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Simulation of the Basin Effects in the Po Plain During the Emilia-Romagna Seismic Sequence (2012) Using Empirical Green’s Functions

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Abstract

The two main earthquakes that occurred in 2012 (May 20 and 29) in the Reggio-Emiliano region (Northern Italy) were relatively small (Mw 6.1 and Mw 5.9) but they generated unexpected damages in a large area around the epicenter. On some stations, the observed seismic levels exceeded design levels recommended by the EC8 seismic code for buildings and civil engineering works. The ground motions generated by the two mainshocks have specific characteristics: the waveforms are mainly controlled by surface waves generated by the deep sedimentary Po plain, by local site effects and also, on some stations, by non-linear behaviors. In this particular context, we test the ability of an empirical Green’s function (EGF) simulation approach to reproduce the recorded seismograms in a large frequency band without any knowledge of the underground medium. We focus on the possibility to reproduce the strong surface waves generated by the basin at distances between 25 and 90 km. We choose to work on the second mainshock of the sequence (Mw 5.9), which occurred on May 29, 2012, because it is better recorded by the seismological networks than the May 20th first mainshock. We use a k-2 kinematic source model to generate a set of 100 slip distributions on the fault plane and choose the recordings of a close-by Mw 3.9 event as EGF. We then generate a set of broad-band seismograms (from 0.2 to 35 Hz) and compare them to the mainshock signals at 15 stations (Seismograms, Fourier spectra, PGA, PGV, duration, Stockwell Transforms) at epicentral distances from 5 to 160 km. We find that the main specific features of the signals are very well reproduced for all the stations within and beyond the basin. Nevertheless, at nearby stations, the PGA values are over-evaluated, which could be explained by the fact that non- linear effects are not taken into account in the simulation process. A better fit was found for a position of the nucleation point to the bottom west of the fault, that suggest a directivity effect of the rupture process of the May 29th event towards the North–East.

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References

  • Aki, K., & Richards, P. G. (2002). Quantitative seismology, 2nd edition, University Science Books, Sausalito, CA.

  • Amato, A., & Mele, F. (2008). Performance of the INGV National Seismic Network from 1997 to 2007. Annals of Geophysics, 51(2–3), 417–431.

  • Anderson, J. G., & Hough, S. E. (1984). A model for the shape of the Fourier amplitude spectrum of acceleration at high frequencies. Bulletin of the Seismological Society of America, 74(5), 1969–1993.

  • Atzori S., Merryman Boncori J., Pezzo G., Tolomeri C., Salvi S. (2012). Secondo Report analisi dati SAR e modellazione della sorgente del terremoto dell’Emilia. INGV (in Italian).

  • Augliera, P., Massa, M., D’Alema, E., & Marzorati, S. (2011). RAIS: a real time strong-motion network in northern Italy. Annals of Geophysics, 54(1), 23–34.

  • Baltay, A., Satoshi I., German P., & G. Beroza (2011). Variability in Earthquake Stress Drop and Apparent Stress: energetic and enervated earthquakes. Geophysical Research Letters 38(6). doi:10.1029/2011GL046698.

  • Beck, J. L., & Hall, J. F. (1986). Factors contributing to the catastrophe in Mexico City during the earthquake of September 19, 1985. Geophysical Research Letters, 13(6), 593–596.

  • Benedetti, L. C., Tapponnier, P., Gaudemer, Y., Manighetti, I., & Van der Woerd, J. (2003). Geomorphic evidence for an emergent active thrust along the edge of the Po Plain: The Broni‐Stradella fault. Journal of Geophysical Research: Solid Earth (1978–2012), 108(B5).

  • Berge, C., Gariel, J. C., & Bernard, P. (1998). A very broad‐band stochastic source model used for near source strong motion prediction. Geophysical research letters, 25(7), 1063–1066.

  • Bernard, P., Herrero, A., & Berge, C. (1996). Modeling directivity of heterogeneous earthquake ruptures. Bulletin of the Seismological Society of America, 86(4), 1149–1160.

  • Bommer, J. J., & Martinez-Pereira, A. (1999). The effective duration of earthquake strong motion. Journal of Earthquake Engineering, 3(2), 127–172.

