to evaluate shear-wave splitting, azimuthal velocity variations, and Stoneley wave reflection coefficients, with fracture density used to assess connectivity and transmissivity. Results show that anisotropy is predominantly governed by fracture intensity and connectivity rather than facies variability. Zone 1 records the strongest anisotropy, while Zone 3 remains nearly isotropic. In contrast, Zone 4 demonstrates poor fracture connectivity reduces anisotropy despite higher fracture counts. Borehole effects in Zone 5 generate apparent anisotropy unrelated to the actual reservoir properties. Overall, anisotropy decreases systematically from Zone 1 to Zone 3, with connectivity and borehole artifacts as decisive modifiers. The above workflow highlights the necessity of integrating geological and geophysical datasets to separate genuine reservoir anisotropy from borehole-related effects, enabling more reliable prediction of fracture permeability and improved reservoir development strategies.

Fractures and tectonic settings cause azimuthal anisotropy in reservoirs. Recognizing the fracture model from the seismic data is a useful tool for identifying the productive zone in reservoirs. We applied azimuthal velocity analysis in seismic processing to improve the image quality and to estimate the anisotropic model parameters. Using azimuthal residual moveout analysis, the direction of azimuthal anisotropy in the reservoir was predicted, and it was found that the results are consistent with fracture orientations obtained from image logs in the reservoirs. Bayes' theorem and a cascaded procedure in least-squares inversion, which matched observed amplitudes to linearized Zoeppritz equations, were used to estimate the elastic moduli as a first step, and the normal and tangential fracture weaknesses were estimated in a second step. Laboratory experiments were carried out on core samples to validate the first-step inversion results. It was found that the propagation wavelets varied in space and reflection time, and so a library of extracted wavelets in the time-frequency domain was used for seismic inversion. Maps of the computed fracture fluid index and estimated fracture weaknesses were used to help to visualize the role of fractures in reservoir productivity, and revealed a consistency with the seismic peak frequency attribute in identifying zones of highly compliant fracture fill. The estimated fracture model demonstrates a good fit with the fractures seen in the available core samples and implies that the fracture fluid index is a useful attribute for determining the productive zones in the reservoir.

The activation of the tectonic setting primarily affects the azimuthal anisotropy, as the poroelastic moduli vary. Seismic imaging to analyze wellbore stability and characterize the reservoirs must take azimuthal anisotropy into account. We investigated the azimuthal anisotropy during seismic processing to show the imaging improvement from isotropy to horizontal transverse isotropy states. We estimated the direction of anisotropy in the reservoir with horizontal transverse isotropy (HTI) moveout analysis and confirmed the results with the direction of active stresses obtained from imaging petrophysical logs and experimental tests. We developed the relationships between strains and stresses in the anisotropy state and combined the results with the failure criterion to express the point for critical pore pressure in breaking onset. We used the experimental analysis to determine the Biot coefficient. We then determined the compliance fractures and the horizontal stresses using the Mohr-Coulomb failure criterion. We evaluated the stresses in isotropic and anisotropic state and analyzed them in reservoir conditions. The study showed that the calculated stresses under anisotropic conditions are 26% higher than under isotropic conditions. This point must be taken into account in the wellbore stability analysis and the reservoir characterization.

Pore types in carbonate reservoirs are more complex than their sandstone counterparts due to the wide spectrum of their depositional environments and their more complicated post-depositional processes. This means that a good knowledge of pore types is vital in determining carbonate formation’s elastic and reservoir properties. This study aims to develop a multi-physics approach to determine pore-type variations in a carbonate reservoir using well log information from one of the oilfields of the Abadan Plain in southwest Iran. Firstly, we determined lithology, porosity, and fluid content by interpreting conventional well logs (gamma ray, resistivity, density, neutron, photoelectric, and P-wave sonic). Then, nuclear magnetic resonance data were used to determine different pore types within the Main Ilam and Sarvak formations. We distinguished between clay, micro, meso, and macro pore types. We confirmed our interpretation results using thin sections, scanning electron microscopy photographs, and pore-size distribution on the available core plugs. Finally, a carbonate rock physics model was employed to model sonic velocities using petrophysical interpretation along with pore-type determination results. A good match between modeled and measured sonic velocities confirmed that using nuclear magnetic resonance data for pore-type determination can reasonably estimate pore-type variations needed for rock physics modeling. The standard industry procedure for carbonate rock physics modeling uses sonic logs, core data, or thin sections to determine pore types. We offer a substitute approach with reasonable accuracy for pore-type modeling needed for carbonate rock physics modeling. We modeled pore types independently from sonic velocity and used them to predict P-wave velocity with a correlation coefficient of 92 and 64 percent accuracy in the Main Ilam and Sarvak formations.

