Poisson deposition models

Fig. 43. Comparison of (a) monolayer and (b) Poisson deposition models of surface site deactivation with experimental aging data (Smith and Wei, 1985).

Another type of Bayesian model that is useful for paieoseismoiogy is an age-depth model for sedimentary sequences. Such models can be used when there are a series of radiocarbon dates in a single sediment column, with depth information. Most commonly, these are used for cores, but could also be applied to other types of section if a single depth scale can be defined. Like other Bayesian models, there needs to be a mathematical model for the deposition process. One such model is the Poisson process model implemented in OxCal. In this model, the assumption is that the deposition is random which allows for flexibility in an otherwise... 

One hypothetical model for the deposition is the purely random Poisson process (Wei, 1984) where any surface is equally likely to be the next deposition site, regardless of whether it is bare alumina or covered by previous depositions. For such a model, the probability of a surface covered with n number of deposits would be... 

Equation (5) is an example of the Poisson process in probability theory [9]. S decays slowly with t, so that enough sites survive even at long times to continue forming new coke. This simple model lends itself naturally to the distinction of coke depositing on clean sites, monolayer coke concentration C , and coke depositing on already-coked sites, multilayer coke concentration Cm- That is, C (/) = CJf) + CM t) at all times. A simple site balance yields... 

One approach in developing a pore-size model is to apply the Poisson polyhedron theory. Each deposited layer in the build-up to make the web is simulated by a two dimensional network of straight lines, a Poisson line network, forming a random distribution of polygons, as depicted in Fig. 8.18 showing two pore sizes defined as the diameter of largest circle inscribed within a given void. 

In these deposition conditions a reasonable model of growth is the vertical stack growth, for which the number of atoms in each stack is a random variable distributed according to Poisson s law." The roughness factor of these films is often very high (say alO) " and increases in proportion to the thickness. 

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