  • Bommer, J. J., Stafford, P. J., & Alarcón, J. E. (2009). Empirical equations for the prediction of the significant, bracketed, and uniform duration of earthquake ground motion. Bulletin of the Seismological Society of America, 99(6), 3217–3233.

  • Bour, M., & Cara, M. (1997). Test of a simple empirical Green’s function method on moderate-sized earthquakes. Bulletin of the Seismological Society of America, 87(3), 668–683.

  • Brune, J. N. (1970). Tectonic stress and the spectra of seismic shear waves from earthquakes. Journal of Geophysical Research, 75(26), 4997–5009.

  • Burrato, P., F. Ciucci, and G. Valensise (2003), An inventory of river anomalies in the Po Plain, Northern Italy: Evidence for active blind thrust faulting, Ann. Geophys., 46(5), 865–882.

  • Castro, R. R., Pacor, F., Puglia, R., Ameri, G., Letort, J., Massa, M., & Luzi, L. (2013). The 2012 May 20 and 29, Emilia earthquakes (Northern Italy) and the main aftershocks: S-wave attenuation, acceleration source functions and site effects. Geophysical Journal International, 195(1), 597–611.

  • Cattari, S., Degli Abbati, S., Ferretti, D., Lagomarsino, S., Ottonelli, D., & Tralli, A. (2014). Damage assessment of fortresses after the 2012 Emilia earthquake (Italy). Bulletin of Earthquake Engineering, 12(5), 2333–2365.

  • Causse, M., Cotton, F., Cornou, C., & Bard, P. Y. (2008). Calibrating median and uncertainty estimates for a practical use of empirical Green’s functions technique. Bulletin of the Seismological Society of America, 98(1), 344–353.

  • Causse, M., Chaljub, E., Cotton, F., Cornou, C., & Bard, P. Y. (2009). New approach for coupling k  2 and empirical Green’s functions: application to the blind prediction of broad-band ground motion in the Grenoble basin. Geophysical Journal International, 179(3), 1627–1644.

  • Causse, M., Cotton, F., & Mai, P. M. (2010). Constraining the roughness degree of slip heterogeneity. Journal of Geophysical Research: Solid Earth (1978–2012), 115(B5).

  • Chaljub, E., Maufroy, E., Moczo, P., Kristek, J., Hollender, F., Bard, P. Y.,… & Chen, X. (2015). 3-D numerical simulations of earthquake ground motion in sedimentary basins: testing accuracy through stringent models. Geophysical Journal International, 201(1), 90–111.

  • Cotton, F., Archuleta, R., & Causse, M. (2013). What is sigma of the stress drop? Seismological Research Letters, 84(1), 42–48.

  • Courboulex, F., Converset, J., Balestra, J., & Delouis, B. (2010). Ground-motion simulations of the 2004 Mw 6.4 les Saintes, Guadeloupe, earthquake using ten smaller events. Bulletin of the Seismological Society of America, 100(1), 116–130.

  • Courboulex F., Dujardin A., Vallée M., Delouis B., Sira C., Deschamps A., Honoré L., Thouvenot F. (2013), High-Frequency Directivity Effect for an Mw 4.1 Earthquake, Widely Felt by the Population in Southeastern France, Bulletin of the Seismological Society of America, 103(6), 3347–3353.

  • Cultrera, G., Faenza, L., Meletti, C., D’Amico, V., Michelini, A., & Amato, A. (2014). Shakemaps uncertainties and their effects in the post-seismic actions for the 2012 Emilia (Italy) earthquakes. Bulletin of Earthquake Engineering, 12(5), 2147–2164.

  • Dan, K., Watanabe, T., Tanaka, T., & Sato, R. (1990). Stability of earthquake ground motion synthesized by using different small-event records as empirical Green’s functions. Bulletin of the Seismological Society of America, 80(6A), 1433–1455.

  • Day, S. M., S. H. Gonzalez, R. Anooshehpoor, and J. N. Brune (2008a), Scale-Model and Numerical Simulations of Near-Fault Seismic Directivity, Bull. Seismol. Soc. Am., 98(3), 1186–1206, doi:10.1785/0120070190.