High-frequency contents of reflections are essential in the investigation and interpretation of thin-bed reservoirs. These beds can be even more complicated in carbonate rocks, as pore geometries influence final seismic responses. To address these complexities, we propose a seismic forward modeling workflow to investigate several thin-bed reservoirs in a carbonate oilfield with variable pore geometries. The new workflow enhances the existing forward models for the investigation of thin beds by integrating seismic petrophysics, geological model building, and 2D finite-difference elastic modeling. We used seismic petrophysics to ensure the consistency between petrophysical well logs and seismic data using rock physics modeling. Then, we introduced a new high-resolution workflow for velocity modeling to build a reliable geological model. Finally, the 2D finite-difference elastic modeling is employed to generate synthetic traces based on our geological model to obtain seismic responses for the existing thin-bed reservoirs. The forward models used in this study are a powerful tool for investigating thin layers because they enable high-resolution investigation of the given geological model in distinguishing lateral and vertical lithofacies changes. The new velocity modeling workflow, implemented in this research, is more reliable and effective than the conventional velocity property modeling approaches, which resulted in synthetic seismic sections with increased lateral and vertical resolutions and enhanced data from a thin bed. The main features of this workflow are the incorporation of well-log data into geological model building, combining the high-resolution data of horizontal seismic stacking velocity with vertical well logging, and the incorporation of a residual model to improve the seismic stacking velocity. We produced a more coherent section resembling the acquired 3D seismic data by applying the proposed workflow to data from an oil carbonate reservoir in the Fahliyan Formation within the Abadan Plain in SW Iran. It is concluded that the higher frequency synthetic sections from the proposed workflow can assist in resolving the seismic interpretation challenges. By applying the proposed workflow to the current data set, four thin-bed carbonate reservoirs were investigated with corresponding thicknesses of approximately 25, and 17 m at peak frequencies of 60, and 90 Hz, respectively.

Permeability is an important factor for reservoir characterization. It is routinely estimated by building a relationship between porosity and permeability. But because of the complexity of the pore types in carbonate reservoirs, sometimes this method does not yield good results. This paper proposes an integrated workflow using rock physics modeling and seismic inversion to estimate the permeability section using core data, petrophysical logs, and seismic data. Our data set belongs to a carbonate reservoir from Abadan Plain and includes three wells and a 2D seismic offset gathers. First, we estimated geophysical pore types (stiff, reference, and cracks) using a pore type inversion algorithm. The validity of the obtained results is investigated using the scanning electron microscope, and thin section images from core samples. Then, the contribution of different pore types to permeability prediction has been investigated and compared to the routine method of permeability prediction using porosity. Analysis of the results at the well locations shows that we achieved better permeability estimation (around 10% improvement in this case) by integrating information of various pore types with the flow capacity. Furthermore, using the proposed method, a permeability section has been generated using the integration of seismic, well logs, and rock physics modeling results for pore types.

Biot's coefficient is an essential factor for estimating reliable-effective stress and an efficient tool in understanding the rock's response to pressure and stress changes. This coefficient is normally considered as a crucial parameter for reservoir geomechanics studies, such as wellbore stability, improving production rate, and hydraulic fracturing of reservoirs. However, its measurement and modeling methods, especially in carbonate rocks, have not been sufficiently studied. The scope of this study is to investigate the relationship between static and dynamic Biot's coefficients for a carbonate oilfield in the southwest of Iran. In this study, 13 core-plug samples were measured from a carbonate oilfield under static and dynamic conditions. Static Biot's coefficient was calculated using stress loading tests and volumetric strain measurements by changing confining and pore pressures. Dynamic Biot's coefficient calculated using ultrasonic measurements under ambient conditions and applying rock physics modeling. We used two workflows based on carbonate rock physics models for two separate pore type models calculation; the first one uses the usual form of Gassmann's theory, and the second one uses its simplified form with a defined C-factor exponent. Then, two dynamic Biot's coefficients were modeled from these pore models along with the calculated grain bulk modulus and the obtained dry bulk modulus. We showed that the dynamic Biot's coefficient in the second approach follows a better agreement with the static Biot's coefficient due to the higher accuracy of the estimated porosity model. Our results also show that static and dynamic Biot's coefficients depend on the pore geometry. As a result, the increasing volume fraction of stiff (moldic and vuggy) pores decreases Biot's coefficient compared to soft (crack) pores. In addition, we used the C-factor parameter calculated from the simplified form of Gassmann's equation to investigate this relationship with the pore geometry. The results showed that C-factor gives a good accuracy for converting dynamic to the static Biot's coefficient based on the pore structure. This, furthermore, was confirmed by the pore model stiffness study. The results of this study can provide the necessary information and relationships for modeling the static Biot's coefficient as an essential parameter in geomechanical studies for exploration and development programs.

