Antonella Cirella 1, Paul Spudich 2 1 INGV, Rome, Italy 2 USGS, Menlo Park, CA Aleatory and Epistemic Uncertainties in Interpolated Ground Motions Example from the Kashiwazaki-Kariwa Nuclear Power Plant Recordings of the July 16, 2007, Niigata-ken Chuetsu-oki, Japan, Earthquake EGU2013, SM2.5, 5932, Vienna

Using an earthquake rupture model to ‘predict’ ground motions at unobserved locations When earthquake occur, we could have a few recordings of ground motion, but not a sites where something interesting and /or bad occurred. (e.g Niigata-ken Chuetsu-oki) EGU2013, SM2.5, 5932, Vienna

Using an earthquake rupture model to ‘predict’ ground motions at unobserved locations Post-Earthquake forensic studies and ‘Shake-Map’ generation rely upon ground-motion interpolation (process to infer, from a set of ground motions, observed at sparse observation locations, the ground motion at a target site where no observation were made during the earthquake) EGU2013, SM2.5, 5932, Vienna

Using an earthquake rupture model to ‘predict’ ground motions at unobserved locations It is now possible to invert observed ground motions to obtain the spatio-temporal behavior of rupture on the causative fault Forward predict ground motions (SA) at unobserved locations But the inversion is inherently non-unique  How large is the scatter in the interpolated ground motions?  Is the scatter of the predicted motions large enough to include the true motions at the target sites?  Is the scatter of the predicted motions at the unobserved site larger than the scatter of the predicted motions at sites having data used in the inversion?  What controls the level of error? EGU2013, SM2.5, 5932, Vienna

A problem in linear inference, except… Theoretically, the process of ground-motion interpolation is an example of linear inference. For a linear problem lacking bounds on the model space, the interpolated ground motion can be completely unbounded. When bounds like positivity and known moment are added as constraints on the model, the interpolated motions may then become bounded, and could be explored using algorithm BVLS of Stark and Parker (1995), which can compute bounds on linear functionals of an inverted model. However, the response spectrum is a nonlinear function of the ground acceleration time series, and consequently we have chosen to investigate the variability of interpolated response spectra using a statistical approach building on a non-linear inversion method (Piatanesi et al, 2007; Cirella et al, 2008) EGU2013, SM2.5, 5932, Vienna

 joint and separate inversion of strong motion, GPS and DInSAR data;  finite fault is divided into sub-faults;  kinematic parameters are allowed to vary within a sub-fault; Kinematic Inversion Technique  Heat-Bath Simulated Annealing algorithm; Model Ensemble Ω = Rupture Models m & Cost Function C(m) Output of kinematic inversion: EGU2013, SM2.5, 5932, Vienna Inverted Parameters: Peak Slip Velocity; Rise Time; Rupture Time; Rake.

EGU2013, SM2.5, 5932, Vienna Kinematic Inversion: 2007 Niigata-ken Chuetsu-oki Earthquake, Mw=6.6  13 stations (surface or borehole strong motion records);  15 GPS stations ;  frequency-band: (0.0÷0.5)Hz;  60 sec (body & surface waves);  all kinematic parameters are inverted simultaneously.

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Cost function for the inversion not using KK data EGU2013, SM2.5, 5932, Vienna 4% above min cost – 8561 models min cost - best fitting model 3 % above min cost – 4897 models 2% above min cost – 1534 models 1% above min cost – 334 models 0.5% above min cost – 122 models

EGU2013, SM2.5, 5932, Vienna Different rupture models can fit the observed data equally well, due to the intrinsic non-uniqueness of the inversion. Waveforms fit for the 4% model ensemble are not obviously worse than for the 1% ensemble.

5% SA Bias (epistemic error) Aleatory error – Nonunique prediction scatter Biases at 2-3 s bigger than nonunique prediction scatter EGU2013, SM2.5, 5932, Vienna Bias as the ratio of the observed response spectrum to the synthetic as a function of period.  quantifies the scatter in the predicted spectral acceleration Form of aleatory uncertainty in the ground motion prediction due to unknown aspects of slip distributions. (data from future EQs will not reduce the uncertainty of this ground motion prediction for this past earthquake)

EGU2013, SM2.5, 5932, Vienna 22% For a true interpolation of a ground motion where there is no observation, the horizontal scatter can be at least 20-25% bigger than the scatter predicted from good fitting models at sites with observed motions. These results are unaffected by the characteristic of the 1g1 data (not used in the inversion!)

