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Cobos, Carlos Manuel (Repsol Services) | Castagna, John P. (U. of Houston)

**Abstract**

The purpose of this paper is to introduce a stochastic seismic inversion algorithm based on Markov Chain Monte Carlo Simulation. The suggested inversion scheme generates a set of possible combinations of rock properties that can explain seismic amplitude responses in terms of lithology, pore structure and fluid variations. The result of the probabilistic seismic inversion is a seismic lithofacies catalog than can describe the elastic response of the studied subsurface interval. The main advantage of this technique is that the results consist of multiple equally probable rock properties models as an alternative to multiple elastic properties scenarios. Therefore, no *post facto* elastic to rock properties conversion is needed. The method might be used either in exploratory areas or hydrocarbon field development. In exploratory areas, the stochastic rock physics inversion can support the evaluation for hydrocarbon potential considering the effects of reservoir properties on seismic signatures for different geologic scenarios and physical conditions, with the prime goal of minimizing uncertainties and risk. In field development areas, stochastic seismic inversion produces multiple equally probable rock properties models that can explain the real 3D seismic response and can be used to constrain possible reservoir models used for hydrocarbon reserve estimation and reservoir production simulation. The probabilistic inversion algorithm was tested on a synthetic model that is based on real well log data. The objective of the synthetic test is to demonstrate the feasibility of the estimation of critical rock properties for hydrocarbon exploration, such as total porosity and reservoir fraction. The synthetic test results confirmed the capability of the proposed inversion technique to accurately predict the rock properties of the reservoir seismic lithofacies, even for seismically thin layers.

**Introduction**

Conventional seismic reservoir characterization (SRC) techniques were developed more than forty years ago for exploration plays where the hydrocarbon’s seismic responses were relatively easy to identify. Early reservoir characterization workflows were usualy based on direct hydrocarbon indicator (DHI) identification techniques centered on post stack seismic amplitude analysis and AVO inversion. DHIs plays are usually related to shallow high porosity reservoirs with significantly lower acoustic impedance than the surrounding rocks. The associated seismic signatures of these hydrocarbon filled high porosity reservoirs can be anomalous high amplitude reflections called “bright spots”. Nowadays, conventional seismic reservoir characterization techniques are becoming obsolete, since the oil industry is moving to explore areas were the hydrocarbons are located in deeper and more complex reservoirs. These new hydrocarbon plays are characterized by low porosity and low permeability reservoirs with near to undetectable pore fluid response. It means that the future seismic reservoir caracterization goal is to predict rock properties such as porosity, lithology and rock fabric of compacted and cemented porous rock. The second more important SRC challenge is to improve the seismic vertical resolution. Currently, seismic inversion resolution is still low for the new exploration/development challenges and improvement of seismic derived elastic parameters is paramount for the application of reservoir properties prediction. Techniques such as stochastic inversion have been initially developed in an attempt to obtain from seismic data quantitative information about subsurface rock properties on a very detailed scale. The goal of this paper is to introduce an inversion technique based on Markov Chain Monte Carlo simulation that can be implemented in a stochastic petrophysical inversion scheme. The stochastic seismic inversion’s objective is to produce a set of equiprobable rock properties volumes that can describe the elastic seismic response of the studied interval and their associated uncertainties. The main advantage of this petrophysical inversion technique is that the results are multiple equally probable rock properties models instead of multiple elastic properties scenarios. Therefore, no elastic to rock properties conversion is needed after the inversion is performed. The method might be used either in exploratory or development areas.

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

**Summary**

Principal component analysis (PCA) can be used to generate frequency-dependent spectral attributes for improved delineation and visualization of frequency-dependent features. A Varimax (Kaiser, 1958) PCA rotation algorithm relates individual principal components (PCs) to characteristic frequency bands. Synthetic and field data results show that Varimax rotated PC spectral attributes effectively respond to geological variations. For a synthetic wedge model, Varimax rotated PC spectral attributes serve well as a thickness indicator. For a real data case, a karst related sink hole is delineated better using Varimax rotated PC attributes than by conventional spectral decomposition or conventional principal component analysis.