  • Day, S. M., Graves, R., Bielak, J., Dreger, D., Larsen, S., Olsen, K. B.,… & Ramirez-Guzman, L. (2008b). Model for basin effects on long-period response spectra in southern California. Earthquake Spectra, 24(1), 257–277.

  • Dolce, M., & Di Bucci, D. (2014). National Civil Protection Organization and technical activities in the 2012 Emilia earthquakes (Italy). Bulletin of Earthquake Engineering, 1–23.

  • Fäh, D., Suhadolc, P., & Panza, G. F. (1994). A hybrid method for the estimation of ground motion in sedimentary basins: quantitative modeling for Mexico City. Bulletin of the Seismological Society of America, 84(2), 383–399.

  • Fletcher, J. B. (2014). Frequency‐dependent effects of rupture for the 2004 Parkfield main shock, results from UPSAR. Journal of Geophysical Research: Solid Earth, 119(9), 7195–7208.

  • Frankel, A. (1995). Simulating strong motions of large earthquakes using recordings of small earthquakes: the Loma Prieta mainshock as a test case. Bulletin of the Seismological Society of America, 85(4), 1144–1160.

  • Frankel, A., Stephenson, W., & Carver, D. (2009). Sedimentary basin effects in Seattle, Washington: Ground-motion observations and 3D simulations. Bulletin of the Seismological Society of America, 99(3), 1579–1611.

  • Gallovič, F., & Brokešová, J. (2004). On strong ground motion synthesis with k  2 slip distributions. Journal of Seismology, 8(2), 211–224.

  • Gallovič, F., & Burjanek, J. (2007). High-frequency directivity in strong ground motion modeling methods. Ann. Geophys, 50(2), 203–211.

  • Gorini, A., Nicoletti, M., Marsan, P., Bianconi, R., De Nardis, R., Filippi, L.,… & Zambonelli, E. (2010). The Italian strong motion network. Bulletin of Earthquake Engineering, 8(5), 1075–1090.

  • Graves, R. W., & Pitarka, A. (2010). Broadband ground-motion simulation using a hybrid approach. Bulletin of the Seismological Society of America, 100(5A), 2095–2123.

  • Hanks, T. C. (1975). Strong ground motion of the San Fernando, California, earthquake: ground displacements. Bulletin of the Seismological Society of America, 65(1), 193–225.

  • Heaton, T. H. (1990). Evidence for and implications of self-healing pulses of slip in earthquake rupture. Physics of the Earth and Planetary Interiors, 64(1), 1–20.

  • Hisada, Y., Aki, K., & Teng, T. L. (1993). 3-D simulations of surface wave propagation in the Kanto sedimentary basin, Japan Part 2: Application of the surface wave BEM. Bulletin of the Seismological Society of America, 83(6), 1700–1720.

  • Honoré, L., Courboulex, F., & Souriau, A. (2011). Ground motion simulations of a major historical earthquake (1660) in the French Pyrenees using recent moderate size earthquakes. Geophysical Journal International, 187(2), 1001–1018.

  • Irikura, K. (1986, December). Prediction of strong acceleration motion using empirical Green’s function. In Proc. 7th Japan Earthq. Eng. Symp (pp. 151–156).

  • Irikura, K. and K. Kamae (1994). Estimation of strong ground motion in broad-frequency band based on a seismic source scaling model and an empirical Green’s function technique, Annali di Geofisica XXXVII, 1721–1743.

  • Joyner, W. B. (2000). Strong motion from surface waves in deep sedimentary basins. Bulletin of the Seismological Society of America, 90(6B), S95–S112.

  • Kagawa, T., Zhao, B., Miyakoshi, K., & Irikura, K. (2004). Modeling of 3D basin structures for seismic wave simulations based on available information on the target area: case study of the Osaka Basin, Japan. Bulletin of the Seismological Society of America, 94(4), 1353–1368.

  • Kanamori, H., & Anderson, D. L. (1975). Theoretical basis of some empirical relations in seismology. Bulletin of the Seismological Society of America, 65(5), 1073–1095.

