Deep mining operations in faulted rock masses are increasingly threatened by fault instability driven by mining-induced stress perturbations. We combine high-resolution microseismic monitoring with three-dimensional numerical modeling to characterize fault slip and subsidence mechanisms at the 8302 working face of the Xinjulong coal mine in China. Full moment tensor inversions of ten representative high-energy seismic (HES) events reveal shear-dominated ruptures around pre-existing faults and tensile-dominated fracturing within the overlying strata. Numerical simulations reproduce the observed spatiotemporal clustering of HES events in areas of elevated and evolving differential stress, delineating progressive fault reactivation during mining. Analysis of asymmetric fault displacements shows subsidence of both the hanging wall and footwall, with greater downward motion on the footwall above the mined-out area. This pattern is atypical for reverse-fault slip and is attributed to stress redistribution following the mining-induced removal of kinematic constraints. Based on these observations, we discuss a targeted blasting strategy to relieve stress in the rock mass and reduce both seismic energy release and event frequency, thereby mitigating the fault-instability hazard. This integrated observational and numerical framework clarifies the interplay among stress redistribution, fault slip, and induced seismicity in deep mining environments and provides a basis for physics-based seismic risk management and hazard reduction.

Phase and group velocities along specific ray directions are needed for qP, qSV and SH-wave traveltime computation in tilted transversely isotropic (TTI) media. The phase and group velocities are not unique functions of the ray direction, but of the slowness direction, so efficient computation of the slowness direction from a given ray direction becomes necessary. The eigenvalue method and the generalized method have been proposed to facilitate the computation by formulating governing equations for the phase angle, which requires efficient root-finding algorithms. In this work, we address this problem in 2-D TTI media by applying Newton's method. For the eigenvalue method, a set of two nonlinear equations for the qP and qSV waves and one nonlinear equation for the SH wave must be solved. For the generalized method, only one nonlinear equation of the phase angle needs to be solved for the qP, qSV and SH waves. Numerical experiments, including phase and group velocity computation and their application in first-arrival traveltime calculation, are performed to verify the effectiveness of the proposed methods.

In this study, we assess the state of the stress field in eastern Türkiye and discuss whether the stress field in the region has changed over time. To assess the governing stress field, we applied stress tensor inversion techniques using focal mechanisms from earthquake catalogs. The focal mechanisms were grouped into subregions based on spatial and temporal factors. We employed a damped regional-scale stress tensor inversion algorithm and an iterative joint inversion technique to determine the stress field for eastern Türkiye. Near the North Anatolian Fault Zone, the stress field exhibits strike-slip faulting with a slight counterclockwise rotation of the principal stress axes. From 1983 to 2016, reverse faulting was observed near Erzincan, transitioning to strike-slip faulting after 2017 due to changes in Smid and Smin axes. Near the East Anatolian Fault Zone, the stress field remains strike-slip, but after two major earthquakes in 2023, normal faulting emerged in areas with longitude less than 37 ^∘E , likely due to stress perturbations. In the easternmost region near the Zagros Fold Belt, reverse faulting dominates the north and south, while strike-slip faulting characterizes the central part. High R-values suggest frequent interchange of Smid and Smin axes. The damped inversion method effectively smoothens stress axis transitions in data-sparse regions but introduces errors in isolated areas, where the iterative method proves more reliable. These findings illuminate eastern Türkiye’s evolving tectonic stress field.

Abstract We investigate the influence of fault roughness on physical damage prior to large laboratory rock failure and the evolution of the local stress field surrounding the fault zone as macroscopic shear slip approaches. To achieve this, we analyze acoustic emission (AE) data from displacement‐driven rock friction experiments conducted on porous sandstone samples containing either a saw‐cut (smooth) or a rough fault. Using high‐quality AE‐derived focal mechanisms and two stress tensor inversion approaches–one considering double‐couple (DC) components and the other one incorporating non‐DC components, we examine the temporal evolution of the local stress tensor for both smooth and rough faults. Our results show no significant differences between the two stress inversion methods, indicating that non‐DC components have no significant influence on the resulting stress tensors in our experiments. As macroscopic shear slip approaches, the principal stress axes surrounding the fault zone gradually rotate, regardless of the initial fault roughness. The observed evolution of stress tensors correlates with the evolving partitioning between volumetric and shear deformation, as derived from moment tensor inversion of AEs. Compared to the smooth fault, the rough fault exhibits higher local stress heterogeneity and more erratic fluctuations in AE source‐related parameters as loading progresses.

