It is a classical result that the elastic moduli of rocks measured with a "static" mechanical press can be substantially smaller than the elastic moduli measured with ultrasonic devices. This result is often incorrectly attributed only to the dispersion effect due to the jump in the frequency band of observation, which is abusively summarized in the terms "static moduli" and "dynamic moduli". Without neglecting the frequency dependence of the mechanical properties, here we show the importance of another fundamental parameter, namely the strain level, to explain this mismatch, which is not commonly appreciated. We propose a theoretical model for describing all these phenomena in arbitrarily anisotropic media. The model is based on the synthesis between viscoelasticy for frequency dependence, and nonlinearity and hysteresis for strain level dependence.


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