Generating Vs from Vp sonic logs. David G. Schieck and Robert R. Stewart INTRODUCTION

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1 Generating Vs from Vp sonic logs David G. Schieck and Robert R. Stewart INTRODUCTION 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.,_ 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 (Ats) to P-wave transit times (Atp) (Ikwaukor, 1988). Ats = ( Arms - Bs/Bp(Atmp)) + Bs/Bp(Atp) Where Atmp and Atms 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 Atmp 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 Atp versus Ats. 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. PROPOSAL It is proposed that the use of Bs/Bp ratios to indicate blocked lithology on the P-wave sonic log may be a viable approach to obtaining S-wave synthetic seismograms. Further, by evaluating the P-SV conversion points in depth, based on the Vp/Vs given by this equation, over a range of source-receiver offsets an accurate P-SV synthetic seismogram may be obtained. 106

2 REFERENCES Corbin, Robert J., 1983, Shear- and compressional-wave surface and downhole tests in Southern Louisiana: presented at the 53rd Annual Meeting, Society of Exploration Geophysics, Las Vegas. Ikwuakor, K.C., 1988, Vp/Vs revisited: Pitfalls and new interpretation techniques: World Oil, Sep. 1988, McCormack, M.d., Dunbar, J.A. and Sharp, W.W., 1984, A case study of su'atigraphicinterpretation using shear and compressional seismic data: Geophysics, 49, Pickett, G.R., 1963, Acoustic character logs and their application in formation evaluation: Journal of Petroleum technology, vol. 15, Rafavich, F.k., Kendall, C.H.St.C. and Todd, T.p., 1984, The relationship between acoustic properties and the petrographic character of carbonate rocks: Geophysics, 49, Limestone 6 --'--Dolomite / ' \ f._-...-'e'-'66 ' -a-c"'_'--v_" 755""--7 " 4 ;_-'_"_ " " O _ v 4,,.'-' 3,4 -._ "_./ // / II" _1.74 / 55 5 #'_." _" "_" _,,.,,5 5 /i An _'"""5,,-,--_ / Vp = Compressional wave velocity Vs = Shear wave velocity 5 _J _.5 Ca Do I I I 1 I 1 I 14,000 15,000 16,000 17,000 18,000 19,000 20,000 vp, ft/sec Figure 1. Plot of Vp/Vs versus compressional wave velocity (Vp) for brine saturated samples (after Rafavich et al., 1984). 107

3 Depth Difference (m) [ I J I /- Difference in Dix "._-- Predicted Depth and 51o _: True Depth (I" E _219 - /\ _= a _ P-Wave Figure 2. Difference in true depth (as measured from VSPs) and predicted depth (calculated from stacking velocities by Dix's equation) for P- and S- wave reflections (after Corbin et al., 1983). 108

4 50 70 o.3d = psi = psi I oeflectave.30=0stress i I T I2 14 I Ccre porosity. % Figure 3. Reciprocal shear wave velocity (Ats) versus core porosity at different effective stresses (Ap) for laboratory measurements on water-saturated dolomites (after Pickett, 1963). Com_'.tess_rlal. avglstope 70 }-- / 80 I 90 F Shear. avg. steppe O0l " _0_ I 1 Effectwe stress = 6,0C3 psi 20' ' I st.lressl= 6._ p?,, ',, i_.[ Ccre porosity. b Figure 4. Reciprocal compressional wave velocity (Atp) and reciprocal shear wave velocity (& ts) versus core porosity for dolomites at effective stress of 6,000 psi (after Pickett, 1963). 109

5 5O & 6O O A d 70 BO A Limestone Dolomile o Clean sands 6, Very limysand 9o I I ,ts. _sec/ft Figure 5. Reciprocal compressional velocity (_tp) versus reciprocal shear velocity (A ts) for laboratory measurements on limestones, dolomites and sands ( after Pickett, 1963). ii0