Article
Geochemistry & Geophysics
Lin Li, Guangzhi Zhang, Xinpeng Pan, Jianxin Liu
Summary: Economic gas production from unconventional shale-gas reservoirs requires hydraulic fracturing to optimize development. An azimuthal seismic data-based estimation of sensitive parameters of fractured sweet spots can be useful. A simplified expression for the saturated stiffness tensor in an HTI model and a three-step azimuthal FCs inversion method for estimating effective stress parameter and fracture weaknesses have been proposed.
SURVEYS IN GEOPHYSICS
(2021)
Article
Energy & Fuels
Zhengqian Ma, Xingyao Yin, Zhaoyun Zong
Summary: In the present study, a method based on AVAaz inversion is proposed to estimate fracture parameters in orthorhombic rock. The relationships of weakness parameters with fracture density are demonstrated, and tangential weakness parameters are identified as preferable indicators. An integrated approach combining azimuthal AEI equation and K-L transform is presented to robustly estimate fracture density and orientation.
JOURNAL OF NATURAL GAS SCIENCE AND ENGINEERING
(2022)
Article
Engineering, Mechanical
Qi Hu, Jeong Whan Yoon, Thomas B. Stoughton
Summary: This study focuses on the analytical determination of anisotropic parameters for the Poly6 yield criterion, which is mathematically equivalent to the Yoshida2013 yield function. Two different calibration methods were used to analytically calibrate the Poly6 yield criterion under associated flow rule, showing its ability to describe stress and strain distributions as well as material anisotropic behaviors effectively.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2021)
Article
Astronomy & Astrophysics
Yang-Ting Chien, Rudi Rahn, Solange Schrijnder van Velzen, Ding Yu Shao, Wouter J. Waalewijn, Bin Wu
Summary: This study overcomes intrinsic limitations of previous research by using a recoil-free axis, achieving unprecedented next-to-next-to-leading logarithmic accuracy with small non-perturbative corrections. The research found that the choice of axis makes the observable robust in the presence of a large background, and the azimuthal angle distribution remains minimally changed when determined using only charged particle tracks.
Article
Geochemistry & Geophysics
Yongjian Zeng, Zhaoyun Zong, Xinpeng Pan
Summary: This study reviews rock-physics characterization methods and inversion techniques for orthorhombic (ORT) anisotropic media. It proposes a Bayesian azimuthal seismic inversion method based on anisotropic perturbations and the iteratively reweighted least-squares (IRLS) algorithm to characterize effective elastic properties of ORT anisotropic media. The effectiveness of the proposed method is demonstrated through applications on synthetic and real data sets.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2023)
Article
Geochemistry & Geophysics
Shichang Li, Yang Zhao, Chenggang Xian, Xing Liang, Jiehui Zhang, Qiya Qiao, Lanlan Yan, Yinhao Shen, Huan Cao
Summary: This study proposes an azimuthal anisotropy-driven ant-tracking scheme for small-scale fracture detection. By utilizing wide-azimuth prestack seismic data and a Bayesian framework, the proposed scheme can accurately identify fractures and optimize fracture detection.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2023)
Article
Geochemistry & Geophysics
Lei Huang, Bo Chen, Xinpeng Pan, Hao Liu, Xinyan Li, Zhishun Liu, Jianxin Liu
Summary: In this study, the fracture weaknesses are estimated using linear seismic inversion based on Bayesian theory in different domains. The results show that the time-domain inversion method has the strongest anti-noise ability, the joint time-frequency inversion method balances between improving the seismic inversion resolution and suppressing random noise, and the Laplace-Fourier domain inversion method reduces the dependence of seismic inversion on the initial model and improves the estimation accuracy.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2023)
Article
Geochemistry & Geophysics
Zhaoyun Zong, Lixiang Ji
Summary: Horizontal layered formations with vertical fractures are suitable for estimating fracture properties in shale reservoirs. A novel reflectivity parameterization approach and pragmatic inversion method are proposed to enhance stability in orthotropic media inversion. Using Bayesian inversion and reducing the number of parameters improves accuracy and feasibility in estimating anisotropic parameters.
