Propensity and Probability in Depositional Facies Analysis and Modeling
- PDF / 2,397,830 Bytes
- 24 Pages / 439.37 x 666.142 pts Page_size
- 17 Downloads / 209 Views
Propensity and Probability in Depositional Facies Analysis and Modeling Y. Zee Ma
Received: 22 January 2009 / Accepted: 29 May 2009 / Published online: 3 September 2009 © International Association for Mathematical Geosciences 2009
Abstract Probabilistic models of geologic phenomena have often been criticized for lack of realism because they do not resemble the “picture” of geology in geoscientists’ minds. A geologic process is a single case, while conventional probabilistic methods assume a certain frequency of events. This is called “the problem of application” of the probability theory to physical sciences by Reichenbach. Propensity concept was proposed by Popper in the late 1950s, as an alternative interpretation of probability, to solve this problem with an emphasis of single cases in quantum physics. Similarly, a reservoir or a geologic process is a single case as there are no two identical reservoirs or processes in nature. The peculiarity of a geologic process as a single case often causes controversies regarding how the probability theory should be applied to geosciences. In this paper, Popper’s propensity concept is introduced to describe geologic depositional environments and facies sequences. As a matter of fact, a geologic process is simultaneously indeterministic and causal. Such a phenomenon has been shown to be well described by the propensity concept in other scientific domains and social applications. Representation of a depositional-facies conceptual or sedimentological model or facies sequences using propensity allows quantitative integration of descriptive geology with facies frequency data at wells. Such integration can produce facies probabilities that convey the descriptive geology. Subsequently, these facies probabilities can be used to constrain stochastic modeling and make a geologic model more realistic. Keywords Geologic conceptual model · Single case probability · Spatial propensity · Probabilistic causality · Abductive inference · Facies frequency · Geostatistical modeling · Declustering Y.Z. Ma () Schlumberger, 6501 S. Fiddler’s Green Cir., Suite 400, Greenwood Village, CO 80111, USA e-mail: [email protected]
738
Math Geosci (2009) 41: 737–760
1 Introduction Although probabilistic methods have been increasingly used in geoscience in the last half century, utilization of the probabilistic approach is still somewhat limited. One of the classical schools of thought is that geology is not random, and therefore, a geologic model should not be built using stochastic methods; and further, for a given reservoir, the geology is unique and the concept of stochastic multiple realizations is flawed. In reality, it is not because geology is random or uncertain that probabilistic methods are used to build geologic models and evaluate the uncertainty, it is because of one’s lack of knowledge about it. Matheron remarked “there is not, nor can there be, any such thing as probability in itself. There are only probabilistic models.” He continued, “Randomness is in no way a uniquely defined or even defin
Data Loading...
