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On the scale dependence of earthquake stress drop

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Abstract

We discuss the debated issue of scale dependence in earthquake source mechanics with the goal of providing supporting evidence to foster the adoption of a coherent interpretative framework. We examine the heterogeneous distribution of source and constitutive parameters during individual ruptures and their scaling with earthquake size. We discuss evidence that slip, slip-weakening distance and breakdown work scale with seismic moment and are interpreted as scale dependent parameters. We integrate our estimates of earthquake stress drop, computed through a pseudo-dynamic approach, with many others available in the literature for both point sources and finite fault models. We obtain a picture of the earthquake stress drop scaling with seismic moment over an exceptional broad range of earthquake sizes (−8 < MW < 9). Our results confirm that stress drop values are scattered over three order of magnitude and emphasize the lack of corroborating evidence that stress drop scales with seismic moment. We discuss these results in terms of scale invariance of stress drop with source dimension to analyse the interpretation of this outcome in terms of self-similarity. Geophysicists are presently unable to provide physical explanations of dynamic self-similarity relying on deterministic descriptions of micro-scale processes. We conclude that the interpretation of the self-similar behaviour of stress drop scaling is strongly model dependent. We emphasize that it relies on a geometric description of source heterogeneity through the statistical properties of initial stress or fault-surface topography, in which only the latter is constrained by observations.

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Acknowledgments

We thank the associate editor and two anonymous reviewers for their useful criticisms, which contributed to improve the manuscript and to make it more accessible to readership. We thank Raul Madariaga, Shamita Das and Jean Virieux for inviting us to attend the symposium to honour the distinguished career of Prof. Raùl Madariaga, where we discussed with numerous scientists and colleagues. We are indebted with all the authors who kindly provided their stress drop estimates (A. Baltay, G. Calderoni, M. Causse, B. Ellsworth, T. Göbel, B. Goertz-Allmann, S. Goodfelow, K. Imanishi, G. Kwiatek, M.P. Mai, L. Malagnini, A. Oth, G. Prieto, T. Uchide, S.H. Yoo and A. Zollo). We thank M.M. Scuderi, C. Collettini, S. Nielsen, G. Di Toro and E. Spagnuolo for the useful discussions.

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  1. Istituto Nazionale di Geofisica e Vulcanologia, Rome, Italy

    Massimo Cocco, Elisa Tinti & Antonella Cirella

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  1. Massimo Cocco
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Correspondence to Massimo Cocco.

Appendix

Appendix

We describe here the details of the calculations performed in this study for the 2009 L’Aquila earthquake. The pseudo-dynamic model is used to infer traction evolution and compute the distribution of dynamic parameters. The kinematic information has been taken from the model proposed by Cirella et al. (2012) jointly inverting GPS, DInSAR and strong motion data. We used the finite difference code proposed by Andrews (1999) and implemented by Tinti et al. (2005a). The adopted fault plane is 28 km long and 17.5 km wide. We adopted the same regularized Yoffe function as source time function (STF), used in Cirella et al. (2012), having a constant time to peak slip velocity equal to 0.225 s. We assume the heterogeneous distribution of peak slip velocity, rise time and rupture time inferred through the inversion of geophysical data. The spatial distributions of these source parameters are interpolated and smoothed for dynamic modelling following the scheme proposed by Tinti et al. (2005a) [see Appendix A in this manuscript]. The original spatial discretization is 3.5 Km. Our discretization interval is 0.35 km in space and 0.02 in time. We used the 1-D Earth model proposed by Herrmann et al. (2011) for central Italy.

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Cocco, M., Tinti, E. & Cirella, A. On the scale dependence of earthquake stress drop. J Seismol 20, 1151–1170 (2016). https://doi.org/10.1007/s10950-016-9594-4

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