Estimation of Pressure-Saturation and Porosity Fields from Seismic AVA Data Using an Ensemble Based Method

<p>Seismic inversion method is widely used to characterize reservoirs and detect zones of interest, i.e., hydrocarbon-bearing zone in the subsurface by transforming seismic reflection data into quantitative subsurface rock properties. The primary aim of seismic inversion is to transform the 3D seismic section/cube into an acoustic impedance (AI) cube. The integration of this elastic attribute, i.e., AI cube with well log data, can thereafter help to establish correlations between AI and different petrophysical properties. The seismic inversion algorithm interpolates and spatially populates data/parameters of wells to the entire seismic section/cube based on the well log information. The case study presented here uses machine learning-neural network based algorithm to extract the different petrophysical properties such as porosity and bulk density from the seismic data of the Upper Assam basin, India. We analyzed three different stratigraphic  units that are established to be producing zones in this basin.</p><p> AI model is generated from the seismic reflection data with the help of colored inversion operator. Subsequently, low-frequency model is generated from the impedance data extracted from the well log information. To compensate for the band limited nature of the seismic data, this low-frequency model is added to the existing acoustic model. Thereafter, a feed-forward neural network (NN) is trained with AI as input and porosity/bulk density as target, validated with NN generated porosity/bulk density with actual porosity/bulk density from well log data. The trained network is thus tested over the entire region of interest to populate these petrophysical properties.</p><p>Three seismic zones were identified from the seismic section ranging from 681 to 1333 ms, 1528 to 1575 ms and 1771 to 1814 ms. The range of AI, porosity and bulk density were observed to be 1738 to 6000 (g/cc) * (m/s), 26 to 38% and 1.95 to 2.46 g/cc respectively. Studies conducted by researchers in the same basin yielded porosity results in the range of 10-36%. The changes in acoustic impedance, porosity and bulk density may be attributed to the changes in lithology. NN method was prioritized over other traditional statistical methods due to its ability to model any arbitrary dependency (non-linear relationships between input and target values) and also overfitting can be avoided. Hence, the workflow presented here provides an estimation of reservoir properties and is considered useful in predicting petrophysical properties for reservoir characterization, thus helping to estimate reservoir productivity.</p>

Seismic inversion in geophysics is a method that uses certain prior information, such as known geological laws and well logging and drilling data, to infer the physical parameters of underground media, such as wave impedance, velocity, and density, from seismic observation data, and thereby obtain the spatial structure and physical properties of underground strata. Seismic inversion is a highly complex problem with multiple solutions, and with the advancement of collection equipment, the volume of geophysical observation data is increasing at an astonishing rate. This presents new challenges for the accuracy and speed of seismic data inversion methods. There is an urgent need to develop intelligent and efficient inversion technologies for seismic inversion.Deep learning networks have powerful nonlinear fitting capabilities and can be used to solve complex nonlinear problems, such as seismic inversion. However, the predictive ability of deep learning networks largely depends on the quantity of training data. In the early stages of oil and gas exploration and development, the amount of well logging label data available for training is very limited, which poses a challenge for the application of deep learning in seismic inversion. Semi-supervised learning seismic inversion methods consider both data mismatch issues and well logging data mismatch issues, and can better adapt to inversion problems in real-world scenarios. Unlike supervised learning approaches, semi-supervised learning does not require a large amount of labeled data, thus it can better handle situations of data scarcity or mismatch.This paper utilizes a semi-supervised learning workflow to perform inversion on post-stack seismic data and has conducted experimental validation on the Marmousi 2 model. The experimental results show that, compared to supervised learning networks, the semi-supervised learning network still exhibits good predictive performance with a limited amount of data, demonstrating better stability in the presence of noise and geological variations, and effectively learns the mapping relationship between seismic data and artificial intelligence. Furthermore, as the amount of training data increases, the performance of the network also improves, confirming the importance of data quantity for training deep learning networks. The application results of the network on actual data indicate that the network has broad application prospects and feasibility. However, since the network is based on a channel-by-channel inversion method, there is still a lack of representation in terms of lateral continuity, which requires further exploration and improvement in subsequent research.

