Effect of Epicenter Data Inconsistency in Determining Bandwidth and Its Subsequent Use in Hazard Analysis for Chennai Using Kernel Smoothing Approach

Effect of Epicenter Data Inconsistency in Determining Bandwidth and Its Subsequent Use in Hazard Analysis for Chennai Using Kernel Smoothing Approach

C. K. Ramanna (Indian Institute of Technology Madras, India) and G. R. Dodagoudar (Indian Institute of Technology Madras, India)
DOI: 10.4018/978-1-4666-9619-8.ch065
OnDemand PDF Download:
$30.00
List Price: $37.50

Abstract

The most important parameter in the kernel density estimator is the bandwidth or spread or window width. The bandwidth of the kernel density estimator, which follows the power law, is determined using the nearest neighborhood technique for the earthquake catalog which is divided into bins. For reliable hazard estimates, the magnitude bins used in developing the power law and estimating the spatial activity rate density function should be the same. It is important that consistency be maintained between the earthquake epicenters used in determining the bandwidth and the epicenters to which the bandwidth is applied subsequently. In this paper, the effect of epicenter data inconsistency on hazard estimates for various return periods for Chennai is evaluated. Two methods of binning are used, one in which the epicenters used in deriving the bandwidth is in line with the epicenters used in arriving at the spatial activity rate and the other where the epicenters used in deriving the bandwidth are just grouped by dividing the catalogue into equal bins. Seismic hazard estimations are compared using these two approaches of forming the magnitude bins for Chennai, Tamil Nadu, India. The peak ground acceleration (PGA) values obtained from Binning Methods 1 and 2 for 475 years return period are 0.0955g and 0.0802g respectively. The difference in PGA and peak spectral acceleration (PSA) from the two binning methods ranges from 20 to 10% with respect to Binning Method 1 for the return periods of 72 to 2475 years.
Chapter Preview
Top

Introduction

Seismic hazard analysis (SHA) plays an important role in the earthquake resistant design of structures by providing a rational value of input hazard parameters such as peak ground acceleration (PGA) or the response spectrum amplitudes at different natural periods. Zonefree technique to seismic hazard analysis is gaining popularity in regions of distributed seismicity. One such zonefree technique most often used (Secanell et al., 2008; Lai et al., 2009; Menon et al., 2010; Ramanna & Dodagoudar, 2012) and also widely studied (Molina et al., 2001; Beauval et al., 2006) is the kernel density estimator to seismic hazard analysis. The kernel estimator has been mainly used to replace the seismicity determined by the Gutenberg-Richter (G-R) recurrence law with a spatially varying seismic activity rate density function. A simple illustration of the kernel density estimator is shown in Figure 1. In this technique, the probability density function (PDF) is determined as the normalized sum of individual function called kernels placed on the data or sample points. The most important parameter in a kernel density estimator is the bandwidth or the spread of the kernels over the epicenters. Figure 2 and Figure 3 illustrate the effect of bandwidth on the final PDF derived. The bandwidth used for each epicenter plays a vital role in arriving at the hazard estimate for a given site and hence it needs to be determined carefully. There are several methods of determining the optimal bandwidth for a data set as summarized by Mugdadi (2004). However, Woo (1996) suggests the use of nearest neighborhood technique for arriving at the bandwidth for a set of epicenters.

Figure 1.

Kernel density estimation concept

Figure 2.

Large bandwidth kernels

Figure 3.

Small bandwidth kernels

Most of the previous studies do not mention the magnitude bins used in deriving the bandwidth parameter. The commonly used program to carry out the seismic hazard estimate using the kernel density estimator is the KERFRACT developed by Woo (1996). However in the program KERFRCAT the spatial activity rate is determined in steps of 0.1 magnitude increment starting from (Mmin ± 0.49) to (Mmax ± 0.49). This study aims at highlighting the effects of not maintaining the consistency in the data used in deriving the bandwidth and the data to which this bandwidth is applied in arriving at the spatial activity rate density function. The effects are shown for every magnitude at the spatial activity rate density function in the form of integrated squared error score and also at the final hazard estimates in the form of PGA and spectral ordinates.

Complete Chapter List

Search this Book:
Reset