## Generating Vs from Vp sonic logs

### David G. Schieck, Robert R. Stewart

The correct identification of primary events on the converted S-wave section in the absence of a VSP or S-wave sonic log may be difficult (Corbin et a1.,1983). Shear wave transit times can be inferred by making lithologic assumptions based on Vp/Vs ratios thus expected (McCormack et al.,1984). However this method is at best qualitative due to the large overlaps in rock lithologies for Vp/Vs ratios as shown by the example in Figure 1 for brine-saturated samples. The accuracy of this ratio may depend on the data quality if based on isochron times or stacking velocities. The errors in this method are demonstrated in Figure 2. Many of the problems in the application of this quantity to exploration may be related to its misinterpretation. A recent redefinition of the Vp/Vs ratio based on Pickett's velocity equation (Pickett, 1963) results in a simple linear equation relating S-wave transit time (ts) to P-wave transit times (tp) (Ikwaukor, 1988).

ts = ( tms - Bs/Bp(tmp)) + Bs/Bp(tp)

Where tmp and tms represent intercept terms; Bs and Bp express the rate of change of effective transit time with porosity as shown in Figure 3. It should also be noted that tms and tmp are relatively constant at all effective stresses while Bs and Bp vary as shown in figure 4. This equation is demonstrated for a series of rock types in figure 5 as a cross plot of tp versus ts. It can be seen that the various rock types can be represented by a linear trend as in the above equation for a given rock type and effective stress. The slopes and intercepts are lithologic indicators.