Seismic reflection amplitude data are increasingly used in reservoir modeling to provide information on changes in earth properties away from well locations. In geostatistical reservoir modeling, the most common application is to use seismic data as background data in some form of comodeling. Seismic data image reflectors and not earth layer properties. Therefore, prior to use in comodeling, seismic data must first be transformed into an earth layer property. Typically, the transform is to acoustic impedance using an appropriate seismic inversion method. Seismic inversion methods generate results that are generally band limited in nature, resulting in limits to vertical resolution. The vertical resolution achieved can be an order of magnitude below the vertical model resolution required from geostatistical reservoir modeling, which is in the order of well-log resolution. Hence, in using seismic data, geostatistical modelers encounter a problem of downscaling, not the more commonly encountered upscaling problem. This difference in scale introduces scatter between the primary data with well-log order resolution and the secondary seismically derived rock property data used in the comodeling. As a result, to preserve vertical heterogeneity, only limited use of the secondary data can be made in comodeling procedures. This results in models that only partially fit the seismic data, i.e., only limited use is made of the seismic information. If the secondary data are more strongly imposed, the fit to the seismic data improves, but the required vertical heterogeneity is not preserved. The inability to overcome this difference in scale issue, therefore, limits the value of the application of comodeling methods to integrate seismic data into reservoir models. One class of geostatistical methods that overcomes this limitation relies on iterative geostatistical modeling. In these methods, referred to as geostatistical seismic inversion, the iterative modeling process is conditioned such that the final models generated closely match the seismic data while maintaining the required vertical heterogeneity. The application of these methods is computationally expensive relative to comodeling methods but is now practical for large models on today's desktop hardware. Relative to comodeling, geostatistical seismic inversion methods make full use of the information carried in the seismic data, resulting in a significant reduction in model uncertainty away from well control.

شکنندگی یکی از مهم‌ترین خصوصیات سنگ می­باشد. تاکنون روشی مستقیم و استاندارد برای به‌دست آوردن شاخص شکنندگی ارائه نشده است. از شاخص شکنندگی بر اساس پارامترهای مقاومت فشارشی تک‌محوره و مقاومت کششی جهت ارزیابی شکنندگی استفاده می­شود. هدف از این مطالعه بررسی مفاهیم شکنندگی ارائه‌شده توسط محققین و استفاده از روش وارون‌سازی لرزه­ای، آنالیز چندنشانگری و شبکة عصبی در میدان ویچررنج (Whicher-Range) واقع در حوضة پرت (Perth Basin) استرالیای غربی می‌باشد. به این منظور دو چاه و یک مقطع لرزه­ای از میدان ویچررنج مورداستفاده قرار گرفت. کمترین شاخص شکنندگی در چاه اول و دوم که با فاصله 1 کیلومتری از هم حفاری شدند، به‌ترتیب با استفاده از مفهوم برابر 69/1 و 67/1 مگاپاسکال که بیانگر شکنندگی کم و بیشترین مقدار آن برابر 78/39 و 15/48 مگاپاسکال که بیانگر شکنندگی زیاد و از نظر حفاری در رتبة حفاری بسیار سخت می­باشد. در مرحلة بعد با استفاده از استخراج موجک و رسم مدل زمین‌شناسی، مدل‌سازی اولیه انجام و سپس امپدانس صوتی حاصل از فرایند وارون‌سازی در کنار دیگر نشانگرها در راستای ساخت ترکیب بهینه از نشانگرها جهت تخمین شاخص شکنندگی استفاده شد. از سه نوع الگوریتم شبکة عصبی جهت تخمین پارامتر هدف از ترکیب بهینه نشانگرهای موجود استفاده می­شود که به‌کمک نرم‌افزار همپسون–راسل و نشانگرهای بهینه­ای، الگوریتم شبکة عصبی تهیه و در نهایت آنالیز چند نشانگری با سه الگوریتم شبکة عصبی مقایسه می‌شود و نتایج بیانگر ضریب همبستگی بیشتر شبکة عصبی احتمالی نسبت به آنالیز چند نشانگری جهت تعیین شاخص شکنندگی است.

