Quantitative gas saturation estimation by frequency‐dependent amplitude‐versus‐offset analysis

Seismic amplitudes contain important information that can be related to fluid saturation. The amplitude‐versus‐offset analysis of seismic data based on Gassmann's theory and the approximation of the Zoeppritz equations has played a central role in reservoir characterization. However, this standard technique faces a long‐standing problem: its inability to distinguish between partial gas and “fizz‐water” with little gas saturation. In this paper, we studied seismic dispersion and attenuation in partially saturated poroelastic media by using frequency‐dependent rock physics model, through which the frequency‐dependent amplitude‐versus‐offset response is calculated as a function of porosity and water saturation. We propose a cross‐plotting of two attributes derived from the frequency‐dependent amplitude‐versus‐offset response to differentiate partial gas saturation and “fizz‐water” saturation. One of the attributes is a measure of “low frequency”, or Gassmann, of reflectivity, whereas the other is a measure of the “frequency dependence” of reflectivity. This is in contrast to standard amplitude‐versus‐offset attributes, where there is typically no such separation. A pragmatic frequency‐dependent amplitude‐versus‐offset inversion for rock and fluid properties is also established based on Bayesian theorem. A synthetic study is performed to explore the potential of the method to estimate gas saturation and porosity variations. An advantage of our work is that the method is in principle predictive, opening the way to further testing and calibration with field data. We believe that such work should guide and augment more theoretical studies of frequency‐dependent amplitude‐versus‐offset analysis.     

Integrating basin modeling with seismic technology and rock physics

We explore the link between basin modelling and seismic inversion by applying different rock physics models. This study uses the E‐Dragon II data in the Gulf of Mexico. To investigate the impact of different rock physics models on the link between basin modelling and seismic inversion, we first model relationships between seismic velocities and both (1) porosity and (2) effective stress for well‐log data using published rock physics models. Then, we build 1D basin models to predict seismic velocities derived from basin modelling with different rock physics models, in a comparison with average sonic velocities measured in the wells. Finally, we examine how basin modelling outputs can be used to aid seismic inversion by providing constraints for the background low‐frequency model. For this, we run different scenarios of inverting near angle partial stack seismic data into elastic impedances to test the impact of the background model on the quality of the inversion results. The results of the study suggest that the link between basin modelling and seismic technology is a two‐way interaction in terms of potential applications, and the key to refine it is establishing a rock physics models that properly describes changes in seismic signatures reflecting changes in rock properties.     

Scale effects on modelling the seismic signature of gas: results from an outcrop analogue

Numerous examples of reservoir fields from continental and marine environments involve thin‐bedded geology, yet, the inter‐relationship between thin‐bedded geology, fluid flow and seismic wave propagation is poorly understood. In this paper, we explore the 4D seismic signature due to saturation changes of gas within thin layers, and address the challenge of identifying the relevant scales and properties, which correctly define the geology, fluid flow and seismic wave propagation in the field. Based on the study of an outcrop analogue for a thin‐bedded turbidite, we model the time‐lapse seismic response to fluid saturation changes for different levels of model scale, and explore discrepancies in quantitative seismic attributes caused by upscaling. Our model reflects the geological complexity associated with thin‐bedded turbidites, and its coupling to fluid flow, which in turn affects the gas saturation distribution in space, and its time‐lapse seismic imprint. Rock matrix and fluid properties are modelled after selected fields to reproduce representative field models with realistic impedance contrasts. In addition, seismic modelling includes multiples, in order to assess their contribution in seismic propagation through thin gas layers. Our results show that multiples could contribute significantly to the measured amplitudes in the case of thin‐bedded geology. This suggests that forward/inverse modelling involving the flow simulation and seismic domains used in time‐lapse seismic interpretation should account for thin layers, when these are present in the geological setting.     

Seismic driven probabilistic classification of reservoir facies for static reservoir modelling: a case history in the Barents Sea

In this paper we present a case history of seismic reservoir characterization where we estimate the probability of facies from seismic data and simulate a set of reservoir models honouring seismically‐derived probabilistic information. In appraisal and development phases, seismic data have a key role in reservoir characterization and static reservoir modelling, as in most of the cases seismic data are the only information available far away from the wells. However seismic data do not provide any direct measurements of reservoir properties, which have then to be estimated as a solution of a joint inverse problem. For this reason, we show the application of a complete workflow for static reservoir modelling where seismic data are integrated to derive probability volumes of facies and reservoir properties to condition reservoir geostatistical simulations. The studied case is a clastic reservoir in the Barents Sea, where a complete data set of well logs from five wells and a set of partial‐stacked seismic data are available. The multi‐property workflow is based on seismic inversion, petrophysics and rock physics modelling. In particular, log‐facies are defined on the basis of sedimentological information, petrophysical properties and also their elastic response. The link between petrophysical and elastic attributes is preserved by introducing a rock‐physics model in the inversion methodology. Finally, the uncertainty in the reservoir model is represented by multiple geostatistical realizations. The main result of this workflow is a set of facies realizations and associated rock properties that honour, within a fixed tolerance, seismic and well log data and assess the uncertainty associated with reservoir modelling.     