The 2021 Fagradalsfjall eruption on Iceland's Reykjanes Peninsula was preceded by an intense seismic swarm, offering an opportunity to investigate fluid dynamics and faulting processes at divergent plate boundary. Here we analysed 1306 full moment tensors of pre-eruption dike-related earthquakes and identified three faulting regimes: strike-slip, normal and reverse, driven by variations in vertical stress and controlled by fluid dynamics and crustal heterogeneity. Systematic volumetric components of these earthquakes revealed both tensile opening and compressive closing of cracks. Notably, crack closing dominated shallow, fractured crust, associated with surface subsidence above the dike, while crack opening occurred within the impermeable crust, suggesting overpressured fluids trapped at structural barriers. These variations highlight the role of fluid-rock interactions and anisotropic permeability in driving fault behaviour. Our results demonstrate that non-double-couple components of earthquakes are sensitive indicators of evolving stress and fluid migration. They provide insights into the mechanics of seismo-volcanic unrest at the slow-spreading rift.

We present an inversion for elastic anisotropy parameters of rocks using a large set of accurate moment tensors (MTs) derived from acoustic emissions (AEs). This method is demonstrated using AEs observed in a sandstone sample during a semi-circular bend test. We inverted 539 highly accurate MTs of AEs and retrieved both the orientation of anisotropy axes and elastic parameters defining the orthorhombic anisotropy within the fracture zone that developed in the sample during the test. The anisotropy results from the presence of aligned cracks in the fracture zone and the background transverse isotropy of the sandstone specimen. The observed anisotropy is moderate, with strengths of 18%, 14% and 21% for the P, S1 and S2 waves, respectively. We show that neglecting this anisotropy introduces a significant bias when estimating crack orientation and tensility from MTs. When anisotropy effects are accounted for by recalculating moment tensors into source tensors, the scatter in crack orientations is reduced, and the slope angle, which characterizes crack tensility, is systematically increased by approximately 10°. Our results confirm that the presented inversion method is a powerful and robust tool, capable of analyzing anisotropy in rocks, even in cases of low anisotropy symmetry.

We investigate the behaviour of photons in Riemann spacetime, focusing on how their velocity and energy are affected by cosmic expansion. Specifically, we examine the differences in energy conservation depending on the cosmological model. Our findings indicate that photons exhibit fundamentally different behaviour based on the chosen metric. In the standard ΛCDM model, which relies on the Friedmann–Lemaître–Robertson–Walker (FLRW) metric, the energy conservation law for redshifted photons is violated. However, in a cosmological model based on the conformal cosmology (CC) metric, this law remains valid. The CC metric offers additional advantages, as it accurately reproduces the cosmological redshift, cosmic time dilation observed in Type Ia supernova light curves, and flat galaxy rotation curves without requiring the introduction of dark matter. These findings underscore the potential significance of the CC metric in cosmological applications.

Large number of accurate focal mechanisms of small and microearthquakes are crucial for investigating regional stress field variations induced by hydraulic fracturing. Based on the seismic records from a dense network for monitoring seismicity in a shale gas extraction and production field in southern Sichuan, we use both waveform inversion and P-wave amplitude inversion to determine the focal mechanisms of five moderate and small earthquakes (5 > M-L > 3). The results obtained by two different methods are compared, and the focal mechanism solutions obtained by waveform inversion are used as references and to compare with the synthetic amplitudes. This enables us to obtain the amplitude calibration factors calculated from the ratio between the theoretical to observed amplitudes of the initial P waves. We apply this approach to inverting for the focal mechanisms of small and microearthquakes (M-L <= 3) using the calibrated P-wave amplitudes and yield reliable focal mechanism solutions of more earthquakes. Our study provides an effective tool for determining focal mechanism solutions of small and microearthquakes, which contributes to the understanding of seismicity induced by hydraulic fracturing and to the mitigation of related seismic hazards.

