Theory Of Seismology Bullen 1980

Bodily Elastic Wave

Following an actual earthquake, the displacement of any point of the Earth’s surface is markedly different from waves through only a homogeneous medium. There are oscillatory movements being due to one or more of the following causes:

(i) the existence of more complicated initial conditions
(ii) fluctuations in the local gravity value during the passage of disturbance
(iii) imperfections of elasticity
(iv) departures from homogeneity within the Earth

In regard to (i), the initial dislocation of material causing the earthquake would normally be spread over a finite interval of time. If there were several distinct movements during this interval, it would be independent of the distance of the point from source of the disturbances.

The effect of gravity fluctuations is also can be neglected as the gravity term has no effect in the propagation os S waves. This is an immediate consequence of the fact that a purely rotational disturbance causes no disturbance in density. Therefore the neglect of gravity effects is unimportant in all ordinary problems on seismological bodily waves. In particular, these effects cannot account for the observed dispersion of these waves.

If we consider several cases other than perfect elasticity assumption (elastic after working, the Jeffreys-Lomnitz law, elasticoviscosity), the onset of a pulse is also sharp as in the perfect elasticity case; and there is no dispersion introduced.

It emerges that the essenial cause of the observed oscillatory movements must be sought in (iv) heterogeneity of the Earth.

We note that these oscillatory movements are observed at points fairly close to the source of an earthquake (as well as at distant points) which indicates the Earth must be markedly heterogeneous. The crustal layer of the Earth (30-40 km thickness) is known for its quite considerable changes in property and likely to account for the observed dispersion bodily waves.

## Seismology and the Earth's Upper Layers The outermost 40 km of the Earth was once thought composed of a comparatively thin crust resting on material in a fluid or near-fluid state. This is not the case and we shall here use the term _crust_ and _crustal layers_ to refer to the part of the Earth above the Mohorovicic discontinuity. Seismological data on the structure of the crust come from several sources, including studies of bodily wavs in the near earthquakes and exploisons, of phases such as _pP_ in deep-focus earthquakes, and of the dispersion of surface waves from distant earthquakes.