Low-frequency approximation

Some complicated details—inflections and inflations of the representing surfaces—occur in the nearest comer of the plots in Figures 4.3 and 4.4, namely, at coio > 1 and cr 3. This is the range that is beyond the scope of the low-frequency approximation, and much so the blocking model. Those results are available only by numerical evaluation since one has to take into account on... 

Raman frequencies (A, Bi ) are doubtless 465—455 cm i in Na2Pt(CN)4 3 H2O and 486—461 cm i in EtiPt. Our study has been limited to EtiPt for technical reasons, but it is certain that comparison of the vuc frequency in different salts would yield important information. The distinction between the two normal modes is based upon the polarization factor and the low-frequency approximation ... 

It is understood that the matrix elements of this operator should be evaluated with the relativistic 4-component wave function. The approximation (163) is called also the low-frequency approximation, since it arises when energy differences tend to zero AE — 0. An expression for the Breit operator suitable for the evaluations with the two-component (nonrelativistic) wave functions follows when we expand also the relativistic wave functions using Eqs(24)-(26) ... 

To deseribe wave propagation in marine sediments mathematieally, various simple to eomplex models have been developed which approximate the sediment by a dilute suspension (Wood 1946) or an elastic, water-saturated frame (Gassmann 1951 Biot 1956a, b). The most common model whieh considers the microstructure of the sediment and simulates frequency-dependent wave propagation is based on Biot s theory (Biot 1956a, b). It includes Wood s suspension and Gassmann s elastic frame model as low-frequency approximations and combines acoustic and elastic parameters - P- and... 

Derive a low-frequency approximate formula of the earth-return impedance from Equation 1.15 under the condition that hg h,-, hj. 

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