Academic literature on the topic 'Angular homogeneity'

Broad temperature and angular phasematching bandwidth, as well as high damage threshold and good homogeneity has made KTiOPO4 (KTP) the most frequently used nonlinear crystal for second harmonic generation (SHG) of 1 µm lasers to the green.

ABSTRACT: The evolution of elastic waves in heterogenous fractured rocks is studied based on numerical simulations. We use the discrete fracture network method to represent the distribution of a natural fracture system and employ the displacement discontinuity method to compute the propagation of elastic waves across individual fractures. The variability of matrix Young's modulus is assumed to obey the Weibull distribution, which is characterized by a homogeneity index m. The rock matrix becomes more heterogeneous as m decreases. The results indicate that the dimensionless angular frequency ῶ = ωZ/κ dominates the wavefield evolution of a plane wave travelling through the heterogeneous fractured rock with less heterogeneous materials (m = 10) or high heterogeneous fractures (ῶ ≥ 1). Here, ω, Z, and κ are the angular frequency, seismic impedance, and fracture stiffness, respectively. As the heterogeneity of the rock materials increases (i.e., m ≤ 5) with small ῶ (say 0.1), both the fracture network and rock matrix jointly dominate the wavefield. An asynchronous arrival phenomenon of wave energy occurs and becomes more significant with an increased ῶ and decreased m. The breakthrough time of elastic wave energy has a positive relationship with ῶ but a negative relationship with m. 1. INTRODUCTION Rock masses typically contain numerous natural fractures of variable lengths, locations, and orientations (Bour et al. 2002; Davy et al. 2010; Lei et al. 2017; Afshari Moein et al. 2019; Miranda et al. 2023). The heterogeneous matrix with spatially varying mechanical parameters is also commonly present (Tang et al. 2000; Molz et al. 2004; Lei and Gao 2019; Yan et al. 2023). The resultant heterogeneities arising from natural fractures and rock materials may significantly affect the seismic wave transport in the subsurface (Sato and Fehler 2009; Hamzehpour et al. 2016; Zhu et al. 2020; Ma et al. 2023; Wang et al. 2023), which has attracted considerable attention from various disciplines such as rock mechanics, geophysics, seismology, and earthquake engineering (Khoshhali and Hamzehpour 2015; Fan et al. 2018; Feng et al. 2020; Zhang et al. 2021). Thus, comprehending the evolution of waves in heterogeneous fractured rocks and quantifying the relationship between wavefield characteristics and rock mass properties are fundamentally important for characterizing crustal heterogeneities in many rock engineering applications. However, the current studies mainly focus on the onefold impact of fracture- (Shao and Pyrak-Nolte 2016; Lei and Sornette 2021; Wang et al. 2023) or material-induced (Allaei and Sahimi 2006; Hamzehpour et al. 2016; Ba et al. 2017; Ma et al. 2023) heterogeneity on the wave transport. The competing roles of the fracture network and rock matrix heterogeneity in the wavefield evolution has not been well revealed.