Introduction

Summary

We use a site-specific rock physics transform between porosity, mineralogy, and fluid and the elastic-wave velocity to invert seismic amplitude data for thickness, clay content, total porosity, and saturation. The implementation is Bayesian, and the results are probabilistic values of the reservoir properties, given seismic measurements and well data. This method is focused on an exploration setting where minimal data exist and requires a prior interpretation of the seismic data. Regularized sampling of the prior distributions is performed within the reservoir to generate a complete set of three-layer earth models, followed by a rock physics transform to elastic properties. Combined with shale properties from well-data for overburden and underlying units, synthetic seismic data accompanies each earth model. Then a full grid search is performed to obtain the synthetic traces that best match the real data. The underlying reservoir properties are used to construct the trace-by-trace posterior distributions. We performed this technique on well and seismic data from offshore west South Africa. The posterior distributions provided the ability to predict measured values of porosity and thickness with uncertain predictions of lithology and saturation.

Quantitative interpretation of geophysical data for hydrocarbon reservoir characterization is a non-unique problem. A solution is to cast the inversion of seismic reflection data for rock properties in terms of probabilities (Tarantola, 1987). The approach taken here is empirical Bayesian, in which the goal is to obtain posterior distributions of reservoir properties given seismic measurements. Specifically, we estimate jointly the conditional probability distribution function of thickness ( H ), clay content (C ), total porosity (f ), and water saturation (SW ), given measured angle-dependent seismic responses ( AN,AM) and calibration well log information. Development of this method was focused on an exploration setting, so assumptions about prior information are as noncommittal as possible. This inversion requires two critical components. First, a site-specific rock physics model is needed that translates all combinations of reservoir properties into elastic properties and thus the seismic domain. This model, calibrated from the input well data, accounts for how the reservoir rock responds to seismic wave propagation. Second, a prior interpretation of the seismic data must provide geo-bodies or horizons corresponding to a potential reservoir unit. These geo-bodies serve to reduce the problem so that the full posterior can be computed.

Bayesian Formulation

In a Bayesian formulation, defining the a prior assumptions is very important (Kass and Wasserman, 1996). To use least-committal priors, we defined them as uniform, independent, and uncorrelated distributions. However, if these parameters were highly correlated, then that correlation structure could be implemented. After the prior distributions were defined, they were regularly sampled to generate the complete set of earth models. This type of sampling meant that each combination of the four reservoir properties was used. Each earth model was effectively a three-layer model, with overburden, reservoir unit and underlying shale. All properties for the overburden and underlying shale units were copied from the calibration well data.

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