Tonga is a part of Tonga-Kermadec, the 2,550 km long subduction system in SW Pacific. It represents a convergent plate boundary and the outcome of the Pacific plate submerging underneath the Australian plate. The Tonga slab subducts steeply into the mantle and is the fastest converging and the most seismically active deep subduction system in the world. In the mantle transition zone, especially at depths greater than 500 km, the geometry of the slab becomes complex, forming separated slab segments. Moreover, it undergoes strong deformation and sharp bending in the north, which results in significantly different course of the southern and northern Tonga slab.We focused on the mantle transition zone in the southern part of Tonga (south of latitude 22°S). We performed stress analysis by inverting focal mechanisms of deep earthquakes available in the Global Centroid Moment Tensor catalog. We focused on depths ranging from 400 to 680 km, where seismic activity forms two subparallel bands of events, in the west and east. We revealed two distinct stress regimes that characterize this deep Tonga double seismic zone and distinguish two slab segments. The stress orientation in the eastern slab segment matches the down-dip compressional stress regime of the subducting slab. However, the stress orientation of the western slab segment is different, with the maximum compression in the vertical direction. This suggests that the western slab segment is no longer connected to the subducting slab. Such findings are also supported by the horizontal westward detachment of the western slab segment at 520 km depth and by substantially different fault orientations in both slab segments. This points not only to the retention of the southern Tonga slab in the mantle transition zone but also to its detachment at the base of the upper mantle with a remnant slab no longer connected to the younger actively subducting slab.

The cosmic time dilation observed in Type Ia supernova light curves suggests that the passage of cosmic time varies throughout the evolution of the Universe. This observation implies that the rate of proper time is not constant, as assumed in the standard FLRW metric, but instead is time-dependent. Consequently, the commonly used FLRW metric should be replaced by a more general framework, known as the Conformal Cosmology (CC) metric, to properly account for cosmic time dilation. The CC metric incorporates both spatial expansion and time dilation during cosmic evolution. As a result, it is necessary to distinguish between comoving and proper (physical) time, similar to the distinction made between comoving and proper distances. In addition to successfully explaining cosmic time dilation, the CC metric offers several further advantages: (1) it preserves Lorentz invariance, (2) it maintains the form of Maxwell’s equations as in Minkowski spacetime, (3) it eliminates the need for dark matter and dark energy in the Friedmann equations, and (4) it successfully predicts the expansion and morphology of spiral galaxies in agreement with observations.

Tonga is a convergent plate boundary between the Pacific and Australian plates and is the fastest and the most seismically active deep subduction system in the world. We focused on southern Tonga (south of latitude 22 degrees S) and the mantle transition zone (depths of 410-670 km), where seismic activity forms two subparallel bands of events in the east and west. We performed stress analysis by inverting focal mechanisms of earthquakes available in the Global Centroid Moment Tensor catalog and revealed two distinct stress regimes in the slab. While the stress orientation in the eastern slab segment conforms to the down-dip compressional stress along the entire slab, the stress orientation in the western slab segment is different, having the maximum compression in the vertical direction. This suggests that the western segment can represent a stagnant slab with flattening and bending, as proposed by modeling studies. Its connection with the younger actively subducting slab is supported by the horizontal westward shift at 520 km depth. The stress analysis also indicates substantially different fault orientations in both segments. In the actively dipping slab, the majority of activated faults are predominantly sub-horizontal. However, they are significantly inclined from vertical in the stagnant slab segment. A higher scatter in fault orientations in the stagnant slab suggests deformation, fragmentation and rheological complexity resulting from bending and flattening. Tonga is a part of Tonga-Kermadec, the 2,550-km long subduction system in SW Pacific. It represents a convergent plate boundary between the Pacific and Australian plates. It is the fastest converging and the most seismically active deep subduction in the world. In the mantle transition zone, especially at depths greater than 500 km, the geometry of the slab becomes complex, forming separated slab segments. We performed stress analysis in the mantle transition zone (depths 410-670 km) with a focus on southern Tonga (south of latitude 22 degrees S) where seismicity forms two subparallel bands of events in the east and west. We inverted publicly available data, focal mechanisms of earthquakes from the Global Centroid Moment Tensor catalog, and revealed two distinct stress regimes. While the stress orientation in the eastern segment matches the down-dip compression of the subducting slab, the stress orientation of the western segment is different with the maximum compression in the vertical direction. This suggests that the western segment represents a stagnant slab with flattening and bending. Such findings are supported by the horizontal westward shift at 520 km depth and by substantially different fault orientations in both segments. We performed stress analysis in southern Tonga mantle transition zone from focal mechanisms of earthquakes listed in Global Centroid Moment Tensor catalog We revealed two distinct stress regimes: down-dip compression matching subducting slab in the east and vertical compression in the west Western segment suggests a stagnant slab with flattening and bending supported by horizontal shift and different fault orientations