Oilfield Places:

- North America > United States > Texas > Fort Worth Basin (0.99)
- North America > United States > Texas > Boonsville Gas Field (0.99)
- North America > United States > Texas > Permian Basin (0.98)

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

An inversion-based algorithm for computing the time-frequency analysis of reflection seismograms using Constrained Least-Squares Spectral Analysis is formulated and applied to modeled seismic waveforms and real seismic data traces. The Fourier Series coefficients are computed as a function of time directly by inverting a basis of truncated sinusoidal kernels for a moving time window. The method results in spectra that have reduced window smearing for a given window length relative to the Discrete Fourier Transform irrespective of window shape, and a time-frequency analysis with a combination of time and frequency resolution that is superior to both the Short Time Fourier Transform and the Continuous Wavelet Transform. The reduction in spectral smoothing enables better determination of the spectral characteristics of interfering reflections within a short window. The degree of resolution improvement relative to the Short Time Fourier Transform increases as window length decreases. As compared to the Continuous Wavelet Transform, the method has greatly improved temporal resolution, particularly at low frequencies.

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

As a seismic wave propagates, it loses energy due to spherical divergence, scattering, intrinsic absorption and reflection at interfaces where rock properties change. The amplitude and frequency responses of the reflected seismic wave are influenced by a variety of factors including: geologic structure, layer thickness, lithology, and pore fluid properties. When the seismic wave travels back to the surface, it also bring back the information related to stratigraphic features, rock property changes and hydrocarbon accumulations. Each reservoir has its own characteristic seismic frequency response because of its unique rock and fluid properties discriminating it from the surrounding environment. We utilize a spectral decomposition method to extract the characteristic frequency components from seismic data and identify low frequency anomalies. To understand the underlying physical factors of the low frequency anomaly, we build a set of wave-equation based synthetic forward modeling. The result of our analysis shows that seismic waves travel more slowly through gas zone than the background material is a main reason for seismic time series delay and low frequency anomaly in the thin layer reservoir. Our explanation has been applied in the analysis of frequency anomalies corresponding to gas-bearing sands in the Gulf of Mexico fields.

Oilfield Places:

- North America > United States > Gulf of Mexico > Green Canyon > Block 517 > King Kong Field (0.98)
- North America > United States > Gulf of Mexico > Green Canyon > Block 473 > King Kong Field (0.98)
- North America > United States > Gulf of Mexico > Green Canyon > Block 472 > King Kong Field (0.98)

Castagna, John P. (Department of Geosciences) | Tai, Shenghong (Department of Geosciences) | Puryear, Charles I. (Department of Geosciences) | Dwan, Fa (Shell International Exploration and Production Company) | Masters, Ron (Shell International Exploration and Production Company)

Various studies have demonstrated the usefulness of spectral decomposition and its associated frequency attributes in seismic interpretation and hydrocarbon exploration. However, many different techniques for spectral decomposition exist in the petroleum industry, creating a need for comparative studies of these techniques to evaluate their utility. In this work, we compare the results of the application of the CWT and MPD algorithms and associated frequency attributes to a complex turbidite model. Our results indicate that better resolution of stratigraphic features is achieved by the MPD algorithm. These improvements include sharper definition of lateral stratigraphic changes and detection of subtle channel features associated with off-peak frequencies. We also show the effective extraction of stratigraphic features associated with off-peak frequencies achieved by principal component analysis. We believe a quantitative assessment of the relationship between the rock properties volume and frequency attributes will provide useful insight during future work.

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (0.94)

Seismic attenuation measurements from surface seismic data using spectral ratios are particularly sensitive to inaccurate spectral estimation. Spectral ratios of Fourier spectral estimates are subject to inaccuracies due to windowing effects, noise, and spectral nulls caused by interfering reflectors. We have found that spectral ratios obtained using continuous wavelet transforms as compared to Fourier ratios are more accurate, less subject to windowing problems, and more robust in the presence of noise.