Comparison of nonunique prediction scatter with aleatory sigma from kinematic and dynamic rupture simulations of ground motions EGU2013, SM2.5, 5932, Vienna A&S 2008 Intra-event  A&S 2008 inter-event  scatter in the predictions due to the non- uniqueness of ‘good’ rupture models Variability of predicted ground motion for a M6.5, by considering uncertainties on EGF’ event & variability of source properties aleatory variability in ground motions calculated for kinematic rupture models and theoretical Green's functions simulate a M6.5 strike-slip and a M6.5 dip-slip quake at different sites, by adopting different slip distributions and different hypocenters. generate source variability by using 2 groups of randomly variable initial stress distributions, input into dynamic rupture simulations to generate variable slip models, with fixed and variable hypo, from which ground motions at different sites were generated. kinematic rupture models contain too much source variability (real earthquake ruptures have correlated source properties ) the correlations of source properties in dynamic models do result in lower ground motion variability our non-uniqueness scatter at 1g1 for the 4% model ensemble approaches the Abrahamson and Silva’s observed inter-event scatter. This means that the non-uniqueness variability of predicted motion at 1g1 is almost as great as the variability of motion incurred by using a different earthquake having the same magnitude and hypocenter to predict the motion at 1g1.

Conclusions We computed the scatter in predictions of SA at 1g1 based on the nonuniqueness of inverted kinematic rupture models of the 2007 Niigata-ken Chuetsu-oki earthquake. The scatter in the predicted horizontal response spectra at 1g1 from the inversion is is about 22% bigger than the scatter of response spectra predicted at the Niigata stations. This result says, that in the case of a true interpolation of a ground motion where there is no observation, the scatter in the horizontal component interpolant can be 20-25% bigger than the scatter in the motions predicted from good fitting models at sites where there were observed motions. We compared our nonuniqueness scatter with aleatory variation of ground motions from kinematic and dynamic rupture models:  aleatory scatter values of the ground motions from kinematic rupture models exceed the empirically observed scatter in response spectra from a standard GMPE (Abrahamson and Silva, 2008), excluding the effects of variable soil amplification. Clearly these kinematic rupture models contain too much source variability; EGU2013, SM2.5, 5932, Vienna

 the aleatory variation of dynamic rupture ground motions is much smaller than that of the kinematic rupture models, indicating that the correlations of source properties in dynamic models result in lower ground motion variability;  our non-uniqueness scatter at 1g1 approaches Abrahamson and Silva’s observed interevent scatter. This means that the variability of predicted motion at 1g1 caused by nonuniqueness in the rupture model is almost as great as the variability of motion incurred by using a different earthquake having the same magnitude and hypocenter to predict the motion at 1g1. The nonunique prediction scatter is a hitherto uninvestigated source of aleatory variability that should be included in studies of aleatory variability which use observed slip distributions with randomized hypocenters. While the bias of interpolated ground motions has not been our main topic of investigation, the biases are of first order importance in the estimation of ground motion at a particular site using interpolation of motion from surrounding stations. EGU2013, SM2.5, 5932, Vienna Spudich P. and A. Cirella., “Aleatory and Epistemic Uncertainties in Interpolated Ground Motions- Example from the Kasiwasaki-Kariwa Nuclear Power Plant recordings of the July 16, 2007 Niigata-ken Chuetsu-oki, Japan, Earthquake”,, submitted to Bulletin of the Seismological Society of America.

Acknowledgements Accelerograms from the KKNPP were provided by the Association of Earthquake Disaster Prevention, Tokyo, Japan, which is the sole distributor of such data. Copyright of all KKNPP data belongs to the Tokyo Electric Power Company. We thank Dr. Kenishi Tsuda of Shimizu Corporation for providing insight into sources of information for this study, and we thank Drs. Arben Pitarka and Enrico Priolo for providing unpublished supplementary materials. This work was supported by the U.S. Nuclear Regulatory Commission (NRC) Office of Research Job Code N6501. EGU2013, SM2.5, 5932, Vienna Spudich P. and A. Cirella., “Aleatory and Epistemic Uncertainties in Interpolated Ground Motions- Example from the Kasiwasaki-Kariwa Nuclear Power Plant recordings of the July 16, 2007 Niigata-ken Chuetsu-oki, Japan, Earthquake”,, submitted to Bulletin of the Seismological Society of America.