AVO study of a gas-hydrate deposit, offshore Costa Rica

Amplitude variation with offset (AVO) analysis and waveform inversion are techniques used to determine qualitative or quantitative information on gas hydrates and free gas in sediments. However, the quantitative contribution of gas hydrates to the acoustic impedance contrast observed at the bottom‐simulating reflector and the reliability of quantitative AVO analyses are still topics of discussion. In this study, common‐midpoint gathers from multichannel wide‐angle reflection seismic data, acquired offshore Costa Rica, have been processed to preserve true amplitude information at the bottom‐simulating reflector for a quantitative AVO analysis incorporating angles of incidence of up to 60°. Corrections were applied for effects that significantly alter the observed amplitudes, such as the source directivity. AVO and rock‐physics modelling indicate that free gas immediately beneath the gas‐hydrate stability zone can be detected and low concentrations can be quantified from AVO analysis, whereas the offset‐dependent reflectivity is not sensitive to gas‐hydrate concentrations of less than about 10% at the base of the gas‐hydrate stability zone. Bulk free‐gas saturations up to 5% have been determined from the reflection seismic data assuming a homogeneous distribution of free gas in the sediment. Assuming a patchy distribution of free gas increases the estimated concentrations up to 14%. There is a patchy occurrence of bottom‐simulating reflectors south‐east of the Nicoya Peninsula on the continental margin, offshore Costa Rica. AVO analysis indicates that this phenomenon is related to the local presence of free gas beneath the gas‐hydrate stability zone, probably related to a focused vertical fluid flow. In areas without bottom‐simulating reflectors, the results indicate that no free gas is present.     

Bayesian inversion of time‐lapse seismic data for the estimation of static reservoir properties and dynamic property changes

Seismic conditioning of static reservoir model properties such as porosity and lithology has traditionally been faced as a solution of an inverse problem. Dynamic reservoir model properties have been constrained by time‐lapse seismic data. Here, we propose a methodology to jointly estimate rock properties (such as porosity) and dynamic property changes (such as pressure and saturation changes) from time‐lapse seismic data. The methodology is based on a full Bayesian approach to seismic inversion and can be divided into two steps. First we estimate the conditional probability of elastic properties and their relative changes; then we estimate the posterior probability of rock properties and dynamic property changes. We apply the proposed methodology to a synthetic reservoir study where we have created a synthetic seismic survey for a real dynamic reservoir model including pre‐production and production scenarios. The final result is a set of point‐wise probability distributions that allow us to predict the most probable reservoir models at each time step and to evaluate the associated uncertainty. Finally we also show an application to real field data from the Norwegian Sea, where we estimate changes in gas saturation and pressure from time‐lapse seismic amplitude differences. The inverted results show the hydrocarbon displacement at the times of two repeated seismic surveys.     

Quantitative estimation of water storage and residence time in the epikarst with time‐lapse refraction seismic

The hydrodynamic characterization of the epikarst, the shallow part of the unsaturated zone in karstic systems, has always been challenging for geophysical methods. This work investigates the feasibility of coupling time‐lapse refraction seismic data with petrophysical and hydrologic models for the quantitative determination of water storage and residence time at shallow depth in carbonate rocks. The Biot–Gassmann fluid substitution model describing the seismic velocity variations with water saturation at low frequencies needs to be modified for this lithology. I propose to include a saturation‐dependent rock‐frame weakening to take into account water–rock interactions. A Bayesian inversion workflow is presented to estimate the water content from seismic velocities measured at variable saturations. The procedure is tested first with already published laboratory measurements on core samples, and the results show that it is possible to estimate the water content and its uncertainty. The validated procedure is then applied to a time‐lapse seismic study to locate and quantify seasonal water storage at shallow depth along a seismic profile. The residence time of the water in the shallow layers is estimated by coupling the time‐lapse seismic measurements with rainfall chronicles, simple flow equations, and the petrophysical model. The daily water input computed from the chronicles is used to constraint the inversion of seismic velocities for the daily saturation state and the hydrodynamic parameters of the flow model. The workflow is applied to a real monitoring case, and the results show that the average residence time of the water in the epikarst is generally around three months, but it is only 18 days near an infiltration pathway. During the winter season, the residence times are three times shorter in response to the increase in the effective rainfall.     

