Summary

The analysis given here considers that an earthquake fault is formed by the superposition of a large number of incremental shear dislocations the sudden release of which produces the earthquake. It is postulated that during an earthquake the incremental dislocations are released in such a way that the average slip is proportional to the square root of the area of slip, and that the probability of release of individual incremental dislocations is such that the probability of a total slip area A is inversely proportional to A. With these two postulates a frequency distribution of earthquakes is derived that agrees with observed data; the Richter magnitude is shown to be essentially a logarithmic measure of the average slip on a fault; and an expression is derived for the energy released by an earthquake that agrees with that derived from consideration of the energy carried in a wave train. Expressions are derived also for the areas of slip during earthquakes, the maximum relative slip, and the average annual, over-all shearing distortion of the state of California and these are in satisfactory agreement with observed behavior. It is assumed that an accelerogram is formed by the superposition of a large number of elemental acceleration pulses random in time. It is shown that this agrees with recorded accelerograms, and an accelerogram composed in this fashion is shown to have the characteristics of actual recorded accelerograms. It is also shown that the maximum ground accelerations in the vicinity of the center of the fault, so far as they are dependent upon the size of the slip area, have essentially reached their upper limits for shocks with areas of slip approximately equal to that associated with the El Centro earthquake of 1940.

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