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This cycling of stress may prolong the release of the pre-stored energy, but it does not add new strain energy to the system. We used a finite element model to explore how stress cycling associated with viscous relaxation may prolong the earthquake sequence Fig. The model setting is similar to that of Kenner and Segall The fault is a km long and 2-km wide elastoplastic vertical zone cutting across the seismogenic upper crust. Below the fault zone is a km wide and km thick weak zone, embedded in the relatively stronger surrounding lower crust and upper mantle.
A range of viscosity values for the weak zone and the surrounding ductile lower lithosphere were tested. The front and back sides are fixed in the x direction and free in the y and z directions. The surface is free; the bottom is fixed vertically but free to move horizontally.
We then explored how viscous relaxation produces repeated earthquakes and what controls the duration of the earthquake sequence. This event causes coseismic loading of the surrounding crust and the underlying ductile lower lithosphere. Viscous relaxation in the lower lithosphere then shifts some of the stress back to the seismogenic upper crust, causing failure of some or all of the fault elements. The cycling of stress between the fault plane and the ductile lower lithosphere continues until the perturbing stress becomes too low to cause further failures Fig.
Simulated earthquake sequences with stress cycling due to viscous relaxation in the ductile lower lithosphere.
However, in this case, as in the model of Kenner and Segall , the stress cycling is assumed to be purely viscoelastic, so strain energy released by rupturing is entirely propagated down into the ductile lower lithosphere and the surrounding crust and later recycled back to the upper crust by viscous relaxation. This is certainly not realistic; during earthquakes, a large portion of strain energy is dissipated in heat and other non-elastic processes, although the energy partition between seismic and aseismic processes is uncertain Kanamori ; Lockner and Okubo , and only a fraction of the strain energy in the upper crust will be eventually used for earthquakes Ward If most of the strain energy is dissipated during ruptures, a more likely scenario Kanamori , the resulting earthquake sequence will end much sooner Fig.
The duration and characteristics of the stress decay process depend also on the rheological structure of the model. In general, the lower the viscosity of the ductile lower lithosphere, the faster the viscous relaxation, and thus the shorter duration of the earthquake sequence. For the results in Fig. We also explored other rheological structures, including a weak zone extending deeper under the NMSZ Zhang et al.
Although the results would vary with rheological values and structures, the general pattern remains the same. The key factor controlling the sequence duration is the fraction of strain energy dissipation during ruptures—the more dissipation, the shorter the sequence. The long aftershock sequences in North China and central US show fundamental differences between earthquakes in mid-continents and at plate boundaries.
The major cause for this difference is the loading conditions Liu et al.
The slow tectonic loading within continents cause long aftershock sequences Stein and Liu , as predicted by the rate and state frictional law Dieterich In contrast, plate boundary faults are loaded more rapidly by steady relative plate motion. Consequently, earthquakes concentrate along the plate boundary faults, and quasi-periodic occurrences may be expected. As long as the relative plate motion continues, so will the earthquake sequences. The situation is quite different in mid-continents, where slow tectonic loading is shared by a complex system of interacting faults spread over a large region.
Each fault is not loaded by steady relative motion between crustal blocks on either side, and its loading rate may be affected by a large earthquake on other faults Li et al. Consequently, individual faults may remain dormant for a long time and then become active for a short period, leading to episodic and spatially migrating earthquakes. Such complex spatiotemporal patterns of large earthquakes are observed in other mid-continents, including Australia and northwestern Europe Camelbeeck et al. Although the repeated large earthquakes in the New Madrid seismic zone during the past millennium may seem to be an exception to this complex pattern of mid-continental earthquakes, they nonetheless differ fundamentally from earthquakes at plate boundary zones because they cannot result from steady tectonic loading.
Whether they release pre-stored strain energy on reactivated faults or have other causes, the transient loading causes a transient earthquake sequence. Using both a simple physics model and a viscoelastic numerical model indicate, we have shown that the current sequence of New Madrid earthquakes is likely ending or has ended. Such results are consistent with geodetic observations that show less than 0. Although the recent seismicity in central US is dominated by the NMSZ earthquakes, paleoseimic evidence indicates large Quaternary earthquakes in other parts of the Mississippi Embayment and beyond Cox et al.
Hence, large earthquakes have roamed between widespread faults in central US, similar to earthquakes in North China. Both the long aftershock sequences of mid-continental earthquakes and their complex spatiotemporal occurrences make hazard assessment, a challenging task even at plate boundaries, even more difficult. Although aftershocks can still be damaging and need to be included in hazard assessment, they are poor predictors of future large earthquakes. Moreover, because large earthquakes tend to migrate between distant faults, large earthquakes in mid-continents often not repeat on the same fault segment within hundreds to thousands of years.
To improve assessments of earthquake hazard, we need to go beyond the current models that treat individual faults or fault segments as isolated systems and focus on cyclic stress buildup and release on these faults. Instead, we have to treat the widespread faults within continents as complex systems and try to understand how the faults interact with each other Li et al. Earthquake records need to be combined with paleoseismic studies to develop a longer earthquake history, and high precision GPS measurements need to go beyond the sites of recent large earthquakes.
All these require time and effort, but realizing the problems of current practice, as we have shown in this study, is the necessary first step toward a better assessment of earthquake hazards. Science J Geophys Res B Google Scholar. Nature — Geological Society of America, Kansas, pp — Pergamon Press, Oxford, p Clark D, McCue K Australian paleoseismology: towards a better basis for seismic hazard estimation. Ann Geophys 46 5 — Geol Soc Am Bull 11 — Dieterich J A constitutive law for rate of earthquake production and its application to earthquake clustering.
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Springer, The Netherlands, pp — EOS 93 45 — Geophys Res Lett L J Geophys Res 88 5 — Luo G, Liu M Stress evolution and fault interactions before and after the great Wenchuan earthquake. Tectonophysics — Ann Rev Earth Planet Sci — Boulder, Colorado, Geol. Am, pp — Parsons T Global Omori law decay of triggered earthquakes: large aftershocks outside the classical aftershock zone.
J Geophys Res B 9 :1—9. Report of the State Investigation Commission, vol. Stein S Disaster deferred: how new science is changing our view of earthquake hazards in the Midwest. Columbia University Press, New York. Stein S, Liu M Long aftershock sequences within continents and implications for earthquake hazard assessment. Seismol Res Lett 80 4 — Tectonophysics —— Bull Seismol Soc Am 92 6 — Seismol Res Lett 77 6 — Eng Geol 55 4 — Bull Seismol Soc Am 90 2 — Ward SN On the consistency of earthquake moment rates, geological fault data, and space geodetic strain; the United States.
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