5.4. Monte Carlo approach to seismic hazard analysis
In this section we are going to look at the generation of hazard curves in yet different representations. The key concept which we will employ here is that of Monte Carlo simulation. We will numerically simulate the earthquake generation processes as well as the generation of ground motion from them (of course only those aspects which we need for the present purpose: magnitudes, distances, and PGA values) through appropriate random process simulations in the computer. The calculation of hazard curves then becomes a very simple numerical book keeping exercise. All we need to do is watch what this model does and count the outcomes.
This strategy will also naturally lead us to an analysis tool to identify the dominant contributions to exceedance rates for a chosen ground motion level, a technique which has become popular in the context of what is known as disaggregation. We have actually used disaggregation techniques before without referring to them as such.
I will eventually get back to where we started our discussion on hazard curves for single sources, namely to the relationship between the hazard curve and the probability density function of expected ground motion at a site of interest. I will show that using this perspective, the hazard curve calculation for the simple situation which we have been discussing so far, can be implemented in a few lines (sic!) of Mathematica code from, which will higlight the underlying mathematical concepts, again from a different perspective.
In order to emphasize the contribution of the two different random processes which we have been dealing with in the context of PSHA, the process to generate magnitudes and distances and secondly the process to generate ground motion values once the magnitudes and distances are known, I will discuss a situation in which it makes sense to separate them sequently. This leads to the concept of real time PSHA (RTPSHA) which can be used in Earthquake Early Warning Systems(e. g. Iervolino et al., 2006, Convertito et al., 2008).
I will conclude this chapter with a some remarks on the advantages and disadvantages of the different representations of hazard curves which we have been discussing in all of chapter 5.
Finally the hazard calculations are extended from PGA to a whole suite of oscillator frequencies. This allows to determine those response spectral values which have the same exceedance rates (or probability). The result is called a uniform hazard spectrum and is discussed in the final subsection.
.............. 5.4. Monte Carlo approach to seismic hazard analysis
.............. 5.4.1. Hazard Analysis as book keeping exercise
.............. 5.4.2. The hazard curve as representation of the ground motion distribution
.............. 5.4.3. Real Time PSHA (RTPSHA)
.............. 5.4.4. Disaggregation
.............. 5.4.5. Synopsis on hazard curves
.............. 5.4.6. The Uniform Hazard Spectrum (UHS)