This idea for this book has grown over the course of several years during which I have worked on projects related to seismic hazard analysis. My academic  training in hazard related issues was originally from a deterministic perspective. Therefore, some of the concepts used in probabilistic seismic hazard analysis (PSHA) were rather new (and partially counterintuitive) to me when more than 12 years ago I was invited to join the Pegasos project (Abrahamson et al., 2002), a SSHAC level 4 probabilistic seismic hazard assessment for the sites of four nuclear power plants in Switzerland. During that time I started to develop some code for seismic hazard analysis and some training material in Mathematica®  which were both originally intended for my own education. Over the years and stimulated by the different projects I worked in since then, the material continued to grow in the number of topics it covered. Gradually, it migrated into the textbook material for  a course in probabilistic seismic hazard analysis which I have been teaching inside and outside of academia for several years. When reading this book as a standalone text, it needs to be stressed up front that it addresses PSHA in ways which are different from what the reader might see in other books and courses on this topic.

Firstly, it focuses on concepts, not on procedures. What I mean by this is that, in contrast to how I originally learned it,  I do not begin to explain PSHA as a sequence of steps which start with the characterisation of the seismic soures, followed by the characterization of the ground-motion model, etc. Based on my own learning and teaching experience I have come to the conclusion that there is enormous benefit to focus on the underlying concepts first and only subsequently discuss the procedures (the “recipes”). This may be considered simply a matter of taste, but procedures can be memorized by simple repetition without having to understand the rational for the individual building blocks. I believe that the mechanics of doing seismic hazard analysis should become obvious from the underlying concepts and not the other way around. As a consequence of this perspective, this book is not aimed at a complete in-depth coverage of all aspects of all real-life PSHAs, nor at discussing the implementation  of PSHA in existing computer codes. It is my hope though  that readers who appreciate the approach  taken here, will also understand why a particular way of implementation may or may not make sense.  

Secondly, in order to accommodate different cognitive preferences and different levels of background knowledge, I introduce the key concepts in PSHA, namely the concepts from which hazard curves are derived, from a number of different perspectives. This was driven by trying to acknowledge that “Learners have different strategies, approaches, patterns of abilities, and learning styles that are a function of the interaction between their heredity and their prior experiences”, (National Research Council, 2000). My goal has also been to first develop the core concepts of seismic hazard analysis from the rather detailed analysis of very simple, but easily understandable “toy problems”. Subsequently, the discussion  is extended to more realistic situations.

Thirdly, people interested in PSHA come from many different backgrounds with very different curricula. In addition, seismic hazard analysis draws from many different fields such as Probability Theory, Earthquake Seismology, Engineering Seismology, and more. As a consequence of this diversity, I make no assumptions about the reader´s prior level of experience. Instead, I have divided the book into two parts:

Part A is aimed at the seismic hazard analysis novice and at readers having some background knowledge in parts of the fields relevant for PSHA. After an introduction it starts out by covering those aspects of probability theory, earthquake seismology, and engineering seismology which are prerequisite for PSHA.  For readers only trying to refresh their memory on particular aspects of these topics, these chapter can be consulted in essentially any order or even skipped at first reading by readers with prior experience in probability theory, earthquake seismology, and engineering seismology. Chapter 5 contains the essential material of part A and, guided by the question “How safe do you want to be?”, focuses on the derivation of  hazard curves from a number of different perspectives. For example, from a probability theoretical perspective,  ground motion (expressed as response spectral amplitudes) in PSHA can be treated as a random variable (RV). Hazard analysis in this framework  becomes an attempt to generate a site specific predictive model for this random variable and  hazard curves are then one of many different ways to  quantify the distribution function of this RV. From a very different, rather pragmatic perspective, hazard curves can simply be understood  as the result of a bookkeeping exercise in which nature is assumed to be observable for long periods of time and one can count how many times over the total observation time  certain ground motion levels are exceeded.  Several of these alternative perspectives are dicussed in chapter 5, hoping to have at least one which is attractive for every reader. Overall, I have tried to keep the discussions in part A to a minimum so that the material can be used as the basis of a "crash course" which can be taught in a few days.  

