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Abstract The paper examines the proposed approach of using T-matrix model to convert dynamic moduli (Young's modulus and Poisson's ratio) determined by sonic well logging to values equivalent to values of static moduli (called effective moduli). The chosen approach is particularly suitable for rock masses consisting of solid rocks with irregular local cracking. The proposed approach is based on the fact that for intact rock with Young's modulus values on the order of several tens of GPa and strength σ c on the order of several tens of MPa, the values of static and dynamic moduli are equivalent. Any fractures in the rock will cause the elastic behaviour to cease being linear and a difference will appear between the values of static and dynamic moduli. It is possible to approximate this difference using the T-matrix model. The starting point for creating a T-matrix model is a simplified layered geological model of a borehole profile. Added to this are values of static moduli determined by a uniaxial compression test on representative samples of the borehole core. Additional input data for calculating the T-matrix model include porosity determined from well logging measurements, and the presence of cracks as interpreted from an acoustic scan of the borehole wall. The given approach is demonstrated in the experimental measurement of a borehole in Silurian limestone. The procedure was verified by comparing the calculated effective moduli with values of static moduli, measured on control samples prepared from borehole core outside the collection intervals of samples used as input for calculation of the T-matrix model. This comparison showed that for majority of samples there was a decrease in the difference from nearly 40% (dynamic moduli) to under 10% (effective moduli). Highlights • Use of a T-matrix model made it possible to approximate static moduli from dynamic moduli. • The curves calculated by the model are significantly more detailed than the original well logging. • The calculated effective values can be used for calculations instead of the static values. [ABSTRACT FROM AUTHOR]

This article compares static moduli determined using uniaxial tests and dynamic moduli calculated from elastic wave propagation velocities. On the example of limestones, we present the fact that for isotropic and intact rock, static and dynamic moduli correspond to each other over a broad range of frequencies. In damaged rock (cracks, weathering), a difference occurs and static moduli decrease. To include the effect of damage, T-matrix model has been selected. Dynamic moduli, porosity, density changes and information about properties of macroscopic cracks are necessary data for model calculation. These data are provided by other well logging methods such as an acoustic log with full waveform registration, density log, neutron log and acoustic scanner. Using all these data, a T-matrix model can predict static moduli from dynamic moduli. As we are dealing with well log data, we calculated vertical component of the elastic tensor only. This component is represented by Young's modulus E and Poisson's ratio ν. The functionality of the model has been verified on real well logging data and corresponding limestone specimens acquired from borehole core. The differences between values of E modulus, originally up to 20 %, decreased to values similar to differences in intact rock, i.e. the order of the first units of percent. In the case of ν values, demonstrable reduction of dynamic values, approaching static values was achieved, the resulting difference being less than 15 %. [ABSTRACT FROM AUTHOR]