A generic probabilistic model for natural hazard assessment

A generic methodology for probabilistic natural hazard assessment is presented. Three area-characteristic recurrence parameters are defined by combining a Poisson process with the relevant natural-hazard-frequency–event-size power law. The distribution of the Poisson process describes the temporal characteristics present in the data and the power law describes the relationship between the frequency of events and the event sizes. The estimates for the mean rate of occurrence λ and the power law parameter b are based on empirical datasets consisting of extreme prehistoric and historical data, along with more-recent instrumental data. Likelihood functions are defined to allow for datasets to be combined and for the application of both maximum likelihood estimation (MLE) and Bayesian inference (BI). The proposed methodology accounts explicitly for aleatory and epistemic uncertainty by making provision for incomplete datasets, uncertainty associated with the observed event sizes, uncertainty associated with the parameters of the applied occurrence and event size distributions, and uncertainty associated with the occurrence of events in the dataset. These types of uncertainty are introduced in the modelling process through convolution and mixture distributions, as well as weighted likelihood functions. Existing techniques to assess the third recurrence parameter, the maximum possible event size x_max, are discussed briefly. The applicability of the proposed methodology is demonstrated by using a synthetic earthquake dataset, real earthquake datasets for Central Italy and the Ceres–Tulbagh region in South Africa, tsunami data for three tsunamigenic regions in the Pacific Ocean, and HAILCAST ensemble re-analysis hail data for Gauteng province, South Africa. Various combinations of the different types of assumptions, data, and uncertainty are investigated. The methodology shows the universality of the power law in assessing natural hazards. In practice, the methodology is not restricted to natural hazard assessment, but can be applied to any instance in which the frequency–event-size relationship follows a power law distribution. To illustrate this statement, financial vehicle loss information related to hail damage, obtained from a short-term insurer in South Africa, is analysed. The versatility of the modelling process provides the researcher with various options to account for incomplete data, as well as data and parameter uncertainty.Thesis (PhD)--University of Pretoria, 2019.• Research and travel were supported by the South African National Research Foundation and the South Africa Statistical Association under the SASA-NFR Grant for Vulnerable Discipline — Academic Statistics 2017. This work is based on research supported wholly or in part by the National Research Foundation of South Africa (Grant Numbers 76906, 96412, 94808 and 103724).• University of Pretoria Natural Hazard Centre, University of Pretoria, Department of Geology.StatisticsPhDUnrestricte

Interpolation in stationary spatial and spatial-temporal datasets

In the early 1950s the study on how to determine true ore-grade distributions in the mining sector, sparked the development of a series of statistical tools that specifically allows for spatial and subsequently spatial-temporal dependence. These statistics are commonly referred to as geostatistics, and has since been incorporated in several fields of study characterized by this dependence. Basic descriptive statistics and mapping tools for geostatistics are defined and illustrated by means of a simulated dataset. The moments are modelled according to predefined conditions and model structures to describe the spatial and spatial-temporal variance in the data. These variograms and covariance structures are subsequently utilized in the least square procedure, namely kriging. At present, kriging is most commonly used in geostatistics for the interpolation and simulation of spatial or spatial-temporal data. The univariate and multivariate spatial and spatial-temporal kriging techniques are tested on the simulated dataset, to demonstrate how interpolation weights are determined according to the lag distances and underlying variance structure. The strength, weaknesses and inherent complexities of the methodologies are highlighted.Dissertation (MSc)--University of Pretoria, 2010.Statisticsunrestricte

Estimation of earthquake hazard parameters from incomplete data files. Part III. Incorporation of uncertainty of earthquake-occurrence model