The transformation of seismic reflection data into quantitative rock properties can be very valuable in all phases of oil and gas exploration and production. In this study, public domain data from Australian offshore have been used to explain the logical workflow, which consists of systematic steps from seismic petrophysics to rock physics modeling and seismic inversion for quantitative rock property estimation. The application of seismic inversion technology offers many rewards, such as: better reservoir definition and management; better resource estimation; and reductions in uncertainty. The main benefit is that it improves direct and intangible interpretation of seismic data to provide meaningful geological boundaries in the subsurface. In order to provide the reliable estimate of rock properties for reservoir modeling the workflow is tested rigorously and divided into three categories which are based on the basic inversion types. The results reveal that relative impedance inversion should be performed first, which then followed by revision of seismic interpretation on impedance data. Full bandwidth rock properties are estimated by deterministic inversion. The results can be improved by several iterations of well to seismic tie, wavelet estimation, and low frequency models. As resolution with accuracy has always been challenging, the stochastic inversion approach is trailered for reservoir characterization and high resolution rock properties have been predicted. This produces a number of possible rock property models, as well as litho facies models and the results can be optionally constrained by the well data. It can be concluded that, to some degree, stochastic inversion is able to overcome the limited seismic bandwidth by integrating the rock physics properties of different lithologies. The examples of seismic inversion are discussed to demonstrate the significant benefits can be obtained by following an optimized workflow that is tailored to deal with the uncertainties that impact the end product. Introduction Seismic surveys are routinely performed to gather information about the geology of hydrocarbon fields. Seismic data, even when it has relatively low resolutions, can still deliver a structural model for the reservoir. The availability and coverage area of the data provides valuable information to constrain the reservoir model. Geophysicists are now able to extract greater quantitative information about reservoir rocks and fluid parameters from seismic data by working backwards using seismic inversion methods. Described as the flip-side of forward modeling, seismic inversion is the process of characterizing rocks and fluids that have produced the seismic data. In a sense, the process involves trying to determine the input (rock properties) by looking at the output (seismic data). It starts with actual measured data, removes the wavelet and derives acoustic impedance from reflection coefficient (Figure-1) with a low frequency model to infer rock properties and deliver earth model.

Seismic impedance inversion is a geophysical technique that transforms seismic data into quantitative subsurface properties, primarily acoustic impedance. This process enables the identification of rock boundaries, hydrocarbon reservoirs, and lithological variations, thus supporting informed drilling decisions and reducing exploration risks. However, conventional inversion methods face limitations such as noise sensitivity, low resolution, and reduced effectiveness in geologically complex areas, often resulting in oversimplified subsurface models. This study addresses these challenges by employing deep learning approaches, specifically LeNet, AlexNet, and conventional CNN architectures, to improve seismic resolution and synthetic seismogram generation. The methodology involves preprocessing seismic and well-log data, calculating acoustic impedance and reflection coefficients, and applying Continuous Wavelet Transform (CWT) for feature extraction. The models are trained using synthetic seismograms and validated against real seismic data. Among the models evaluated, AlexNet demonstrates superior performance in seismic data reconstruction, achieving the lowest MSE (0.0031), RMSE (0.0557), and MAE (0.052), along with the highest R2 score (0.993). The proposed technique demonstrates superior predictive accuracy, refined subsurface characterization, and reduced geological risk, thereby establishing a robust benchmark for advanced geophysical data analysis.

