Accelerating moment release revisited: Examples of application to Italian seismic sequences

From simple considerations we propose a revision of the AcceleratingMoment Release (AMR) methodology for improving our knowledge of seismic sequences and then, hopefully in a close future, to reach the capability of
predicting the main-shock location and occurrence with sufficient accuracy. The proposed revision is based on the introduction of a “reduced” Benioff strain for the earthquakes of the seismic sequence where, for the same
magnitude and after a certain distance from the main-shock epicentre, the closer the events the more they are weighted. In addition,we retain the usual expressions proposed by the ordinary AMRmethod for the estimation
of the corresponding main-shock magnitude, although this parameter is the weakest of the analysis. Then, we apply the revised method to four case studies in Italy, three of which are the most recent seismic sequences of
the last 9 years culminating with a shallow main-shock, and one is instead a 1995–1996 swarm with no significant main-shock. The application of the R-AMRmethodology provides the best results in detecting the precursory
seismic acceleration,when comparedwith those found by ordinaryAMR technique.We verify also the stability of the results in space, applying the analysis to real data with moving circles in a large area around each mainshock
epicentre, and the efficiency of the revised technique in time, comparing the results with those obtained when applying the same analysis to simulated seismic sequences.

Atkinson, G.M., Silva, W., 2000. Stochastic modeling of California ground motions. Bull.
Seismol. Soc. Am. 90, 255–274.
Benioff, H., 1949. Seismic evidence for the fault origin of oceanic deeps. Geol. Soc. Am.
Bull. 60, 1837–1856.
Benioff, H., 1951. Global strain accumulation and release as revealed by great earthquakes.
Geol. Soc. Am. Bull. 62, 331–338.
Ben-Zion, Y., Lyakhovsky, V., 2002. Accelerated seismic release and related aspects of
seismicity patterns on earthquake faults. Pure Appl. Geophys. 19, 2385–2412.
Bowman, D.D., Ouillon, G., Sammis, C.G., Sornette, A., Sornette, D., 1998. An observational
test of the critical earthquake concept. J. Geophys. Res. 103 (24), 359–24,372.
Boore, D.M., 2003. Simulation of ground motion using the stochastic method. Pure Appl.
Geophys. 160, 635–676.
Brehm, D.J., Braile, L.W., 1998. Intermediate-term earthquake prediction using precursory
events in the New Madrid Seismic Zone. Bull. Seismol. Soc. Am. 88 (2),
564–580.
Brehm, D.J., Braile, L.W., 1999. Intermediate-term earthquake prediction using the modified
time-to-failure method in Southern California. Bull. Seismol. Soc. Am. 89 (1),
275–293.
Brodsky, E.E., 2011. The spatial density of foreshocks. Geophys. Res. Lett. 38, L10305
(10109/2011GL047253).
Bufe, C.G., Varnes, D.J., 1993. Predictive modelling of the seismic cycle of the greater San
Francisco Bay region. J. Geophys. Res. 98 (B6), 9871–9883.
Bufe, C.G., Nishenko, S.P., Varnes, D., 1994. Seismicity trends and potential for large earthquakes
in the Alaska–Aleutian region. Pure Appl. Geophys. 142 (1), 83–99.
Calcagnile, G., Panza, G.F., 1981. The main characteristics of the lithosphere–
asthenosphere system in Italy and surrounding regions. Pure Appl. Geophys. 119,
865–879.
Campbell, K.W., Bozorgnia, Y., 2008. NGA ground motion model for the geometric mean
horizontal component of PGA, PGV, PGD and 5% damped linear elastic response spectra
for periods ranging from 0.01 to 10 s. Earth Spectra 24 (1), 139–171.
Chouliaras, G., 2009. Seismicity anomalies prior to the 13 December 2008, Ms = 5.7
earthquake in Central Greece. Nat. Hazards Earth Syst. Sci. 9, 501–506.
Cicerone, R.D., Ebel, J.E., Britton, J., 2009. A systematic compilation of earthquake precursors.
Tectonophysics 476 (3–4), 371–396.
De Santis, A., Cianchini, G., Qamili, E., Frepoli, A., 2010. The 2009 L'Aquila (Central Italy)
seismic sequence as a chaotic process. Tectonophysics 496, 44–52.
Di Giovambattista, R., Tyupkin, Yu.S., 1999. The fine structure of the dynamics of seismicity
before M = 4.5 earthquakes in the area of Reggio Emilia (Northern Italy). Ann.
Geofis. 42 (5), 897–909.