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Supplementary Material. Modelli Invertiti con & senza kkp con relativi fit figure 7 e 8. Confronto valori di cost function: figure 9. Formule SA(T=2sec);. Formule scatter, bias.. Confronto con gli altri lavori: figure necessarie EGU2013, SM2.5, 5932, Vienna

random model m0 START + = Strong motion L1+L2 norm To quantify the misfit… GPSL2norm C(m) DInSARL2norm + Forward Modeling: Compsyn Misfit computation Loop over parameters (Vr,…) Loop over model values Loop over iterations Loop over temperatures end end end end Simulated annealing Heat-bath algorithm Kinematic Inversion Technique Stage I: Building Model Ensemble-HB Simulated Annealing EGU2013, SM2.5, 5932, Vienna

 Best Model  Average Model:  Standard Deviation: Output of kinematic inversion: Ω Model Ensemble Ω = Rupture Models m & Cost Function C(m) Kinematic Inversion Technique Stage II: Appraisal of the Ensemble EGU2013, SM2.5, 5932, Vienna

Kinematic Inversion: 2007 Niigata-ken Chuetsu-oki Earthquake, Mw=6.6  13 stations (surface or borehole strong motion records);  15 GPS stations ;  frequency-band: (0.02÷0.5)Hz;  60 sec (body & surface waves);  W=31.5km; L=38.5km;  =3.5km;  all kinematic parameters are inverted simultaneously.  South-East Dipping Fault; July 16-th 2007

Best Model: E(m)=0.3 Average Model: E(m)=0.4 The ensemble-averaged model better represents the stable The ensemble-averaged model better represents the stable features of the rupture history. features of the rupture history. The best fitting model might contain an extreme configuration of model parameters;

Strong Motion GPS Comparison between synthetics (red) and observed (blue) waveforms. Comparison between synthetics (white) and observed (red) coseismic horizontal displacement.

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Formula SA

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Comparison of nonunique prediction scatter with aleatory sigma from kinematic and dynamic rupture simulations of ground motions EGU2013, SM2.5, 5932, Vienna

Results 1.Almost all of the aleatory scatter values of the ground motions from kinematic rupture models exceed the blue dashed line, which is the empirically observed scatter in response spectra, excluding the effects of variable soil amplification. Clearly these kinematic rupture models contain too much source variability. Abrahamson (personal communication) has speculated that real earthquake ruptures have correlated source properties (for example, local rupture velocity and peak slip velocity at the same point, for example) that are not present in the kinematic rupture models, leading to excessive variation in the kinematic rupture models and resulting ground motion. 2.The aleatory variation of Ripperger’s ground motions is much smaller than that of the kinematic rupture models, indicating that the correlations of source properties in dynamic models do result in lower ground motion variability, although we must bear in mind that Ripperger’s variability of stress drop is less than a factor of two, in other words, rather low. 3.Ripperger’s variability is comparable to the empirical variability. Abrahamson and Silva’s blue dashed line includes the effects of variable source properties (for example, stress drop) as well as variations like directivity amplification that vary from site to site in a single earthquake. Ripperger’s variability for variable hypocenter location agrees rather well with the blue dashed line. However, Ripperger’s result for fixed hypocenter is a bit bigger than the empirically observed earthquake-to-earthquake variation (red dashed line), despite Ripperger’s rather small stress drop variation. 4.Our nonuniqueness scatter at 1g1 for the 4% model ensemble approaches Abrahamson and Silva’s observed interevent scatter. This means that the nonuniqueness variability of predicted motion at 1g1 is almost as great as the variability of motion incurred by using a different earthquake having the same magnitude and hypocenter to predict the motion at 1g1. (We make the ‘same hypocenter’ restriction because differences in directivity contribute to the intraevent error that is characterized by the ‘total’ sigma curve in the figure.) Of course, this observation depends on the choice of the 4% ensemble which is arbitrary. 5.Spectral acceleration predictions based on ground motion inversions and dynamic simulations might be less accurate than simply predicting the spectral acceleration from a GMPE such as Abrahamson and Silva (2008) with a directivity correction (for example, Somerville et al., 1997). (Or maybe the GMPE sigma is too small?) EGU2013, SM2.5, 5932, Vienna