Over the last project six months, our project activities have concentrated on three areas: (1) performing a stochastic inversion of pattern 16 seismic data to deduce reservoir permeability, (2) development of the geochemical inversion strategy and implementation of associated software, and (3) completing the software implementation of TProGS and the geostatistical analysis that provides the information needed when using the software to produce realizations of the Midale reservoir. The report partially the following deliverables: D2: Model development: MCMC tool (synthetic fluid chemistry data); deliverable completed. D4: Model development/verification: MCMC tool (TProGS, field seismic/chemistry data) work product; deliverable requirements partially fulfilled. D5: Field-based single-pattern simulations work product; deliverable requirements partially fulfilled. When completed, our completed stochastic inversion tool will explicitly integrate reactive transport modeling, facies-based geostatistical methods, and a novel stochastic inversion technique to optimize agreement between observed and predicted storage performance. Such optimization will be accomplished through stepwise refinement of: (1) the reservoir model - principally its permeability magnitude and heterogeneity - and (2) geochemical parameters - primarily key mineral volume fractions and kinetic data. We anticipate that these refinements will facilitate significantly improved history matching and forward modeling of CO{sub 2} storage. Our tool uses the Markov Chain Monte Carlo (MCMC) methodology. Deliverable D1, previously submitted as a report titled ''Development of a Stochastic Inversion Tool To Optimize Agreement Between The Observed And Predicted Seismic Response To CO{sub 2} Injection/Migration in the Weyburn-Midale Project'' (Ramirez et al., 2009), described the stochastic inversion approach that will identify reservoir models that optimize agreement between the observed and predicted seismic response. The software that implements this approach has been completed, tested, and used to process seismic data from pattern 16. A previously submitted report titled ''Model verification: synthetic single pattern simulations using seismic reflection data'', Ramirez et al. 2010, partially fulfilled deliverable D3 by summarizing verification activities that evaluate the performance of the seismic software and its ability to recover reservoir model permeabilities using synthetic seismic reflection data. A future progress report will similarly describe summarizing verification activities of the geochemical inversion software, thereby completing deliverable D3. This document includes a chapter that shows and discusses permeability models produced by seismic inversion that used seismic data from pattern 16 in Phase 1A. It partially fulfills deliverable D5: Field-based single-pattern simulations work product. The D5 work product is supposed to summarize the results of applying NUFT/MCMC to refine the reservoir model and geochemical parameters by optimizing observation/prediction agreement for the seismic/geochemical response to CO{sub 2} injection/migration within a single pattern of Phase 1A/1B. A future progress report will show inversion results for the same pattern using geochemical data, thereby completing deliverable D5. This document also contains a chapter that fulfills deliverable D2: Model development: MCMC tool (synthetic fluid chemistry data). The chapter will summarize model development activities required to facilitate application of NUFT/MCMC to optimize agreement between the observed and predicted geochemical response to CO{sub 2} injection/migration. Lastly, this document also contains a chapter that partially fulfills deliverable D4: Model development/verification: MCMC tool (TProGS, field seismic/chemistry data) work product. This work product is supposed to summarize model development activities required for (1) application of TProGS to Weyburn, (2) use of TProGS within the MCMC tool, and (3) application of the MCMC tool to address field seismic and geochemical data. The chapter included here fulfills requirements 1 and 2. Requirement 3 will be addressed in a future progress report.

High Resolution, Simultaneous VSP and Land Seismic Acquisition

In a previous work (Luo et al., 2016), we proposed an ensemble 4D seismic history matching framework, which has some relatively new ingredients, in terms of the type of seismic data in choice, the way to handle big seismic data and related data noise estimation, and the use of a recently developed iterative ensemble history matching algorithm. In seismic history matching, it is customary to use inverted seismic parameters as the observations. In doing so, extra uncertainties may arise during the inversion processes. We avoid such intermediate inversion processes by adopting amplitude versus angle (AVA) data. To handle the big-data problem in seismic history matching, we adopt a wavelet-base sparse representation procedure. Concretely, we apply a discrete wavelet transform to seismic data, and estimate noise in resulting wavelet coefficients. We then use an iterative ensemble smoother to history-match leading wavelet coefficients above a certain threshold value. In the previous work (Luo et al., 2016), we applied the proposed framework to a 2D synthetic case. In the current study, we extend our investigation to the 3D Brugge benchmark case. Numerical results indicate that, the proposed framework is very efficient in handling big seismic data, while achieving reasonably good history matching performance.

