Seismic To Simulation - MCMC Geostatistical Inversion

MCMC Geostatistical Inversion

In the next step of seismic to simulation, seismic inversion techniques combine well and seismic data to produce multiple equally plausible 3D models of the elastic properties of the reservoir. Seismic data is transformed to elastic property log(s) at every trace. Deterministic inversion techniques are used to provide a good overall view of the porosity over the field, and serve as a quality control check. To obtain greater detail needed for complex geology, additional stochastic inversion is then employed.

Geostatistical inversion procedures detect and delineate thin reservoirs otherwise poorly defined. Markov chain Monte Carlo (MCMC) based geostatistical inversion addresses the vertical scaling problem by creating seismic derived rock properties with vertical sampling compatible to geologic models.

All field data is incorporated into the geostatistical inversion process through the use of probability distribution functions (PDFs). Each PDF describes a particular input data in geostatistical terms using histograms and variograms, which identify the odds of a given value at a specific place and the overall expected scale and texture based on geologic insight.

Once constructed, the PDFs are combined using Bayesian inference, resulting in a posterior PDF that conforms to everything that is known about the field. A weighting system is used within the algorithm, making the process more objective.

From the posterior PDF, realizations are generated using a Markov chain Monte Carlo algorithm. These realizations are statistically fair and produce models of high detail, accuracy and realism. Rock properties like porosity can be cosimulated from the elastic properties determined by the geostatistical inversion. This process is iterated until a best fit model is identified.

Inversion parameters are tuned by running the inversion many times with and without well data. Without the well data, the inversions are running in blind-well mode. These blind-well mode inversions test the reliability of the constrained inversion and remove potential biased.

This statistical approach creates multiple, equi-probable models consistent with the seismic, wells, and geology. Geostatistical inversion simultaneously inverts for impedance and discrete properties types, and other petrophysical properties such as porosity can then be jointly cosimulated.

The output volumes are at a sample rate consistent with the reservoir model because making synthetics of finely sampled models is the same as from well logs. Inversion properties are consistent with well log properties because the histograms used to generate the output rock properties from the inversion are based on well log values for those rock properties.

Uncertainty is quantified by using random seeds to generate slightly differing realizations, particularly for areas of interest. This process improves the understanding of uncertainty and risk within the model.