abstract.tex

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Common procedures in seismic signal processing require the use of filters to restrict or eliminate the energy contribution of undesired wavelengths, or to facilitate the analysis of signals within specific frequency bandwidths. It is well-known that the selection of filters and filter parameters has a strong influence on the characteristics of the filtered signal. This selection is, however, often done based on traditional practices rather than on a careful quantitative measure of the desirable outcome characteristics of the filtered signals, and its relation to the unfiltered data. Particular filters and parameters have therefore become ingrained in earthquake science and engineering practices where other more appropriate alternatives would easily yield better, more accurate results. We present a procedure for the optimal selection of filter parameters using a genetic algorithm, which minimizes the residual energy of a filtered signal with respect to the original data---as seen through an ideal filter in the frequency domain, but including provisions to minimize undesirable effects in the time domain. The procedure can be applied to a single signal, or to a family of signals. This is relevant because it is often necessary to find the best filtering parameters for a collection of records, and not just for an isolated signal. We test the proposed approach on a collection of synthetically generated tapered white noises and show that among commonly used filter families, infinite impulse response elliptic filters offer the best results, as opposed to other commonly used filters such as Butterworth and Chebyshev. We also shown how the use of optimally selected filters is important in ground motion validation through goodness-of-fit criteria, and make recommendations for the selection of filter parameters for more general use.


% OLD ABSTRACT by Naeem


% The validation of ground motion synthetics has received increased attention over the last few years due to advances in physics-based deterministic and hybrid simulation methods. Validation of synthetics is necessary in order to determine whether the available simulation methods are capable of faithfully reproducing the characteristics of ground motions from past earthquakes. Some validation methods use filters to evaluate the quality of the fit between synthetics and data within different frequency bands. This is done, primarily, to weight the contribution of different wavelengths so that low frequencies are given more weight than high frequencies. One particular method of interest is the goodness-of-fit (GOF) criterion introduced by Anderson (2004). In this method, the degree of similarity between two signals is quantified by means of a set of ten (error) metrics which are projected on a 0?10 scoring scale. These metrics are based on ground motion characteristics commonly used in seismology and earthquake engineering. The scores are used to evaluate each given pair of signals in the three components of motion and within different frequency ranges. The scores of each frequency band, component, and metric are then combined to obtain a final GOF score. In this paper we study the sensitivity of the GOF scores, and thus the sensitivity of the validation itself, to the filtering process when different filter parameters are considered. Our initial analysis of results shows that GOF methods are susceptible to the design of filters. The filter?s order, for instance, seems to significantly affect the interpretation of the validation especially for metrics that are time-dependent (e.g., peak ground response). We evaluate the implications of the variability in GOF scores on the 60 randomly generated (white noise) waves. We calculated the best parameters to each filter through Genetic Algorithm. We test best sets of parameters on two case studies of the 2008 Mw 5.4 Chino Hills earthquake, and Broadband Platform, investigate the sensitivity of GOF criteria to the type of filters used to decompose the signals. We analyze the consistency and correlation of the results obtained using various metrics by means of a filtering fitting function. Our work indicates that elliptic infinite impulse response filters lead to more reliable results, over other more commonly used filters; and the filtering parameters are mainly dependent on filtering bandwidth. We provide relationships to select the most accurate parameters of elliptic filter.