SECT. 1] SUB-OCEANIC STRUCTURAL EXPLORATION BY SEISMIC SURFACE WAVES 



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Unfortunately, with existing techniques, it is not possible to deduce earth 

 structure directly from a measurement of the dispersion, i.e. a plot of group 

 and/or phase velocity as a function of period. Instead, dispersion curves are 

 computed for a variety of theoretical models, and then compared with the 

 experimental data. This process is repeated until a good fit is obtained. In 

 selecting models for computation it is frequently possible to use information 

 from other sources, for example, seismic refraction data, and thereby to narrow 

 the number of possible solutions, and hence to increase the accuracy of the 

 surface-wave technique. 



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E 



o 



> 

 Q. 



o 



V- 



CI 



10 



20 



30 

 Period (sec) 



40 



50 



Fig. 2. Theoretical group -velocity (solid lines) and phase-velocity (dashed lines) disper- 

 sion curves for the first three modes of Love waves on a half-space with single 

 surface layer. The shear velocities are /Si = 3.6 km/sec for the layer and ^82 = 4.68 km/ 

 sec for the underlying material. The thickness of the layer is 35 km. Density ratio is 

 pi\p\—\.W. The fundamental mode curves cover the entire range of frequencies 

 reaching the velocity ^2 at infinite period. The second and third modes have a cut-off 

 or maximum possible period at which the group and phase velocities equal ^1. This 

 structural configuration is a simple approximation of the continental crust over- 

 lying the upper mantle. Waves corresponding to these three modes of propagation 

 have been observed from natural earthquakes, the fundamental mode being very 

 commonly observed. 



Theoretical considerations of surface-wave propagation in a horizontally 

 stratified wave guide produce, among other things, a most important relation 

 called the period equation, i.e. the relation between phase, and indirectly 

 group, velocity and wave period. A brief discussion of this theory and of 

 methods of finding and solving a period equation are given by Haskell (1953) 

 and Dorman (1962). Solution of this period equation gives various "allowed" 

 values of velocity and period. These values, frequently called normal modes, 

 may be thought of in much the same way as are the normal modes of an organ 



5 S. Ill 