Part B adresses more advanced and partially highly specialized topics, for example a theoretical treatment of  the relationship between Fourier spectra and response spectra, a discussion on ground-motion model selection, on ground-motion model adjustment,  some thoughts on hazard model testing, and an in-depth discussion of uncertainties. In the latter case the guiding  question is "How certain do you want to be that the chosen safety level is met?". The selection of the topics in part B  is certainly biased by the challenges which we faced in projects in which I participated. Some of the issues are currently still unresolved such as the adjustment of empirical ground-motion prediction equations for application in regions different from the host region of the data from which they were generated.

Finally, this book is completely written in Mathematica® and produced in the open CDF format (, which can be read with the free CDF Player® ( It contains a combination of textbook material, interactive exercises and interactive walk-through tutorials which make heavy use of Mathematica´s dynamic interactivity. This type of interactivity is different from the pre-generated interactivity often found in  electronic books, where it comes in the form of pre-generated animations or movies. While these elements are a step forward from the traditional paper-textbook mindset which come as a one way conversation in which the narrative content is fixed by the author and static, it still maintains the role of the reader as pure recipient, because the interactivity is pre-generated and all the assumptions which go into an interactive figure for example are  still fixed by the author. When I learn a new topic, I usually have a lot of  “What if?”-questions, which often lead me to programming to explore these questions by small scale simulations. In particular with topics such as PSHA, I find such exercises very helpful to develop some intuition for the behaviour of a system in simple situations. The interactive material here is at least partially aimed at addressing “What if?”-questions, which is possible because the interactivity in CDF-documents can be computed and does not have to be pre-generated. This allows the reader to take on a completely new role in learning because assumptions going into an interactive element (“knowledge apps”) don´t need to be fixed, which allows the reader to interactively explore "What if?"-questions. In such an environment, the author takes on the role of a curator of  information while the readers become an active part in the learning process who may even design their own exercises.

In conclusion, I have tried to make this the book on PSHA which I would have liked to have had when I started to become involved in this topic nearly fifteen years ago, but done with the tools of today. I hope you´ll enjoy it.

Potsdam, Summer 2013

Frank Scherbaum


Abrahamson, N. A., P. Birkhauser, M. Koller, D. Mayer-Rosa, P. M. Smit, C. Sprecher, S. Tinic, and R. Graf. (2002). PEGASOS- A comprehensive probabilistic seismic hazard assessment for nuclear power plants in Switzerland. Paper presented at the 12 ECEE, London.

National Research Council (2000). How People Learn: Brain, Mind, Experience, and School: Expanded Edition. Washington, DC: The National Academies Press.‬


Parts of this book have been shaped a lot by contributions from some of my collaborators during the last years. Nico Kuehn,  University of Potsdam,  shares intellectual ownership on the inital versions of a number of the interactive features in the main chapter of Part A. I also owe him gratitude for lots of stimulating discussions on PSHA-related isues over the course of the years we worked together and for keeping the whole group up-to-date on the latest blog news on uncertainties, Bayesianism vs Frequentist, and biking.

Annabel Händel, University of Potsdam, did such a phantastic job in programming and documenting of all the signal processing tools needed for strong motion processing in Mathematica for her thesis, that it stimulated me to add a chapter on strong motion processing to part A. I am grateful for her generosity to let me use her codes but also for her comments on the initial version of this book.

This book would not have come into existence without my participation in the Pegasos project (Abrahamson et al., 2002). In particular the stimulating discussions with Julian Bommer, Hilmar Bungum, and Fabrice Cotton during the project workshops and the technical guidance by  Norm Abrahamson on all imagineable aspects of engineering seismology and seismic hazard analysis have shaped how I look at PSHA today and have continuously motivated me to learn more about this field.

I am indebted to Adrian Rodriguez-Marek for taking the time to critically read through  the first version of part A (despite it being in a rather rough state). His  feedback was extremely helpful to remove oversights and  to take out some of the  “rough edges” in the presentation.

This book has also been influenced considerably by the interaction with Fabrice Cotton and Céline Beauval from Grenoble University in the context of jointly teaching a 1-week course on PSHA at the master level. Most influential, however, has been the interaction with my students, who continue to stimulate me with their fresh look at old problems and by teaching me what works in education and what not.  For this I am extremely grateful.

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