Di Giovambattista, R., Tyupkin, Yu.S., 2001. An analysis of the process of acceleration
of seismic energy emission in laboratory experiments on destruction of rocks
and before strong earthquakes in Kamchatka and in Italy. Tectonophysics 38,
339–351.
Di Giovambattista, R., Tyupkin, Yu.S., 2004. Seismicity patterns before the M = 5.8 2002,
Palermo (Italy) earthquake: seismic quiescence and accelerating seismicity.
Tectonophysics 384, 243–255.
Dobrovolski, I.P., Zubkov, S.I., Miachin, V.I., 1979. Estimation of the size of earthquake
preparation zones. Pure Appl. Geophys. 117, 1025–1044.
Douglas, J., 2011. Ground-motion Prediction Equations 1964–2010, PEER 2011/102.
Pacific Earthquake Engineering Research Center College of Engineering University
of California, Berkeley, p. 443.
Felzer, K.R., Brodsky, E.E., 2006. Decay of aftershock density with distance indicates triggering
by dynamic stress. Nature 441, 735–737.
Freed, A.M., 2005. Earthquake triggering by static, dynamic, and postseismic stress transfer.
Annu. Rev. Earth Planet. Sci. 33, 335–367.
Gasperini, P., 2001. The attenuation of seismic intensity in Italy: a bilinear shape indicates
the dominance of deep phases at epicentral distances larger than 45 km. Bull.
Seismol. Soc. Am. 91 (4), 826–841.
Geller, R.J., Jackson, D.D., Kagan, Y.Y., Mulargia, F., 1997. Earthquakes cannot be predicted.
Science 275 (5306), 1616.
Graiser, V., Kalkan, E., Lin, K.-W., 2013. Global ground motion prediction equation for
shallow crustal regions. Earth Spectra 29 (3), 777–791.
Guilhem, A., Bürgmann, R., Freed, A.M., Tabrez, Ali S., 2013. Testing the accelerating moment
release (AMR) hypothesis in areas of high stress. Geophys. J. Int. 195 (2),
785–798. http://dx.doi.org/10.193/gji/ggt298.
Hardebeck, J., Felzer, K.R., Michael, A.J., 2008. Improved tests reveal that the accelerating
moment release hypothesis is statistically insignificant. J. Geophys. Res. 113,
B08310.
Harmsen, S., 1997. Estimating the diminution of shear-wave amplitude with distance:
application to the Los Angeles, California, urban area. Bull. Seismol. Soc. Am. 87 (4),
888–903.
Hough, S., 2009. Predicting the Unpredictable: The Tumultuous Science of Earthquake
Prediction. Princeton University Press.
Jaumè, S.C., Sykes, L.R., 1999. Evolving towards a critical point: a review of accelerating
moment release prior to large and great earthquakes. Pure Appl. Geophys. 155,
279–306.
Jiang, C., Wu, Z., 2006. Benioff strain release before earthquakes in China: accelerating or
not? Pure Appl. Geophys. 163, 1965–1976.
Jones, L., Molnar, P., 1979. Some characteristics of foreshocks and their possible
relation to earthquake prediction and premonitory slip on fault. J. Geophys. Res. 84,
3569–3608.
Kagan, Y., Knopoff, L., 1978. Statistical study of the occurrence of shallow earthquakes.
Geophys. J. R. Astron. Soc. 55, 67–86.
Keilis-Borok, V.I., Kossobokov, V.G., 1990. Premonitory activation of earthquake flow:
Algorithm M8. Phys. Earth Planet. Inter. 61, 73–83.
King, G.C.P., Bowman, D.D., 2003. The evolution of regional seismicity between
large earthquakes. J. Geophys. Res. 108 (B2), 2096. http://dx.doi.org/10.1029/
2001JB000783.
Kossobokov, V.G., 2013. Earthquake prediction: 20 years of global experiment. Nat.
Hazards 69, 1155–1177.
Lamb, D., Easton, S.M., 1984. Multiple Discovery: The Pattern of Scientific Progress.
Avebury Press, Amersham.
Lippiello, E.,Marzocchi,W., de Arcangeli, L., Godano, C., 2012. Spatial organization of foreshocks
as a tool to forecast large earthquakes. Sci. Rep. 2, 846. http://dx.doi.org/10.
1038/srep00846.
López Casado, C.,Molina Palacios, S., Delgado, J., Peláez, J.A., 2000. Attenuation of intensity
with epicentral distance in the Iberian Peninsula. Bull. Seismol. Soc. Am. 90 (1),
34–47.
