Brune Model Research Articles

The Impact of Source Time Function Complexity on Stress-Drop Estimates

ABSTRACT Earthquake stress drop—a key parameter for describing the energetics of earthquake rupture—can be estimated in several different, but theoretically equivalent, ways. However, independent estimates for the same earthquakes sometimes differ significantly. We find that earthquake source complexity plays a significant role in why theoretically (for simple rupture models) equivalent methods produce different estimates. We apply time- and frequency-domain methods to estimate stress drops for real earthquakes in the SCARDEC (Seismic source ChAracteristics Retrieved from DEConvolving teleseismic body waves, Vallée and Douet, 2016) source time function (STF) database and analyze how rupture complexity drives stress-drop estimate discrepancies. Specifically, we identify two complexity metrics—Brune relative energy (BRE) and spectral decay—that parameterize an earthquake’s complexity relative to the standard Brune model and strongly correlate with the estimate discrepancies. We find that the observed systematic magnitude–stress-drop trends may reflect underlying changes in STF complexity, not necessarily trends in actual stress drop. Both the decay and BRE parameters vary systematically with magnitude, but whether this magnitude–complexity relationship is real remains unresolved.

Сейсмотектонические деформации и сброшенные напряжения землетрясений Центрального Тянь-Шаня

Based on the seismic moment tensor (SMT) data of 270 earthquakes in the Central Tien Shan, which occurred from 1978 to 2021 and include 63 events from the Global Centroid Moment Tensor catalog and 207 events from the works of Aleksander D. Kostyuk and Naylya A. Sycheva, the focal parameters (seismotectonic deformations (STD), kinematic and dynamic parameters, source radius, and stress drop) were calculated. The STD calculation was based on the approaches proposed in the studies of Yuriy V. Riznichenko and Sergei L. Yunga. The area under consideration is characterized by such deformation modes as thrust, transpression, underpression, and oblique. The distribution of the Lode–Nadai coefficient was calculated and plotted. A significant part of the study area is characterized by simple compression deformation, dominated by simple compression and simple shear. To calculate the stress drop , the values of the scalar seismic moment M0, which are determined in the SMT calculation, and the source radii r, which are calculated on the basis of theoretical and experimental models of the dependence of the source radius on the moment magnitude, were used. The radii r and stress drops  were calculated for two models of earthquake sources: the Brune model and the Madariaga–Kaneko–Shearer model. A catalog of dynamic parameters was compiled. The comparison of the kinematic and dynamic parameters of earthquakes was carried out, and the relationship of the dropped stresses with the type of movement in the source, as well as with the Lode–Nadai coefficient, was established. The results obtained in the study can be useful for specialists in other fields of knowledge – geodesy, geology, and geophysics.

Spectral Characteristics of Hydraulic Fracturing-Induced Seismicity Can Distinguish between Activation of Faults and Fractures

Abstract Analysis of earthquake spectra can aid in understanding source characteristics like stress drop and rupture complexity. There is growing interest in probing the similarities and differences of fault rupture for natural and human-induced seismic events. Here, we analyze waveform data from a shallow, buried geophone array that recorded seismicity during a hydraulic fracturing operation near Fox Creek, Alberta. Starting from a quality-controlled catalog of 4000 events between magnitude 0 and 3.2, we estimate source-spectral corner frequencies using methods that account for the band-limited nature of the sensor response. The stress-drop values are found to be approximately self-similar, but with a slight magnitude dependence in which larger events have higher stress drop (∼10 MPa). Careful analysis of the relative corner frequencies shows that individual fault and fracture segments experienced systematic variations in relative corner frequency over time, indicating a possible change in the stress state. Clustering analysis of source spectra based on the relative proportion of high- and low-frequency content relative to the Brune model further shows that event complexity evolves over time. In addition, the faults produce earthquakes with systematically larger stress-drop values than the fractures. Combined, these results indicate that the features activated by hydraulic fracturing experience observable changes in source behavior over time and exhibit different properties depending on the orientation, scale, and fabric of the structural feature on which they occur.

