Iterative Geostatistical Seismic Inversion Research Articles

SmoGSI: smoothed multiscale iterative geostatistical seismic inversion

Iterative geostatistical seismic inversion is a vital technique for estimating subsurface properties. However, a conventional single-scale strategy faces challenges in preserving large-scale geological features due to the limited restoration of the type of data template, and conventional multiscale strategies face the challenge in that it is easy to lose the large-scale structure that was previously preserved. This paper introduces a novel smoothed multiscale strategy aimed at overcoming these limitations, which comprises two components: Simulated annealing at the coarsest scale and smooth conversation between two scale grids. This approach offers a smoother way to simultaneously retain large-scale and small-scale structures, improving the overall accuracy of the subsurface property estimations. To validate the effectiveness of our approach, we apply it to both synthetic and real examples. The results show that the simulated annealing strategy at the coarsest scale grid explores the prior space and finds the best large structures to avoid the generated models trapping in the local minimal. Meanwhile, the smooth conversation strategy between two scale grids helps us avoid the damage of the coarser structure. It can be explained that a large weight is assigned to the coarse structure at the beginning of the conversation of two grid scale, reducing the likelihood of the replacing proposed local small-scale geological patterns, which prone to be accepted in the conventional multiscale strategies. The combination of the two strategies used in the proposed smoothed multiscale strategy displays a significant improvement in subsurface property estimation accuracy compared to traditional multiscale strategies. This innovation can have far-reaching implications, benefiting a wide range of geophysical applications and contributing to more accurate and informed decision-making in geological and hydrogeological assessments.

Updating Local Anisotropies with Template Matching During Geostatistical Seismic Inversion

Iterative geostatistical seismic inversion methods are widely used to predict petro-elastic rock properties from seismic reflection data. When the model perturbation technique uses two-point geostatistics, these methods struggle to reproduce complex and nonstationary geological environments such as faults, folds and highly variable depositional systems. These limitations are often due to the use of a global variogram model to express the expected spatial continuity pattern of the property of interest. In complex geological environments a global variogram model might be unable to detect local heterogeneities and rapid variations of lithology, and result in nonrealistic geological models. Local heterogeneities might be predicted from the data using seismic attribute analysis, which can be imposed during geostatistical seismic inversion as local anisotropy models. In these approaches, the information about the local spatial continuity patterns is fixed and will guide and condition the entire inversion procedure, which can lead to errors and uncertainty in areas where this approach is not appropriate due to high local uncertainty of geological features, given the poor signal-to-noise ratio of the data or the presence of important geological features below the seismic resolution. This work proposes an iterative geostatistical seismic inversion method which iteratively updates the local spatial continuity models based on the trace-by-trace misfit between observed and predicted seismic data. The update of the local spatial continuity models aims at surpassing the limitations of the seismic inversion methods that use a fixed a priori variogram model. The method is successfully illustrated in a challenging two-dimensional synthetic data set and in a real case application. The results demonstrate the benefit of updating iteratively the imposed local spatial continuity patterns based on the data misfit. The inverted models are capable of better predicting the location of faults and reproducing the continuity of sinuous channels.

Iterative geostatistical seismic inversion with rock-physics constraints for permeability prediction

Accurate prediction of the spatial distribution of subsurface permeability is a fundamental task in reservoir characterization and monitoring studies for hydrocarbon production and CO2geologic storage. Predicting permeability over large areas is challenging, due to their high variability and spatial anisotropy. Common approaches for modeling permeability generally involve deterministic calculations from porosity using precalibrated rock-physics models (RPMs) or geostatistical cosimulation methods that reproduce observed experimental porosity-permeability relationships. Instead, we have predicted permeability from seismic data using an iterative geostatistical seismic inversion method that combines the advantages of rock-physics and geostatistical modeling methods. First, we simulate facies through 1D vertical Markov chain simulations. Then, permeability, porosity, and acoustic impedance are sequentially generated and conditioned to the previously simulated facies model. An RPM is used to evaluate the misfit between the permeability predictions obtained from geostatistical cosimulation at the well locations and well-log values computed from the acoustic impedance. The residuals of the misfit function are used as conditioning constraints in the stochastic update of the models in the subsequent iteration. The outcome of our methodology is a set of multiple geostatistical realizations of facies, permeability, porosity, and acoustic impedance conditioned to seismic data and constrained by an RPM. We first illustrate the method on a synthetic 1D example and compare it to a traditional geostatistical inversion approach. We then apply our inversion to a 3D real data set to assess the methodology performance with scarce conditioning data and in the presence of noise.

