Hi Mohamad, I'm afraid that you need a bit more than just a Shear DT log to obtain the compressional one. Shear and compressional velocities are to some extend independent from each other. As you can see for example here http://petrowiki.org/Compressional_and_shear_velocities
in the equations (5) and (7) if we are talking about homogeneous isotropic materials. Could you be a bit more specific about your problem? For example what properties are know about the material waves are propagating in.
Thank you Mr. Simurda for your answer. I want to calculate elastic modulus ( Bulk and Young's and poison ratio modulus) from sonic logs. And I have just Compressional DT log data. So I want to calculate Shear DT log from these, and then calculate elastic modulus.
I believe you need more than just shear DT log. Shear and compressional velocities (logs) are both dependent on more than just one parameter and as I said, are to some extend independent of each other. One way how to see this is from the equations 5,7 from the previous post. Both velocities are functions of density(rho), shear modulus(mu) and compressional velocity is also function of lame's first parameter(lambda). Now say someone would give you only the shear wave velocity and asked you to calculate compressional velocity. Then from the equations just given you are lacking density and lame's first parameter to give the answer.
I agree with the with the previous two gentleman. It is the correct advice and procedure. When you do the calculations, a "rule of thumb" is that the S-wave is about 1.73 times slower than the P-wave. Your answers should be somewhere around in this region for a check. BUT remember it is not exact. The equations above will give you more correct answers.