Introduction - Extreme Events: A Physical Reconstruction and Risk Assessment - page 6

Frequency of occurrence
(decreasing)
Figure 1.2. Typical relationship between event magnitude and frequency. Note that
larger magnitude events occur less frequently than smaller magnitude events.
any one year always remains the same. In fact, its probability of occurrence
is regarded as remaining the same for any period of time. This remains the
case if the event occurs independently of prior events and therefore, like the
toss of a coin, occurs randomly within any given period of time. If external
factors influence the occurrence of that event then it will not be occurring
independently of a specified period of time. To once again use the coin tossing
analogy, if something influences the outcome of the tosses of a coin for some
specific period of time then we can no longer say that the outcome is a random
occurrence. We know that this is unlikely to be the case when tossing a coin,
but it is a very real possibility with respect to the occurrence of natural hazards
over time.
There are statistical measures, such as Bayesian analyses, which do assume
that prior events influence the occurrence of subsequent events and these are
sometimes used in risk assessments of some natural hazards such as earth-
quakes. Bayesian analysis is usually only used for hazards that have known
build-up and relaxation times, as occurs for example when crustal stresses along
afault or tectonic plate boundary build to the point of release causing an earth-
quake. Following the earthquake, it takes some time for those stresses to once
again build to a level to induce the next earthquake. So the time between earth-
quakes is not random and the probability of an earthquake occurring at that
specific location is reduced for a period and hence varies over time. This can
be called a conditional probability. Other hazards, such as many atmospheric
hazards, however, where such processes are thought not to operate, are gener-
ally regarded as occurring randomly with respect to previous events and in this
sense randomly with respect to time.
High-magnitude events usually occur less frequently than low-magnitude
events. A typical distribution of events over time is shown in Figure 1.2.Itis