Time-lapse seismic data has been widely used for the detailed reservoir characterization, and data assimilation algorithms are commonly used for petroleum reservoir history matching of production data. However, hardly any seismic data has been integrated into the reservoir inverse modeling workflow, due to the large data size, finer gridding, and especially the scarcity in time of the seismic data. Popular ensemble-based reservoir inverse modeling methods such as ensemble Kalman filter (EnKF) also face the problems of high computational cost due to the storage of the intermediate variables, restarting the reservoir simulating process and the inconsistency of the full-step and step-wise simulations. The intrinsic sequential data assimilations characteristics of the EnKF set obstacles to assimilate 4D seismic data. The alternative method can be the ensemble smoother (ES), which is an ensemble based method for data assimilation. The ES is based on a Bayesian updating scheme of the reservoir model to match the production history and improve the production forecast. To improve the algorithm convergence, a multiple data assimilation (MDA) method was proposed by Emerick and Reynolds (2012a). The algorithm we used is called ensemble smoother with multiple data assimilation (ESMDA), we modified the ESMDA to integrate the geophysical data, and created the new workflow to history match both the production and geophysical data. The available production data is well measurements, including oil production rate, well water cut and bottom-hole pressure, as well as time-lapse geophysical data, including P-wave impedance. In this paper, we first formulated the mathematical descriptions of ESMDA, we then down-scaled the seismic data, and modified the data assimilation algorithms, illustrated the history matching workflow for both production and geophysical data, finally, we showed how it works with a case study on a water flooding operation in a synthetic reservoir. In comparison, we also showed the history matching only on the production data, which yields an inferior results than the one matches both production and seismic data.

Seismic inversion is an important processing step for characterizing reservoirs with properties predicted away from well controls. A new approach to inversion and reservoir modeling is based on a nonlinear multitrace seismic inversion algorithm. Neural-network solutions for the inversion problem exist, whereby a multiattribute analysis increases output reliability. A more robust 3D working method is proposed that uses a simple nonlinear operator. The method is fast, user friendly, and cost effective. Initial input is formed by poststack seismic data and relevant well logs (e.g., acoustic impedance). The latter serve as a training and control point set to calculate optimized weights in the neural-network scheme. The nonlinear output operator trans-forms the seismic data into the desired log-response equivalent. Crucial is finding a real regional minimum for the difference between the computed synthetic and the recorded seismic traces at the target location. Intelligent data decimation eliminates the number of unknown coefficients in the operator computation. Moreover, it speeds up the true 3D minicube processing. Genetic inversion can be applied to properties other than acoustic impedance. However, these attributes should have a meaningful physical relationship to the seismic data, e.g., porosity, density, and saturation. Geologic modeling constitutes the last step of the inversion workflow. The geologic model is populated stochastically with relevant reservoir properties. The capabilities of the genetic inversion were tested on a semicontrolled seismic example and a real case study across the Shtokman gas field, Russia.

Time-lapse (4D) seismic inversion is the leading method to quantitatively monitor fluid-flow dynamics in the subsurface, with applications ranging from enhanced oil recovery to subsurface CO2 storage. The process of inverting 4D seismic data for reservoir properties is a notoriously ill-posed inverse problem due to the band-limited and noisy nature of seismic data and inaccuracies in the repeatability of 4D acquisition surveys. Consequently, ad-hoc regularization strategies are essential for the 4D seismic inverse problem to obtain geologically meaningful subsurface models and associated 4D changes. Motivated by recent advances in the field of convex optimization, we propose a joint inversion-segmentation algorithm for 4D seismic inversion that integrates total variation and segmentation priors as a way to counteract missing frequencies and present noise in 4D seismic data. The proposed inversion framework is designed for poststack seismic data and applied to a pair of seismic volumes from the open Sleipner 4D seismic data set. Our method has three main advantages over state-of-the-art least-squares inversion methods. First, it produces high-resolution baseline and monitor acoustic models. Second, it mitigates nonrepeatable noise and better highlights real 4D changes by leveraging similarities between multiple data. Finally, it provides a volumetric classification of the acoustic impedance 4D difference model (4D changes) based on user-defined classes (i.e., percentages of speedup or slowdown in the subsurface). Such advantages may enable more robust stratigraphic/structural and quantitative 4D seismic interpretation and provide more accurate inputs for dynamic reservoir simulations. Alongside presenting our novel inversion method, we introduce a streamlined data preprocessing sequence for the 4D Sleipner poststack seismic data set that includes time-shift estimation and well-to-seismic tie. Finally, we provide insights into the open-source framework for large-scale optimization that we used to implement the proposed algorithm in an efficient and scalable manner.

