ShakeCast’s primary product is the potential impacts list, generated by calculating the probability that real-time shaking levels have exceeded a facility’s physical limits. ShakeCast users define these limits by uploading fragility profiles of their facilities. Generally determined by an engineer, a facility’s fragility is a correlation of some shaking value in a particular metric (ex. PGA, MMI) to a damage state, taking into account some uncertainty in that value.
When a ShakeMap is generated after an earthquake, ShakeCast will search this map for the shaking measurements (or estimates) nearest to the facilities in its database. These values can then be compared to cumulative distribution functions (CDFs) for each facility to determine the probability of the facility being in a specific damage state. Figure 1 shows an example of this comparison from the HAZUS manual.
Figure 1: HAZUS example of CDF curves intersecting with shaking of various strengths1
pyCast uses this same method to generate its inspection priorities. It generates these CDF curves using Python’s built in error function (math.erf). The relationship between the error function and CDF is
Eq. 1
and pyCast’s implementation of this calculation is shown in figure 2.
Figure 2: Example of CDF implementation in pyCast and an intersecting shaking level of 6 MMI
The probability of the facility being in an inspection state can then be described by the CDF curves at a measured shaking level. Since the CDF cannot account for additional states, the final probability for any state is equal to the value of the CDF at the specific shaking level minus the probability of all higher damage states. This is described by
Eq. 2
.
Entering the data from Figure 2 into Equation 2, the inspection priority of the facility for this event can be determined and is realized in Figure 3.
Figure 3: The probability of an example facility requiring an inspection after experiencing 6 MMI Shaking
pyCast will award the facility the inspection priority with the highest probability, favoring the higher in the event of two states being equally the most likely. For smaller shaking levels, the probability of exceeding even the lowest state may be quite small; in this case, the facility is most likely in a “No Priority” inspection state. The facility is then designated a “weight” based on it’s damage state
Eq. 3
.
After all the facilities encompassed by a ShakeMap are processed, a notification is generated. The list of facilities included in this notification are sorted in reverse order by their weight.
1: Federal Emergency Management Agency (FEMA), 2001. Earthquake Model, Hazus–MH 2.1 Technical Manual, Online.