Laboratory measurements of seismic attenuation and Young's modulus dispersion in a partially and fully water‐saturated porous sample made of sintered borosilicate glass

We measured the extensional‐mode attenuation and Young's modulus in a porous sample made of sintered borosilicate glass at microseismic to seismic frequencies (0.05–50 Hz) using the forced oscillation method. Partial saturation was achieved by water imbibition, varying the water saturation from an initial dry state up to ～99%, and by gas exsolution from an initially fully water‐saturated state down to ～99%. During forced oscillations of the sample effective stresses up to 10 MPa were applied. We observe frequency‐dependent attenuation, with a peak at 1–5 Hz, for ～99% water saturation achieved both by imbibition and by gas exsolution. The magnitude of this attenuation peak is consistently reduced with increasing fluid pressure and is largely insensitive to changes in effective stress. Similar observations have recently been attributed to wave‐induced gas exsolution–dissolution. At full water saturation, the left‐hand side of an attenuation curve, with a peak beyond the highest measured frequency, is observed at 3 MPa effective stress, while at 10 MPa effective stress the measured attenuation is negligible. This observation is consistent with wave‐induced fluid flow associated with mesoscopic compressibility contrasts in the sample's frame. These variations in compressibility could be due to fractures and/or compaction bands that formed between separate sets of forced‐oscillation experiments in response to the applied stresses. The agreement of the measured frequency‐dependent attenuation and Young's modulus with the Kramers–Kronig relations and additional data analyses indicate the good quality of the measurements. Our observations point to the complex interplay between structural and fluid heterogeneities on the measured seismic attenuation and they illustrate how these heterogeneities can facilitate the dominance of one attenuation mechanism over another.     

Seismic attenuation,normal moveout stretch,and low‐frequency shadows underlying bottom simulating reflector events

In many cases, the seismic response of bottom‐simulating reflectors is characterised by low frequencies called “low‐frequency shadow”. Generally, this phenomenon is interpreted as attenuation due to partial saturation with free gas. Actually, this frequency loss may have multiple causes, with a normal moveout stretch as a possible candidate. To analyse this phenomenon, we compute synthetic seismograms by assuming a lossy bottom‐simulating layer, with varying quality factor and thickness, bounded by the upper hydrate‐brine/gas‐brine and lower gas‐brine/brine interfaces. First, we estimate the shift of the centroid frequency of the power spectrum as a function of the travelled distance of the seismic pulse. Then, we perform one‐dimensional numerical experiments to quantify the loss of frequency of the seismic event below the bottom‐simulating reflector as a function of the quality factor of the bottom‐simulating layer and its thickness (due to wave interference). Then, we compute shot gathers to obtain the stacked section, with and without the normal moveout stretch correction and with and without the presence of wave attenuation in the bottom‐simulating layer. The results indicate that the low‐frequency shadow due to the normal moveout stretch is stronger than that due to attenuation and may constitute a false indicator of the presence of gas. In fact, often, the low‐frequency shadow overlies events with higher frequencies, in contradiction with the physics of wave propagation. This is particularly evident when the low‐frequency shadow is so extensive that the presence of high frequencies below cannot be justified by the acquisition geometry.     

Exploring seismic inversion methodologies for non‐stationary geological environments: a benchmark study between deterministic and geostatistical seismic inversion

This paper presents a comparison between subsurface impedance models derived from different deterministic and geostatistical seismic inversion methodologies applied to a challenging synthetic dataset. Geostatistical seismic inversion methodologies nowadays are common place in both industry and academia, contrasting with traditional deterministic seismic inversion methodologies that are becoming less used as part of the geo‐modelling workflow. While the first set of techniques allows the simultaneous inference of the best‐fit inverse model along with the spatial uncertainty of the subsurface elastic property of interest, the second family of inverse methodology has proven results in correctly predicting the subsurface elastic properties of interest with comparatively less computational cost. We present herein the results of a benchmark study performed over a realistic three‐dimensional non‐stationary synthetic dataset in order to assess the performance and convergence of different deterministic and geostatistical seismic inverse methodologies. We also compare and discuss the impact of the inversion parameterisation over the exploration of the model parameter space. The results show that the chosen seismic inversion methodology should always be dependent on the type and quantity of the available data, both seismic and well‐log, and the complexity of the geological environment versus the assumptions behind each inversion technique. The assessment of the model parameter space shows that the initial guess of traditional deterministic seismic inversion methodologies is of high importance since it will determine the location of the best‐fit inverse solution.     

