A novel inversion method for the laboratory determination of Thomsen's δ anisotropy parameter on cylindrical rock specimens from ultrasonic data has been recently reported in the literature. We further assessed this method through a direct comparison of the results of the traditional method (involving a single off-axis P-wave velocity measurement at 45°) and the new method (involving 65 P-wave velocity measurements at several angles to the symmetry axis). We prepared and characterized two vertical shale specimens from the same preserved vertical core to assess their similarity in terms of structure, mineralogy, porosity, and density. The shale was assumed to be transversely isotropic in view of the observed (horizontal) bedding. We subjected both specimens to the same brine saturation and effective stress state. Using the two methods, we obtained similar results for Thomsen's α (vertical P-wave) and ε (P-wave anisotropy) parameters. However, a significant discrepancy was observed for Thomsen's δ parameter: We obtained results of 0.13 using the new method and 0.39 using the traditional method. As a result of the overdetermined nature of the P-wave velocity measurements used in the new method, we believe that the corresponding δ value is more reliable. Also, the value derived with the new testing method seems to match more closely the reported field data.
SUMMARY This paper reports a new approach for the estimation of Thomsen anisotropy parameters and symmetry axis orientation from ultrasonic P‐wave traveltime measurements on transversely isotropic shale samples of arbitrary geometry. This approach can be used for core samples cut in any direction with respect to the bedding plane, because no a priori assumption regarding the symmetry axis orientation is made. This orientation is rather part of the solution of the inverse problem together with the anisotropy parameters themselves. Very fast simulated reannealing is used to search for the best possible estimate of the model parameters. The methodology is applied to spherical and cylindrical anisotropic shale samples.
A B S T R A C TThe aim of this paper is to understand the seismic anisotropy of the overburden shale in an oilfield in the North West Shelf of Western Australia. To this end, we first find the orientation of the symmetry axis of a spherical shale sample from measurements of ultrasonic P-wave velocities in 132 directions at the reservoir pressure. After transforming the data to the symmetry axis coordinates, we find Thomsen's anisotropy parameters δ and ε using these measurements and measurements of the shear-wave velocity along the symmetry axis from a well log. To find these anisotropy parameters, we use a very fast simulated re-annealing algorithm with an objective function that contains only the measured ray velocities, their numerical derivatives and the unknown elasticity parameters. The results show strong elliptical anisotropy in the overburden shale. This approach produces smaller uncertainty of Thomsen parameter δ than more direct approaches.
Our aim is to understand the stress-dependent seismic anisotropy of the overburden shale in an oil field in the North West Shelf of Western Australia. We analyze data from measurements of ultrasonic P-wave velocities in 132 directions for confining pressures of 0.1-400 MPa on a spherical shale sample. First, we find the orientation of the symmetry axis, assuming that the sample is transversely isotropic, and then transform the ray velocities to the symmetry axis coordinates. We use two parameterizations of the phase velocity; one, in terms of the Thomsen anisotropy parameters a, b, e, d as the main approach, and the other in terms of a, b, g, d. We invert the ray velocities to estimate the anisotropy parameters a, e, d, and g using a very fast simulated reannealing algorithm. Both approaches result in the same estimation for the anisotropy parameters but with different uncertainties. The main approach is robust but produces higher uncertainties, in particular for g, whereas the alternative approach is unstable but gives lower uncertainties. These approaches are used to find the anisotropy parameters for the different confining pressures. The dependency of P-wave velocity, a, on pressure has exponential and linear components, which can be contributed to the compliant and stiff porosities. The exponential dependence at lower pressures up to 100 MPa corresponds to the closure of compliant pores and microcracks, whereas the linear dependence at higher pressures corresponds to contraction of the stiff pores. The anisotropy parameters e and d are quite large at lower pressures but decrease exponentially with pressure. For lower pressures up to 10 MPa, d always is larger than e; this trend is reversed for higher pressures. Despite the hydrostatic pressure, the symmetry axis orientation changes noticeably, in particular at lower pressures.
In this paper we present a new approach to the estimation of the Thomsen anisotropy parameters and symmetry axis coordinates from the P-wave traveltime measurements on cylindrical shale samples. Using the tomography-style array of transducers, we measure the ultrasonic P-wave ray velocities to estimate the Thomsen anisotropy parameters for a transversely isotropic shale sample. This approach can be used for core samples cut in any direction with regard to the bedding plane, since we make no assumption about the symmetry axis directions and will estimate it simultaneously with the anisotropy parameters. We use the very fast simulated re-annealing to search for the best possible estimate of the model parameters. The methodology was applied to a synthetic model and an anisotropic shale sample.
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