Transient Velocity of Oceanic Lithosphere: a Mechanism for Remote Triggering of Earthquakes

A sequence of large earthquakes along the Aleutian arc and Kurile-Kamchatka trench from 1952 to 1965 released interplate stresses accumulated over a much longer period prior to the sequence. The subsequent evolution of postseismic deformation of the Pacific lithosphere has been predicted using a viscoelastic coupling model consisting of a purely elastic oceanic lithosphere overlying a viscoelastic asthenosphere with viscosity = 5 $\times$ 10¹⁷ Pa s. Southward propagation of both postseismic strain and velocity fronts is consistent with patterns of (apparently triggered) earthquake occurrence along western North America over the past 30 years, including accelerations in California seismicity from about 1979 to 1994. The model is consistent with observed anomalous velocity of broadly distributed Pacific geodetic sites and suggests that stress redistribution following earthquakes may produce tangible effects over a spatial scale of 1000's of km.

Ever since the theory of plate tectonics established that Earth's outer shell consists of numerous plates moving in a rigid fashion averaged over long periods of time, the question has naturally arisen: how do the plates move over short periods of time? For example, the long term convergence rate between the Pacific and North American plates at the Aleutian arc or the sliding rate of these two plates along the San Andreas fault can be accurately predicted from a model in which both large plates are behaving rigidly. However, the slip history of a point near such a plate boundary will be highly non-uniform with time (e.g., Savage, 1983), and short term "transient" motions are a common feature around plate boundaries. Since such transients typically follow earthquakes and exhibit nonlinear time dependence, in continental crustal deformation studies they have been frequently attributed to relaxation of the lower crust and upper mantle. Such an elastic lithosphere - viscoelastic asthenosphere coupling model was, in fact, originally developed to explore transient stress propagation through the oceanic lithosphere and its potential for influencing the occurrence of earthquakes on the borders of an oceanic plate (e.g., Elsasser, 1969; Anderson, 1975). Historically, relatively little attention has been devoted to stress diffusion through the ocean basins compared with continental lithosphere because of the relative lack of geodetic observations.

Romanowicz (1993) speculated that long range coupling between oceanic and continental lithosphere may follow alternating 20 year cycles on a global scale based on 20th century seismicity patterns. Pollitz, Bürgmann, and Romanowicz (1998) performed a focussed test of this possibility within the northern Pacific Basin and its eastern boundary, western North America. They used stress sources consisting of the coseismic stresses generated by the large 1952 Kamchatka, 1957 Aleutian, 1964 Alaskan, and 1965 Rat Island earthquakes (Figure 15.1) and a number of smaller interplate events. Their preferred viscoelastic coupling model consisted of a 62 km - thick oceanic lithosphere underlain by a 160 km thick asthenosphere with viscosity = 5 $\times$ 10¹⁷ Pa s. Time-dependent stress diffusion through the Pacific oceanic lithosphere following this earthquake sequence can be tracked by surface horizontal dilatational strain rate $\dot\Delta$ (Figure 15.1), which clearly demonstrates stress propagation towards the S/SE at an average propagation rate of $\sim$ 100 km/yr over the past 30 years.

This pattern bears a direct relationship to the horizontal velocity field. Points near the Aleutian arc tend to move in quickly towards the N/NW in the early relaxation phase, and points far to the south are not yet moving significantly. Between these two regions must lie a region of tension, i.e., positive $\dot\Delta$ . As relaxation progresses, the northward pull of the combined earthquake sources is gradually manifested at points further south, increasing their velocities and pushing the front of maximal $\dot\Delta$ towards the south with time.

**Figure:15.1** (A) Rupture areas of major subduction events along the Aleutian arc and Kamchatka trench from 1952 to 1965. Arrows give the direction of slip associated with each of the four events considered, with length proportional to total seismic moment. Numerals adjacent to these arrows specify the seismic moment in units of 10²⁰ N m. (B-D) Net postseismic velocity and dilatational strain rate $\dot\Delta$ over the northern Pacific and eastern Arctic basins driven by combined subduction events projected onto a sphere centered on 50 $\deg$ N, 155 $\deg$ W as evaluated at three different times. Deformation is evaluated at Earth's surface. Heavy lines denote the fault planes used to model the subduction events. Locally large velocities near the rupture zones have been truncated at a maximum of 5 cm/yr for visual simplicity.
$\begin{figure}% \begin{center} \epsfig{file=figs/bsl98_fredp_fig1.ps, width=13cm} % \end{center}\end{figure}$

Although this is useful for demonstrating the pulse-like behavior of the stress diffusion process, we believe that earthquake triggering potential at affected plate boundaries is most closely related to the absolute postseismic velocity of the adjacent oceanic lithosphere. Around the San Andreas fault system, transient oceanic velocity according to our model reached a maximum $\sim$ 3 mm/yr in 1980-85 off northern California and $\sim$ 2 mm/yr in 1985-90 off southern California, adding constructively to the background relative plate motion. Both transient velocity and integrated velocity (accumulated displacement) as a function of time are compared with California seismicity rates in Figure 15.2. This comparison suggests a close connection between transient displacement and triggered California seismicity which may be part of a larger consistent pattern of triggered seismicity along western North America during southward passage of the strain/velocity front through the Pacific Basin.

Our viscoelastic coupling model suggests a rather low viscosity for the oceanic asthenosphere, though recent independent constraints on asthenospheric viscosity are at most a factor of 2 to 5 higher (Davaille and Jaupart, 1994; Hirth and Kohlstedt, 1996). The model predicts well anomalous geodetic velocities within the Pacific Basin observed from 1984 to 1997. Future tests of this model may ultimately depend on following the slow decay in transient velocity at these oceanic geodetic sites over the coming two decades.

**Figure:15.2** Equivalent magnitude M of summed seismic moment M₀ within binned 5-year intervals in northern California (latitudes 35-39 $\deg$ N) and southern California (32-35 $\deg$ N), derived from all regional earthquakes within boxed region of Figure 15.1 of magnitude >=5.0 (USGS NEIC; NCEDC) and the averaged seismic moment formula of Hanks and Kanamori (1979). Time-dependent transient velocity and displacement of the adjacent Pacific margin lithosphere is superimposed.
$\begin{figure}% \begin{center} \epsfig{file=figs/bsl98_fredp_fig2.ps, width=8cm} % \end{center}\end{figure}$

References

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Elsasser, W.M., Convection and stress propagation in the upper mantle, in The Application of Modern Physics to the Earth and Planetary Interiors, edited by S.K. Runcorn, pp. 223-246, John Wiley, New York, 1969.

Hanks, T.H. and H. Kanamori, A moment magnitude scale, J. Geophys. Res., 84, 2348, 1979.

Hirth, G., and D.L. Kohlstedt, Water in the oceanic upper mantle: Implications for rheology, melt extraction and the evolution of the lithosphere, Earth Planet. Sci. Lett., 144, 93-108, 1996.

Pollitz, F.F., R. Bürgmann, and B. Romanowicz, Viscosity of oceanic asthenosphere inferred from remote triggering of earthquakes, Science, 280, 1245-1249, 1998.

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Savage, J.C., A dislocation model of strain accumulation and release at a subduction zone, J. Geophys. Res., 88, 4984-4996, 1983.