SEISMIC METHODS 929 



measurements of the velocity of sound in the mine pillars from which the laboratory 

 samples were taken. From a knowledge of the velocity of sound in a particular rock 

 as a function of pressure (laboratory measurement) and the velocity of sound in an 

 underground pillar composed of the same rock (mine measurement), the pressure 

 on the underground rock pillar can be inferred, t 



A direct and relatively simple method for measuring the variation of elastic wave 

 velocity with pressure utilizes rocks cut in the form of rectangular prisms. Known 

 amounts of pressure are applied to the ends of the rock specimen by means of a 

 mechanical press. The prism of known dimensions and density is caused to vibrate 

 in one of its fundamental modes of vibration and the frequency of vibration is de- 

 termined. The elastic wave velocity for any pressure can be computed from well- 

 known relationships expressing the velocity as a function of frequency, density, and 

 geometrical dimensions. For example, if the prism is supported at its ends and if 

 the driving force is applied at the center of the prism so as to cause the prism to 

 vibrate as a unit with its two points of support as nodal points, the elastic wave 

 velocity V of the prism material is given by the relation 



IT t 



where L is the length of the column, / the frequency of vibration, and / the thickness 

 of the column. 



Earthquake Insurance. — The appalling loss of Hfe and the damage 

 to property caused by earthquakes has led the governments of several 

 countries, notably the United States, Japan and Germany, to institute 

 investigations of methods of minimizing this damage.* Studies of the 

 damage produced during the San Francisco earthquake of 1906, the 

 Santa Barbara earthquake of 1925, and the Long Beach earthquake of 

 1933, have shown that the damage was due largely to the collapse of 

 poorly constructed structures not designed to withstand earthquake forces 

 and to fires which could not be controlled because of the failure of water 

 supplies. These studies, therefore, indicated that one very important 

 method of minimizing the damage is to construct buildings in earthquake 

 areas which are as earthquake-resistant as feasible.t From afti engineering 

 design viewpoint, this is accomplished by so constructing the building that 

 it will not be markedly affected by the natural frequency of vibration 

 common to earthquakes in the area. 



An important economic problem associated with earthquakes concerns 

 insurance. Logically, earthquake insurance rates for buildings in a given 

 area should vary according to their susceptibility to earthquake damage. 

 For example, if the natural period** of vibration of a building is the same 

 as the ground period set up by most earthquakes in the area in which the 



t L. Obert, "Measurement of Pressures on Rock Pillars in Underground Mines," U. S. Bureau 

 of Mines, Report of Investigations 3444, April, 1939. 



* It has been estimated that during the last two centuries on the average some 



thirty thousand persons were killed each year by earthquake phenomena. 



t M. H. Gilmore, "Earthquake Investigations," Geophysics, Vol. II, No. 3, July, 1937, 

 pp. 253-264. 



** It will be recalled that the period of a vibration is equal to the reciprocal of 

 the frequency. 