Summary Acoustic impedance (AI) is often inversely proportional to porosity. This has led to a seismic reservoir characterization technology where the AI from seismic inversion is used to predict porosity away from well locations. The porosity is typically predicted from the absolute seismic AI derived from a model based inversion (MBI). There is an inherent error in AI derived from MBI due to the accuracy of the low frequency model (LFM) provided to the inversion engine, introducing an additional error in the predicted porosity. Here we show an use of relative AI after seismic Coloured Inversion to predict porosity in a target zone. This is possible if the seismic data have good low frequency content and if the target zone is small and appropriate for the field development. Within a zone of interest the sensitivity to the effects of the LFM is minimum and therefore relative AI can be sufficient to predict porosity. An Eagle Ford Shale example from the South Texas is used in this study.

Summary The seismic data spectral inversion method, arisen in recent years, can improve the resolution of seismic data for obtaining reservoir characteristics. It does not rely on prior information such as well-logging data. By using partial spectrum information from the input seismic trace data, a sparse reflectivity series can be inverted. The inverted reflectivity series can be used to improve the resolution and impedance inversion for thin layer reservoir prediction. In this paper, we implement seismic spectral inversion based on a compressed sensing algorithm, which can solve the ill-posed problem of the inversion process. In the process of inversion, we introduce a quadratic spectrum method to calculate the spectrum of seismic wavelet in the frequency domain, which can stabilize the inversion and handle real field data. Synthetic and real field seismic data examples show that the proposed spectral inversion based on compressed sensing algorithm is stable and effective. Moreover, the real field data inversion results show a good signal-to-noise ratio (SNR) and lateral continuity.

Seismic formation pressure logs are derived from seismic data in this study. The main objective is to delineate the distribution of overpressured zones in the subsurface, and seismic data from Offshore Louisiana are used to illustrate the proposed approach. The seismic data processing consists of velocity modeling, wavelet processing, and seismic inversion. From the acoustic impedances produced by seismic inversion, seismic velocity and density "logs" are derived at every CDP location using a relationship between sonic velocities and acoustic impedances (AI). Seismic formation pressure logs are computed against depth, making use of the above seismic velocity and density logs. Formation pressure logs are calculated assuming that compressional velocity, mean density, and depth are proportional to formation pressure. These logs are constrained at every depth point by estimated matrix and fluid compressional velocities (Vmax and Vmin). Vmax and Vmin are derived using porosity and sonic well log information. Results include profiles of seismic velocity logs, seismic density logs, and seismic formation pressure logs for two intersecting seismic lines from Offshore Louisiana. One well is used to constrain the data processing. The seismic formation pressure sections delineate a large region of overpressured shales in the subsurface. INTRODUCTION An important parameter in hydrocarbon exploration and exploitation is formation (or pore) pressure. In particular, detection of abnormally high formation pressures, or "overpressured" zones, can provide valuable information for exploration and exploitation purposes. High formation pressures are common in the Gulf of Mexico. Overpressured sediments are generally caused by a sequence of events wherein water becomes. trapped by faults or nonpermeable barriers in sediments at depth where, otherwise, the water would have been forced out by normal increasing overburden pressure (Bilgeri and Ademeno, 982). Abnormal fluid pressure is also caused by release of water into the pore system during clay diagenesis (smectiteillite transformation), and other mechanisms as listed in Bruce, 1984. High formation pressures cause major changes in subsurface rock parameters. In overpressured shales (Which contain pressured water), seismic velocity is lower, density is lower, and porosity is higher than if the pressured water had been able to escape (Bilgeri and Ademeno, 1982). Detection of overpressured sediments can also contribute to the overall analysis of hydrocarbon potential of a basin. Abnormal pressures exert partial control on the type and quantity of hydrocarbons accumulated because pressure potential determines the direction of fluid flow, and overpressuring partly controls the geometry of growth faults and related folds in basins where shale structures are the dominant type formed (Bruce, 1984). In the area of hydrocarbon exploitation, knowledge of formation pressure distribution can aid in conducting safe and efficient drilling operations. In this study, several recent advances in velocity modeling, seismic wavelet deconvolution, and inversion are incorporated to more accurately derive velocity and density "logs" from seismic data in both time and depth domains. (In his paper, seismically derived "logs" refers to a derived section where each output trace, or "log", has been generated from one CDP in the original seismic section).