In this paper, we study the tectonic stress around the South Caspian Basin (SCB), which includes the Kopeh Dagh, Alborz, Talesh, eastern Greater Caucasus mountain belts, the Apsheron sill, and the Balkhan-Ashkabad fault zone. We apply the stress inversion to focal mechanisms of 410 mainshocks that have occurred over the last 69 years. These mechanisms indicate that the surrounding fault zones of the SCB exhibit diverse types of faulting, ranging from thrust to strike-slip, normal, and their combinations. The results of the stress inversion align with the kinematics of the major fault zones bounding the SCB and emphasize the spatial heterogeneity of the stress field in this region. The region is predominantly under compression, but transpressive and strike-slip regimes are also present. This highlights the role of obliquely oriented basement faults with respect to the maximum horizontal compressive stress (SHmax) in accommodating deformation through convergent zones. The orientation of the SHmax is in the NE to NNE direction in the Kopeh Dagh, Alborz, Talesh, and Ashkabad-Balkhan fault zones, being rotated to NNE-N in the Greater Caucasus. The orientation of the SHmax relative to the convergence direction of the Arabian and Eurasian plates indicates that the Arabian-Eurasian oblique convergence-derived tectonic stress is the primary contributor to the total stress and deformation in this region.

In this study, we determine the stress release from the 2003 Bam earthquake (Mw 6.6) by applying the stress inversion technique to focal mechanisms of 199 aftershocks. There is no evidence of significant surface faulting that can be used to study the faulting pattern of the Bam fault zone. Therefore, we applied two independent methods for identifying the faulting pattern in this zone: the instability criterion based on the analysis of orientations of nodal planes of focal mechanisms with respect to the regional stress, and the Fry method based on the analysis of spatial clustering of aftershock foci. The results show that the fault associated with the 2003 Bam earthquake is well oriented for shearing under the present-day regional stress. We identified four sets of faults with a close angular relation to the maximum horizontal compression ( SH max ) that have been (re)activated. These faults include strike-slip (right lateral and left lateral), thrust, and normal faults that are oriented approximately oblique, perpendicular, and parallel relative to the SH max , respectively. The direction of the SH max is N31° E. Based on the results, we propose to apply the instability criterion and the Fry method to seismic data as two valuable and independent techniques in order to constrain the kinematic and active faulting in the area.

The anisotropy of elastic properties, including seismic velocities, has already been investigated in the lab over past seven decades. Here, we present a review related to the development of a unique apparatus for the detailed measurement of seismic velocity anisotropy. Its originality lies in measuring velocities on spherical specimens, which allows for determination of the velocity anisotropy as a function of confining pressure loading with high resolution. The 132 directions, covering the sphere in a regular 15° net of meridians and parallels, have proven to be optimal with respect to common heterogeneities of investigated rocks. The device was designed and the first measurements were performed by a research team of the Institute of Geophysics in Prague (Babuška, Pros and Klíma) in 1968, shortly following many pioneer velocity anisotropy studies. Since then, almost 100 papers have been published using the velocity anisotropy measured with this unique device. The review consists of three separate but mutually interconnected parts: (i) historical development; (ii) microstructural insights from an ultrasonic velocity measurement perspective; (iii) macroscale applications to practical problems in geophysics, structural geology and rock mechanics.

ABSTRACT We present the elastic anisotropy of two rock samples from two underground research laboratories (URL) that are focused mainly on the investigation of functionality of deep repositories: (1) BUK sample – migmatized paragneiss, typical for the test site of the URL Bukov, Czech Republic; (2) GRM sample - Central Aare granite, a predominant host rock of the URL Grimsel, Switzerland. We used a detail ultrasonic measurement of P and S wave velocity to obtain a general form of stiffness tensor with 21 independent elastic constants for selected pressure levels from 0.1 to 100 MPa. The transformation of tensor to its principal coordinate systems shows: the Bukov migmatized gneiss is orthorhombic, whereas the Grimsel granite is transversely isotropic under atmospheric pressure. The anisotropy strength of both rocks decreases with applied confining pressure due to closing of preferentially oriented cracks. Grimsel granite becomes almost isotropic at high pressures. A great part of anisotropy in the Bukov paragneiss remains even under high pressures due to its texture. Both rocks are anisotropic under the equivalent of the overburden pressure acting at the in-situ URL conditions. INTRODUCTION Rocks, in general, display elastic anisotropy, as a combined effect of preferential orientations of their constituents: crystals, mineral grains and microcracks (eg. Babuska and Cara, 1991). This anisotropy depends on acting stresses, as was demonstrated by the pressure dependence of seismic velocities (eg. Pros et al. 1998). At lower pressures (<50 MPa), the elasticity and its anisotropy is controlled by the cracks with characteristic exponential increase in seismic velocity. Above the crack closing pressure, the velocity/pressure relation becomes linear depending on rock matrix (crack free) properties. The ultrasonic sounding is a laboratory technique to determine the anisotropic elastic constants for a different symmetry types, most commonly the transverse isotropy (Sarout et al., 2007) or orthorhombic symmetry (Sano et al., 1992). With decreasing level of symmetry, the number of independent elastic constants is increasing up to 21, for the most general case of triclinic symmetry. Lokajicek and Svitek (2015) presented an experimental approach to estimate such a stiffness tensor estimated from the ultrasonic sounding performed on the spherical specimen in 132 independent directions for three waves with different wave polarizations (P, SH, SV). In this experiment, the symmetry type or its orientation does not have to be known/supposed before the experiment, or may even change with the applied pressure (Lokajicek et al., 2020). The obtained general stiffness tensor can be simplified for the higher symmetries by rotation into its principal coordinate system (Aminzadeh et al., 2022).

