# Probabilistic Aggregation of Uncertain Geological Resources

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## Abstract

Commodities such as oil and gas occur in isolated reservoirs or accumulations, more generically called basic units here. To understand a study area’s economic potential and to craft plans for exploration and development, resource analysts often aggregate (sum, accumulate) basic unit magnitudes in distinct spatial subsets of the study area and then appraise the total area’s potential by summing these intermediate sums. In a probabilistic approach, magnitudes are modeled as random variables. Some have asked, “Do different methods of partitioning basic units into subsets lead to different probability distributions for the sum of all basic unit magnitudes?” Any method of aggregation of basic unit magnitudes which obeys the rules of probability leads to the same probability distribution of the sum of all unit magnitudes as that computed by direct summation of all basic unit magnitudes. A Monte Carlo simulation of a synthetic example in which the magnitude of resource in each unit is marginally lognormal and pairwise correlations among basic unit magnitudes are specified illustrates key features of probabilistic aggregation. The joint distribution of certain pairs of aggregates are closely approximated by a bivariate lognormal distribution.

## Keywords

Aggregation matrix Single-stage aggregation Multiple-stage aggregation Lognormality## Notes

### Acknowledgments

The U. S. Geological Survey requires a preliminary internal review before any paper can be published in a scientific journal (http://pubs.usgs.gov/circ/1367/). We wish to thank Emil Attanasi, David Root and Peter Warwick for their insightful suggestions.

## References

- Anscombe FJ (1973) Graphics in statistical analysis. Am Stat 27(1):17–21Google Scholar
- Blondes MS, Brennan ST, Merrill MD, Buursink ML, Warwick PD, Cahan SM, Cook TA, Corum MD, Craddock WH, DeVera CA, Drake RM, Drew LJ, Freeman PA, Lohr CD, Olea RA, Roberts-Ashby TL, Slucher R, Varela BA (2013a) National assessment of geologic carbon dioxide storage resources—methodology implementation: U.S. Geological Survey Open-File Report 2013-1055, p 26. http://pubs.usgs.gov/of/2013/1055/OF13-1055.pdf
- Blondes MS, Schuenemeyer JH, Drew LJ, Warwick PD (2013b) Probabilistic aggregation of individual assessment units in the U.S. Geological Survey national CO
_{2}sequestration assessment. Energy Proc 37:5110–5117CrossRefGoogle Scholar - Blondes MS, Schuenemeyer JH, Olea RA, Drew LJ (2013c) Aggregation of carbon dioxide sequestration storage assessment units. Stoch Environ Res Risk Assess 27:1839–1859CrossRefGoogle Scholar
- Carter PJ, Morales E (1998) Probabilistic addition of gas reserves within a major gas project. In: Paper presented at the Society of Petroleum Engineers Asia Pacific Oil and Gas Conference and Exhibition, p 8. SPE paper 50113Google Scholar
- Collett T (2008) Assessment of gas hydrates on the North Slope, Alaska, 2008. US Geological Survey Fact 2008-3073, p 4. https://pubs.usgs.gov/fs/2008/3073/pdf/FS08-3073_508.pdf
- Crovelli RA, Balay RH (1991) A microcomputer program for energy assessment and aggregation using the triangular probability distribution. Comput Geosci 17(2):197–225CrossRefGoogle Scholar
- Daneshkhah A, Oakley JE (2010) Eliciting multivariate probability distributions. In: Böcker K (ed) Rethinking Risk Measurement and Reporting, vol I. Risk Books, LondonGoogle Scholar
- Delfiner P, Barrier R (2008) Partial probabilistic addition: a practical approach for aggregating resources. SPE Reserv Eval Eng 11(2):379–386Google Scholar
- Kaufman GM (2016) Generalizations of intra-class correlation matrices (unpublished working paper)Google Scholar
- Kaufman GM (2018) Properties of sums of geologic random variables. In: Daya Sagar BS, Cheng Q, Agterberg F (eds) Handbook of Mathematical Geosciences: fifty years of IAMG, Chapter 5. 50th Anniversary volume (forthcoming)Google Scholar
- Klett TR, Gautier DL (2009) Assessment of undiscovered petroleum resources of the Barents Sea. U.S. Geological Survey Fact Sheet 2009-3037, p 4. http://pubs.usgs.gov/fs/2009/3037/pdf/FS09-3037.pdf
- Meyer MA, Booker JM (2001) Eliciting and analyzing expert judgement: a practical guide. ASA-SIAM series on Statistics and Applies Probabilities, Alexandria, VA, p 459Google Scholar
- Miller BM, Thomsen HL, Dolton GL, Coury AB, Hendricks TA, Lennartz FE, Powers R, Sable EG, Varnes KI (1975) Geological estimates of undiscovered oil and gas resources in the United States. United States Geological Survey Circular 725, p 78, 3 mapsGoogle Scholar
- O’Hagan A, Buck CE, Daneshkhah A, Eiser JR, Garthwaite PH, Jenkinson DJ, Oakley JE, Rakow T (2006) Uncertain judgements: eliciting experts’ probabilities. Wiley, Chichester, p 321CrossRefGoogle Scholar
- Pike R (2008) How much oil is really there? Making correct statistics bring reality to global planning. Significance 5:149–152CrossRefGoogle Scholar
- Schuenemeyer JH (2005) Methodology for the 2005 USGS assessment of undiscovered oil and gas resources, Central North Slope, Alaska. U.S. Geological Survey Open-File Report 2005-1410, p 82. https://pubs.usgs.gov/of/2005/1410/of2005-1410.pdf
- Schuenemeyer JH, Gautier DL (2010) Aggregation methodology for the Circum-Artic resource appraisal. Math Geosci 42(5):583–594CrossRefGoogle Scholar
- U.S. Geological Survey Geologic Carbon Dioxide Storage Resources Assessment Team (2013) National Assessment of Geologic Carbon Dioxide Storage Resources-Results: U.S. Geological Survey Circular 1386, p 41. http://pubs.usgs.gov/circ/1386/pdf/circular1386.pdf
- Van Elk JF, Gupta R (2010) Probabilistic aggregation of oil and gas field resource estimates and project portfolio analysis. SPE Reserv Eval Eng 13(1):72–81Google Scholar
- Wilcox RR (2016) Introduction to robust estimation and hypothesis testing, 4th edn. Academic Press, Cambridge, p 786Google Scholar