Propagation characteristics of acoustic waves in a borehole surrounded by a viscoelastic medium with horizontal cracks
水平裂纹粘弹性介质包围的钻孔中声波传播特性
水平亀裂のある粘弾性媒体に囲まれたボアホール内の音波の伝播特性
수평 균열이 있는 점탄성 매질로 둘러싸인 시추공에서 음파의 전파 특성
Características de propagación de ondas acústicas en un pozo rodeado de un medio viscoelástico con grietas horizontales
Caractéristiques de propagation des ondes acoustiques dans un forage entouré d'un milieu viscoélastique à fissures horizontales
Особенности распространения акустических волн в скважине, окруженной вязкоупругой средой с горизонтальными трещинами
Chong-Wang Yue 岳崇旺 ¹, Xiao-Chun Li 李晓春 ², Ji-Shan Xu 徐继山 ³, Bo Feng ¹
¹ School of Geology Engineering and Geomatics, Chang’an University, Xi'an, Shanxi, 710054, China
中国 陕西 西安 长安大学地质工程与测绘学院
² Inner Mongolia coal geological exploration (Group) company with limited liability, Bayannur, China
中国 巴彦淖尔 内蒙古煤炭地质勘查（集团）有限责任公司
³ School of Resources and Geosciences, China University of Mining and Technology, Xuzhou, 221116, China
中国 徐州 中国矿业大学资源与地球科学学院
Because of the viscous properties of rock, a viscoelastic model is closer to the real situation of rock media than an elastic model is. Cracks in the media are common geophysical phenomena. In particular, horizontal cracks are widely developed in the thin interbeds of sedimentary rock. Taking a Cole—Cole viscoelastic medium as the background medium, we compute the frequency-dependent velocities, quality factors, anisotropy coefficients, crack densities, and crack aspect ratios of P- and S-waves based on Hudson’s theory.
We give the velocity-stress staggered finite-difference equations of the elastic wave propagation in a cylindrical coordinate system for a viscoelastic medium with horizontal cracks and numerically simulate acoustic propagation in the cracked medium with different crack densities and aspect ratios.
The simulation results indicate that as the crack density increases outside a borehole the P- and S-wave velocities decrease and their amplitudes increase, in a borehole the P- and S—wave velocities and amplitudes decrease; as the crack aspect ratios increases outside a borehole the P-wave velocities decrease, its amplitudes change little and the S-wave amplitudes and velocities change little, in a borehole the P-wave velocities and amplitudes decrease and the S-wave velocities in a borehole change little, and the S-wave amplitudes decrease.
