As per ASTM D4428M-14 and IS 13372 (Part 2): 1992 (RA2001), the Modulus of shear, bulk, and elasticity can be calculated directly from Vp and Vs. How can I calculate specific moduli such as the tangent shear modulus, rotational shear modulus, modulus reduction, constrained modulus, and secant modulus based on the cross-hole seismic test (based on the velocity of P and S waves & Poisson's ratio)?
Please share your thoughts and literature on the above-stated-problem.
Kaustubh Sane, glad to meet you.
If you are looking for an answer related with seismic elastic characterization and mechanical properties of reservoirs, it can be estimates by static methods founded on laboratory triaxial tests or dynamic one’s estimation using compressional wave, refracted shear wave, and Stoneley wave properties in-situ well logging. If you have Vp, Vs, and density, you can derivate a whole set of rock properties, such as acoustic and shear impedances, shear and bulk modulus, LMR, etc., in order to analyse and estimate for example, the sonic porosity from P-wave slowness and secondary porosity by combining sonic porosity with neutron and density porosity data; of course, as a geophysicist, derivate the time-to-depth correlation for seismic interpretation and characterization. It is not usual to applying secant and tangent modulus of elasticity in reservoir seismic characterization, even acoustic, elastic, AVO. In any case, it would be possible to determine for example:
Secant Modulus of Elasticity: it is a measure of how a material deforms under stress. It is calculated by taking the slope of the line that connects the origin (0,0) on the stress-strain curve to a specific point on the curve. The secant modulus represents the average rigidity of the material over a specific strain range. It is often used to describe the initial rigidity of the material. Knowing the secant modulus helps engineers understand how the material behaves under different loading conditions and can be used to predict the response of concrete structures to various loads.
Tangent Modulus of Elasticity: It is the slope of the stress-strain curve at a specific point. It represents the instantaneous rigidity of the material at that point. - Unlike the secant modulus which provides an average rigidity over a range of strain, the tangent modulus gives the rigidity of the material at a specific point along the stress-strain curve. - The tangent modulus is particularly useful in analysing the behaviour of concrete structures at critical points, such as at the onset of cracking or failure.
I attached a little more explanation related with concrete structural materials.
Best regards, Mario E. Sigismondi
Thanks, Mario Emilio Sigismondi for sharing the information on the topic.
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