Attenuation tomography: An application to gas-hydrate and free-gas detection

We estimate the quality factor (Q) from seismic reflections by using a tomographic inversion algorithm based on the frequency‐shift method. The algorithm is verified with a synthetic case and is applied to offshore data, acquired at western Svalbard, to detect the presence of bottom‐simulating reflectors (BSR) and gas hydrates. An array of 20 ocean‐bottom seismographs has been used. The combined use of traveltime and attenuation tomography provides a 3D velocity–Q cube, which can be used to map the spatial distribution of the gas‐hydrate concentration and free‐gas saturation. In general, high P‐wave velocity and quality factor indicate the presence of solid hydrates and low P‐wave velocity and quality factor correspond to free‐gas bearing sediments. The Q‐values vary between 200 and 25, with higher values (150–200) above the BSR and lower values below the BSR (25–40). These results seem to confirm that hydrates cement the grains, and attenuation decreases with increasing hydrate concentration.     

Accelerating the T‐matrix approach to seismic full‐waveform inversion by domain decomposition

A seismic variant of the distorted Born iterative inversion method, which is commonly used in electromagnetic and acoustic (medical) imaging, has been recently developed on the basis of the T‐matrix approach of multiple scattering theory. The distorted Born iterative method is consistent with the Gauss–Newton method, but its implementation is different, and there are potentially significant computational advantages of using the T‐matrix approach in this context. It has been shown that the computational cost associated with the updating of the background medium Green functions after each iteration can be reduced via the use of various linearisation or quasi‐linearisation techniques. However, these techniques for reducing the computational cost may not work well in the presence of strong contrasts. To deal with this, we have now developed a domain decomposition method, which allows one to decompose the seismic velocity model into an arbitrary number of heterogeneous domains that can be treated separately and in parallel. The new domain decomposition method is based on the concept of a scattering‐path matrix, which is well known in solid‐state physics. If the seismic model consists of different domains that are well separated (e.g., different reservoirs within a sedimentary basin), then the scattering‐path matrix formulation can be used to derive approximations that are sufficiently accurate but far more speedy and much less memory demanding because they ignore the interaction between different domains. However, we show here that one can also use the scattering‐path matrix formulation to calculate the overall T‐matrix for a large model exactly without any approximations at a computational cost that is significantly smaller than the cost associated with an exact formal matrix inversion solution. This is because we have derived exact analytical results for the special case of two interacting domains and combined them with Strassen's formulas for fast recursive matrix inversion. To illustrate the fact that we have accelerated the T‐matrix approach to full‐waveform inversion by domain decomposition, we perform a series of numerical experiments based on synthetic data associated with a complex salt model and a simpler two‐dimensional model that can be naturally decomposed into separate upper and lower domains. If the domain decomposition method is combined with an additional layer of multi‐scale regularisation (based on spatial smoothing of the sensitivity matrix and the data residual vector along the receiver line) beyond standard sequential frequency inversion, then one apparently can also obtain stable inversion results in the absence of ultra‐low frequencies and reduced computation times.     

Modulus defect,velocity dispersion and attenuation in partially-saturated reservoirs of Jurassic sandstone,Indus Basin,Pakistan

Partially saturated reservoirs are one of the major sources of seismic wave attenuation, modulus defect and velocity dispersion in real seismic data. The main attenuation and dispersion phenomenon is wave induced fluid flow due to the heterogeneity in pore fluids or porous rock. The identification of pore fluid type, saturation and distribution pattern within the pore space is of great significance as several seismic and petrophysical properties of porous rocks are largely affected by fluid type, saturation and fluid distribution pattern. Based on Gassmann-Wood and Gassmann- Hill rock physics models modulus defect, velocity dispersion and attenuation in Jurassic siliclastic partially-saturated rocks are studied. For this purpose two saturation patterns - uniform and patchy - are considered within the pore spaces in two frequency regimes i.e., lower frequency and higher frequency. The results reveal that at low enough frequency where saturation of liquid and gas is uniform, the seismic velocity and bulk modulus are lower than at higher frequency where saturation of fluid mixture is in the form of patches. The velocity dispersion and attenuation is also modeled at different levels of gas saturation. It is found that the maximum attenuation and velocity dispersion is at low gas saturation. Therefore, the dispersion and attenuation can provide a potential way to predict gas saturation and can be used as a property to differentiate low from high gas saturation.     

