Fuzzy Probability Approach in Seismic Hazard Analysis

Abstract

Seismic hazard assessment like many other problems in seismology is a complicated problem, owing to the variety of parameters affecting the occurrence of the earthquake. Assessment of seismic hazard based on the theory of probability becomes hard particularly under highly uncertain conditions, i.e., where neither the statistical data nor the physical knowledge required for a purely probabilistic risk analysis is sufficient. Insufficiency of information will afflict the calculated risk probabilities with imprecision and will to the underestimation of the risk. This uncertainty, which is a result of vagueness and incompleteness of the data, should be considered in a rationale way. Essentials of seismic hazard analysis are identified and the concept of fuzzy logic is applied to seismic hazard analysis, generalizing the conventional probabilistic seismic hazard analysis (PSHA) to fuzzy probabilistic seismic hazard analysis (FPSHA). The β and λ values which are the input parameters for the PSHA are evaluated using earthquake data for the Warangal region. The uncertainty associated with these values will be too high for a site with moderate earthquake activity, and the previous earthquake data is scarce. Fuzzy logic will help in containing these uncertainties by its property of considering the possibility of a certain event occurring. This study presents an approach for seismic hazard analysis based on fuzzy set theory. Seismic activity is based on the seismic activity rate, λ, which is equal to the number of events with magnitudes equal to or greater than a defined magnitude level, say M₀, during a specified time period, T; the parameter b or β (β = b ln10). The variables β and λ are first converted into Gaussian fuzzy sets using α-cut method. The ranges of β and λ are chosen based on previous studies. The fuzzified variables are used in seismic hazard analysis. The outputs are defuzzified using the center of area method, and fuzzy hazard curve is developed for the study region. The output is compared with PSHA results. The horizontal PGA expected in Warangal on stiff ground, with a 10% probability of exceedance in 50 years (which corresponds to a return period of 475 years) is 0.0836 g, whereas, that with a 2% probability of exceedance in 50 years (return period = 2475 years) is 0.153 g.