An algorithm for the calculation of bed thickness, reflection coefficients, and time location is described and applied. The algorithm is derived from the amplitude spectrum and has been tested on thin beds below one-quarter wave-length with variable reflection coefficient ratios. While the results have been very encouraging thus far, further testing is warranted.

Sinha, Satish K. (School of Geology and Geophysics, University of Oklahoma, Norman, OK) | Routh, Partha S. (Dept. of Geosciences, Boise State University, Boise, ID) | Anno, Phil D. (Seismic Imaging and Prediction, ConocoPhillips., Houston, TX) | Castagna, John P. (University of Houston, Houston, TX.)

**Summary**Average instantaneous attributes of time-frequency decompositions are useful in revealing the time varying spectral properties of seismic data. In the continuous wavelet transform (CWT), a time signal is decomposed into a time-scale spectrum or a scalogram; unlike a timefrequency spectrum or a spectrogram from the short time Fourier transform (STFT). Although there are various approaches of converting a time-scale spectrum into a timefrequency spectrum we introduce new mathematical formulas to calculate spectral attributes from the scalogram. In this process, we bypass the conversion of a scalogram into a time-frequency spectrum and provide average spectral attributes based on scale. The attributes are: center frequency, dominant frequency, and spectral bandwidth. Since these attributes are based on the CWT, computation of these attributes avoids subjective choice of a window length.

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (0.93)

The estimation of fluid properties from indirect geophysical data is limited by, and should account for, the uncertainty of the measurements. However only in recent years has this lead to results in this field tied to their corresponding uncertainty of outcome. This study presents a stochastic inversion, from geophysical data, and a quantified probability of the fluid modulus within target layers of two different hydrocarbon bearing fields. The probabilistic inversion method based on Gassmann's equation, as described by White and Castagna (2002), is applied.

Oilfield Places:

- North America > United States > Texas > Moneywort > Frio Formation (0.99)
- Europe > Norway > North Sea > Northern North Sea > Troll Oil and Gas Field > Troll West Formation (0.99)
- Europe > Norway > North Sea > Northern North Sea > Troll Oil and Gas Field > Troll East Formation (0.99)
- Europe > Norway > North Sea > Northern North Sea > Troll Oil and Gas Field > Brent Formation (0.99)

Burnett, Michael D. (Fusion Petroleum Technologies, Inc.) | Castagna, John P. (Fusion Petroleum Technologies, Inc.) | Camargo, German (Fusion Petroleum Technologies, Inc.) | Chen, He (Fusion Petroleum Technologies, Inc.) | Sanchez, Julian Juarez (Petroleos Mexicanos) | Santana, Alberto (Petroleos Mexicanos) | Hernandez, Efrain Mendez (Petroleos Mexicanos)

A reservoir study was conducted at Gaucho field in the Chiapas of Southern Mexico with the primary objective being to determine porosity in the base of the upper Cretaceous carbonate in order to facilitate further field development. Conventional seismic impedance inversion alone did not adequately predict porosity nor did neural network predictions with conventional seismic attributes. Spectral decomposition, seismic impedance inversion, and neural network inversion were integrated to produce an estimated porosity cube at the target level that provided excellent porosity indication in validation wells. The lateral variation of porosities within the area range from about 2% to more than 30%. Thus, the application of these techniques allowed final adjustment of drilling locations in order to capture the maximum local porosity possible. Resulting porosity maps within the field area are shown to have important implications for field development and further exploration in this area. This study defines a relationship between porosity thickness and peak frequency, and between the magnitude of the average effective zone porosity and peak amplitude. Additionally, the study illustrates the importance of training a neural network properly with (1) appropriate input attributes, and (2) utilization of wells which cover the spectrum of possible porosity encountered in the area. We show how such a methodology can be applied to carbonate reservoirs to distinguish locations with minimal to no effective porosity from areas with excellent porosity where additional development drilling can be fruitful.

SPE Disciplines: