Problems in parameter estimation in probabilistic seismic hazard analysis and some solutions

Abstract

Probabilistic Seismic Hazard Analysis (PSHA) is not a new study field — indeed, it dates from the late 1960s. However, the original and introductory study paid scant attention to a crucial aspect, namely the estimation of the model parameters. Consequently, over the ensuing five decades, Parameter Estimation in Probabilistic Seismic Hazard Analysis (PE-PSHA) has not gained due recognition as an independent field of study. A review of the relevant body of literature indicates that PE-PSHA is not yet regarded as an entity, a coherent body of literature, or a study field. This study aims to introduce PE-PSHA as a distinct field of study. In 1968, Cornell introduced what is known today as Probabilistic Seismic Hazard Analysis (PSHA). Although a landmark study, it is peculiar and even astonishing that Cornell (1968) simply ignored the crucial aspect of parameter estimation of models. This aspect and the implications of ignoring the importance of parameter estimation are discussed in detail in this thesis. Seismicity modelling in general and the classic Cornell–McGuire procedure are introduced, which provides the platform for the introduction of the parameters typically associated with it, usually referred to as seismicity parameters. Subsequently, each parameter is discussed in detail, clarifying the development of estimation techniques, as well as the problem areas that could be identified. In some instances, solutions are put forward, either as own research by the author or gleaned from the literature. A discussion is presented on the magnitude of completeness (𝑚𝑐) of seismic catalogues, along with a critical analysis of the estimation techniques currently employed. Concerns about some of these methods are discussed comprehensively and clarified by detailed argument. The two principal model parameters are discussed, namely the Gutenberg–Richter 𝑏-value and the rate of seismicity (RoS). A review of the estimation techniques of these parameters is presented, as well as the problems encountered. This review also serves as an overview of the historical development of the estimation of the two parameters. Various solutions have been put forward to some of the problems encountered; however, these solutions are not being employed. Subsequently, some estimators for the 𝑏-value for incomplete catalogues are compared. The maximum possible earthquake magnitude for a given area (𝑚𝑚𝑎𝑥) from the seismic catalogue data is discussed. A few procedures (or estimators) have been proposed, although only by a few researchers. The estimators are discussed in some detail and are analysed critically, among which are methods newly investigated by the author. The concept of seismic zones is discussed, as, although seismic zones are not parameters, the delineation of seismic sources is a modelling procedure that requires estimation from the catalogue data similar to estimating parameters (this can be regarded as a generalised part of parameter estimation). The practice of seismic zoning based largely on expert opinion is analysed critically, and a number of alternatives are discussed. In the conclusion to the study, the need for PE-PSHA to be regarded as an entity, or separate field of study, is highlighted. In addition, the discussed problems and solutions are reviewed, and recommendations are made. Finally, possible future research areas are pointed out.