It is important to study the fracture mechanism of fractured rocks. Uniaxial compression tests and discrete element numerical simulations were conducted on sandstone specimens with fixed dip angles and parallel fractures. With the help of acoustic emission detection technology, the effects of different fracture spacings and number of fractures on the mechanical properties, fracture mechanism and acoustic emission full dynamic time-varying evolution of sandstone were investigated. The results show that: there is an obvious correlation between the number of fractures and elastic modulus and no obvious correlation with strength. There is no clear relationship between fracture spacing, elastic modulus, and peak strength. The fracture spacing determines the basic type of crack aggregation, and the number of cracks mainly affects the diversity of crack aggregation types. Spalling damage mainly occurs at the middle position of through-bridge shear cracks, and plate crack damage mainly occurs at the position on both sides of the specimen. Through-bridge shear cracks are a common type of crack in specimens containing parallel fractures, which influence the initiation location of the main shear crack and the damage mechanism of the specimen, and affect the overall strength of the specimen by changing the local narrowest width of the "column" structure. There is a mutual excitation between the tension and shear cracks, and each sudden increase in the shear-tension crack ratio corresponds to a macroscopic rupture of the specimen. The multifractal parameters of acoustic emission can provide a more detailed description of signal complexity. The abrupt changes in the time-varying multifractal parameters Deltaalpha and Deltaf(alpha) can serve as short-range prediction indicators for disaster occurrences. © 2025. The Author(s).

为提高微震源定位精度,构建精细化微震波速度模型,基于层状均匀介质假设,定义震波等效传播路径和等效波速,分段构建采空塌陷区“三带”波速模型.开展室内相似材料模型试验,实测人工震源微震信号,依据波速模型计算震波传播等效波速,分析

The analytical representation and underlying mechanism of displacement fields induced by point source are of notable engineering significance and value. The displacement field generated by a point source consists of an irrotational longitudinal wave induced by a dilatational source and a rotational shear wave excited by a torsional source. The D'Alembert solution accounting for geometric attenuation is applied to the formulation of spherical longitudinal waves from point sources and 2-dimensional (2D) transverse waves from point sources. Moreover, the relationship between this solution and the governing differential equation for 2D point-source shear waves is elucidated. By employing the stream function for 2D shear waves and the potential function for spherical longitudinal waves, both derived from a D'Alembert-type solution, and integrating relevant results from fluid mechanics, the complex potentials corresponding to displacement flux sources and displacement vortex sources are obtained. Based on the commonality between point-source vector elastic wave fields and other point-source vector fields encountered in engineering, the displacement field generated by point source is expressed-according to Helmholtz's theorem-as a superposition of an irrotational field and a solenoidal field. The irrotational field is excited by a displacement flux source, while the solenoidal field is generated by a displacement vortex source. The steady-state results obtained from the finite element method are consistent with those derived from the analytical solution, validating the correctness of the theoretical derivation. Consequently, the analytical representation and physical mechanism of the displacement field induced by the point source are established.

微震定位方法是微震监测技术的重要组成部分,其关键是定位震源位置。利用空间网格划分并计算网格交点目标函数值,对微震定位目标函数二维及三维空间分布进行了分析,并据此获取了目标函数连续且极小值唯一、单轴收敛范围逐步减小、各轴

Seismic source location is a classic inverse problem in seismology. In mathematical physics, inverse problems have multiple natural solutions. The objective of this study was to develop a generic theory and method of seeking the true solution from multiple solutions for the location of a coal mine seismic source in an idealized velocity structure model of a coal mine with a small scale and complex geological environment. Starting from the simplest velocity structure model, the complexity of the model gradually increased, until it approached the real velocity structure model, i.e., the multilayered horizontal and inclined velocity structure model, in order to find a generic method for solving the multi-solution inverse problem of coal mine seismic source location. Specifically, the wavefront distribution equation in a two-layer horizontal medium was derived and then expanded to any multi-layer horizontal medium. Based on this equation, a positive definite nonlinear equation system was established from the perspective of any observation system. The equation system contained four unknown variables of the spatiotemporal position of the seismic source. To determine the spatiotemporal parameters of the seismic source, nonlinear equations for four stations were required. To solve the nonlinear equation system, an initial iteration value was determined. In order to reduce the difficulty of determining the initial iteration value, the variable substitution method was used to reduce the number of location parameters. By rotating the original geodetic coordinate system of the station to be parallel and orthogonal to the medium interface, the wavefront method was extended to inclined medium. In conclusion, in this study, the problem of coal mine seismic source location in a multi-layer horizontal or inclined medium was effectively solved. The method proposed in this study provides a reference for solving the true solution from multiple solutions for the location of a coal mine seismic source in small-scale coal mines with complex geological environments. © The Author(s) 2024.

The geological structure of the goaf overlying rock is complex, a consequence of coal mining that has modified the original stratified structure of the sedimentary strata. To enhance the accuracy of microseismic source location in such intricate geological formations, a wave velocity model for the "three zones" goaf was constructed based on natural divisions within the strata using Snell's law and assuming a homogeneous medium. The model took into account the effects of rock deformation and fracture development, enabling the derivation of formulas for microseismic wave propagation path and travel time calculation. Additionally, the concept of equivalent wave velocity was defined. An indoor simulation test using similar materials was conducted to establish a geological model of the goaf. By comparing the errors between the theoretical and measured values of equivalent wave velocity, assessing the locating effects before and after implementing the wave velocity model of the goaf, and verifying the feasibility of the model, it was demonstrated that establishing a wave velocity model based on the characteristics of the strata structure was crucial for improving the accuracy of the microseismic source location. Notably, as the propagation path of microseismic waves in the goaf increased, the equivalent wave velocity decreased. The wave velocity structure in the goaf exhibited nonuniformity, with the relative error between the theoretical and measured values of equivalent wave velocity being limited to 10 %. The incorporation of this established wave velocity model into the location method resulted in a substantial 58.57 % increase in locating accuracy. © 2024