A Time-Domain Approach for Accurate Spectral Source Estimation with Application to Ridgecrest, California, Earthquakes

ABSTRACTWe determine the seismic moment and corner frequency of earthquakes using narrowband, time-domain measurements of the maximum shear-wave displacement amplitude. Each S wave is passed through a set of one-octave band-pass filters between 0.25 and 32 Hz to measure the peak amplitude on the horizontal components. Following the development of Richter (1935) local magnitude scale, we derive a functional form of maximum amplitude versus distance, but separately for each frequency band, and use them to estimate wave attenuation as a function of frequency and distance. Attenuation is a strong function of frequency, approximately proportional to 1/f, with path averaged Q increasing (attenuation decreasing) with propagation distance. We use these empirical attenuation curves to correct the time-domain peak amplitudes to a reference distance of 10 km to recover the source spectrum. We find that the spectral shape is consistent with the Brune model, showing a well-defined plateau at low frequency and a decay at high frequency proportional to ω−2. We use the median spectrum for stations at distances up to 120 km for each event to measure the moment and corner frequency. This time-domain method provides a reliable and efficient way to accurately measure earthquake source parameters.

Characterizing Multisubevent Earthquakes Using the Brune Source Model

ABSTRACTAlthough the Brune source model describes earthquake moment release as a single pulse, it is widely used in studies of complex earthquakes with multiple episodes of high moment release (i.e., multiple subevents). In this study, we investigate how corner frequency estimates of earthquakes with multiple subevents are biased if they are based on the Brune source model. By assuming complex sources as a sum of multiple Brune sources, we analyze 1640 source time functions of Mw 5.5–8.0 earthquakes in the seismic source characteristic retrieved from deconvolving teleseismic body waves catalog to estimate the corner frequencies, onset times, and seismic moments of subevents. We identify more subevents for strike-slip earthquakes than dip-slip earthquakes, and the number of resolvable subevents increases with magnitude. We find that earthquake corner frequency correlates best with the corner frequency of the subevent with the highest moment release (i.e., the largest subsevent). This suggests that, when the Brune model is used, the estimated corner frequency and, therefore, the stress drop of a complex earthquake is determined primarily by the largest subevent rather than the total rupture area. Our results imply that, in addition to the simplified assumption of a radial rupture area with a constant rupture velocity, the stress variation of asperities, rather than the average stress change of the whole fault, contributes to the large variance of stress-drop estimates.

Characteristics of stress field and crustal kinematics of the southern region of Sichuan-Yunnan block, southern Tibet Plateau

The Red River fault is a massive tectonic shear zone of the Sichuan-Yunnan block, southern Tibet Plateau. The target area of this study is the Red River fault's middle-northern section and adjacent areas. Considering the spatial difference of tectonic structures and the inhomogeneity of focal mechanism solutions, we divided the target area into three structural units: the northern extension area, the middle strike-slip movement area, and the west complex rupture area. The study is carried out on the basis of zoning. Using the CAP method to invert the focal mechanism of moderate earthquakes and the principal compressive and tensile stress. Restoring the seismic source spectrum of small and medium earthquakes, then inversion the stress drops in three sub-units based on Brune model using digital waveform records. Our study suggests that: (1) Many high-stress drop earthquakes occurred in the transitional areas from the Weixi-Qiaohou fault to the Red River fault and from the Chuxiong fault to the Qujiang fault, also occurred in the Changning-Baoshan-Yongping area, revealing a large accumulation of local tectonic stress. (2) Some events with Δσ ≥ 20 MPa have occurred in the prominent low-speed anomaly area, indicating that a passive deformation crossed the Red River fault and extended to the west. Yangbi MS 6.4 earthquake (2021) occurred in a strongly locked area with high potential earthquake risk. (3) In the north of the study region, the movement of the Sichuan-Yunnan block to SE-SSE orientation was governed by the dextral strike-slip movement of the NW strike fault; in the middle region, the SE-orientated movement of the block relative to the South China block was governed by the sinistral slip movement of the SN-strike faults; and in the west region, the tectonic stress was governed by clockwise rotation of the block and the sinistral slip movement of the NE strike faults. We suggest that strike slip and rotation of the Red River fault's middle section may drive and aggravate passive movement in the north section, resulting in locally geophysical field responses. Therefore, the potential risk of a large earthquake in the middle-northern section of the Red River fault should be monitored.