  • Kawase, H. (1996). The cause of the damage belt in Kobe:“The basin-edge effect,” constructive interference of the direct S-wave with the basin-induced diffracted/Rayleigh waves. Seismological Research Letters, 67(5), 25–34.

  • Kohrs-Sansorny, C., Courboulex, F., Bour, M., & Deschamps, A. (2005). A two-stage method for ground-motion simulation using stochastic summation of small earthquakes. Bulletin of the Seismological Society of America, 95(4), 1387–1400.

  • Koketsu, K., & Miyake, H. (2008). A seismological overview of long-period ground motion. Journal of Seismology, 12(2), 133–143.

  • Lai, C. G., Bozzoni, F., Mangriotis, M. D., & Martinelli, M. (2014). Soil liquefaction during the May 20, 2012 M5. 9 Emilia earthquake, Northern Italy: field reconnaissance and post-event assessment. Earthquake Spectra, In-Press.

  • Liberatore, L., Sorrentino, L., Liberatore, D., & Decanini, L. D. (2013). Failure of industrial structures induced by the Emilia (Italy) 2012 earthquakes. Engineering Failure Analysis, 34, 629–647.

  • Luzi, L., S. Hailemikael, D. Bindi D, F. Pacor, F. Mele, F. Sabetta (2008), ITACA (ITalian Accelerometric Archive): A Web Portal for the Dissemination of Italian Strong-motion Data, Seismological Research Letters, 79(5), 716–722. Doi: 10.1785/gssrl.79.5.716

  • Luzi, L., Pacor, F., Ameri, G., Puglia, R., Burrato, P., Massa, M.,… & Castro, R. (2013). Overview on the Strong‐Motion Data Recorded during the May–June 2012 Emilia Seismic Sequence. Seismological Research Letters, 84(4), 629–644.

  • Malagnini, L., Herrmann, R. B., Munafò, I., Buttinelli, M., Anselmi, M., Akinci, A., & Boschi, E. (2012). The 2012 Ferrara seismic sequence: Regional crustal structure, earthquake sources, and seismic hazard. Geophysical Research Letters, 39(19).

  • Maufroy, E., Chaljub, E., Hollender, F., Kristek, J., Moczo, P., Klin, P.,… & Bard, P. Y. (2015). Earthquake Ground Motion in the Mygdonian Basin, Greece: The E2VP Verification and Validation of 3D Numerical Simulation up to 4 Hz. Bulletin of the Seismological Society of America.

  • Milana, G., Bordoni, P., Cara, F., Di Giulio, G., Hailemikael, S., & Rovelli, A. (2014). 1D velocity structure of the Po River plain (Northern Italy) assessed by combining strong motion and ambient noise data. Bulletin of Earthquake Engineering, 12(5), 2195–2209.

  • Molinari, I., Argnani, A., Morelli, A., & Basini, P. (2015). Development and Testing of a 3D Seismic Velocity Model of the Po Plain Sedimentary Basin, Italy. Bulletin of the Seismological Society of America, 105(2A), 753–764.

  • Moretti, M., Abruzzese L., Zeid, N. A., Augliera, P., Azzara, R. M., Barnaba, C., Benedetti, L., Bono, A., Bordoni, P., Boxberger, T., Bucci, A., Cacciaguerra, S., Calò, M., Cara, F., Carannante, S., Cardinale, V., Castagnozzi, A., Cattaneo, M., Cavaliere, A., Cecere, G., Chiarabba, C., Chiaraluce, L., Ciaccio, M. G., Cogliano, R., Colasanti, G., Colasanti, M., Cornou, C., Courboulex, F., Criscuoli, F., Cultrera, G., D’Alema, E., D’Ambrosio, C., Danesi, S., De Gori, P., Delladio, A., De Luca, G., Demartin, M., Di Giulio, G., Dorbath, C., Ercolani, E., Faenza, L., Falco, L., Fiaschi, A., Ficeli, P., Fodarella, A., Franceschi, D., Franceschina, G., Frapiccini, M., Frogneux, M., Giovani, L., Govoni, A., Improta, L., Jacques, E., Ladina, C., Langlaude, P., Lauciani, V., Lolli, B., Lovati, S., Lucente, F. P., Luzi, L., Mandiello, A., Marcocci, C., Margheriti, L., Marzorati, S., Massa, M., Mazza, S., Mercerat, D., Milana, G., Minichiello, F., Molli, G., Monachesi, G., Morelli, A., Moschillo, R., Pacor, F., Piccinini, D., Piccolini, U., Pignone, M., Pintore, S., Pondrelli, S., Priolo, E., Pucillo, S., Quintiliani, M., Riccio, G., Romanelli, M., Rovelli, A., Salimbeni, S., Sandri, L., Selvaggi, G., Serratore, A., Silvestri, M., Valoroso, L., Van der Woerd, J., Vannucci, G., & Zaccarelli, L. (2012). Rapid response to the earthquake emergency of May 2012 in the Po Plain, northern Italy. Annals of Geophysics, 55(4).

