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Dynamics of Elongated Earthquake Ruptures

Weng, Huihui and Ampuero, Jean-Paul (2019) Dynamics of Elongated Earthquake Ruptures. Journal of Geophysical Research. Solid Earth, 124 (8). pp. 8584-8610. ISSN 2169-9313.

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The largest earthquakes propagate laterally after saturating the fault's seismogenic width and reach large length‐to‐width ratios L/W. Smaller earthquakes can also develop elongated ruptures due to confinement by heterogeneities of initial stresses or material properties. The energetics of such elongated ruptures is radically different from that of conventional circular crack models: they feature width‐limited rather than length‐dependent energy release rate. However, a synoptic understanding of their dynamics is still missing. Here we combine computational and analytical modeling of long ruptures in three dimension (3D) and 2.5D (width‐averaged) to develop a theoretical relation between the evolution of rupture speed and the along‐strike distribution of fault stress, fracture energy, and rupture width. We find that the evolution of elongated ruptures in our simulations is well described by the following rupture‐tip‐equation‐of‐motion: G_c = G₀(1-v_rW/v²s γ/Aα^P_s) (1) where G_c is the fracture energy, G₀ is the steady state energy release rate, v_s is the S wave speed, v_r is the rupture speed, v_r = dv_r/dt is the rupture acceleration, and γ/Aα^P_s is a known function of rupture speed. The steady energy release rate is limited by rupture width as G₀ = γ∆τ²W/μ, where γ is a geometric factor, ∆τ is the stress drop (spatially smoothed over a length scale smaller than W), and μ is the shear modulus. If G_c is a constant and exactly balanced by G₀, the rupture can in principle propagate steadily at any speed. If G_c increases with rupture speed, steady ruptures have a well‐defined speed and are stable. When G_c ≠ G₀, the rupture acquires an inertial effect: the rupture‐tip‐equation‐of‐motion depends explicitly on rupture acceleration. This inertial effect does not exist in the classical theory of dynamic rupture in 2‐D unbounded media and in unbounded faults in 3D, but emerges in 2‐D bounded media or, as shown here, as a consequence of the finite rupture width in 3D. These findings highlight the essential role of the seismogenic width on rupture dynamics. Based on the rupture‐tip‐equation‐of‐motion we define the rupture potential, a function that determines the size of next earthquake, and we propose a conceptual model that helps rationalize one type of “supercycles” observed on segmented faults. More generally, the theory developed here can yield relations between earthquake source properties (final magnitude, moment rate function, radiated energy) and the heterogeneities of stress and strength along the fault, which can then be used to extract statistical information on fault heterogeneity from source time functions of past earthquakes or as physics‐based constraints on finite‐fault source inversion and on seismic hazard assessment.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Weng, Huihui0000-0002-2936-2342
Ampuero, Jean-Paul0000-0002-4827-7987
Additional Information:© 2019 American Geophysical Union. Received 13 MAR 2019; Accepted 21 JUL 2019; Accepted article online 30 JUL 2019; Published online 14 AUG 2019. The open‐source software SPECFEM3D used in our 3‐D dynamic rupture simulations is available from the Computational Infrastructure for Geodynamics at We express our deepest gratitude in memory of Dimitri Komatitsch, whose pioneering work on the spectral element method in seismology and generous development of SPECFEM3D enabled a whole generation of computational seismology studies, including ours. The open‐source software SEMLAB for 2.5‐D dynamic rupture simulations based on the spectral element method is available at The SPECFEM3D simulations were conducted in the Cluster THERA in Géoazur. This work was supported by the French government through the Investments in the Future project UCAJEDI (ANR‐15‐IDEX‐01) managed by the French National Research Agency (ANR). J.P.A. acknowledges partial funding from NAM (Nederlandse Aardolie Maatschappij). All data of dynamic models are generated from numerical simulations. All figures are produced by using Generic Mapping Tools (GMT). We benefited from discussions with Robert Viesca, M.P.A. van den Ende, and Hongfeng Yang. We thank Eric Dunham and Raul Madariaga for their informative reviews.
Group:Seismological Laboratory
Funding AgencyGrant Number
Agence Nationale pour la Recherche (ANR)ANR‐15‐IDEX‐01
Nederlandse Aardolie MaatschappijUNSPECIFIED
Issue or Number:8
Record Number:CaltechAUTHORS:20191107-080445605
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Official Citation:Weng, H., & Ampuero, J.‐P. (2019). The dynamics of elongated earthquake ruptures. Journal of Geophysical Research: Solid Earth, 124, 8584–8610.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99721
Deposited By: Tony Diaz
Deposited On:07 Nov 2019 18:10
Last Modified:07 Feb 2020 21:05

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