Static moduli

Static and dynamic moduli are the same for a homogeneus, elastic material. Thus, if there is a discrepancy between these values, it is probably related to the heterogeneous microstructure of the rock.1

Some of the relationships between static and dynamic moduli are shown below.

Bulk Modulus

Converting the dynamic bulk and Young’s moduli to static moduli (for low-frequency applications), we have

Young's Modulus

Lacy (Sandstone, 1996)

where E_dyn and E_sta are in Mpsi. The parameter 0.0293 has a unit of 1/Mpsi and the parameter 0.4533 is unitless.

This equation was obtained through curve fitting of dynamic test data from an ultrasonic technique covering a range of Young’s modulus values from 60000 psi to 8 Mpsi.2

Lacy (Shale, 1996)

where E_dyn and E_sta are in Mpsi. The parameter 0. 0428 has a unit of 1/Mpsi and the parameter 0. 2334 is unitless.

This equation was obtained through curve fitting of dynamic test data using an ultrasonic technique covering a range of Young’s modulus values from 1 Mpsi to 11 Mpsi.3