An inversion for Biot parameters in water-saturated sand

Abstract

The discrepancy between acoustic measurements and the theoretical predictions was investigated in the case of water-saturated sand. Two theoretical models were considered: visco-elastic and poro-elastic solid models. The visco-elastic solid model could not be reconciled with reflection loss measurements and was rejected. The poro-elastic solid model using Biot's theory [J. Acoust. Soc. Am. 103, 2723-2729 (1998)] as formulated by Stoll [J. Acoust. Soc. Am. 70, 149-156 (1981)] was an improvement. It was investigated using an inversion process. Operative values of grain bulk modulus and the frame bulk and shear moduli of water-saturated sand were inverted from simple measurements--reflection loss, compressional and shear wave speeds and attenuations. Although the inversion process is nonlinear, in practice, it is well behaved and converges quite rapidly to a unique solution. The issue of imprecisely known parameter values was handled in a probabilistic manner. The inversion results, using published laboratory and in situ measurements, showed that further improvement was needed. In an attempt to find a solution, two possible hypotheses are put forward. (1) Composite materials: The possibility that the frame may contain fluid and that the pore fluid may contain loose grains. (2) Independent coefficient of fluid content: The possibility that porosity may change with pore fluid pressure. Inversion results were encouraging for both hypotheses. It is difficult to say which of the two hypotheses is superior, and the two hypotheses are not mutually exclusive. The new hypotheses represent a significant advance because they have the potential to resolve the remaining discrepancies. At this stage, alternative interpretations of the data are possible.