Hi Mohamad,

the paper of Castagna et al. (1985) is probably a good starting point if you want to use empirical relations between vp and vs. What other well log data are available to you?

 J. P. Castagna, M. L. Batzle, and R. L. Eastwood (1985). ”Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks.” Relationships between compressional‐wave and shear‐wave velocities in clastic silicate rocks, 50(4), 571-581.

doi: 10.1190/1.1441933

http://library.seg.org/doi/abs/10.1190/1.1441933

http://www.ipt.ntnu.no/pyrex/stash/GPY00571.pdf

Thank you Mr.Fuchs

I have most of conventional logs ( GR, RHOB, NPHI, Resistivity logs).

Well, density might be valuable. Check out the CREWES Research Report 10 (1998) from Potter and Stewart I have found. Equation 6 in this report gives you a relation between density and vs. I don't know if there is a full paper available.

Density predictions using V P and V S sonic logs

Colin C. Potter and Robert R. Stewart

ABSTRACT

We use P-wave, V P , and S-wave, V S , velocity logs to predict density, ρ, values. In particular, Gardner's and Lindseth's empirical relationships are used to estimate the coefficients for P-wave and S-wave data and to investigate the relationship between P-wave and S-wave velocities and bulk densities. The data is from four wells in the Blackfoot field and one in the Chin Coulee area of Alberta. The S-wave velocities give a good approximation to Gardner's relationship and we find that ρ=0.37V S 0.22 . The variance or scatter about the best-fit line for predicting densities for both Gardner's and Lindseth's relationship is better for S-wave than P-wave velocities. We suggest there is a relation between S-wave impedance and density and that S-wave velocity can be used to predict density.

http://www.crewes.org/ForOurSponsors/ResearchReports/abstract.php?file=/ForOurSponsors/ResearchReports/1998/1998-10.pdf

http://www.crewes.org/ForOurSponsors/ResearchReports/reports.php?year=1998

Castagna, J.P., M.L. Batzle, and T.K. Kan, 1993. Rock physics - The link between rock properties and AVO response, in J.P. Castagna and M.M. Backus, editors, Offset‐Dependent Reflectivity - Theory and Practice of AVO Analysis: Investigations in Geophysics No. 8. Society of Exploration Geophysicists, Tulsa. p. 135-171.

Mavko, G., T. Mukerji, and J. Dvorkin, 2003, The rock physics handbook: Tools for seismic analysis of porous media: Cambridge University Press.

http://library.seg.org/doi/abs/10.1190/1.9781560802624.ch2

It is pretty hard to do without actually having some shear wave data to build an empirical correlation. If you have DTC data only, and no DTS at all in any nearby wells, then it is very difficult. Castagna is a good way for when you have DTC and DTS data to build a correlation. Similarly, if you have DTS data and a number of different logs, then you can try building a prediction using neural networks, or genetic algorithms or other methods.

One other reference worth having a look at is:

Lee, M. W., 2010, Predicting S-Wave Velocities for Unconsolidated Sediments at Low Effective Pressure: USGS Scientific Investigations report 2010-5138.