Spectral characteristics of P-and S-wave quarry blasts in Aswan region, South Egypt

The Aswan broadband seismic network, consisting of high-sensitivity sensors with dense stations coverage, provided the opportunity to study and analysed the spectral properties of the quarry blasts in the Aswan region, southern Egypt. We comprehensively analysed 757 digital seismograms from 128 quarry blasts with local magnitude (ML) between 1.7 and 3.1 during time span from 2010 to 2021. A Generalized Inversion Technique (GIT) constrained by a reference site is applied to isolate the attenuation, site responses of the seismic stations, and the source spectra from the observed seismograms by means of iterative least square analysis. The displacement source spectra for P-and S-waves are computed for all quarry blasts based on the theoretical omega-square seismic source model (Brune's model). The spectral analysis demonstrated that both P-and S-waves displacement source spectra of the quarry blasts used in this study have low corner frequency values. The corner frequency of the quarry blasts used in this study ranged from 1.0 to 2.6 Hz and from 1.5 to 4.6 Hz for P-and S-waves, respectively. The P-and S-wave corner frequency ratio (fCP/fCS) is computed for each event. We obtained that the fCP/fCS ratio is less than 1.0 Hz for 106 events (94%) and equal to 1.0 Hz and less than 1.2 Hz for only six selected data events (6%). The analysis indicates that the observed displacement source spectra show discrepancies with the omega-square type spectrum, and they generally have a steep fall off at high frequencies. We also found that the selected quarry blasts have a narrow seismic moment range (from 2.03E+11 to 1.35E+12 Nm), and stress drop values range from 0.001 to 0.023 MPa. The distribution of the used quarry blast stress drop demonstrated a self-similar character.

Radiated seismic energy and source damage evolution from the analysis of simulated dynamic rupture and far-field seismograms

SUMMARY We present results on radiated seismic energy during simulations of dynamic ruptures in a continuum damage-breakage rheological model incorporating evolution of damage within the seismic source region. The simulations vary in their initial damage zone width and rate of damage diffusion with parameter values constrained by observational data. The radiated energy recorded at various positions around the source is used to calculate seismic potency and moment. We also calculate the normalized radiated energy from the source, in a way that allows comparing between results of different simulations and highlighting aspects related to the dilatational motion during rupture. The results show that at high-frequencies, beyond the dominant frequency of the source ($( {f > 3{f}_d} )$, the damage process produces an additional burst of energy mainly in the Pwaves. This eccess of high-frequency energy is observed by comparing the radiated energy to a standard Brune's model with a decay slope of the radiated energy of n = 2. While the Swaves show good agreement with the n = 2 slope, the Pwaves have a milder slope of n = 1.75 or less depending on the damage evolution at the source. In the used damage-breakage rheology, the rate of damage diffusivity governs the damage evolution perpendicular to the rupture direction and dynamic changes of the damage zone width. For increasing values of damage diffusivity, dilatational energy becomes more prominent during rupture, producing a high-frequency dilatational signature within the radiation pattern. The high-frequency radiation pattern of the Pwaves includes two main lobes perpendicular to the rupture direction, reflecting high-rate local tensile cracking during the overall shear rupture process. Analysing the possible existence and properties of such high-frequency radiation pattern in observed Pwaves could provide important information on earthquake source processes.

Variability of Spectral Estimates of Stress Drop Reconciled by Radiated Energy

ABSTRACTA review of a collection of theoretical source spectral models revealed: (1) Despite the well-known variation in predicting static stress drop Δσs from the seismic moment and corner frequency, all models, especially the three conventional models, suggest that earthquakes radiate about half of the available strain energy into the surrounding medium. This similarity justifies a less model-dependent approach to estimate Δσs, though estimates for natural earthquakes rely on apparent seismic radiation efficiency (=2σa/Δσs; σa is apparent stress of an earthquake). (2) When one attempts to use Δσs and spectral models to make predictions, such as apparent stress σa, there is a model-dependent discrepancy between the σa inferred from theoretical energy partitioning and the σa predicted using spherical mean corner frequency. Their ratio cp varies significantly from 1.0 for the Brune (1970, 1971) model to 6.38 for the Madariaga (1976) model. If one uses spectral models to predict the ground motion, cp must be considered. (3) We infer that the constancy of the “stress parameter” (Δσ˜) found in engineering seismology (e.g., Boore, 1983; Atkinson and Beresnev, 1998) is similar to having constant apparent stress, σa (e.g., Ide and Beroza, 2001). The observation that Δσ˜ is generally larger than the average static stress drop Δσs for global M >5.5 shallow crustal earthquakes in active tectonic regions implies that these earthquakes radiate, on average, more seismic energy than predicted from the conventional dynamic crack models.