Most probabilistic seismic-hazard analysis procedures require that at least three seismic source parameters be known, namely the mean seismic activity rate λ, the Gutenberg–Richter b-value, and the area-characteristic (seismogenic source) maximum possible earthquake magnitudemmax. In almost all currently used seismic-hazard assessment procedures that utilize these three parameters, it is explicitly assumed that all three remain constant over time and space. However, closer examination of most earthquake catalogs has indicated that significant spatial and temporal variations existed in the seismic activity rate λ, as well as in the Gutenberg–Richter b-value. In this study, the maximum likelihood estimation of these earthquake hazard parameters considers the incompleteness of the catalogs, the uncertainty in the earthquake magnitude determination, as well as the uncertainty associated with the applied earthquake-occurrence models. The uncertainty in the earthquake-occurrence models is introduced by assuming that both the mean seismic activity rate λ and the Gutenberg–Richter b-value are random variables, each described by the gamma distribution. This approach results in the extension of the classic frequency–magnitude Gutenberg–Richter relation and the Poisson distribution of the number of earthquakes with their compounded counterparts (Benjamin, 1968; Campbell, 1982, 1983). The proposed procedure was applied in the estimation of the seismicity parameters in an area that had experienced the strongest and most devastating earthquake in contemporary South African history, namely the 29 September 1969 Mw 6.3 Ceres–Tulbagh event. In this example, it was shown that the introduction of uncertainty in the earthquake-occurrence model reduced the mean return periods, leading to an increase of the estimated seismic hazard. Additionally, this study confirmed that accounting for magnitude uncertainties had the opposite effect, that is, it brought about increases in the return periods, or, equivalently, a reduction of the estimated seismic hazard.The National Research Foundation of South Africa (Grant Numbers 76906 and 94808).http://www.seismosoc.orgpublications/bssa/am2016Geolog

Extension of the Aki-Utsu b-value estimator for incomplete catalogs

The Aki (1965) maximum likelihood estimate of the Gutenberg–Richter b-value is extended for use in the case of multiple catalogs with different levels of completeness. The most striking feature of this newly derived estimator is its simplicity—it is more manageable than the well-known and already easy to use Weichert (1980) solution to the analogs problem. In addition, confidence intervals for the newly derived estimator are provided.http://www.seismosoc.orgpublications/bssa/am2017Geolog

Estimation techniques for seismic recurrence parameters for incomplete catalogues

Please read the abstract in the article.http://link.springer.com/journal/10712hj2021Geolog

Probabilistic tsunami hazard assessment from incomplete and uncertain historical catalogues with application to tsunamigenic regions in the Pacific Ocean

The paper presents a new method for empirical assessment of tsunami recurrence parameters, namely the mean tsunami activity rate λT, the Soloviev–Imamura frequency–magnitude power law bT-value, and the coastline-characteristic, maximum possible tsunami intensity imax. The three coastline-characteristic recurrence parameters are estimated locally by maximum likelihood techniques using only tsunami event catalogues. The method provides for incompleteness of the tsunami catalogue, uncertainty in the tsunami intensity determination, and uncertainty associated with the parameters in the applied tsunami occurrence models. Aleatory and epistemic uncertainty is introduced in the tsunami models by means of the use of mixture distributions. Both the mean tsunami activity rate λT of the Poisson occurrence model, and the bT-value of the Soloviev–Imamura frequency–intensity power law are random variables. The proposed procedure was applied to estimate the probabilities of exceedance and return periods for tsunamis in the tsunamigenic regions of Japan, Kuril–Kamchatka, and South America.The National Research Foundation of South Africa (Grant Numbers 76906 and 94808).https://link.springer.com/journal/242018-08-30hj2017GeologyStatistic

Energetic and spatial characterization of seismicity in the Algeria–Morocco region

