Sparse-spike seismic inversion with semismooth newton algorithm solver

Ore-controlling structures of sandstone-hosted uranium deposit in the southwestern Ordos Basin: Revealed from seismic and gravity data

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 inversion methods are routinely used to estimate attributes such as P-impedance, S-impedance, density, P-wave and S-wave velocity, and elastic impedances from seismic and well log data. These attributes help to understand subsurface lithology and fluid content. There are several types of seismic inversion methods available in which model-based inversion has got more attention. In the present study, the model-based inversion and geostatistical methods namely probabilistic neural network (PNN), multi-layer feed-forward neural network (MLFN) and radial basis function neural network (RBFNN) are implemented to estimate acoustic impedance, porosity, density, gamma-ray volume and P-wave velocity in the inter-well region of the F-3 block, Netherlands. The aim of the study is to predict a number of petrophysical parameters and demonstrate how they can be used to interpret seismic reflection data. A comparative study is also performed to estimate the best suitable method to predict various petrophysical parameters. The assessment of inverted results demonstrates that the impedance in the region varies from 2550 m/s*g/cc to 6150 m/s/*g/cc, which is relatively low and indicates the presence of loose formation in the area. The correlation between synthetic seismic trace and initial seismic trace is estimated to be 0.98, and the synthetic relative error as 0.19, indicating excellent algorithm output. Further, the assessment of the geostatistical methods is carried out to predict petrophysical parameters in conjunction with Multi-Attribute Transform Analysis. The analysis shows that among the geostatistical methods, the PNN provides slightly better results. The petrophysical parameters that are estimated in this study are porosity, density, gamma-ray, and P-wave velocity volumes. These parameters reinforce the interpretation of seismic data, which is a significant step in any project of exploration and production. The technique is first implemented to the composite traces near to the well location, and the findings are analysed with well log data. Second, the entire seismic section is inverted for porosity, density, gamma-ray, and P-wave velocity after achieving satisfactory outcomes in the first step. The assessment demonstrates very high-resolution subsurface petrophysical parameters which strengthen the seismic data interpretation.

A new methodology for frequency bandwidth enhancement using 3D layered reflectivity inversion is demonstrated in this paper. The inversion is used to obtain layered reflectivity and then band-limited to the outer bounds of the input seismic. The 3D reflectivity inversion starts with a thin layer model based on the geological picks following the structural and stratigraphic trends. The initial thickness of the thin layers is determined by the frequency bandwidth of the seismic data, and the inversion process orients them conformably to stratigraphic layers in the subsurface. The thickness and impedance of each layer (and hence interface reflection coefficient) is perturbed and the corresponding modelled synthetic is compared to the seismic data in a volumetric fashion to minimise the misfit (Walia, 2001). This contributes to the removal of tuning effects and provides a reflectivity sequence with a much higher frequency bandwidth than the seismic data. Subsequently, the reflection series is band-limited to obtain higher resolution seismic data. The limits of bandwidth enhancement is selected by correlating the enhanced seismic to well logs and VSPs. The comparison of seismic profiles attribute maps and correlation with well data presented in this paper confirm that this process has resolved real seismic events. This resulted in confident picking of top and base of individual sand units, consequently providing better maps of the reservoir sands. Application to Seismic Data Rigorous study of this technique on several 3D data volumes from the North Sea and Ecuador’s Oriente Basin have produced very encouraging results in terms of resolving Top/Base of producing thin sands, improving structural features and complex-fault definition. Fig. 1 shows a simple workflow of the methodology. An initial model, based on the main geological horizons and log data, is input to the inversion process. The inversion process describes the existing zero-phase 3D volume by a discrete number of thin (half of time-thickness of the input wavelet) layers (Ricker, 1953). Each layer consists of two parameters, the time thickness and initial impedance and hence reflection coefficient value at the interface of every bin location. During the inversion process both the parameters are perturbed within pre-defined constraints based on well log data. Convergence to the final solution is achieved using a full 3D algorithm based on simulated annealing. The resulting layered structure provides an effective resolution of typically an eighth of the wavelength (Gluck et al, 1997; Widess, 1973). The data reduction implicit in the layer definition makes this algorithm extremely robust to noise. This inverted reflectivity is then band-limited such that the enhanced seismic has a broader frequency bandwidth than the input seismic. Fig. 2 shows a comparison of the seismic data from the Oriente Basin before Hz dB

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.