  • Mucciarelli, M., & Liberatore, D. (2014). Guest editorial: The Emilia 2012 earthquakes, Italy. Bulletin of Earthquake Engineering, 12(5), 2111–2116.

  • Olsen, K. B., & Archuleta, R. J. (1996). Three-dimensional simulation of earthquakes on the Los Angeles fault system. Bulletin of the Seismological Society of America, 86(3), 575–596.

  • Pacor, F., R. Paolucci, L. Luzi, F. Sabetta, A. Spinelli, A. Gorini, M. Nicoletti, S. Marcucci, L. Filippi, M. Dolce (2011), Overview of the Italian strong motion database ITACA 1.0, Bulletin of Earthquake Engineering, 9(6), 1723–1739. Doi: 10.1007/s10518-011-9327-6

  • Pavic, R., Koller, M. G., Bard, P. Y., & Lacave-Lachet, C. (2000). Ground motion prediction with the empirical Green’s function technique: an assessment of uncertainties and confidence level. Journal of Seismology, 4(1), 59–77.

  • Penna, A., Morandi, P., Rota, M., Manzini, C. F., da Porto, F., & Magenes, G. (2014). Performance of masonry buildings during the Emilia 2012 earthquake. Bulletin of Earthquake Engineering, 12(5), 2255–2273.

  • Pezzo, G., Boncori, J. P. M., Tolomei, C., Salvi, S., Atzori, S., Antonioli, A.,… & Giuliani, R. (2013). Coseismic deformation and source modeling of the May 2012 Emilia (Northern Italy) earthquakes. Seismological Research Letters, 84(4), 645–655.

  • Saraò, A., & Peruzza, L. (2012). Fault-plane solutions from moment-tensor inversion and preliminary Coulomb stress analysis for the Emilia Plain. Annals of Geophysics, 55(4).

  • Sato, T., Graves, R. W., & Somerville, P. G. (1999). Three-dimensional finite-difference simulations of long-period strong motions in the Tokyo metropolitan area during the 1990 Odawara earthquake (MJ 5.1) and the great 1923 Kanto earthquake (MS 8.2) in Japan. Bulletin of the Seismological Society of America, 89(3), 579–607.

  • Shapiro, N. M., Singh, S. K., Almora, D., & Ayala, M. (2001). Evidence of the dominance of higher-mode surface waves in the lake-bed zone of the Valley of Mexico. Geophysical Journal International, 147(3), 517–527.

  • Shaw, B. E., Richards‐Dinger, K., & Dieterich, J. H. (2015). Deterministic model of earthquake clustering shows reduced stress drops for nearby aftershocks. Geophysical Research Letters.

  • Shi, Z., and S. M. Day (2013). Rupture dynamics and ground motion from 3-D rough-fault simulations, J. Geophys. Res. 118, 1–20.

  • Somerville, P., Irikura, K., Graves, R., Sawada, S., Wald, D., Abrahamson, N.,… & Kowada, A. (1999). Characterizing crustal earthquake slip models for the prediction of strong ground motion. Seismological Research Letters, 70(1), 59–80.

  • Sorrentino, L., Liberatore, L., Decanini, L. D., & Liberatore, D. (2014). The performance of churches in the 2012 Emilia earthquakes. Bulletin of Earthquake Engineering, 12(5), 2299–2331.

