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

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 (M_min ± 0.49) to (M_max ± 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.