Channel facies, of the most prevalent stratigraphic features, are essential from the perspective of hydrocarbon exploration. However, measuring edge features using the gradient vector's calculation in an individual pixel mainly produces edge borders with pixel resolution even in images with low noise levels. This paper introduces a novel seismic attribute based on the partial area effect algorithm assuming a particular discontinuity in the edge location to extract the buried channel boundaries. First, the Sobel-based edge detector extracts the pixels' partial derivatives as probable channel boundaries. Then, the direction and the dimension of the postulated partial area effect mask in the local maxima points are deliberated to elicit the edge curve coefficients as the perfect edge positions. The proposed algorithm was implemented on a synthetic time slice comprising two-channel events with varying thicknesses and sinuosity. The procedure was also investigated on two high-cut frequency filtered datasets from the Penobscot prospect in the Nova Scotia Basin accommodating canyon-channel events. The proposed algorithm was then compared to the prominent gradient-based edge detectors (Canny, Prewitt, and Sobel) and some conventional seismic attributes (apparent dip, most negative curvature, and similarity). The results showed that applying the nominated algorithm could provide an improved map of buried channels less affected by the coherent noise and acquisition footprints. The partial area effect algorithm also successfully localized more true-positive edge points and fewer false-positive ones in the synthetic and field seismic data examples.

For addressing the behavior of a reservoir with different fluid types, the Biot-Gassmann equation often is the base of the practical simulation. Despite the prevalence application of this equation with the isotropy conditions, the unforeseen errors always expose in simulation results because of the anisotropy state in reality. We investigated the anisotropy model with the integration of two analytical strategies using a three-component VSP data set. We obtained an initial anisotropy model in the region of acquired walkaway VSP using slowness polarization inversion, and updated the anisotropy model with the application of anisotropy ray-tracing and tomography. We applied a layer-stripping approach to the anisotropy model during raytracing to optimize the inversion. Given a computed geomechanical model and extracted rock properties of a carbonate reservoir, we developed the anisotropy Biot-Gassmann model, for finding the elastic moduli. We used the substitution strategy to generate the dynamic model of elastic moduli. We showed how the compressional modulus and rigidity change with the anisotropy model in different fluid content. We found that integration of slowness polarization and raytracing tomography increases the maneuverability to control the predicted anisotropy model and intensifies the convergence rate of the inverse problem. We observed that the isotropy assumption in modeling the elastic parameters makes around 8-10 % drift value in compressional modulus relevant to the reality, whereas rigidity showed reluctant behavior to fluid.

Buried channels are considered stratigraphic traps, essential in petroleum exploration and drilling hazard management. A thorough investigation of the buried channels provides helpful information about the sedimentation processes and the marine currents. Hand-operated interpretation of channels is sometimes labor-intensive and time-consuming, particularly in areas with complex geological patterns or low signal-to-noise ratios. However, automatic feature extraction is a task-on-demand. Channel boundaries, depicted as curvy and curvilinear events on time slices, are called edges in image processing, where amplitudes intensively vary. This paper provides an improved edge delineation algorithm with a sub-pixel resolution for an enhanced channel boundary depiction. The partial area effect, in combination with a unique edge linking technique, is proposed to strengthen the connectivity of edge segments and the fidelity of edge outlines. First, a gradient-directed partial area effect mask was employed in the edge area of interest to extract the edge position in each pixel with relatively high precision and less affected by environmental noise. Then, an edge linking algorithm based on the edge segments' distance was applied to the partial area effect's results to connect the circular arc edges detected. Field tests were carried out on synthetic and field data sets containing several channelized features with differing widths and tortuosity. The proposed sub-pixel procedure afforded more precise and cost-effective outcomes than approaches with pixel resolutions. The quantitative validation tests using root mean square error, peak signal-to-noise ratio, structural similarity index, and Pearson correlation coefficient revealed that the proposed approach exceeded the traditional edge measures and seismic attributes by detecting more reliable edge points. Finally, we tested the proposed algorithm on synthetic and field seismic data sets containing salt domes and fault events to determine its applicability for localizing other geological features. The detected edges were quantitatively validated based on the manually interpreted events. The salt and fault boundaries detected by the proposed algorithm have relatively high coincidences with their ground truths.