因存在断层和岩层间层理面等不连续界面，天然岩体并非均匀连续介质，声发射信号经过断层和层理面时传播规律必然会发生改变，因此研究断层中声发射信号的传播规律成为岩石力学的重点课题之一。基于惠更斯原理对含断层的非均匀介质条件下的波面方程进行推导，并通过室内相似模拟模型试验制作45°、60°、75°以及其他类型断层试件，结合超声波测速仪和DS5-16B全信息声发射信号分析仪对跨断层的声发射信号进行监测和记录，采用非线性拟合和Matlab软件数值计算的方式，研究不同倾角的断层、层理面数量对声发射信号传播速度以及信号特征的影响。研究结果表明：声发射信号的传播速度随着断层倾角的增大逐渐增加，传播速度与断层倾角呈正相关，断层倾角越大信号传播速度越快，信号穿过断层后传播速度会发生衰减，断层倾角越大速度衰减比例越小，层理面会使传播速度发生衰减，单个层理面对速度的影响较小，两个层理面对速度的影响较大；断层会使信号的最大幅值减小，主频率降低，频率区间向低频方向移动，断层倾角越大，最大幅值、主频率、频率区间越大。一个层理面对信号的影响较小，与无层理面的信号时频特征基本相同，两个层理面对信号的影响较大，会使信号的最大幅值、主频、频率区间有较大幅度的减小；断层的存在会导致声发射信号的瞬时能量发生巨大衰减，倾角越小衰减越为严重。研究成果可为射线理论下波速模型的建立提供理论依据。

In order to investigate the energy attenuation of microseismic signal in the "three-zone" structure of goaf, a similar model test of the overburden of goaf is proposed to collect the artificially excited microseismic signals propagated through the structure of goaf. The relationship between the central frequency and energy of the modal components of the microseismic signal via variational mode decomposition (VMD) is analysed. The optimum number of modal components of the microseismic signal is determined according to the central frequency method, and the energy of each component is calculated for the under-decomposition, optimum decomposition and over-decomposition states of the microseismic signal. The relationship between the energy of each modal component and the central frequency distribution is fitted for the optimum decomposition state of the signal under each source, and the energy of each modal component is analysed for different propagation states of the microseismic signal in the "three-zone" structure. The effect of each structural layer on the energy of the microseismic signal under different propagation states of the "three-zone" structure is analyzed. The results of the study show that: (1) The number of effective modes of the artificially excited vibration signal in the VMD process ranges from 6 to 11, and the energy of the microseismic signal varies significantly with the number of modes. (2) The power function can be used to fit the modal energy versus frequency of the microseismic signal, and the fitting state is good (the coefficient of determination is greater than 0.9), in which the low-frequency modal component contains nearly 50% of the total energy of the signal. The Gaussian function can be used to fit the distribution performance of the energy of each component of the source in the frequency domain, and the fitting state is good and shows the Gaussian single-peak characteristic. (3) The microseismic signal traverses through the "three-zone" structure of goaf, and the energy of the microseismic signal decreases as the distance between the source location and the sensor increases. The collapse zone has a significant attenuating effect on the signal compared to the fracture zone and the bending zone. The energy of the microseismic signal does not change as it passes through the "three-zone" structure of goaf. © 2024 Biodiversity Research Center Academia Sinica. All rights reserved.

为构建煤矿小尺度区域微震波传播速度模型，提高矿井含采空区复杂地质结构内微震源定位精度。依据矿山采空区覆岩“三带”岩层变形、层面离层、层内断裂和裂隙发育以及岩体扩容等特征，构建圆弧层面波速模型，分区描述采空区覆岩波速结构。并提出采用考虑岩层变形特征的微震波绕射传播路径增量和基于时间平均方程的裂隙岩层波速折减进行波速模型修正。基于层状均匀介质假设和斯奈尔定律，推导微震波传播路径和走时计算公式，并计算各传播方向上的异向等效波速。基于到时理论定位原理，选择以实测到时差与理论走时差之差构建震源求解目标函数，采用模式搜索算法进行震源位置求解。形成了基于采空区覆岩异向波速模型的微震源定位方法。通过三维算例和煤矿地面微震监测定位应用，验证了所提方法的可行性与定位效果。研究表明：（1）由于煤矿地质环境中采空区遍布和微震波经由采空区传播的必然性，针对煤矿含采空区复杂地层结构特征，建立相应的异向波速模型，是提高矿山环境下微震源定位精度的关键；（2）采空区覆岩波速模型充分考虑了岩层形态、离层、断裂、裂隙发育和岩体扩容等对微震波传播路径和等效波速的影响，并通过定量确定微震波传播绕射路径增量和岩层波速折减，宏观表现出采空区地层结构的典型波速异向特征；（3）针对分层介质下的震源定位，在三维算例中选用异向等效波速模型的定位方法相较于全局平均波速模型，定位结果的平均误差由9.7558 m降至0.4186 m，有效降低了定位误差；（4）以矿井大能量微震事件的井下微震定位结果为参照，在现场地面微震监测中应用采空区覆岩波速模型，得出该模型定位结果较待定波速而言更接近现场调查结果中确定的煤岩体破裂影响范围。综上，对于依赖波速模型的定位方法，根据地质结构特征建立相应的异向波速模型是高效开展微震监测，提高微震源定位精度的突破点之一。