Deep physics-aware stochastic seismic inversion

Seismic inversion allows the prediction of subsurface properties from seismic reflection data and is a key step in reservoir modeling and characterization. With the generalization of machine learning in geophysics, deep learning methods have been proposed as efficient seismic inversion methods. However, most of these methods lack a probabilistic approach to deal with the uncertainties inherent in the seismic inversion problem and/or rely on complete and representative training data, which often is partially or scarcely available. We have explored the ability of deep convolutional neural networks to extract meaningful and complex representations from spatially structured data, combined with geostatistical simulation, to efficiently invert poststack seismic data directly for high-resolution models of acoustic impedance. Our model incorporates physics constraints and sparse direct measurements while leveraging the use of imprecise but widely distributed indirect measurements as represented by the seismic data. The models generated with geostatistical simulation provide additional information with higher spatial resolution than the original seismic data and allow assessing uncertainty in the model predictions by generating multiple realizations of the subsurface properties. Our method can (1) provide an uncertainty assessment of the predictions, (2) model the complex and nonlinear relationship between data and model, (3) extend the seismic bandwidth at low and high ends of the frequency parameters spectrum, and (4) lessen the need for large, annotated training data. Our method is applied to a 1D synthetic example and a real 3D application example from a Brazilian reservoir. The predicted impedance models are compared with those obtained from a full iterative geostatistical seismic inversion. Our method allows retrieving similar models but has the advantage of generating alternative solutions in greater numbers, providing a larger exploration of the model parameter space in less time than the iterative geostatistical seismic inversion.

Geostatistical Seismic Rock Physics AVA Inversion With Data-Driven Elastic Properties Update

Geostatistical seismic rock physics amplitude-versus-angle (AVA) inversion allows the joint prediction of rock and fluid properties from seismic reflection data. In these seismic inversion methods, the model perturbation and update occur iteratively in the petrophysical domain. A facies-dependent precalibrated rock physics model is applied to the simulated rock properties to calculate elastic properties. Synthetic seismic reflection data are computed from these elastic models. The rock physics models are calibrated at the well locations and act as the link between the rock and the elastic domains, remaining unchanged during the inversion procedure: the convergence of the inversion and the geological plausibility of the inverted rock property models depend on the quality of the calibration and available well-log data. To overcome this limitation, account for calibration errors and geological scenarios not sampled at the well locations, we introduce an iterative geostatistical seismic AVA inversion where the elastic predictions from a facies-dependent precalibrated rock physics model are updated iteratively, based on the mismatch between observed and synthetic data. We assume an initial <inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> <i>priori</i> uncertainty in the rock physics model and update it iteratively based on the data mismatch. The proposed method is applied in a 1-D synthetic example to illustrate the concept and validate the method. Then, we apply the inversion method to a 3-D real data set. In this application, we use a blind well to assess locally the performance of the technique. The results show that the parameters of space exploration is not compromised by the rock physics model&#x2019;s uncertainty.