  • Stockwell, R. G., Mansinha, L., & Lowe, R. P. (1996). Localisation of the complex spectrum: the S transform. Journal of Association of Exploration Geophysicists, 17(3), 99–114.

  • Trifunac, M. D., & Brady, A. G. (1975). A study on the duration of strong earthquake ground motion. Bulletin of the Seismological Society of America, 65(3), 581–626.

  • Vallée, M. (2013). Source time function properties indicate a strain drop independent of earthquake depth and magnitude. Nature communications, 4.

  • Vuan, A., Klin, P., Laurenzano, G., & Priolo, E. (2011). Far-source long-period displacement response spectra in the Po and Venetian Plains (Italy) from 3D wavefield simulations. Bulletin of the Seismological Society of America, 101(3), 1055–1072.

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Acknowledgments

We thank all the persons and organisms involved in the post-seismic experiment, the processing and the distribution of data. A special thanks to Francesca Pacor for her help, and to Giovanna Cultrera for fruitful discussions. This work was supported by the SIGMA project http://www.projet-sigma.com/. The post-seismic intervention of the French team was supported by the Institut National des Sciences de l’Univers CNRS-INSU.

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24_2015_1233_MOESM1_ESM.pdf

Supplementary material 1 (PDF 1847 kb) Figure S1: Velocity time series of the Mw 5.9 event. Left: East-West component, Center: North-South component, right: vertical component. PGV are denoted by yellow dots, and the larger PGV for a station is denoted by a red dot

24_2015_1233_MOESM2_ESM.pdf

Supplementary material 2 (PDF 1961 kb) Figure S2: Determination of the apparent corner frequencies of the EGF for the five closest stations. This determination is done by fitting a theoretical ω−2 model (Brune, 1970) in displacement on the Fourier displacement spectra of the two horizontal components

24_2015_1233_MOESM3_ESM.pdf

Supplementary material 3 (PDF 172 kb) Figure S3: Fourier spectra of the Mw 3.9 event used as EGF (bold line) and of the noise (thin line). Both are NS component of acceleration. A vertical line is drawn at 0.2 Hz, which delimits the lower frequency for which this study is relevant

24_2015_1233_MOESM4_ESM.pdf

Supplementary material 4 (PDF 112 kb) Figure S4: Comparison of Fourier velocities spectra of East-West components. Spectra from the Mw 5.9, May 29, 2012 event are represented in continuous bold green line. Spectra from the 100 EGF simulations are represented in gray, and the simulation with the selected slip distribution (Fig. 2a) is represented in dotted black line. The EGF spectra are represented in thin green line and the ω−2 model is represented by a brown line

24_2015_1233_MOESM5_ESM.pdf

Supplementary material 5 (PDF 517 kb) Figure S5: Comparison between observed velocity time series (cm/s) for the Mw 5.9, May 29, 2012 event (left) and EGF simulations for the selected slip distribution (Figure 2a) (right). Both figures present the East-West component. Yellow dots indicate PGV. Data and simulations are both bandpass filtered between 0.2 and 35 Hz

24_2015_1233_MOESM6_ESM.pdf

Supplementary material 6 (PDF 1403 kb) Figure S6: Comparison between observed velocity time series (cm/s) for the Mw 5.9, May 29, 2012 event (left) and EGF simulations for the selected slip distribution (Figure 2a) (right). Both figures present the vertical component. Yellow dots indicate PGV. Data and simulations are both bandpass filtered between 0.2 and 35 Hz

24_2015_1233_MOESM7_ESM.pdf

Supplementary material 7 (PDF 1455 kb) Figure S7: Comparison between Stockwell transforms of observed velocity time series (NS component) and EGF simulation for the selected slip distribution for stations, T0817 at 33.1 km (a), TGG at 79.4 km (b) and VOBA at 99.2 km (c)

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Dujardin, A., Causse, M., Courboulex, F. et al. Simulation of the Basin Effects in the Po Plain During the Emilia-Romagna Seismic Sequence (2012) Using Empirical Green’s Functions. Pure Appl. Geophys. 173, 1993–2010 (2016). https://doi.org/10.1007/s00024-015-1233-4

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