{'fraction_non_alphanumeric': 0.020699172033118676, 'fraction_numerical': 0.0, 'mean_word_length': 5.109550561797753, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Bulk modulus for fluid-saturated rocks at intermediate frequencies: modification of squirt flow model proposed by Gurevich et al.


 Squirt flow is an essential cause of wave dispersion and attenuation in saturated rocks. The squirt flow model, proposed by Gurevich et al., has been widely applied to explain the wave dispersion and associated attenuation for saturated rocks at sonic and seismic frequency bands. In this model, the saturated bulk modulus is obtained by taking the partially relaxed frame bulk modulus as the dry frame modulus into Gassmann's formula with the mineral bulk modulus as the matrix bulk modulus. However, because of the weakening effect of soft pores on rock matrix bulk modulus, the model cannot accurately predict the saturated bulk modulus when the soft-pore fraction (the ratio of the soft porosity to total porosity) becomes large. We modified this model following Gurevich et al. by setting a different boundary condition. The modified squirt flow model can obtain correct saturated bulk modulus for large soft-pore fractions in the full range of frequencies, showing excellent consistency with the predictions of Gassmann, Mavko & Jizba (modified) at both low- and high-frequency limits, respectively. Modelling results show that the saturated bulk moduli and their dispersions calculated by the original and modified models exhibit little difference when the soft-pore fraction is small. Under this condition, the original model is as effective and accurate as the modified one. When the soft-pore fraction becomes larger, the differences in the bulk moduli and their dispersions become substantial, suggesting the original model is not applicable any longer. Furthermore, the differences calculated for the intermediate frequency range is even more obvious than other ranges, suggesting that the modified model should be used to calculate the bulk modulus and the dispersion in this frequency range. In summary, the modified squirt flow model can extend the original model's applicable range in terms of soft-pore fraction and has a potential application in rocks having a relatively large amount of soft-pore fraction such as basalts.