Model reduction in geostatistical seismic inversion with functional data analysis

In subsurface modeling and characterization, predicting the spatial distribution of subsurface elastic properties is commonly achieved by seismic inversion. Stochastic seismic inversion methods, such as iterative geostatistical seismic inversion (GSI), are widely applied to this end. Global iterative GSI methods are computationally expensive because they require, at a given iteration, the stochastic sequential simulation of the entire inversion grid at once multiple times. Functional data analysis (FDA) is a well-established statistical method suited to model long-term and noisy temporal series. This method allows us to summarize spatiotemporal series in a set of analytical functions with a low-dimension representation. FDA has been recently extended to problems related to geosciences, but its application to geophysics is still limited. We have developed the use of FDA as a model reduction technique during the model perturbation step in global iterative GSI. FDA is used to collapse the vertical dimension of the inversion grid. We illustrate our hybrid inversion method with its application to 3D synthetic and real data sets. The results indicate the ability of our inversion methodology to predict smooth inverted subsurface models that match the observed data at a similar convergence as obtained by a global iterative GSI, but with a considerable decrease in the computational cost. Although the resolution of the inverted models might not be enough for a detailed subsurface characterization, the inverted models can be used as a starting point of global iterative GSI to speed up the inversion or to test alternative geologic scenarios by changing the inversion parameterization and obtaining inverted models in a relatively short time.

Geostatistical Seismic Inversion for Temperature and Salinity in the Madeira Abyssal Plain

A two-dimensional multichannel seismic reflection profile acquired in the Madeira Abyssal Plain during June 2016 was used in a modeling workflow comprising seismic oceanography processing, geostatistical inversion and Bayesian classification to predict the probability of occurrence of distinct water masses. The seismic section was processed to image in detail the fine scale structure of the water column using seismic oceanography. The processing sequence was developed to preserve, as much as possible, the relative seismic amplitudes of the data and enhance the shallow structure of the water column by effectively suppressing the direct arrival. The migrated seismic oceanography section shows an eddy at the expected Mediterranean Outflow Water depths, steeply dipping reflectors, which indicate the possible presence of frontal activity or secondary dipping eddy structures, and strong horizontal reflections between intermediate water masses suggestive of double diffuse processes. We then developed and applied an iterative geostatistical seismic oceanography inversion methodology to predict the spatial distribution of temperature and salinity. Due to the lack of contemporaneous direct measurements of temperature and salinity we used a global ocean model as spatial constraint during the inversion and nearby contemporaneous ARGO data to infer the expected statistical properties of both model parameters. After the inversion, Bayesian classification was applied to all temperature and salinity models inverted during the last iteration to predict the spatial distribution of three distinct water masses. A preliminary interpretation of these probabilistic models agrees with the expected ocean dynamics of the region.

Geostatistical Seismic Inversion with Self-Updating of Local Probability Distributions

Three-dimensional subsurface elastic models inverted from seismic reflection data are the basis of the geo-modeling workflow. These models are often used to predict the spatial distribution of reservoir rock properties such as porosity, volume of minerals and fluid saturations. Stochastic seismic inversion methods are important modeling tools, as they allow one to infer high-resolution subsurface models and assess uncertainties related to the spatial distribution of the inverted petro-elastic properties. Within this framework, iterative geostatistical seismic inversion methods use stochastic sequential simulation and co-simulation as a model generation and perturbation technique based on the mismatch between synthetic and real seismic data. This work proposes an alternative approach of iterative geostatistical seismic inversion based on the concept of self-updating of local probability distributions of the elastic property of interest to be inverted. The model perturbation is conditioned by local probability distribution functions, which are iteratively updated based on the data misfit at previous iterations. This approach allows for better exploration of the model parameter space, avoiding local fast convergence at early steps of the inversion, and wider exploration of the model parameter space. The method is applied to a two-dimensional nonstationary synthetic dataset and to a three-dimensional real case example with a blind well test.