Machine learning of source spectra for large earthquakes

SUMMARYThe shape of earthquake source spectra, traditionally fit by physics-based models, contains important parameters to constrain rupture dimension, duration and geometry. Here we apply machine learning (ML) to derive single- and double-variable data-driven models of source spectra from 3675 Mw > 5.5 global earthquakes, assuming that the Fourier transform of source time functions represent earthquake source spectra below 1 Hz. The single-variable ML model, in the same degree of freedom as the Brune model, improves the goodness of fit by 8.5 per cent. Specifically, the ML model fits the data without systematic bias, whereas the Brune model tends to underestimate at intermediate frequencies and overestimate at high frequencies. The latter discrepancy cannot be modelled by increasing the fall-off exponent in the Brune- or the Boatwright-type models. The double-variable ML model is compared to existing double-corner-frequency models and is found to capture the second-order features such as the subtle curvature differences around the corner. Our results demonstrate that unsupervised ML can extract hidden global characteristics of high-dimensional data and provide observational evidence to amend existing physical models.

Rupture properties and safety assessment of raw coal specimen rupture process under true triaxial hydraulic fracturing based on the source parameters and magnitude

To realize the safety assessment and risk management of the raw coal specimen rupture process under true triaxial hydraulic fracturing, the AE parameters and source parameters were obtained based on the AE monitoring of raw coal specimen rupture under true triaxial hydraulic fracturing. Throughout the process of hydraulic fracturing, the variation rule of AE parameters and the spatio-temporal distribution of the AE events induced by hydraulic fracturing of raw coal under true triaxial stress were studied. Then, based on the Brune model and grid search method, the source parameters and moment magnitude of raw coal specimens rupture under true triaxial hydraulic fracturing were obtained, and the relationship between the seismic moment and the other source parameters was analyzed. Finally, the source parameters relating AE events in raw coal specimens rupture under true triaxial hydraulic fracturing and micro-earthquakes induced by hydraulic fracturing were compared and investigated; the relationship between Mw (moment magnitude) and ML (local magnitude) of AE events of raw coal specimens rupture under true triaxial hydraulic fracturing was revealed. The results show that: the AE locating results are generally consistent with the actual rupturing of raw coal specimens. The source displacement spectrum of raw coal specimens rupture under true triaxial hydraulic fracturing is in good accordance with predictions made using the Brune model. By calculating the source parameters and moment magnitude, the source scale of hydraulic fracturing of raw coal specimens under true triaxial stress can be evaluated accurately. Source parameters such as corner frequency and apparent stress of raw coal specimen decrease linearly with the increase of seismic moment, and the source radius and source energy increase linearly with the increase of seismic moment; the stress drop tends to fluctuate around a certain value. The source properties of hydraulic fracturing of raw coal specimens under true triaxial stress can be evaluated. The seismic source properties relating AE events in raw coal specimens rupture under true triaxial hydraulic fracturing and micro-earthquakes induced by hydraulic fracturing are different. Considering Mw, ML1 can be better used to calculate the magnitude of AE events of raw coal specimens rupture during true triaxial hydraulic fracturing. These results can reveal the source properties throughout the rupturing of raw coal specimens during true triaxial hydraulic fracturing, and evaluate the safety of rupture process.

Stress drops of hydraulic fracturing induced microseismicity in the Horn River basin: challenges at high frequencies recorded by borehole geophones

