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Unsymmetric compressibility matrix to model P-wave attenuation

Abstract

In double permeability models, the first and second porosities are represented by the main pores and fissures, respectively. The constitutional relation in the models suffers from a disadvantage that the compressibility matrix is symmetric which is incompatible with classic poroelasticity. This study aims to improving the double permeability models not only to well predict the measured velocity and attenuation at ultrasonic frequency, but also to yield the classic Gassmann velocity at the low frequency limit. The first porosity in this paper refers to the main pore space, while the second porosity refers to throat (between grains) and fissures. Our improvements in this paper include: (1) the compressibility matrix is unsymmetric for the model to automatically yield Gassmann velocity at the low frequency limit; (2) squirt coefficient is got from dimensional analysis; and (3) the compressibility coefficients are qualitatively constrained based on rock physics. For simplicity, permeabilities of the first and second porosities are set to zero because local squirt between them is dominant in P-wave attenuation. The wavenumber equation yields one fast P-wave and one slow P-wave (which has zero velocity due to vanishing permeabilities). Two core samples (Berea sandstone and Boise sandstone) with the measured data are used for illustration. The results show that the improved model successfully predicts both velocity and the quality factor of ultrasonic P-wave in the two sandstones, being superior to the previous models.

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Acknowledgements

The research was sponsored by National Natural Science Foundation of China under Grant 42064006. The authors would like to thank S.R. Pride and J.G. Berryman for the contribution that their articles in Physical Review in 2003 reminded them of the idea of unsymmetric compressibility matrix. Sincere thanks to Editor, Norbert Péter Szabó and two anonymous reviewers for their positive comments and constructive suggestions.

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Correspondence to Guangquan Li.

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Li, G., Mu, Y. & Xie, C. Unsymmetric compressibility matrix to model P-wave attenuation. Acta Geod Geophys 56, 407–424 (2021). https://doi.org/10.1007/s40328-021-00344-6

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Keywords

  • Double porosity
  • P-wave
  • Squirt
  • Constitutional relation
  • Gassmann velocity