Comparison between four quantitative goodness-of-fit criteria for acceleration time series

Earthquake studies often use different models to simulate acceleration time series and analyse earthquake consequences. These simulated accelerations are then generally validated against experimental data or data from recordings in the field. In order to assess the effectiveness of these simulations, a method is needed to compare between acceleration time series and quantify the similarities. Many previous studies merely qualitatively assess performance based on the match of shape and magnitude aspects. To minimize the subjective nature of these choices, various authors have proposed numerical “goodness-of-fit” criteria to quantify the similarity between two acceleration time series. This paper summarises and compares four existing goodness-of-fit criteria that have different output presentations, including parameter scores and misfit distribution over a time-frequency representation. A sensitivity analysis is used to evaluate how different factors – including amplitude, phase, and frequency – influence the criteria evaluation results. The Anderson (2004) and Olsen & Mayhew (2010) criteria both have 10 parameters and easily identify the amplitude mismatch. The Kristeková et al. (2009) criterion generates plots to visualise the envelope and phase misfit distribution over both time and frequency domains. It has two parameters that respond, independently to amplitude and phase mismatch. The Zeghal et al. (2018) criterion uses three parameters to compare the acceleration time series in the frequency domain, but the proposed metrics are not able to identify the amplitude mismatch.