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The Three Elements of Structural Geology Part 1, #41849 (2016).
Terry Engelder
Search and Discovery.com
... the Kronecker delta. Second rank tensor -- In general, if a property, T, relates two vectors P = [p1,p2,p3] and Q = [q1,q2,q3] in such a way...
2016
Recommendations From Error Analysis of Single Well Microseismic Data With Full-Wavefield Moment Tensor Inversion: A Case Study
Juan M. Lorenzo, Trudy L. Watkins, Arash Dahi Taleghani
Unconventional Resources Technology Conference (URTEC)
...e and receiver 0 ๐๐ ๐๐ ๐๐ โ ๐๐ ๐ฟ?? ๐๐๐?? = ๏ฟฝ (Kronecker delta) 1 ๐๐ ๐๐ ๐๐ = ๐๐ ๐๐ = Density of medium ๐๐ = ๐ผ๐ผ = ๐ฝ๐ฝ = ๐?...
2017
A Dynamic Fractal Permeability Model for Heterogeneous Coalbed Reservoir Considering Multiphysics and Flow Regimes
Jianwei Tian, Jishan Liu, Derek Elsworth, Yee-Kwong Leong, Wai Li, Jie Zeng
Unconventional Resources Technology Conference (URTEC)
..., ๏ฎ is Poisson's ratio of coal matrix, ๏ก is Biot coefficient, (1) p is pore pressure, K is bulk modulus๏ผ ๏ค ij is Kronecker delta, ๏ฅ s is the sorption...
2019
Regional Top Seal Capacity Analysis in JS-1 Ridge, Offshore Madura Involving Seal Geometry, Capilary Seal, Hydrofracturing Analysis, and Natural Fracture Modelling
Khadafi, Agus M. Ramdhan, Riszky B. Risyad, Andri Akbar, Ghufron Fauzi
Indonesian Petroleum Association
... = Shear modulus = Lamรฉ constant = Kronecker delta Freeman et al. (2015) demonstrated a strong correlation between observed fracture intensity...
2021
Observations and Modeling of Fiber-Optics Strain on Hydraulic Fracture Height Growth in HFTS-2
Jiehao Wang, Yunhui Tan, Peggy Rijken, Xinghui Liu, Amit Singh, Yan Li
Unconventional Resources Technology Conference (URTEC)
..., ๐ ๐ is the initial pore pressure, E is the elastic modulus, ๐ is the Poissonโs ratio, ๐ถ is a Biotโs constant, and ๐น ๐๐ is the Kronecker delta. The relationship...
2021
Investigation of Parent-Child Well Fracturing Interference in Depleted Shale Oil Reservoirs in a Faulted Region with Strong Tectonic Stresses
Xuyang Guo, Jiawei Li
Unconventional Resources Technology Conference (URTEC)
... for the elastic problem; ๐ผ is the Biot coefficient; ๐บ is the strain tensor; ๐น is the Kronecker delta function. The x stress component at a certain...
2024
High-precision seismic imaging for complex deep structures in the hydrocarbon exploration using a coherent-stacking-based least-squares migration
Jidong Yang, Jianping Huang, Tengfei Lin, Zhenchun Li, and Liang Chen
AAPG Bulletin
... in the half-opening angle domain, which has the following expression in acoustic medium as where f(t) is the source time function, is the Kronecker delta...
2024
Multiscale Seismic Models of Complex Fracture Networks
Richard L. Gibson Jr., Yalchin Efendiev, Judith Chester, Yongchae Cho, Edith Sotelo
Unconventional Resources Technology Conference (URTEC)
... and strain tensor components, and ๐ฟ!" is the Kronecker delta. The body force term is represented by fi, ๐ is mass density, and ๐ and ๐ denote Lamรฉ...
2017
Time-lapse impedance variations using DAS VSP data during CO2 injection at the CMC Newell County Facility, Alberta, Canada
Yichuan Wang, Donald C. Lawton
International Meeting for Applied Geoscience and Energy (IMAGE)
... elements of strain tensor, and ๏คij is the Kronecker symbol (๏คij = 1 for i = j, and ๏คij = 0 for i โ j). From equations 2 and 3, the traction on the flat...
2023
The emergence and impact of scientific machine learning in geophysical exploration
Umair bin Waheed
International Meeting for Applied Geoscience and Energy (IMAGE)
... to solve for higher frequencies in a computationally tractable manner. In a similar vein, Waheed (2022) used Kronecker Neural Networks formed...
2023
Breakthrough in Hydraulic Fracture & Proppant Mapping: Achieving Increased Precision with Lower Cost
Matthew Dawson, Gรผnther Kampfer
Unconventional Resources Technology Conference (URTEC)
... t : : : : : : : : : : : stress tensor Kronecker delta porosity drained bulk modulus undrained bulk modulus bulk modulus of the solid constituent...
2016
Robust multichannel prestack AVA inversion based on elastic L1/2 norm
Nanying Lan
International Meeting for Applied Geoscience and Energy (IMAGE)
... ๏ฉ where B = kron ๏จ I N ๏ดN , D๏ข ๏ฉ , D๏ข ๏ฝ kron ๏จ I 3๏ด3 , D ๏ฉ , kron ๏จ ๏ง,๏ง ๏ฉ is the 1/ 2 Kronecker product operator, ๏ง 1/ 2 is the L1/2 norm...