Main, I.G., 1999. Applicability of time-to-failure analysis to accelerated strain before
earthquakes and volcanic eruptions. Geophys. J. Int. 139, F1–F6.
Malagnini, L., Herrmann, R.B., 2000. Ground-motion scaling in the region of the 1997
Umbria–Marche Earthquake (Italy). Bull. Seismol. Soc. Am. 90, 1041–1051.
Malagnini, L., Herrmann, R.B., Di Bona, M., 2000. Ground-motion scaling in the Apennines
(Italy). Bull. Seismol. Soc. Am. 90, 1062–1081.
Malagnini, L., Akinci, A., Herrmann, R.B., Pino, N.A., Scognamiglio, L., 2002. Characteristics
of the ground motion in Northeastern Italy. Bull. Seismol. Soc. Am. 92 (6),
2186–2204.
Marsan, D., Lengline, O., 2010. A new estimation of decays of aftershock density with distance
to the main-shock. J. Geophys. Res. 115, B09302. http://dx.doi.org/10.1029/
2009JB007119.
McCaffrey, R., 2011. Earthquakes and crustal deformation. In: Gupta, H.K. (Ed.), Encyclopedia
of Solid Earth Geophysics. Springer, pp. 218–226.
Mele, G., Rovelli, A., Seber, D., Barazangi, M., 1997. Lateral variations of Pn propagation in
Italy: evidence for a high-attenuation zone beneath the Apennines. Geophys. Res.
Lett. 23 (7), 709–712.
Merton, R.K., 1963. Resistance to the systematic study of multiple discoveries in science.
Eur. J. Sociol. 4, 237–282.
Mignan, A., 2011. Retrospective on the accelerating seismic release (AMR) hypothesis:
controversy and new horizons. Tectonophysics 505, 1–16.
Mignan, A., 2012. Seismicity precursors to large earthquakes unified in a stress accumulation
framework. Geophys. Res. Lett. 39, L21308. http://dx.doi.org/10.1029/
2012GL053946.
Mignan, A., 2014. The debate on the prognostic value of earthquake foreshocks: a metaanalysis.
Sci. Rep. 4, 4099. http://dx.doi.org/10.1038/srep04099.
Mogi, K., 1969. Some features of recent seismic activity in and near Japan (2), Activity
before and after great earthquakes. Bull. Earthq. Res. Inst., Univ. Tokyo 47,
395–417.
Morasca, P., Malagnini, L., Akinci, A., Eva, C., 2004. Characteristics of ground motion in
Northern Apennines (Lunigiana–Garfagnana, Tuscany, Italy), Sept. 1st–6th 2002, ESC
Meeting (Genoa, Italy).
Morasca, P.,Malagnini, L., Akinci, A., Spallarossa, D., Herrmann, R.B., 2006. Ground-motion
scaling in the western Alps. J. Seismol. 10, 315–333.
Morasca, P., Zolezzi, F., Spallarossa, D., Luzi, L., 2008. Groundmotionmodels forMolise region
(Southern Italy). Soil Dyn. Earthq. Eng. 28, 198–211.
Nanjo, K.Z., Rundle, J.B., Holliday, J.R., Turcotte, D.L., 2005. Pattern Informatics and its
application for optimal forecasting of large earthquakes in Japan. Pure Appl. Geophys.
163, 2417–2432.
Ogburn, W.F., Thomas, D.S., 1922. Are inventions inevitable? A note on social evolution.
Polit. Sci. Q. 37 (1), 83–98.
Papadopoulos, G.A., 1988. Long-term accelerating foreshock activity may indicate the occurrence
time of a strong shock in the western Hellenic Arc. Tectonophysics 152,
179–192.
Papazachos, B.C., 1974. On certain aftershock and foreshock parameters in the area of
Greece. Ann. Geofis. 27, 497–515.
Papazachos, C., Papazachos, B., 2001. Precursory accelerated Benioff strain in the Aegean
area. Ann. Geophys. 44, 461–474.
Pasyanos, M.E., 2011. A case for the use of 3D attenuation models in groundmotion
and seismic-hazard assessment. Bull. Seismol. Soc. Am. 101 (4),
1965–1970.
Plastino, W., Bella, F., Catalano, P.G., Di Giovambattista, R., 2002. Radon groundwater
anomalies related to the Umbria–Marche, September 26, 1997, earthquake. Geofis.
Int. 41 (4), 369–375.
Reid, H.F., 1910. The mechanics of the earthquake. Carnegie Inst. Wash. Publ. 87
(192 pp.).
