Ezequiel F. Gonzalez

Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: A review

There are various approaches for quantitative estimation of reservoir properties from seismic inversion. A general Bayesian formulation for the inverse problem can be implemented in two different work flows. In the sequential approach, first seismic data are inverted, deterministically or stochastically, into elastic properties; then rock-physics models transform those elastic properties to the reservoir property of interest. The joint or simultaneous work flow accounts for the elastic parameters and the reservoir properties, often in a Bayesian formulation, guaranteeing consistency between the elastic and reservoir properties. Rock physics plays the important role of linking elastic parameters such as impedances and velocities to reservoir properties of interest such as lithologies, porosity, and pore fluids. Geostatistical methods help add constraints of spatial correlation, conditioning to different kinds of data and incorporating subseismic scales of heterogeneities.

Statistical rock physics Combining rock physics, information theory, and geostatistics to reduce uncertainty in seismic reservoir characterization

“Any physical theory is a kind of guesswork. There are good guesses and bad guesses. The language of probability allows us to speak quantitatively about some situation which may be highly variable, but which does have some consistent average behavior…. Our most precise description of nature must be in terms of probabilities.” —Richard Feynman This paper presents snapshots of current and emerging trends in applied statistical rock physics for reservoir characterization. By integrating fundamental concepts and models of rock physics, statistical pattern recognition, and information theory with seismic inversion and geostatistics, we can quantify and reduce uncertainties in reservoir management. Rock physics allows us to link seismic response and reservoir properties and to extend the available data to generate training data for the classification system. Seismic imaging brings indirect, but nevertheless spatially exhaustive, lateral and vertical information about reservoir properties that are not available from pinpoint well data. Classification and estimation methods based on computational statistical techniques such as nonparametric Bayesian classification, bootstrap, and neural networks help quantitatively measure interpretation uncertainty and the mis-classification risk at each spatial location. Geostatistical stochastic simulations add spatial correlation and small-scale variability which is hard to identify from seismic only because of the limits of resolution. Combining deterministic physical models with statistical techniques leads to new methods for interpretation and estimation of reservoir rock properties from seismic data. These formulations identify the most likely interpretation, the uncertainty of the interpretation, and guide quantitative decision analysis. Subsurface heterogeneity delineation is a key factor in reliable reservoir characterization. These heterogeneities occur at various scales and can include variations in lithology, pore fluids, clay content, porosity, pressure, and temperature. Some methods used in seismic reservoir characterization are purely statistical. Others are deterministic, based on physical models (theoretical, laboratory). Each group of techniques can have some …

Seismic inversion combining rock physics and multiple-point geostatistics

A novel inversion technique combines rock physics and multiple-point geostatistics. The technique is based on the formulation of the inverse problem as an inference problem and incorporates multiple-point geostatistics and conditional rock physics to characterize previously known geologic information. The proposed implementation combines elements of sampling from conditional probabilities and elements of optimization. The technique provides multiple solutions, all consistent with the expected geology, well-log data, seismic data, and the local rock-physics transformations. A pattern-based algorithm was selected as the multiple-point geostatistics component. Rock-physics principles are incorporated at the beginning of the process, defining the links between reservoir properties (e.g., lithology, saturation) and physical quantities (e.g., compressibility, density), making it possible to predict situations not sampled by log data. Results for seismic lithofacies inversion on a synthetic test and a real data application demonstrate the validity and applicability of the proposed inversion technique.

Near and far offset P-to-S elastic impedance for discriminating fizz water from commercial gas

In many practical situations when the objective is to differentiate between high and low gas concentrations, using P-to-P (PP) seismic data alone may not be enough to successfully complete the task. The abrupt reduction in P-wave velocity (VP) with the first few percent of gas controls the seismic response. Therefore, usually only the presence of gas, but not the saturation, can be detected with PP seismic. This well known physical phenomena can be modeled by Gassmanns equation, and was documented by Domenico in 1976. In contrast, density (ρ) varies more gradually and linearly with gas saturation, while S-wave velocity (VS) does not vary much. As noted by Berryman et al. (2002), the linear behavior of ρ with saturation makes seismic attributes that are closely related to density useful proxies for estimating gas saturation. Attempting to extract and to use information about rock density from AVO analysis or inversion has not been a successfully robust approach in many cases because of limitations in data...

Similarity analysis; a new tool to summarize seismic attributes information

Seismic attribute analysis is generally performed by correlating various attributes with reservoir properties. Even though experienced interpreters may have developed a good intuition about which attributes usually exhibit good correlation with particular reservoir properties, correlations between attributes and reservoir properties cannot be extrapolated from one reservoir to another. The analysis becomes more difficult as the number of attributes becomes larger, since the interpreter has to rely less on his/her experience and more on the actual correlations found in the data. Although some of the attributes seem to provide different information about lateral changes in the study area, they also contain redundant information that makes the analysis even more awkward.