2023
Prediction and attenuation method of surface-related multiple based on characteristic reflector
Jian Xiang, Huazhong Wang, Chengliang Wu
International Meeting for Applied Geoscience and Energy (IMAGE)
..., representing local data and multiple models, respectively, D and M are the mean of D and M respectively; โ denotes Kronecker product, ๏ง F denotes...
2024
Prestack joint inversion based on multi-components seismic data using analytical solution of 1D elastic wave equation
Weiheng Geng, Wenkai Lu, Jingye Li, Xiaohong Chen, Yinshuo Li, Lei Han, Cao Song
International Meeting for Applied Geoscience and Energy (IMAGE)
... PP ๏ญ G PP (m) 2 2 m 2๏ณ PP ๏ซ ๏ก 2 2๏ณ PS (c) 2 d PS ๏ญ G PS (m) 2 ๏ซ ๏ข 2 ๏ญ Cm1 m ๏ญ ฮผ 2 (5) 2 where Cm represents the Kronecker inner product...
2024
Thermodynamic Behavior of Liquid-Supercritical CO2 Fracturing in Shale
Xiaojiang Li, Gensheng Li, Wei Yu, Haizhu Wang, Kamy Sepehrnoori, Zhiming Chen, He Sun, Shikun Zhang
Unconventional Resources Technology Conference (URTEC)
... , (10) where ฯ ij is stress notation, Pa; ฮป is Lamรฉโs first parameter, GPa; ฮต vol is volumetric strain, dimensionless; ฮด ij is Kronecker symbol; G is Lamรฉ...
2017
Accurate Estimation of Tubular Fluid Flow Friction Loss During Liquid-supercritical CO2 Fracturing and Transportation
Xiaojiang Li, Gensheng Li, Kamy Sepehrnoori, Wei Yu, Haizhu Wang, Qingling Liu, Hongyuan Zhang, Zhiming Chen
Unconventional Resources Technology Conference (URTEC)
... is Kronecker symbol. Because the direct numerical simulation (DNS) of the Navier-Stokes equations for turbulent flow is extremely difficult, which makes...
2017
Geomechanical Analysis of Caprock and Fault Stability in a Full 3D Field Model During CO2 Geological Storage
Enyi Yu, Shilong Liu, Zongyang Li, Dong Zhang, Hui Wu, Yuan Di
Carbon Capture, Utilization and Storage (CCUS)
... ๐ is the effective stress, ๐ผ is the Biotโs coefficient of rock saturated with water, ๐ is the fluid pressure, and ๐น is the Kronecker symbol...
2024
Elastic full-waveform inversion using random space shift
Yuhui Yao, Jizhong Yang, Yuzhu Liu
International Meeting for Applied Geoscience and Energy (IMAGE)
... ๐)(*+ = ๐๐ฟ)( ๐ฟ*+ + ๐(๐ฟ)* ๐ฟ(+ + ๐ฟ)+ ๐ฟ(* ), (2) where ๐ and ๐ are the Lame coefficients, and ๐ฟ)( is the Kronecker function. CEFWI aims to minimize the residuals between observed...
2022
Characterization of Thermal Evolution of Pores and Fluids in Shales Using NMR 2D Measurement
Han Jiang, Hugh Daigle, Boyang Zhang, Xiao Tian
Unconventional Resources Technology Conference (URTEC)
..., and Carlos Torres-Verdรญn. "Multidimensional NMR inversion without Kronecker products: Multilinear inversion." Journal of Magnetic Resonance 269 (2016...
2018
A High-Frequency NMR Investigation of Eagle Ford Shale Cores
Jyoti Swarup Singh Kanwar, Azra Tutuncu, Yuan Yang
Unconventional Resources Technology Conference (URTEC)
...., Ravi, V. R., and Torres-Verdin, C. 2016. Multidimensional NMR Inversion without Kronecker Products: Multilinear Inversion. Journal of Magnetic...
2019
The Three Elements of Structural Geology, #41849 (2017).
Terry Engelder
Search and Discovery.com
... into one equation where the symbol, dij, is called the Kronecker delta. Second rank tensor -- In general, if a property, T, relates two vectors P...
2017
Fracture characterization at multiple scales using borehole images, sonic logs, and walkaround vertical seismic profile
Romain Prioul, Jeroen Jocker
AAPG Bulletin
... with an excess compliance term Sijkl because of the presence of fractures or cracks.withwhere ij is the Kronecker function, ij is a second-rank...
2009
Pore-scale Evaluation of Nuclear Magnetic Resonance Measurements in Organic-Rich Mudrocks Using Numerical Modeling
Saurabh Tandon, Zoya Heidari, Hugh Daigle
Unconventional Resources Technology Conference (URTEC)
... and Discovery Article, 40855, 1-32. Medellรญn, D., Ravi, V. R., and Torres-Verdรญn, C. 2016. Multidimensional NMR inversion without Kronecker products...
2017
Elastic Wave Propagation Mechanisms in High-Temperature Deep Hydrocarbon Reservoirs Exhibiting Three-Phase Fluids
Jidong Gao, Bin Yuan, Wei Zhang, Hongbin Zhang, Caili Dai, Baohua Wang, Yuyang Liu
Unconventional Resources Technology Conference (URTEC)
... derivative for spatial variables; d is the Kronecker operator; ui , u j are solid displacements in different directions, m; U ik , U jk are fluid...
2025
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