Richards-Dinger, K., Stein, R.S., Toda, S., 2010. Decay of aftershock density with distance
does not indicate triggering by dynamic stress. Nature 467, 583–586.
Riguzzi, F., Crespi,M., Devoti, R.,Doglioni, C., Pietrantonio, G., Pisani, A.R., 2013. Strain
rate relaxation of the normal and thrust faults in Italy. Geophys. J. Int. 195,
815–820.
Rundle, J.B., Klein,W., Turcotte, D.L.,Malaud, B.D., 2000. Precursory seismic activation and
critical point phenomena. Pure Appl. Geophys. 157, 2165–2182.
Saito, M., 1969. Forecasting time of slope failure by tertiary creep. Proc. 7th Internat. Conf.
on Soil Mechanics and Foundation Engineering 2, pp. 677–683.
Sarlis, N., Skordas, E., Lazaridou,M., Varotsos, P., 2008. Investigation of seismicity after the
initiation of a seismic electric signal activity until the main shock. Proc. Jpn. Acad. Ser.
B 84, 331–343.
Scholz, C.H., 2002. The Mechanics of Earthquake and Faulting vol. xxiv. Cambridge Univ.
Press, Cambridge/New York (471 pp.).
Schorlemmer, D., Mele, F., Marzocchi, W., 2010. A completeness analysis of the National
Seismic Network of Italy. J. Geophys. Res. 115, B04308. http://dx.doi.org/10.1029/
2008JB006097.
Shearer, P.M., 2009. Introduction to Seismology. 2nd ed. Cambridge Univ. Press, p. 396.
Stefànsson, R., 2011. Advances in Earthquake Prediction. Springer-Verlag, Berlin
Heidelberg.
Todorovska, M.I., 2011. Earthquake damage: detection and early warning in man-made
structures. In: Meyers, R.A. (Ed.), Extreme Environmental Events. Springer,
pp. 150–174.
Tokarev, P.I., 1963. On a possibility of forecasting of Bezymianny volcano eruptions according
to seismic data. Bull. Volcanol. 26, 379–386.
Toutain, J.-P., Baubron, J.-C., 1998. Gas and geochemistry and seismotectonics: a review.
Tectonophysics 304, 1–27.
Tzanis, A., Makropoulos, K., 2002. Did the 7/9/1999 M5.9 Athens Earthquake come with a
warning? Nat. Hazards 27, 85–103.
Tzanis, A., Vallianatos, F., 2003. Distributed power-law seismicity changes and crustal
deformation in the SW Hellenic Arc. Nat. Hazards Earth Syst. Sci. 3, 179–195.
Utsu, T., 1961. A statistical study of the occurrence of aftershocks. Geophys. Mag. 30,
521–605.
Varnes, D.J., 1989. Predicting earthquakes by analysing accelerating precursory seismic
activity. Pure Appl. Geophys. 130 (4), 661–686.
Varotsos, P.A., Sarlis, N.V., Skordas, E.S., Uyeda, S., Kamogawa, M., 2010. Natural-time
analysis of critical phenomena: the case of seismicity. EPL 92, 29002.
Varotsos, P.A., Sarlis, N.V., Skordas, E.S., Uyeda, S., Kamogawa, M., 2011. Natural time
analysis of critical phenomena. Proc. Natl. Acad. Sci. U. S. A. 108, 11361–11364.
Vere-Jones, D., Robinson, R., Yang,W., 2001. Remarks on the accelerated moment release
method: problems of model formulation, simulation and estimation. Geophys. J. Int.
144, 517–531.
Voight, B., 1989. A relation to describe rate-dependent material failure. Science 243,
200–203.
Wessel, P., Smith,W.H.F., 1998. New improved version of the generic map tools released.
EOS Trans. AGU 79, 579.
Yamashita, T., Knopoff, L., 1987. Models of aftershock occurrence. Geophys. J. 91, 13–26.
Yamashita, T., Knopoff, L., 1989. A model of foreshock occurrence. Geophys. J. 96,
389–399.
Zaliapin, I., Keilis-Borok, V., Axen, G., 2002. Premonitory spreading of seismicity over the
faults' network in southern California: precursor accord. J. Geophys. Res. 107 (B10),
2221. http://dx.doi.org/10.1029/2000JB000034.
Zhou, S.Y., Johnston, S., Robinson, R., Vere-Jones, D., 2006. Tests of the precursory AMR
using a synthetic seismicity model. J. Geophys. Res. 111, B05308. http://dx.doi.org/
10.1029/2005JB003720.