SUMMARYThe ground motions caused by seismicity associated with fluid injection can pose a significant hazard. Borehole geophone arrays can provide access to tiny seismic events, which can extend the investigated magnitude range. However, the high frequency phase arrivals (i.e., >100 Hz) also present challenges associated with high frequency cut-offs (fmax), stronger attenuation and resonances within geophones. These effects limit our ability to accurately constrain attenuation models and high frequency source parameters. We investigate 112 −0.6 $\le \, M_{\rm w}\, \le$ 0.7 seismic events and calculate corner frequencies and stress drops from 90 of these events recorded during hydraulic fracturing treatment in the Horn River basin, British Columbia. High frequency resonances (>250 Hz) caused by spurious frequency excitation and/or coupling issues can significantly distort the shape of phase arrival spectra and affect source parameter estimates. Critically, resonances vary in strength between (nearly) colocated events, which may compromise the validity of a spectral ratio approach. For stations showing the cleanest spectra, the Brune model provides a decent fit to the displacement spectra. However, bandwidth limitations, low signal-to-noise ratios, high frequency cut-offs and significant attenuation still hinder our ability to retrieve high frequency source parameters. We find that a frequency independent Qp = 180 ± 40 provides a reasonable model for crustal attenuation but the large uncertainty caused by resonances prevents a robust constraint. From those events that show the best fits, we find a mean Madariaga corner frequency of 210 Hz ± 30 from P-phase arrivals, which is in the range of expected values if self-similarity extends into negative magnitudes. We also calculate a mean stress drop of 1.6 MPa ± 1.2, which is within the tectonic range but slightly lower than other deeper regional studies, which can be explained by lower effective stresses and/or a lower crustal shear strength. We find no evidence for a change in stress drop with depth or distance from the point of injection. A plausible explanation is that effective stresses are lowered relatively quickly over the entire fault zone via direct hydraulic connections. However, the large uncertainties make it difficult to interpret source parameter variability in detail. For high resolution monitoring and source properties of microseismicity, there is an urgent need for high quality high frequency recordings unaffected by spurious frequencies.

Source parameters and scaling relations for small to moderate earthquakes in theIndo‐BurmaRanges,North‐east India, and its seismotectonic implications

The Indo‐Burma Ranges (IBRs) and its surrounding North‐east India is one of the seismotectonically active subduction systems in the world, where the Indian Plate is subducting beneath the Sunda Plate. This has resulted in major earthquakes in the past. In this study, spectral analysis of S‐wave has been used to investigate the source parameters for local earthquakes (3.3 ≤ MD ≤ 5.8) exclusively in the Indo‐Burma region fusing a network of six stations by adopting the Brune model. The corner frequencies (fc) of the events are varied from 0.6 to 3.2 Hz. The estimated source parameters lie in the range from 9 × 1013–3.7 × 1017 N m, 0.2–35.1 MPa, 410–1,956.4 m, 0.002–1.196 m, and 2.9–13.5 Hz for seismic momentM0, stress drop (Δσ), source radius, source dislocation, and maximum cut‐off frequency (fmax), respectively. The scaling relation betweenM0andfchas been derived asM0 = 1.622 × 1016 fc−5.298. The scaling relations ofM0withfmaxand stress drop have also been derived. The high‐stress drops (>10 MPa) were at a depth zone of ~40–60 km, while the stress drops were less than 4.0 MPa beyond this depth, indicating the shallow and deeper portion of the lithosphere to be relatively brittle. We postulate that this could occur due to a complex detachment process as a result of slab tearing in the region. The upper boundary of stress drop was found to have an increasing trend with the focal depth of the earthquakes. The empirical relations betweenM0 − MDandMW − MDhave also been derived for the IBRs. The estimated source parameters and scaling relations will be useful in estimations of lithospheric strength, simulation of strong ground motion in the IBRs, and calibrating the coefficient of the local earthquakes in the IBR and its surrounding region.

Rupture process assessment of rock bursts in a coal mine: Inversion of source parameters and the slip distribution on the rupture surface

To assessment the source parameters and slip distribution on the rupture surface of a rock burst event in Qianqiu coal mine, and verify the accuracy of the source parameters and slip distribution on the rupture surface, four rock burst events in Qianqiu coal mine were selected for source analysis. Firstly, the source parameters of four rock burst events in Qianqiu coal mine were obtained based on the Brune model. Then, the rupture scale and average slip on the rupture surface of seismic source were identified by using the established relationship between rupture scale and moment magnitude. Finally, based on the k2 rupture-slip model and the obtained source parameters, the slip distribution on the rupture surface was inverted to reveal the slip-rupture process of the source, and the accuracy of the seismic source parameters and the slip distribution on the rupture surface was verified based on the in-situ rupture-slip behavior. The results show that: the source parameters can be calculated using the Brune model and grid search method; the rupture scale and average slip on the rupture surface were obtained by establishing the relationship between the moment magnitude and the rupture scale of the source; based on the k2 rupture-slip model and the scale of rupture, the slip distribution on the rupture surface of a microseismic event in a coal mine can be deduced by inversion. The calculated source parameters and slip distribution of four rock burst events are consistent with the actual records of such events in a coal mine, which further verifies the accuracy of the source parameters and slip distribution of rock burst events. These results can be used to quantify and evaluate the rupture properties, scale and process of a rock burst, and provide reference for further study of the evolution process and risk assessment of rock burst events in coal mine.