In general only a single 3D seismic data set is used for the characterization of the static properties of a reservoir, even though these static properties could be integrated with dynamic properties. But sometimes, more than one 3D seismic data volume has been acquired over the same field after the production starts. We propose to use these additional data not only to understand the dynamic properties of the reservoir using a time-lapse seismic analysis as presented last year, but to improve the accuracy of the initial reservoir description and study its sensitivity to the input data during the optimization process. Using two 3D seismic data sets acquired over a field in the Gulf of Mexico, this paper demonstrates a method to improve the porosity map obtained from the geostatistical characterization of the base 3D seismic data set by an analysis of the second 3D data volume. It is not possible using just the base data to differentiate factors such as fluid content and pressure from the geostatistical porosity characterization. But by using the flow information from the wells and the second 3D seismic data which was acquired after the production started, it is possible to decouple the porosity, fluid contents and even pressure. Consequently, it provides a more representative porosity characterization compared to using a single 3D seismic data set. The relative permeability curves are optimized by comparing actual time-lapse seismic and production data to synthetic ones generated with a Gassmann rock physics model. P. 527

Optimised spectral merge of the background model in seismic inversion

A 3D integrated saturation model was built for the Sierras Blancas Formation of the Neuquén Basin, Argentina. The saturation model was based on core, logs and seismic data. History match of reservoir pressure and well productivities were taken into account to accurately determine the gas in place and productive reservoir boundaries, specifically using 3D seismic water saturation in the gas condensate formation. The Sierras Blancas Formation is an eolian deposit. In tight, wet and diagenetically altered regions, the seismic inversion porosity and acoustic impedance based models were not adequate to describe the gas in place distribution. Further, the effective gas permeabilities in the tighter part of the reservoir are a strong function of the initial water saturation as evidenced by fewer condensate and water blocking problems of horizontal wells that navigated through low water saturation, high permeability regions. Any relationship between seismic impedance and porosity correlation degraded in areas affected by secondary diagenetic processes therefore necessitating the use of a saturation parameter. 30 vertical wells that had DT curves were selected based on their production and spatial location in order to establish a correlation between log saturation and seismic attributes. Seismic saturation cubes were generated by multiattribute seismic analysis and resampled into the simulation scale model. Log saturations were then co-kriged with the 3D seismic saturation. Water saturations obtained from the initialized simulation scale model were compared with the 2D saturation logs, the 3D seismic and the geological model scales. An objective function was defined to match the 3D seismic water saturation with the initialized simulation model water saturation. Model parameters were iterated until a satisfactory match with the initialized simulation model was obtained.By focusing the saturation match at the initialization stage, seismic, geological, petrophysical and SCAL models were ensured to be consistent prior to the full history match. Well history matching was consequently achieved much more simply and quickly. This paper presents a new detailed methodology of 3D pseudo-seismic water saturation generation, modeling and simulation used to accurately define OGIP, the productive boundaries of the reservoir, and to design trajectories for new horizontal wells.

A geostatistical method is used to generate a family of petrophysical models of the subsurface from which synthetic seismic traces are computed. Comparison of these synthetic traces with the actual seismic trace selects the petrophysical models that are explaining the seismic data. From these selected models, the uncertainty of an inversion is obtained. The method is applied to investigate the errors introduced in the petrophysical models when the inversion is performed with a wavelet that is not representative for the seismic data. Next, the method is applied on time‐lapse seismic data to invert for small production introduced changes under the level of inversion uncertainty.

CO2 storage capacity estimation through static reservoir modelling: A case study of the lower Cretaceous Gage Sandstone reservoir in the offshore Vlaming Sub-basin, Perth Basin, Australia

In this paper a technique for non-hyperbolic automatic velocity analysis of seismic data based on reflectivity series has been introduced. Maximizing coherence measures either considering hyperbolic or non-hyperbolic arrival times for velocity analysis has been studied by researchers (Fomel and Stovas 2010). The difference of our method is that we used the reflectivity series of the near offset trace in a common depth point (CDP) gather to guide the non-hyperbolic curves for semblance evaluation. Instead of windowing the traces by equal time gates, we follow the reflectivity series and compute the semblance function within a time range almost equal to the seismic wavelet width. However, the semblance is calculated directly from seismic gather not the reflection coefficients. Guiding reflectivity series is determined by the Sparse Spike Deconvolution which is introduced by Hondori et al. 2011. After evaluating semblance for all the trial velocities in a window, the next spike leads the reflection fitting function. Hence, the total number of semblance computation will decrease and the processing cost will be less than conventional methods.

Delhi Field is located in northeastern Louisiana. The reservoir is the Holt-Bryant zone that consists of Upper Cretaceous (Tuscaloosa) and Lower Cretaceous (Paluxy) sandstones. Currently, the field is undergoing a tertiary CO2 flood of the Holt-Bryant zone for enhanced oil recovery. To better understand the complexity of the reservoir, seismic and well log data were used to determine petrophysical properties within the reservoir. Correlations were established between: density and gamma ray; P-impedance and porosity. Pre-stack, model-based inversion was performed on the seismic data to obtain volumes of density and P-impedance. At the same time, synthetic seismic traces were created by changing the petrophysical properties, and correlations found previously were examined again.

