Abstract
SUMMARYNumerical simulations of earthquake ground motions are used both to anticipate the effects of hypothetical earthquakes by forward simulation and to infer the behaviour of the real earthquake source ruptures by the inversion of recorded ground motions. In either application it is necessary to assume some Earth structure that is necessarily inaccurate and to use a computational method that is also inaccurate for simulating the wavefield Green's functions. We refer to these two sources of error as ‘propagation inaccuracies’, which might be considered to be epistemic. We show that the variance of the Fourier spectrum of the synthetic earthquake seismograms caused by propagation inaccuracies is related to the spatial covariance on the rupture surface of errors in the computed Green's functions, which we estimate for the case of the 2009 L'Aquila, Italy, earthquake by comparing erroneous computed Green's functions with observed L'Aquila aftershock seismograms (empirical Green's functions). We further show that the variance of the synthetic seismograms caused by the rupture variability (aleatory uncertainty) is related to the spatial covariance on the rupture surface of aleatory variations in the rupture model, and we investigate the effect of correlated variations in Green's function errors and variations in rupture models. Thus, we completely characterize the variability of synthetic earthquake seismograms induced by errors in propagation and variability in the rupture behaviour. We calculate the spectra of the variance of the ground motions of the L'Aquila main shock caused by propagation inaccuracies for two specific broad-band stations, the AQU and the FIAM stations. These variances are distressingly large, being comparable or in some cases exceeding the data amplitudes, suggesting that the best-fitting L'Aquila rupture model significantly overfits the data and might be seriously in error. If these computed variances are typical, the accuracy of many other rupture models for past earthquakes may need to be reconsidered. The results of this work might be useful in seismic hazard estimation because the variability of the computed ground motion, caused both by propagation inaccuracies and variations in the rupture model, can be computed directly, not requiring laborious consideration of multiple Earth structures.
Highlights
Numerical simulations of earthquake ground motions are used both to anticipate the effects of hypothetical earthquakes (e.g. Graves & Pitarka 2014) by forward simulation and to infer the behaviour of the real earthquake source ruptures by the inversion of recorded ground motions (e.g. Olson & Apsel 1982)
In seismic hazard studies using synthetic seismograms (e.g. Wang & Jordan 2014; Villani & Abrahamson 2015) the error in the synthetic earthquake seismograms caused by inaccuracies in the Earth structure and in the computational methods is not considered
We investigate the total variability of a synthetic seismogram for a large earthquake, which is caused by errors in the wave propagation model and by the natural variability of the earthquake source
Summary
Numerical simulations of earthquake ground motions are used both to anticipate the effects of hypothetical earthquakes (e.g. Graves & Pitarka 2014) by forward simulation and to infer the behaviour of the real earthquake source ruptures by the inversion of recorded ground motions (e.g. Olson & Apsel 1982). We use this with a frequency-domain version of the time-domain Yagi & Fukahata (2011) theory to derive the expected variance γ 2 caused by Green’s function error in the Fourier amplitude spectra of ground motions from a larger (non-point) earthquake that we seek to model This variance might possibly be useful both in ground motion inversions and in seismic hazard studies. The first term on the right-hand side of the equal sign is just the slip-velocity model ‘convolved’ with the erroneous numerical Green’s function, in other words it is the usual finite-fault forward synthetic in this type of inversion. While it is reasonable to guess that the Green’s function error is proportional to the maximum value of the theoretical Green’s function, it is preferable to measure the actual error, which we do later in this paper
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.