Adding geologic prior knowledge to Bayesian lithofluid facies estimation from seismic data

AbstractUsing inverted seismic data from a turbidite depositional environment, we have determined that accounting only for rock types sampled at the wells can lead to biased predictions of the reservoir fluids. The seismic data consisted of two volumes resulting from a (multi-incidence angle) sparse-spike amplitude variation with offset inversion. Information from a single well (well logs and petrological analysis) was used to define an initial set of lithofluid facies that characterized rock type and porefill fluid to emulate a typical exploration setting. Based on our geologic understanding of the study area, we have augmented this initial model with lithofluid facies expected in the given depositional environment, yet not sampled by the well. Specifically, the new lithofluid facies accounted for variations in the mixture type and proportions of shales and sands. The elastic property distributions of the new lithofluid facies were modeled using appropriate rock-physics models. Finally, a geologically co...

AVO signatures of Eastern Venezuela gas sands: Feasibility and uncertainty estimation

The goal of this paper is to quantitatively model the expected AVO response of gas sands in an Eastern Venezuela field. The modeling includes not only the deterministic synthetic response computed from sonic logs, but also Monte-Carlo simulations in order to asses the uncertainty and variability in the AVO signature. This kind of stochastic analysis of the variability is very important for making decisions about the usefulness of AVO techniques in this particular region.

Importance of Geological and Rock Physics Prior Information for Lithology and Pore Fluid Estimation from Inverted Seismic Data: Exploration in a Turbidite Reservoir Case Study

Using inverted seismic data from a turbidite depositional environment, we show that accounting only for rock types sampled by wells can lead to biased predictions of the reservoir’s fluids. As it is common in an exploration setting, information from a single well (well logs and petrological analysis) was used to define a set of initial facies that combine lithology and fluids in a single reservoir property. Based on our understanding of the depositional environment, we augmented our model with expected lithofacies and associated elastic properties, which were not sampled by the well (here different types/proportions of sand-shale mixtures). Given a geologically consistent, spatially variant, prior probability of facies occurrence, Bayesian estimation of each facies probability was computed at every sample of the inverted seismic data. In this study, we used deterministic seismic inversion to produce the input data for our analysis, which is customary in similar field studies. Accounting for the augmented geological prior we were able to generate a scenario consistent with all available data, which supports further development of the field. In contrast, the purely data driven Bayesian classification (well log and seismic) would lead to downgrading of the prospectivity of the field in our case. Based on our findings, we argue that lack of data in Quantitative Interpretation needs to be counterweighted by robust geological prior information In order to risk geological scenarios without bias in exploration settings. In this work, using inverted seismic data from a turbidite depositional environment, we show that accounting only for rock types sampled at the wells can lead to biased predictions of the reservoir fluids. We propose two critical improvements on the purely data-driven approach: first we extend the rock physics model with facies expected in the depositional environment but not sampled by wells, and second we impose a spatially variant prior probability density of lithologies and fluids. Accounting for the augmented geological prior in this way, we were able to generate a scenario consistent with all available data that supports further development of the field. In contrast, the purely data-driven Bayesian classification (well log and seismic) would lead to downgrading the prospectivity of this field.

Rock Physics And Multiple-point Geostatistics For Seismic Inversion

Summary This paper presents a novel inversion technique that combines rock physics and multiple-point geostatistics (MPG) in a Bayesian framework. The proposed method can be applied in its current implementation to any inverse problem that can be approximated as a series of 1D forward-modeling operators. Rock-physics principles are incorporated at the beginning of the process, defining the links between reservoir properties (e.g., lithology, saturation) and physical properties (e.g., compressibility, electrical conductivity). MPG is used to define and explore the space of solutions. The method can be extended to satisfy multiple physical constraints simultaneously; in other words, the solutions can be conditioned with different types of geophysical data. Results of two synthetic tests and a real data application are presented to demonstrate the validity and applicability of the proposed inversion technique.

Facies classification using P-to-P and P-to-S AVO attributes

Summary It is well known that S (shear wave) information can sometimes be decisive for successfully identifying different facies in a reservoir using seismic methods. With the use of multicomponent receivers, it is possible to record converted S waves, even when using conventional P wave source. In this paper we present a linear approximation of the Zoeppritzs equation for the reflectivity of converted P-S waves. Similar to Shueys equation for the P-P case, the proposed P-S reflectivity approximation defines a gradient (E). In practice, E can be derived from the amplitudes of a particular seismic event in the traces of converted CDP gathers, with a least squares technique. Using real well logs and the Bayesian non-parametric classification methods we quantified the classification success rate. In cases where P-P AVO Shueys parameters A and B are less reliable (more uncertainty in their estimation, because of noise) than E, the facies classification could be improved by including the P-S gradient. This situation could occur in reservoirs with gas chimneys, for example. We estimated the added value of the P-S gradient, for reducing uncertainty in seismic facies discrimination with AVO parameters.