# Seismological and Engineering Demand Misfits for Evaluating Simulated Ground Motion Records
## 1 Introduction  
Earthquakes are amongst the most destructive natural hazards and disasters resulting in major seismic losses to the built environment. Many researchers have studied the hazard and intensity proposed by large and destructive earthquakes (e.g., [1, 2, 3, 4]). In most engineering applications, ground motion time histories are required in order to perform time history analyses of geotechnical or structural systems (e.g., [5, 6, 7, 8, 9]). In regions of sparse ground motion networks or lack of potential large earthquakes, simulated ground motion time histories have been increasingly recommended in earthquake engineering practice in recent years (e.g., [10, 11]). Depending on the solution approach, ground motion simulation methods can be deterministic, stochastic or hybrid. The low frequencies, which are solved mostly by deterministic methods, need precise source and velocity models (e.g., [12, 13, 14, 15, 16, 17, 18]). On the other hand, incoherency of the phase angles can be modeled using stochastic approaches (e.g., [19, 20, 21, 22, 23, 24, 25, 26, 27, 28]). In order tomodel the broadband frequency range, hybrid ground motion simulation techniques are introduced (e.g., [29; 30; 31; 32; 33]). During recent years, validation of ground motion simulation records has gained considerable interest among many researchers (e.g., [34; 35; 36]). Since accuracies and computational costs of different ground motion simulation techniques vary, investigation of the efficiency of the simulated seismological measures compared to the real values is essential. Recently, a few studies have investigated the Goodness of Fit (GOF) criteria between real and simulated time histories based on characteristics of the seismic waveforms (e.g., [37; 38; 39]). In these studies, GOF evaluation has been accomplished generally through ground motion intensity measures such as Fourier amplitude, peak ground intensity values or duration. However, the main concern in engineering practice is that simulated ground motion records may not be representative of real ones when estimation of structural seismic demand is required (e.g., [40; 41]). Further investigation is necessary to evaluate alternative structural responses (i.e., elastic and inelastic spectral values as well as seismic energy contents) obtained from simulated records against those from corresponding recorded motions. The objective of this study is to evaluate suitability of seismologically validated simulated ground motion records corresponding to the selected past events in the prediction of alternative engineering demand parameters. Evaluation of the simulated time histories is accomplished through the definition of different seismological and engineering demand misfits. The misfits are defined in terms of both log-scale misfits and GOF scores using the approach proposed by [PERSON] and [PERSON] [39]. For misfit evaluation, the seismological measures employed here consist of duration, peak ground motion amplitudes and frequency as well as energy content of the records while the engineering demand parameters include Single Degree of Freedom (SDOF) structural responses in terms of both elastic and inelastic spectral acceleration, spectral velocity and seismic input energy contents. Simulated records corresponding to the three past events with different source mechanisms in regions of different geological features are selected in this study. The 1992 Erzincan earthquake with a moment magnitude of 6.6 [42], which occurred in the eastern part of North Anatolian Fault Zone (NAFZ) in Turkey on a strike-slip fault mechanism, is selected as the first case study. The second case study is the 1999 Duzce event which occurred in the western part of NAFZ with Mw = 7.1 on the same fault mechanism [43]. The last case study is considered as the 2009 L'Aquila (Italy) earthquake with Mw = 6.3 [44] which occurred on a normal fault zone.