SEPT. 1] SEIRMir REFRAOTTON AND REFLRf'TTON MEASTTREAIENTS 5 



Layer 2 at zero distance between shot and detector. Similarly, the Rn intercept 

 represents the travel time for a normal incidence reflection from the top of 

 Layer 3. Higher order reflections from these interfaces determine hyperbolic 

 curves which intercept the ordinate at times 'InhijCi and 2n[{hi-\-h2)IC\C2\ 

 and are asymptotic to the first-order curves. The number and strength of 

 reflections received from each shot will depend on absorption, scattering and 

 spreading losses in Layers 1 and 2 and on reflectivity and scattering at the 

 interfaces. In the cases we consider here, the 1-2 interface is the water- 

 sediment boundary and the coefficient of reflectivity for it can be expressed by 

 Rayleigh's equation for plane waves incident on a boundary between two non- 

 rigid compressible media with velocities and densities Ci, pi and ('2, pz and 

 angle of incidence dc 



J. _ (p2C2/piCi)-[l+tan2^,(l-g2^/(7i2)]V2 

 ' (p2C2/piCi) + [l+tan2^i(l-C22/Ci2)]'// ^ f 



This shows that the coefficient of reflectivity is a function of the angle of 

 incidence, di, and of the ratio of acoustic impedances, pC, between the two 

 media. 



In many oceanic areas where Ci<C2 and piCi < p^lCh, K increases from some 

 finite value at di = to unity at ^j = sin~i (C1/C2), where total reflection occurs. 

 In other areas there is evidence that the velocity in the uppermost sediments is 

 lower than in the water, in which case total reflection occurs only at grazing 

 incidence. The reader is referred to Officer (1958) for a treatment of reflectivity 

 which considers various ratios of C\ and C2, and of p\Ci and P2C2. For the 

 deeper interfaces, where rigidity becomes an important factor, other complica- 

 tions are introduced into the consideration of reflectivity, owing to the fact 

 that some of the energy in the incident wave can now go into a refracted 

 compressional wave, as before, and in addition, into reflected and refracted 

 shear waves. Reference is made to Nafe (1957) who investigated reflection and 

 transmission coefficients at an interface between two solids for several values 

 of velocity and density appropriate to crustal layering. 



In the time-distance graph, it is obvious that if the intercepts of Ri and Rn 

 are measured and C'l and C2 are known, the thickness of Layer 1 and of Layer 2 

 can be computed directly. In marine operations, C'l is the speed of sound in 

 the water and can be computed from hydrographic data. In some cases C2 

 can be measured directly by refracted waves, but, particularly in deep ocean 

 areas, the velocity contrast between Layers 1 and 2 is small and it is usually 

 necessary to derive the value of C2 by comparison of the Rn curve with a 

 family of theoretical curves computed for various assumed velocities and 

 thicknesses of Layer 2. 



Fig. 2, taken from Katz and Ewing (1956), shows theoretical curves for the 

 relationship of three different values oi liijhi and five diff'erent values of C'2/Ci 

 to Rin (reflection from sea bottom) and Run — Rin (time difference between 

 bottom and sub-bottom reflection). Observed values of Rin and Rim — Rjn 

 plotted on the same scale will determine a curve similar to one of these. The 