The impact of a priori elastic models into iterative geostatistical seismic inversion

In reservoir modelling and characterization, the integration of geological information within seismic inversion is critical to efficiently obtain accurate inverted models. The existing knowledge about the subsurface geology should be gathered and used as conditioning data to generate robust a priori models. Usually, these models explain the expected background trend of the subsurface property of interest. One of the main differences between deterministic and iterative geostatistical seismic inversion methods is how the a priori knowledge about the spatial continuity pattern of the subsurface elastic property to be inferred, is used as constraint for the inversion. Deterministic approaches use explicit a priori models, often low-frequency models, to represent the geological background of the inverted properties. On the other hand, iterative global geostatistical seismic inversion methods do not include explicitly a priori models, since the spatial continuity pattern of the elastic property to be inverted is described exclusively by a variogram model. This work explores the impact of using explicit a priori models when integrated into iterative geostatistical seismic inversion methods. Three a priori models were built with different techniques and incorporated into the inversion process using two distinct methodologies: the first directly constrains the generation of elastic models, using stochastic sequential simulation with simple kriging with locally varying means; alternatively, these a priori models are also incorporated as part of a multi-objective function, accounting for both data and model deviations. All scenarios are applied to a synthetic case study, and those with the best results are then applied to a three-dimensional real dataset. The results of this work illustrate the drawbacks and advantages of using explicit a priori models in iterative geostatistical seismic inversion, highlighting the impact on the reproduction of channels under complex and heterogeneous siliciclastic geological environments and the need of reliable a priori models for accurate predictions about the subsurface.

Strategies for integrating uncertainty in iterative geostatistical seismic inversion

Iterative geostatistical seismic inversion integrates seismic and well data to infer the spatial distribution of subsurface elastic properties. These methods provide limited assessment to the spatial uncertainty of the inverted elastic properties, overlooking alternative sources of uncertainty such as those associated with poor well-log data, upscaling, and noise within the seismic data. We have expressed uncertain well-log samples, due to bad logging reads and upscaling, in terms of local probability distribution functions (PDFs). Local PDFs are used as conditioning data to a stochastic sequential simulation algorithm, included as the model perturbation within the inversion. The problem of noisy seismic and narrow exploration of the model parameter space, particularly in the early steps of the inversion, is tackled by the introduction of a cap on local correlation coefficients (CCs) responsible for the generation of the new set of models during the next iteration. We evaluate a single geostatistical framework with application to a real case study. When compared against a conventional iterative geostatistical seismic inversion, the integration of additional sources of uncertainty increases the match between real and inverted seismic traces and the variability within the ensemble of models inverted at the last iteration. The selection of the local PDFs plays a central role in the reliability of the inverted elastic models. Avoiding high local CCs at early stages of the inversion increases convergence in terms of global correlation between synthetic and real seismic reflection data at the end of the inversion.

Geostatistical rock physics AVA inversion

Reservoir models are numerical representations of the subsurface petrophysical properties such as porosity, volume of minerals and fluid saturations. These are often derived from elastic models inferred from seismic inversion in a two-step approach: first, seismic reflection data are inverted for the elastic properties of interest (such as density, P-wave and S-wave velocities); these are then used as constraining properties to model the subsurface petrophysical variables. The sequential approach does not ensure a proper propagation of uncertainty throughout the entire geo-modelling workflow as it does not describe a direct link between the observed seismic data and the resulting petrophysical models. Rock physics models link the two domains. We propose to integrate seismic and rock physics modelling into an iterative geostatistical seismic inversion methodology. The proposed method allows the direct inference of the porosity, volume of shale and fluid saturations by simultaneously integrating well-logs, seismic reflection data and rock physics model predictions. Stochastic sequential simulation is used as the perturbation technique of the model parameter space, a calibrated facies-dependent rock physics model links the elastic and the petrophysical domains and a global optimizer based on cross-over genetic algorithms ensures the convergence of the methodology from iteration to iteration. The method is applied to a 3D volume extracted from a real reservoir dataset of a North Sea reservoir and compared to a geostatistical seismic AVA.

