Phenomenological models for estimating and constraining c13 for transversely isotropic hydrocarbon source rocks

Hydrocarbon source rocks can be adequately approximated as transversely isotropic (TI) media. The elastic properties of a TI medium are defined by five stiffness parameters: c11, c33, c44, c66, and c13. The laboratory estimation of c11, c33, c44, and c66 is straightforward, with each of the stiffness parameters determined by a single velocity measurement in an orthogonal direction. For c13, we need the information of c11, c33, c44, and at least one oblique velocity. Consequently, it is usually more difficult to estimate c13 than the other stiffness parameters in the laboratory, and it is even more challenging to acquire it from the field. Therefore, it is important to find the relations between c13 and the other stiffness parameters so that c13 can be estimated from the orthogonal elastic tensor elements c11, c33, c44, and c66 that can be much more economically and reliably acquired. There are phenomenological models for estimating c13 from the other stiffness parameters, but their accuracy is not always satisfactory. We found that c13 has strong correlations with c33 − 2 c44 and c11 − 2 c66, and that c33 − 2 c44 generally underestimates c13 and c11 − 2 c66 generally overestimates c13. The average of c33 − 2 c44 and c11 − 2 c66 can be a much more precise phenomenological model to approximate c13. We also found that c11 − 2 c66 is generally greater than c33 − 2 c44 for hydrocarbon source rocks. Therefore, we evaluated that c13 should lie between c33 − 2 c44 and c11 − 2 c66 for hydrocarbon source rocks.

Calculation method and characteristic analysis of dispersion curves of Rayleigh channel waves in transversely isotropic media

Coal seams have beddings and fissures and are typically anisotropic media. Current channel wave theories are mainly based on isotropic media, and few studies exist on the dispersion characteristics of Rayleigh channel waves in anisotropic models, such as transversely isotropic (TI) media. We chose the generalized reflection-transmission coefficient method to solve the dispersion curves of Rayleigh channel waves in TI media. However, it is difficult to solve the associated dispersion equations of Rayleigh channel waves using this method directly. Therefore, we have extended the generalized reflection-transmission coefficient method and determined the improved accuracy through numerical simulation. We analyzed the dispersion characteristics of Rayleigh channel waves of several typical coal seam models in TI media. The results showed that in the three-layer model, the difference in fundamental-mode dispersion curves between vertically transversely isotropic (VTI) media and isotropic media was relatively small; however, the differences in the higher order dispersion curves were slightly larger. The difference in the Airy phase velocity between horizontal transversely isotropic (HTI) and isotropic media was relatively large. When the coefficient of variation in the qP waves ([Formula: see text]) was greater than 0, the fundamental-mode and first-order phase velocity curves of HTI media exhibited an evident intersection at the head end. In the dirt-band-containing coal seam model, within the 350 and 550 Hz band, the high-frequency velocity of fundamental-mode phase velocity curve of isotropy and HTI media was slightly higher than the low-frequency velocity, which is a notable phenomenon.