918 MISCELLANEOUS GEOPHYSICAL METHODS [Chap. 12 



and the response of the structure (or model) is recorded at one or several 

 points. The records give the variation of amplitude with frequency and 

 (when several detectors are used) the variation of amplitude with vertical 

 elevation and horizontal direction. Buildings and other structures may 

 have different frequencies in different directions. Different harmonics 

 may appear for different modes of vibration (see page 912). In dynamic 

 investigations, harmonics are more readily segregated than in free vibra- 

 tion records and may not even appear when outside the range of the 

 vibrator. Evaluation of the vibration records yields resonance frequency, 

 natural frequency, damping, and magnification for any point. These 

 quantities are usually combined by plotting the response curve, that is, a 

 curve giving relative amplitude (and magnification) as a function of fre- 

 quency. Earthquake or vibration damage for a given structure is depend- 

 ent on its response function*" and therefore on its degree of tuning in respect 

 to prevalent ground frequencies. Hence, the damage is larger if the ratio 

 of building to ground frequency is near 1 and if damping is small. Since, 

 in turn, the response of the ground to earthquake waves increases with 

 the ability of layers to oscillate, earthquake damage is controlled largely 

 by local geologic factors. This is well illustrated by the example of two 

 Japanese earthquakes*^ which, though originating about 1100 km apart, 

 caused maximum damage in virtually the same area. 



The vertical component of earthquake or other vibrations is believed to 

 be comparatively ineffective; most structures are damaged primarily by 

 horizontal motion. For the duration of a vibration, a structure is sub- 

 jected to a strain whose magnitude depends on the vibration amplitude at 

 the particular point, and damage results when the ultimate stress of the 

 building material is exceeded. This has been verified by dynamic building 

 tests in areas where earthquakes of known intensity had occurred and 

 where, therefore, the building amplitude (which follows from the response 

 function of the building for an earthquake of given strength) could be 

 correlated with the observed damage. Calculations*^ showed that the 

 ultimate stress of the material actually had been exceeded where destruc- 

 tion occurred. The importance of resonance between building and ground 

 may be seen from the fact that for a brick house the critical ground ampli- 

 tude (just causing damage) is 53 microns at resonance and as much as 75 

 centimeters off resonance. 



The seismic resistance of a structure may be calculated for sinusoidal 

 ground motion and for simple modes of vibration, provided the response 



so Ramspeck, Zeit. Geophys., 9(1/2), 44-59 (1933). 

 " H. Martin, Zeit. Geophys., 12(7/8), 335 (1936). 

 ** Ramspeck, loc. cit. 