Geostatistical seismic inversion for frontier exploration

Numerical 3D high-resolution models of subsurface petroelastic properties are key tools for exploration and production stages. Stochastic seismic inversion techniques are often used to infer the spatial distribution of the properties of interest by integrating simultaneously seismic reflection and well-log data also allowing accessing the spatial uncertainty of the retrieved models. In frontier exploration areas, the available data set is often composed exclusively of seismic reflection data due to the lack of drilled wells and are therefore of high uncertainty. In these cases, subsurface models are usually retrieved by deterministic seismic inversion methodologies based exclusively on the existing seismic reflection data and an a priori elastic model. The resulting models are smooth representations of the real complex geology and do not allow assessing the uncertainty. To overcome these limitations, we have developed a geostatistical framework that allows inverting seismic reflection data without the need of experimental data (i.e., well-log data) within the inversion area. This iterative geostatistical seismic inversion methodology simultaneously integrates the available seismic reflection data and information from geologic analogs (nearby wells and/or analog fields) allowing retrieving acoustic impedance models. The model parameter space is perturbed by a stochastic sequential simulation methodology that handles the nonstationary probability distribution function. Convergence from iteration to iteration is ensured by a genetic algorithm driven by the trace-by-trace mismatch between real and synthetic seismic reflection data. The method was successfully applied to a frontier basin offshore southwest Europe, where no well has been drilled yet. Geologic information about the expected impedance distribution was retrieved from nearby wells and integrated within the inversion procedure. The resulting acoustic impedance models are geologically consistent with the available information and data, and the match between the inverted and the real seismic data ranges from 85% to 90% in some regions.

Hybrid Global Stochastic and Bayesian Linearized Acoustic Seismic Inversion Methodology

Seismic inversion is an important technique for reservoir modeling and characterization due to its potential in inferring the spatial distribution of the subsurface elastic properties of interest. Two of the most common seismic inversion methodologies within the oil and gas industry are iterative geostatistical seismic inversion and Bayesian linearized seismic inversion. Although the first technique is able to explore the uncertainty space related with the inverse solution in a more comprehensive way, it is also very computationally expensive compared with the Bayesian linearized approach. In this paper, we introduce a novel hybrid seismic inversion procedure that takes advantage of both the frameworks: an iterative geostatistical seismic inversion methodology is started from an initial guess model provided by a Bayesian inversion solution. Also, we propose a new approach to model the uncertainty of the retrieved inverse solution by means of kernel density estimation. The proposed approach is implemented in two different real data sets with different signal-to-noise ratios. The results show the robustness of the hybrid inverse methodology and the usefulness of modeling the uncertainty of the retrieved inverse solution.

Geostatistical Seismic Inversion with Direct Sequential Simulation and Co-simulation with Multi-local Distribution Functions

Stochastic sequential simulation is a common modelling technique used in Earth sciences and an integral part of iterative geostatistical seismic inversion methodologies. Traditional stochastic sequential simulation techniques based on bi-point statistics assume, for the entire study area, stationarity of the spatial continuity pattern and a single probability distribution function, as revealed by a single variogram model and inferred from the available experimental data, respectively. In this paper, the traditional direct sequential simulation algorithm is extended to handle non-stationary natural phenomena. The proposed stochastic sequential simulation algorithm can take into consideration multiple regionalized spatial continuity patterns and probability distribution functions, depending on the spatial location of the grid node to be simulated. This work shows the application and discusses the benefits of the proposed stochastic sequential simulation as part of an iterative geostatistical seismic inversion methodology in two distinct geological environments in which non-stationarity behaviour can be assessed by the simultaneous interpretation of the available well-log and seismic reflection data. The results show that the elastic models generated by the proposed stochastic sequential simulation are able to reproduce simultaneously the regional and global variogram models and target distribution functions relative to the average volume of each sub-region. When used as part of a geostatistical seismic inversion procedure, the retrieved inverse models are more geologically realistic, since they incorporate the knowledge of the subsurface geology as provided, for example, by seismic and well-log data interpretation.