We estimate the energetic and spatial characteristics of seismicity in the Algeria–Morocco region using a variety of seismic and statistical parameters, as a first step in a detailed investigation of regional seismic hazard. We divide the region into five seismotectonic regions, comprising the most important tectonic domains in the studied area: the Moroccan Meseta, the Rif, the Tell, the High Plateau, and the Atlas. Characteristic seismic hazard parameters, including the Gutenberg–Richter b-value, mean seismic activity rate, and maximum possible earthquake magnitude, were computed using an extension of the Aki–Utsu procedure for incomplete earthquake catalogs for each domain, based on recent earthquake catalogs compiled for northern Morocco and northern Algeria. Gutenberg–Richter b-values for each zone were initially estimated using the approach of Weichert (Bull Seismol Soc Am 70:1337–1346, 1980): the estimated b-values are 1.04 ± 0.04, 0.93 ± 0.10, 0.72 ± 0.03, 0.87 ± 0.02, and 0.77 ± 0.02 for the Atlas, Meseta, High Plateau, Rif, and Tell seismogenic zones, respectively. The fractal dimension D2 was also estimated for each zone. From the ratio D2/b, it appears that the Tell and Rif zones, with ratios of 2.09 and 2.12, respectively, have the highest potential earthquake hazard in the region. The Gutenberg–Richter relationship analysis allows us to derive that in the Tell and Rif, the number of earthquake with magnitude above Mw 4.0, since 1925 normalized to decade and to square cell with 100-km sides is equal to 2.6 and 1.91, respectively. This study provides the first detailed information about the potential seismicity of these large domains, including maximum regional magnitudes, characteristics of spatial clustering, and distribution of seismic energy release.The Algerian CRAAG, the Spanish Seismic Hazard and Active Tectonics research group, and the Spanish MINECO CGL2015- 65602-R project.http://link.springer.com/journal/110692018-04-30hb2016Physic

A scenario approach to estimate the maximum foreseeable loss for buildings due to an earthquake in Cape Town

A methodology for the assessment of the probable maximum loss associated with an earthquake is described and applied to the Cape Town central business district. The calculations are based on the effect of the two largest earthquakes that occurred in Milnerton in 1809 and Ceres–Tulbagh in 1969. The investigation concludes that if buildings and infrastructure in an area follow the SANS Standard 10160 for seismic loading of 0.1 g, they are exposed to significant seismic risk. The main purpose of this research is not the accurate quantification of expected losses to Cape Town’s infrastructure, but to raise awareness between civil engineers, the insurance industry and disaster management agencies that seismic hazard is an issue in South Africa and must be considered as a potential threat to its residents and infrastructure.http://www.actuarialsociety.org.za/Professionalresources/SAActuarialJournal.aspxam201

A review of biophysical and socio-economic effects of unconventional oil and gas extraction - implications for South Africa

The impacts associated with unconventional oil and gas (UOG) extraction will be cumulative in nature and will most likely occur on a regional scale, highlighting the importance of using strategic decision-making and management tools. Managing possible impacts responsibly is extremely important in a water scarce country such as South Africa, versus countries where more water may be available for UOG extraction activities. This review article explains the possible biophysical and socioeconomic impacts associated with UOG extraction within the South African context and how these complex impacts interlink. Relevant policy and governance frameworks to manage these impacts are also highlighted.The Water Research Commission, South Africa, is thanked for providing funding for this research.http://www.elsevier.com/locate/jenvman2017-12-31hb2017Geolog

Vulnerability mapping as a tool to manage the environmental impacts of oil and gas extraction

Various biophysical and socio-economic impacts may be associated with unconventional oil and gas (UOG) extraction. A vulnerability map may assist governments during environmental assessments, spatial planning and the regulation of UOG extraction, as well as decision-making around UOG extraction in fragile areas. A regional interactive vulnerability map was developed for UOG extraction in South Africa. This map covers groundwater, surface water, vegetation, socio-economics and seismicity as mapping themes, based on impacts that may emanate from UOG extraction. The mapping themes were developed using a normative approach, where expert input during the identification and classification of vulnerability indicators may increase the acceptability of the resultant map. This article describes the development of the interactive vulnerability map for South Africa, where UOG extraction is not yet allowed and where regulations are still being developed to manage this activity. The importance and policy implications of using vulnerability maps for managing UOG extraction impacts in countries where UOG extraction is planned are highlighted in this article.The Water Research Commission, South Africahttp://rsos.royalsocietypublishing.orgam2018Geolog