We propose a novel method for studying the λ/μ ratio, the vP/vS ratio and Poisson's ratio of rocks based on the determination of highly accurate moment tensors of acoustic emissions (AEs). The validity of the method is verified on observations of 539 AEs recorded in a sandstone sample during a semi-circular bend test. We show that the sandstone exhibits the so-called bi-modular behaviour indicating that rock parameters significantly differ under compressive and tensile stress regimes. In addition, the zone characterized by highly tensile fractures is auxetic. For increasing shear component in AEs, Poisson's ratio increases and the auxetic effects disappear. The proposed approach for determining the λ/μ, vP/vS, and Poisson's ratios using AEs is fully independent of standard techniques based on measuring deformation of rock samples. The approach might find applications in detailed studies of rock behaviour under various stress conditions, in particular, in assessing the bi-modularity of rocks measured during a single experiment.

SUMMARY As an alternative to the moment tensor (MT) model for earthquake sources, the shear-tensile-compressive (STC) model offers a kinematic description of the source mechanism and leads to a more robust inversion problem. However, the premise of the source inversion based on STC is to ensure the accuracy of parameter $\kappa $ defined as the ratio of the Lamé constants, $\kappa $=$\lambda /\mu $, in a fault zone. In this study, we carry out a series of synthetic experiments using P-wave amplitudes in source mechanism inversions based on both the STC and MT models, and consider the influence of noise, the uncertainties in source locations and in the velocity model. We show that the nonlinear STC inversion with an appropriate value of $\kappa $ leads to more accurate result compared to the linear MT inversion. We also propose a new joint-STC inversion method to jointly invert for parameter $\kappa $ and the remaining parameters of the STC model (magnitude and the strike, dip, rake and slope angles). The results indicate that our proposed method yields robust results for both the parameter $\kappa $ and focal mechanisms. We apply our joint-STC inversion method to field microearthquake data observed in the West Bohemia region to validate some of the conclusions drawn from the synthetic experiments.

Modified Newtonian equations for gravitational orbits in the expanding Universe indicate that local gravitationally bounded systems like galaxies and planetary systems are unaffected by the expansion of the Universe. This result is derived for the space expansion described by the standard FLRW metric. In this paper, the modified Newtonian equations are derived for the space expansion described by the conformal cosmology (CC) metric. In this metric, the comoving and proper times are different similarly as the comoving and proper distances. As shown by Vavryčuk (Front. Phys. 2022), this metric is advantageous, because it properly predicts the cosmic time dilation, and fits the Type Ia supernova luminosity observations with no need to introduce dark energy. Surprisingly, the solution of the equations for gravitational orbits based on the CC metric behaves quite differently than that based on the FLRW metric. In contrast to the common opinion that local systems resist the space expansion, they expand according to the Hubble flow in the CC metric. The evolution of the local systems with cosmic time is exemplified on numerical modelling of spiral galaxies. The size of the spiral galaxies grows consistently with observations and a typical spiral pattern is well reproduced. The theory predicts flat rotation curves without an assumption of dark matter surrounding the galaxy. The theory resolves challenges to the ΛCDM model such as the problem of faint satellite galaxies, baryonic Tully-Fisher relation or the radial acceleration relation. Furthermore, puzzles in the solar system are successfully explained such as the Faint young Sun paradox or the Moon’s and Titan’s orbit anomalies.