Article
Geochemistry & Geophysics
Li Lin, Zhang GuangZhi
Summary: Accurate estimation of fracture parameters and Differential Horizontal Stress Ratio (DHSR) is crucial for subsurface fracture prediction and hydraulic fracturing. In this paper, the Extended Elastic Impedance (EEI) is extended from isotropic media to Horizontal Transverse Isotropic (HTI) media, introducing the concept of Extended Azimuthal Elastic Impedance (EAEI). A novel approach using the Fourier Coefficient (FC) of EAEI is proposed to estimate fracture parameters and DHSR. The results of synthetic data example and field data application demonstrate the effectiveness of the proposed approach in guiding the lateral identification of fracture development areas and favorable fracturing areas.
CHINESE JOURNAL OF GEOPHYSICS-CHINESE EDITION
(2022)
Article
Geochemistry & Geophysics
Xinpeng Pan, Zhishun Liu, Pu Wang, Ying Zheng, Lei Li, Xun Wang, Zhenwei Guo, Jianxin Liu
Summary: Horizontally transverse isotropy (HTI) induced by vertical or subvertical aligned fractures is common in unconventional fractured shale oil or gas reservoirs. Understanding fracture properties and in situ stresses is essential for optimizing well planning, hydraulic fracturing, and seismic inversion in these types of reservoirs.
Article
Mathematics
Johnny Rodriguez-Maldonado, Cornelio Posadas-Castillo, Ernesto Zambrano-Serrano
Summary: This paper presents a methodology to obtain the Fourier coefficients and the derivative Fourier coefficients from an input signal. The proposed Taylor-Kalman-Fourier algorithm achieves noise reduction and sidelobe suppression advantages, and a null-flat frequency response. The method also provides a more significant decrement in the inter-harmonic amplitude and an expanded neighborhood of the null-flat frequency compared to the Kalman-Fourier algorithm.
Article
Mathematics
Yuri F. Bilu, Sanoli Gun, Sunil L. Naik
Summary: In this article, the authors investigate a non-Archimedean analogue of a question posed by Atkin and Serre. They derive lower bounds for the largest prime factor of non-zero Fourier coefficients of non-CM normalized cuspidal Hecke eigenforms of even weight k >= 2, level N with integer Fourier coefficients. The authors show that for such a form f and for any real number epsilon > 0, the largest prime factor of the p-th Fourier coefficient a(f) (p) of f satisfies P(a(f) (p)) > (log p)(1/8) (log log p)(3/8-epsilon) for almost all primes p. This improves on previous bounds. They also investigate a number field analogue of a recent result regarding the largest prime factor of a(f) (p(m)) for m >= 2.
MATHEMATISCHE ANNALEN
(2023)
Article
Chemistry, Multidisciplinary
Peitao Wang, Cao Liu, Zhenwu Qi, Zhichao Liu, Meifeng Cai
Summary: This paper proposes a rough discrete fractures network (RDFN) characterization method based on the Fourier transform method. By changing the different Fourier series values, the unified characterization of the complex geometric fracture network is achieved. The study findings suggest that the geometry of the joint network significantly influences the strength and failure modes of jointed rock masses, and the orientation of the fracture sets plays a crucial role in the failure modes of opening.
APPLIED SCIENCES-BASEL
(2022)
Article
Mathematics, Applied
Peter J. Cho, Seokho Jin, Subong Lim
Summary: This paper deals with the first sign change problem of the real Fourier coefficients a(n) of a cusp form f(z) = En>0 a(n)qn with weight k on Gamma 0(N), and provides a bound for arbitrary N. The results of this study are of great significance for solving the sign change problem.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Sindhu Nagaraja, Ulrich Roemer, Hermann G. Matthies, Laura De Lorenzis
Summary: This study investigates variational phase-field formulations to model zigzag crack patterns in cubic materials. The main objectives are to analyze the behavioral aspects predicted by two fourth-order models and guide the calibration of their unknown parameters, as well as to transition from a deterministic to a stochastic model by introducing a material-related random field. Statistical moments of the phase-field variable are estimated using Monte Carlo, randomized quasi-Monte Carlo, and stochastic spectral methods. The stochastic approach holds significant promise in enabling meaningful predictions of anisotropic fracture with phase-field models.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)