Theory of earthquakes — IV. General implications for earthquake prediction

Abstract

The scale invariant inclusion theory of failure is applied to the general problem of precursors that precede failure. A precursor is defined to be an effect produced within a physical system which indicates that the process leading to failure of the system has begun. Precursors are grouped into three classes.Class I precursors refer to long-term indicators of impending failure. These may includev _p/v_s, long-term tilt, and crustal uplift anomalies observed to precede some major shallow earthquakes by afew years. Class II precursors refer to short-term indicators of failure and include: S-bend tilt, electromagnetic radiation, radon emanations, and seismicity changes that have been reported to precede major earthquakes by afew hours. Class III precursors refer tovery short-termphenomena such as long-period (strain) waves,rapid changes in surface ground tilts, and seismicity increase in the hypocentral region that are predicted by the inclusion theory to precede major shallow earthquakes by afew seconds.

The physical processes that occur within the inclusion zone of an impending failure that indirectly produce the class II precursors are used with the scale invariant properties of failure to show that their time duration is a direct measure of the average length of the cracks that comprise the inclusion zone. This result is used to derive the precursor time-‘fault’ length relationship that has been observed to hold for class I precursors of shallow earthquakes, mine failures, and laboratory size failures of rock. The physical model proposed for producing class I, class II, and indirectly, the class III precursors leads to six results when both the Utsu relationship between aftershock area and earthquake magnitude and the Gutenberg-Richter energy-magnitude relationship are satisfied. (1) The seismic efficiency factor for failures satisfying the constraints of the inclusion theory is approximately 0.40%. (2) The energy radiated by aftershocks will be at least 1.0% of the energy radiated bythe mainshock. (3) An upper limiting magnitude of any aftershock in the aftershock sequence isM−1.6, whereM is the mainshock magnitude. (4) The time durations of all three precursor classes are shown to be shortened (or lengthened) by a factor inversely proportional to the rate of increase (or decrease) of the far-field stresses during the time duration of the precursor. Changes in far-field stresses, such as might occur to tidal effects, are shown to be of particular importance in initiating class II precursors, and it is shown that tidal stresses provide a mechanism for triggering large earthquakes (M≥6.0) in regions that are at the point of incipient failure. Thus, class II precursors may give the appearance of being independent of magnitude for large earthquakes. (5) When fluids are present in the focal volume of the mainshock, the predicted magnitude, calculated by class I precursors, will always be larger than the observed magnitude. (6) Seismic events that produce the inclusion zone of the impending mainshock will not be followed by aftershocks. These events are predicted to be characterized by anomalously long rupture lengths.

The inclusion theory is shown to provide a physical basis for criteria required to predict failure. The implications of the inclusion theory to the problem of earthquake prediction are discussed. The theory is applied to existing earthquake-prone regions.