Validation of the laboratory measurements at seismic frequencies using the Kramers-Kronig relationship

Abstract

© 2016. American Geophysical Union. All Rights Reserved. We present a simple procedure concerning the application of the Kramers-Kronig relation for the validation of the laboratory measurements of the extensional attenuation and Young's modulus carried out on the solid specimens at seismic frequencies. The local approximation of the Kramers-Kronig relationship was applied to verify the seismic-frequency measurements conducted on four specimens: a viscoelastic polymethyl-methacrylate (PMMA) sample, and two water- and one glycerol-saturated sandstone samples. The experimental tests were performed at various axial (PMMA sample) and confining (sandstone samples) pressures. The measurements conducted on the PMMA sample and saturated sandstones revealed prominent extensional attenuation and significant dispersion of the Young's modulus. Our analysis shows that the quantitative relationship between the extensional attenuation and the Young's modulus is consistent with the causality principle presented by the Kramers-Kronig relationship. No particular physical models implying any constraints on the physical properties of the samples are required for this validation.