CuAP. 9] SEISMIC METHODS 591 



initial phase difference is not much different from that for 0° difference. 

 H. W. Koch and W. Zelle/" have calculated onset records for ground 

 motions of gradually increasing amplitudes composed of two portions, 

 X sin Oil and — Xe""' ', where e' is the damping factor of the ground motion. 



C. The Mechanical Seismograph 



In principle a mechanical seismograph consists of a mass suspended by 

 a spring. To it may be added a lever or mirror system. This then repre- 

 sents a mechanical seismograph with a mechanical or optical recording sys- 

 tem. The mass may also carry inductive, capacitive, or reluctance trans- 

 ducers; it then constitutes a mechanical seismograph with an electrical 

 recording system, sometimes referred to merely as an electrical seismo- 

 graph, detector, or geophone. Whatever the arrangement for mechanical 

 magnification or electrical transmission, th& characteristics of a seismo- 

 graph are determined in the main by its mechanical design. The following 

 is a brief discussion of suspensions used in their relation to the frequency 

 characteristics of exploration seismographs. 



The sensitivity of a seismograph to ground vibrations depends on its 

 deflection for a given load, which is inversely proportional to its natural 

 frequenc}^ It is, therefore, impossible to combine high (mechanical) sensi- 

 tivity with high natural frequency. The following relations exist between 

 spring constant c (force-producing unit elongation), load on the end of a 

 spring F, natural frequency co, and deflection a: 



m am Wq 



where wo = 27r/o . 



For a leaf spring of rectangular section with the length I, breadth &, 

 thickness h, Young's modulus E, and sectional moment of inertia J, the 

 spring constant c = 3EJ/^^ Since / = hh^/l2, c = Eh{h/lf /4, so that 

 the natural frequencj^ 



2./, = .. = 1 /f(f)'. (9-90« 



When a light mass is suspended at the end of the spring, 30 per cent 

 of the mass of the spring should be added to it. For steel springs Young's 

 modulus is closely enough 2 X 10^^ dynes • cm ~^ (if the geometric dimen- 

 sions are expressed in cm and masses in g). In horizontal seismometers 



56 Zeit. Geophys., 12(6/6), 220-228 (1936). 



