The Rock Physics Handbook should help! Chapter 2:

Book The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media

As you are interested in Geomechanic, have a look at Mark D. Zoback's book 'Reservoir Geomechanic s'. You may want to try an online couse.

https://www.mooc-list.com/instructor/mark-d-zoback

For understanding rock mechanics and its relation to other physical properties it is imperative that we should understand the physical properties of rocks and their evaluation.

This can be best achieved through the petrophysical assessment of rocks in which various physical parameters like density, conductivity, magnetic characteristics, pore volume etc are in detail covered through various measurements ranging from electrical to nuclear magnetic resonance.

I will recommend the following book published by Elsevier -

Physical Properties of Rocks: Fundamentals and Principles of Petrophysics by Juergen H. Schon

With this parameters determined then you need to covert them to actual rock properties, if you are to do a geomechanical analysis then this is done mainly for the stress field and then other properties such as strength, deformation (i.e. Young modulus and Poisson ratio), other properties such as Biot constant can also be derived. Be aware that this conversion is carried out in a lot of cases using correlations so try to find one that works for you, in other words that you can validate through other routes such as laboratory testing. I hope it helps

Just to add to Juan's comment. Be aware that the dynamic properties derived directly from log data are often very different from the static properties that you would measure from core testing - there are good physical reasons why this should be the case. For example the dynamic Young's modulus derived from log data is often 2 to 3 times greater than the static value in weak sandstones. Petroleum Related Rock Mechanics, Fjaer & Holt, 2nd Edition 2008 or Fundamentals of Rock Mechanics, Jaeger and Cook, 4th Edition, 2007.