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The Dilatancy -Diffusion Hypothesis
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Earth Sciences

The dilatancy-diffusion hypothesis and earthquake predictability

Profile image of Ian G MainIan G Main

2012, Geological Society, London, Special Publications

https://doi.org/10.1144/SP367.15
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Abstract
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The dilatancy-diffusion hypothesis, initially proposed as a basis for earthquake prediction, has come under scrutiny due to its failure to demonstrate valid precursors at the crustal scale. Despite early optimism, subsequent studies show an absence of detectable precursory behaviors, leading to a re-evaluation of the hypothesis. This analysis encourages exploration of new avenues to better understand the physics underlying earthquakes and improve predictability.

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THEORETICAL BASIS OF SOME EMPIRICAL RELATIONS IN SEISMOLOGY
E S

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Mo, magnitude Ms, energy Es and fault dimension L (or area S) are discussed on the basis of an extensive set of earthquake data (M s >= 6) and simple crack and dynamic dislocation models. The relation between log S and log M o is remarkably linear (slope ~ 2/3) indicating a constant stress drop Aa; Atr = 30, 100 and 60 bars are obtained for inter-plate, intra-plate and "average" earthquakes, respectively. Except for very large earthquakes, the relation M s ~ (2/3) log M o ~ 2 log L is established by the data. This is consistent with the dynamic dislocation model for point dislocation rise times and rupture times of most earthquakes. For very large earthquakes M s ~ (1/3) log M o ,,~ log L ~ (1/3) log E s. For very small earthquakes M s ~ log M o ,~ 3 log L ~ log E s. Scaling rules are assumed and justified. This model predicts log E s ~ 1.5 M s ,-~ 3 log L which is consistent with the Gutenberg-Richter relation. Since the static energy is proportional to 0L 3, where ~ is the average stress, this relation suggests a constant apparent stress ~/¢i where r/ is the efficiency. The earthquake data suggest r/0 ~ ½ Atr. These relations lead to log S ,,~ M s consistent with the empirical relation. This relation together with a simple geometrical argument explains the magnitude-frequency relation log N N -Ms.

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