The application of three-dimensional (3-D) seismic methods to reservoir characterisation has gained wide acceptance in the last ten years. Almost seventy-five percent of additional reserves are now found in mature areas by redefining reservoir boundaries and internal heterogeneities using surface and crosswell seismic methods. However the implementation of, in particular, 3-D seismic methods can be very expensive and can rival the cost of drilling a dry hole. A solution to the problem is to physically model a reservoir in the laboratory and to collect simulated seismic reflection data over the model. Then conventional, or unconventional, seismic processing techniques can be applied to the data prior to embarking on costly field seismic data collection. The physical modelling experiments enable an improved and corrected image of the subsurface to be developed, and a more effective drilling program to be designed. We briefly review the 3-D seismic method and indicate its value in reservoir characterisation. Examples will be given of models developed for experiments in fault plane analysis and for imaging beneath high velocity near surface layers. Introduction The 3-D seismic method was first shown to be viable for subsurface imaging in the early 1970s (Ref. 1). This was the first successful application of physical modelling to solving 3-D seismic problems. The fact that the 3-D method has been rapidly accepted in the last 10 years has been documented (Ref. 2). The conclusion is that '3-D seismic surveys have become a cost-effective tool for mapping hydrocarbon reservoirs and can have a major impact on the volume of reserves estimated'. The method needs the subsurface area of interest to be spatially sampled correctly with seismic traces. in marine operations this may be achieved with a ship towing many cables, such that each source and receiver combination represent a sample point. In land operations various positionings of sources and receivers may be used such that an area of the subsurface is 'covered' with seismic traces. The examples in this paper show two very different applications of 3-D seismic to solving reservoir problems, both of which required the extensive application of physical models. Fault Plane Analysis. When a seismic wave meets an acoustic contrast it may be reflected and/or refracted. If a wave reaches a fault with a relatively high impedance contrast across it, it will refract through the fault plane, resulting in a change in the travel path of the wave. When common midpoint gathers are produced, the wave refracting across the fault can cause changes in the trace gathers which can affect 'reflections' within the gather. When the data are stacked the result can give a different appearance to the image. Such a change could be the presence of an apparent fault at depth, which is in fact an artefact of the stacking process. When computing the reserves in a reservoir the assumption of the presence of such a fault could lead to incorrect reserve estimates. Consequently, it is very important to determine whether such an artefact does, or does not, exist. Two dimensional (2-D) seismic data collected across a fault plane containing such an impedance contrast in the shallow section will produce a false image of a fault (Ref. 3). 3-D data collected along strike to the fault will not have raypaths passing through the fault plane. so these data will not create such an artefact. A 2-D section can be reconstituted from the 3-D data, along the plane of the original 2-D line, without the artefact indicating that the 'fault' does not exist. P. 81

Summary We propose an ensemble based seismic inversion framework to estimate static and dynamic reservoir parameters such as saturation, pressure and porosity fields using seismic data. The proposed method has certain novelties, in terms of the choice of seismic data, as well as uncertainty quantification of the estimates. Further, the method uses reservoir-engineering data as the prior information (such as pressure-saturation data) from reservoir simulation model to constrain the inversion process. Many conventional seismic inversion algorithms are deterministic in nature, and thus they pay less attention to uncertainty quantification. To quantify the uncertainties in the estimates, we adopt an iterative ensemble smoother as the inversion algorithm. Compared to the conventional deterministic inversion algorithms, this ensemble-based method is a derivative-free and non-intrusive approach, and has better capacity of uncertainty quantification. On the other hand, inverted seismic parameters, such as acoustic impedance, are often adopted as the data in inversion. In doing so, extra uncertainties may arise during the inversion processes. Here, we avoid such intermediate inversion processes by adopting amplitude versus angle (AVA) data. To handle the big-data problem in the AVA inversion process, we adopt a wavelet based sparse representation procedure ( Luo et al., 2016 ). Precisely, we apply a discrete wavelet transform to the AVA data, and estimate noise in the resulting wavelet coefficients. We then use the leading wavelet coefficients above a certain threshold value as the data in inversion. We apply the proposed framework to a 2D synthetic model for a proof-of-concept study. This reservoir model consists of three phases (water, oil and gas), and is a vertical section of a 3D Norne field model. We also test the performance of the framework in the 3D Brugge benchmark case that consists of two phases (water and oil). The numerical results from both cases indicate that the proposed framework can integrate the reservoir-engineering data as prior knowledge with seismic data, while achieving reasonably good estimates of both static and dynamic reservoir variables.

A new method for characterizing architectural elements of fractured-cavernous carbonate reservoirs was proposed, with application to an Ordovician reservoir in the Tahe Oilfield, Tarim basin. The new method integrates observations from outcrop analogs and concepts from modern karst theory for the mapping and modeling of fractured-cavernous reservoirs. In this paper, fractured-cavernous reservoirs were divided into 4 architectural element types—underground river caverns, sinkholes, discrete internal caverns, and faults. Architectural elements of the Ordovician reservoir in Tahe oilfield were identified and characterized by integrating well logs and seismic data. A new method constrained by faults, karst zones, and seismic acoustic impedance data, was introduced to build a 3D model of architectural elements of fractured-cavernous reservoir in the S48 unit of Tahe Oilfield. A porosity model was then derived from the architectural element model using facies-constrained method. The research provides a work-flow for the characterization of fractured-cavernous reservoirs and determining optimal methods for maximizing oil recovery in the study area or in similar areas.