Search

In laboratories, core cannot always be cut exactly along the axis of symmetry (normal to the bedding plane), which leads to a minor core cutting rotation (CCR) error. The presence of a small CCR error can give rise to an error in computation of anisotropic parameters, which will result in erroneous P-wave and S-wave velocities (V P, V SV and V SH). In this study, we test the sensitivity of Thomson's anisotropic parameters, epsilon (ε), gamma (γ) and delta (δ), to the CCR error. In the vertical transverse isotropy (VTI) system where no rotation exists, values of ε , γ and δ will not vary with azimuth. Similarly, in VTI the values of V P, V SV and V SH, measured at orientations with respect to the axis of symmetry, will also not vary with azimuth. We modelled and analysed the error generated, in anisotropic parameters and phase velocities, due to rotation error of 5° on VTI ANNIE model data, and the Niobrara Shale core sample measurements. For these two cases, we obtained values of P-wave and S-wave velocities along with anisotropy parameters ε , γ and δ , at 0°, 45° and 90° orientations with respect to the axis of symmetry, before and after a rotation of 5°, for different azimuth directions. This study shows that, when the CCR error exists, ε , γ and δ vary with azimuth. For Niobrara Shale samples, we observed that, among all three Thomsen's parameters δ is the most sensitive parameter to the CCR error; when we varied azimuth, we observed a sign change of δ from positive to negative. For ε and γ , variation in azimuth lead to only slight changes in values without any change of sign. The CCR error affects V P and V s measurements the most at 45° orientation, and the least at 90° orientation. The maximum error occurred at 0° azimuth, whereas the minimum error occurs at 90° azimuth. This analysis suggests that, if core cutting rotation exists, phase velocities should be measured at 90° azimuth for accurate results. In laboratories, core cannot always be cut exactly along the axis of symmetry (normal to the bedding plane), which leads to a minor core cutting rotation error. This paper investigates the sensitivity of Thomson's anisotropic parameters, epsilon (ε), gamma (γ) and delta (δ), to the cutting error. [ABSTRACT FROM AUTHOR]

Noise reduction is important for signal analysis. In this paper, we propose a hybrid denoising method based on thresholding and data-driven signal decomposition. The principle of this method is to reconstruct the signal with previously thresholded intrinsic mode functions (IMFs). Empirical mode decomposition (EMD) based methods decompose a signal into a sum of oscillatory components, while variational mode decomposition (VMD) generates an ensemble of modes with their respective centre frequencies, which enables VMD to further decrease redundant modes and keep less residual noise in the modes. To illustrate its superiority, we compareVMDwithEMDas well as its derivations, such as ensembleEMD(EEMD), complete EEMD (CEEMD), improved CEEMD (ICEEMD) using synthetic signals and field seismic traces. Compared with EMD and its derivations, VMD has a solid mathematical foundation and is less sensitive to noise, while both make it more suitable for non-stationary seismic signal decomposition. The determination of mode number is key for successful denoising. We develop an empirical equation, which is based on the detrended fluctuation analysis (DFA), to adaptively determine the number of IMFs for signal reconstruction. Then, a scaling exponent obtained by DFA is used as a threshold to distinguish random noise and signal between IMFs and the reconstruction residual. The proposed thresholded VMD denoising method shows excellent performance on both synthetic and field data applications. [ABSTRACT FROM AUTHOR]