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5

The basic principles of seismic hazard analysis

Engineers design for ground motion, not for earthquakes

N.  Abrahamson

Seismic hazard analysis deals with the hazard generated by strong ground shaking. Earthquakes or other  sources of seismic waves are the reason for the hazard, but it is the effect, the corresponding ground motion, that actually constitutes the hazard. This is an important distinction which cannot be overemphasized. Seismic hazard is a site dependent quantity, the properties of which are controlled by physical processes at the source, by properties of the medium through which the waves propagate and by local site conditions. A brief introduction into the seismological aspects of seismic hazard analysis can be found in chapter 3.

Although seismic hazard analysis can be explained procedurally as a sequence of steps which start with the characterisation of the seismic source(s), followed by the characterisation of the ground motion, I believe (very much in line with the epigraph) that it facilitates the understanding to approach seismic hazard analysis conceptually by thinking about ground motion first. The way ground motion is parametrised in  the context of seismic hazard analysis differs considerably from the way it is treated in classical seismology. In engineering seismology and seismic hazard analysis, the most popular ground motion intensity parameters are related to response spectral amplitudes. This might be an unfamiliar concept to some non-engineers who might be more familiar with Fourier spectra. Those readers are referred to chapter 4 for a brief introduction into the concept of elastic response spectrum and the  processing steps necessary to derive them. Here, seismic hazard will be addressed from a ground motion perspective and furthermore from within a probabilistic framework. Therefore, the type of hazard analysis which is discussed below can be referred to as probabilistic seismic hazard analysis, often simply called PSHA.

Loosely speaking, PSHA is aimed at the determination of statistical properties of ground shaking which is expected to occur at a site of interest. The adjective "probabilistic" in PSHA refers to the fact that, mathematically speaking,  the chosen ground motion intensity parameter is treated as a random variable (RV). The concept of a random variable is the  key mathematical concept in PSHA. An introduction into this and other essential aspects of probability theory, needed to understand the fundamental concepts of PSHA, is given in chapter 2. In contrast to a normal variable, a random variable does not have a specific value but is described by a distribution function which defines a range of values together with a "likelihood" to obtain a particular value. In the probabilistic framework, the goal of seismic hazard analysis can be stated as the attempt to derive a model for the distribution function of a random variable. From this function, all desired representations, for example the often used hazard curve, can be derived by simple mathematical operations.

In this chapter you will be made familiar with the concept of hazard curves from a number of different perspectives.  In other words, you will be made familiar with hazard curves in very different representations. The reason for taking this approach is to acknowledge that humans have different cognitive preferences and different ways of learning. Some of us learn best through theoretical derivations, some through incremental examples, some through synoptic ones, and so forth. I hope that the diversity of  perspectives taken here has something to offer for everybody.

Frank Scherbaum (2015), Fundamental concepts of Probabilistic Seismic Hazard Analysis, Hazard Classroom Contribution No. 001