The Energy Release in Earthquakes, and Subduction Zone Seismicity and Stress in Slabs

Citation

Vassiliou, Marios Simou (1983) The Energy Release in Earthquakes, and Subduction Zone Seismicity and Stress in Slabs. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/yp4p-t246. https://resolver.caltech.edu/CaltechTHESIS:10282019-161929138

Abstract

Part I

Earthquake energy calculations are generally made through an empirical application of the familiar Gutenberg-Richter energy-magnitude relationships. The precise physical significance of these relationships is somewhat uncertain. We make use here of the recent increases in knowledge about the earthquake source to place energy measurements on a sounder physical basis. For a simple trapezoidal far-field displacement source-time function with a ratio x of rise time to total duration T₀, the seismic energy E is proportional to 1/[x(1-x)²] M²₀/T³₀, where M₀ is seismic moment. As long as x is greater than 0.1 or so, the effect of rise time is not important. The dynamic energies thus calculated for shallow events are in reasonable agreement with the estimate E ≈ (5 x 10^-5)M₀ based on elastostatic considerations. Deep events, despite their possibly different seismological character, yield dynamic energies which are compatible with a static prediction similar to that for shallow events. Studies of strong-motion velocity traces obtained near the sources of the 1971 San Fernando, 1966 Parkfield, and 1979 Imperial Valley earthquakes suggest that even in the distance range of 1-5 km., most of the radiated energy is below 1-2 Hz. in frequency. Far field energy determinations using long period WWSSN instruments are probably not in gross error despite their bandlimited nature. The strong motion record for the intermediate depth Bucharest earthquake of 1977 also suggests little teleseismic energy outside the pass-band of a long period WWSSN instrument.

Part II

The pattern of seismicity as a function of depth in the world, and the orientation of stress axes of deep and intermediate earthquakes, are explained using viscous fluid models of subducting slabs, with a barrier in the mantle at 670 km. 670 km is the depth of a seismic discontinuity, and also the depth below which earthquakes do not occur. The barrier in the models can be a viscosity increase of an order of magnitude or more, or a chemical discontinuity where vertical velocity is zero. Log N versus depth, where N is the number of earthquakes, shows (1) a linear decrease to about 250-300 km depth, (2) a minimum near that depth, and (3) an increase thereafter. Stress magnitude in a subducting slab versus depth, for a wide variety of models, shows the same pattern. Since there is some experimental evidence that N is proportional to e^kσ, where k is a constant and σ is the stress magnitude, the agreement is encouraging. In addition, the models predict down-dip compression in the slab at depths below 400 km. This has been observed in earlier studies of earthquake stress axes, and we have confirmed it via a survey of events occurring since 1977 which have been analyzed by moment tensor inversion. At intermediate depths, the models predict an approximate but not precise state of down-dip tension when the slab is dipping. The observations do not show an unambiguous state of down-dip tension at intermediate depths, but in the majority of regions the state of stress is decidedly closer to down-dip tension than it is to down-dip compression. Chemical discontinuities above 670 km, or phase transitions with an elevation of the boundary in the slab, predict, when incorporated into the models, stress peaks which are not mirrored in the profile of seismicity versus depth. Models with an asthenosphere and mesosphere of appropriate viscosity can not only explain the state of stress observed in double Benioff zones, but also yield stress magnitude profiles consistent with observed seismicity. Models where a nonlinear rheology is used are qualitatively consistent with the linear models.

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