Bulk modulus which relates seismic attributes to rock and fluid properties is considered as an important parameter for seismic reservoir characterisation workflows, and can provide useful information for such studies. However, its measurement and modelling approaches are yet to be sufficiently addressed and discussed especially for carbonate rocks. In this research, in order to provide more information about bulk modulus, nine samples from a carbonate oilfield were subjected to static and dynamic investigations under dry and saturated conditions. Then, the dynamic modulus was calculated using well log data and ultrasonic measurements. In order to obtain static data, multi-stage triaxial compression tests were performed on the vertical plugs extracted from conventional cores taken at different selected depths. The results showed that static and dynamic bulk moduli follow similar trends, although the value of dynamic modulus is usually higher. Furthermore, several empirical relationships based on simple linear regression and forward and backward stepwise multiple linear regressions were developed to relate measured static and dynamic bulk moduli for the given field, then proposed equations were evaluated by ANOVA analysis. Besides, dry and saturated bulk moduli were modelled using Xu and Payne rock physics model. Here, saturated bulk modulus was modelled using either dynamic or static dry bulk moduli within the Gassmann's theory. It is observed that Gassmann's equation gives a more accurate result using dynamic data rather than static ones. The poor Gassmann's equation prediction under static condition could be attributed to microcracks in the samples and the uncertainty associated with this theory for complex pore geometry. The outcomes of this study can, furthermore, provide the necessary information and relationships for rock physics (e.g. shear wave estimating and fluid substitution modelling) and geomechanical (e.g. CO2 injection and compaction forecast) studies for exploration and development programs.

ABSTRACTThe propagation of seismic waves through a saturated reservoir compresses the fluid in the pore spaces. During this transition, parts of seismic energy would be attenuated because of intrinsic absorption. Rock physics models make the bridge between the seismic properties and petrophysical reality in the earth. Attenuation is one of the significant seismic attributes used to describe the fluid behaviour in the reservoirs. We examined the core samples using ultrasonic experiments at the reservoir conditions. Given the rock properties of the carbonate reservoir and experiment results, the patchy saturation mechanism was solved for substituted fluid using the theory of modulus frequency. The extracted relationship between the seismic attenuation and water saturation was used in time–frequency analysis. We performed the peak frequency method to estimate theQfactor in the Gabor domain and determined the water saturation based on the computed rock physics model. The results showed how the probable fault in the reservoir has stopped the fluid movement in the reservoir and caused touching the water‐bearing zone through drilling.

Faults are natural tectonic events as planar features along which rock units are moved. The patterns of these planes on seismic sections include linear or curvilinear features that are called edge in image processing, where amplitudes sharply change. In seismic data, these edge features made by fault traces are usually detected by seismic attributes, which need complex mathematical calculation such as a dip-steered cube. In this study, we introduce faults as global anomalies which disturb the normal interaction of seismic reflectors. Here, the normal interaction means the absence of intensive changes in reflectors trend in seismic sections. Fault detection as a global anomaly is done by the Gaussian process regression model (GPR), which is a nonparametric probabilistic model based on Bayesian statistics supporting noisy (Gaussian noise) and sparse features in data. In data mining, anomaly detection identifies items or events that do not match an expected pattern in a dataset. Global anomalies are sparse and affect a wide range of normal trends of data which are also held by fault features in seismic data. In this study, the GPR-based anomaly detection algorithm was implemented on the 3D seismic data of the Gulf of Mexico containing normal growth faults and a salt dome to detect salt boundary and fault traces in seismic data. In this respect, the reflections from rock units and fault features were taken into account as normal interactions and global anomalies, respectively, because faults disrupted the normal trend of reflectors in seismic sections. To detect fault locations, the location of a voxel in voxel grid where it is a part of fault in seismic data, after smoothing the seismic data, a Gaussian process (GP) model was trained on seismic data, attempting to describe the seismic amplitude data as a multivariate Gaussian model. However, GP regression fails to describe the seismic data at fault locations. Thus, the failure of the GP in the regression step was analyzed to separate the probable fault points, highlighted by calculating the variance of the GPR results. Finally, the detected probable fault points were improved and separated from background results by implementing a consistent reconstruction morphological algorithm. The results were validated using a similar structural index method, mean square error, and power signal to noise ratio indices in comparison with interpreted faults, implying the superiority of the proposed method in comparison with seismic attributes. The faults detected by the proposed method have the most structural similarity to faults interpreted. This similarity has improved by 22% compared to used attributes.