The magnitude M of an earthquake, on modern variants of the Richter scale, is a quantitative measure of the strength of the seismic waves it creates. The earthquake’s seismic-wave energy release can be estimated using a rough semi-empirical formula due to Bath (1966):

The largest earthquakes have magnitude ∼9.5.

One type of earthquake is caused by slippage along a fault deep in the crust. Suppose that most of the seismic power in an earthquake with M ∼ 8.5 is emitted at frequencies ∼1Hz and that the quake lasts for a time T ∼ 100 s. If C is an average wave speed, then it is believed that the stress is relieved over an area of fault of length ∼CT and a depth of order one wavelength (Fig. 12.8). By comparing the stored elastic energy with the measured energy release, make an estimate of the minimum strain prior to the earthquake. Is your answer reasonable? Hence estimate the typical displacement during the earthquake in the vicinity of the fault. Make an order-of magnitude estimate of the acceleration measurable by a seismometer in the next state and in the next continent. (Ignore the effects of density stratification, which are actually quite significant.)

Fig. 12.8

Transcribed Image Text:

E = 105.24+1.44MJ. (12.63)