Geostatistical seismic Amplitude‐versus‐angle inversion

Seismic inversion plays an important role in reservoir modelling and characterisation due to its potential for assessing the spatial distribution of the sub‐surface petro‐elastic properties. Seismic amplitude‐versus‐angle inversion methodologies allow to retrieve P‐wave and S‐wave velocities and density individually allowing a better characterisation of existing litho‐fluid facies. We present an iterative geostatistical seismic amplitude‐versus‐angle inversion algorithm that inverts pre‐stack seismic data, sorted by angle gather, directly for: density; P‐wave; and S‐wave velocity models. The proposed iterative geostatistical inverse procedure is based on the use of stochastic sequential simulation and co‐simulation algorithms as the perturbation technique of the model parametre space; and the use of a genetic algorithm as a global optimiser to make the simulated elastic models converge from iteration to iteration. All the elastic models simulated during the iterative procedure honour the marginal prior distributions of P‐wave velocity, S‐wave velocity and density estimated from the available well‐log data, and the corresponding joint distributions between density versus P‐wave velocity and P‐wave versus S‐wave velocity. We successfully tested and implemented the proposed inversion procedure on a pre‐stack synthetic dataset, built from a real reservoir, and on a real pre‐stack seismic dataset acquired over a deep‐water gas reservoir. In both cases the results show a good convergence between real and synthetic seismic and reliable high‐resolution elastic sub‐surface Earth models.     

The 4D seismic signature of oil–water contact movement due to natural production in a stacked turbidite reservoir

Combined time‐lapse reservoir simulation and seismic modelling has been performed on both 1D and 3D models of a channelized turbidite reservoir. The models have been built using core, log, laboratory and seismic data from the Nelson Field (central North Sea) as a template. Oil and water movement in the main channels, channel margins and interchannel regions is investigated, with a particular focus being the effect of poor net‐to‐gross. The analysis confirms that saturation effects dominate the response whilst stress‐sensitivity effects play a minor role. The trough–peak signature in the seismic difference volumes formed by the sweep of the water can be continued and mapped slightly further than the channel margins. This characteristic 4D signature remains roughly intact, despite the complicated depositional architecture, and accurately delineates the area of moved fluid, but it needs additional calibration to combat the detrimental influence of the low net‐to‐gross. Signal strength is largely dependent on reservoir quality, but is also compromised by the net‐to‐gross, fluid distribution and, more critically, by the exact timing of the seismic survey. For example, a region of bypassed oil zone remains undetected as it forms early during the production. This work demonstrates that to understand fully the 4D signature at a quantitative level requires adequate knowledge of the fluid properties, but also, more critically, the geology.     

The application of well logging and seismic modeling to assess the degree of gas saturation in Miocene strata (Carpathian Foredeep, Poland)

The presence of natural gas in the pore space of reservoir rocks results in a significant decrease in P-wave velocity. Even low gas saturation can generate seismic anomalies (DHI) and false image of gas accumulation of economic importance. This article presents an attempt to evaluate gas saturation from 2D seismic section in the Miocene sandstone strata in the south-eastern part of the Carpathian Foredeep. The ESTYMACJA program and the Biot-Gassmann model were used to study the dependence between elastic parameters and saturating fluids (water and gas) recorded in wells. Series of calculations was carried out using a method of fluid substitution for various gas saturation. The applicability of seismic data for evaluating gas saturation of reservoir beds was assessed with the use of 1D modelling (synthetic seismograms) and 2D modelling (theoretical seismic section) calculated for different gas saturation. The proposed methodology can be used to identify low and high gas-saturated zones and contour the reservoir.     

中深层天然气藏地震预测技术研究

济阳坳陷天然气资源丰富,已在多个层系发现了不同类型的中深层天然气藏,由于气藏地质条件、地震反射复杂,针对不同的气藏需采用不同的地震预测技术。本文在中深层天然气藏地质特点分析的基础上进行了岩石物理、地震反演、地震属性等预测技术研究,结果表明：中层气藏储层物性较好,储层与围岩的岩石物理参数差异明显,应用亮点、AVO、叠前弹性阻抗反演技术可较好地识别预测三角洲砂岩气藏;针对深层低孔低渗砂岩气藏,地震属性及多属性反演是有效的储层预测技术,并预测了孤北地区二叠系有利储集相带分布,结合构造分析,指出了孤北地区深层气勘探方向。