Spatiotemporal Evolution of Microseismicity Seismic Source Properties at the Irpinia Near-Fault Observatory, Southern Italy

ABSTRACTWe estimate the source parameters of small-magnitude earthquakes that occurred during 2008–2020 in the Irpinia faults area (southern Italy). We apply a spectral decomposition approach to isolate the source contribution from propagation and site effects for ∼3000 earthquakes in the local magnitude range between ML 0 and 4.2. We develop our analyses in three steps. First, we fit the Brune (1970) model to the nonparametric source spectra to estimate corner frequency and seismic moment, and we map the spatial distribution of stress drop across the Irpinia area. We found stress drops in the range 0.4–8.1 MPa, with earthquakes deeper than 7 km characterized by higher average stress drop (i.e., 3.2 MPa). Second, assuming a simple stress-release model (Kanamori and Heaton, 2000), we derive fracture energy and critical slip-weakening distance. The spatial variability of stress drop and fracture energy allows us to image the present stress conditions of fault segments activated during the 23 November 1980 Ms 6.9 earthquake. The variability of the source parameters shows clear patterns of the fault mechanical properties, suggesting that the Irpinia fault system can be divided into three main sectors, with the northern and southern ones showing different properties from the central one. Our results agree with previous studies indicating the presence of fluids with different composition in the different sectors of the Irpinia fault system. In the third step, we compare the time evolution of source parameters with a time series of geodetic displacement recorded near the fault system. Temporal trends in the correlation between geodetic displacement and different source parameters indicate that the poroelastic deformation perturbation generated by the karst aquifer recharge is modulating not only the occurrence rate of microseismicity (D’Agostino et al., 2018) but may lead to rupture asperities with different sizes and characteristics.

Source parameters and focal mechanism of ruptures in coal and sandstone specimens under uniaxial loading based on acoustic emission signals

To investigate the source properties and focal mechanism of coal and sandstone specimen rupture under uniaxial loading, acoustic emission (AE) testing of sandstone and coal specimen rupture under uniaxial loading was conducted. The spatio-temporal evolution of AE parameters in the rupture process was determined through the AE testing of coal and sandstone specimen rupture under uniaxial loading. The source parameters of sandstone and coal specimen rupture were then calculated and analyzed using the Brune model and grid-search method. Finally, the focal mechanism of sandstone and coal specimen rupture was deduced by inversion and compared based on source parameters and moment tensor inversion. The results show that: the rupture morphology of sandstone specimens differs from that of coal specimens; the source displacement spectra of sandstone and coal specimens under uniaxial loading are in good agreement with the Brune model. The corner frequency of coal and sandstone specimens decreases linearly with the increase of seismic moment; source radius and energy increase linearly with increasing seismic moment; the stress-drop fluctuates around a certain value. For events of the same magnitude, the corner frequency, energy, and source radius of sandstone specimens at rupture are greater than those of coal specimens at rupture, but the stress-drop in sandstone specimens (at rupture) is smaller than that occurring in coal specimens. In the middle and early stages of rupture, the coal and sandstone specimens mainly undergo shear failure. Shear-tension and shear-compression failures occur in the later stage of rupture. These results can be used to quantify and evaluate the source properties and focal mechanism of small-scale specimens at rupture.

Study on the rupture properties and automatic identification model of micro-earthquakes and blasting events in a coal mine

Source location is the key step of microseismic monitoring. The monitored microseismic signals are often mixed with unrecognized blasting interference signals, which affect the results of microseismic monitoring and location. Therefore, it is very important to extract the characteristic parameter information to identify the microseismic signal and blasting signal. The rupture processes during micro-earthquakes and blasting events in a coal mine are complicated and have different characteristics, which seriously affects the safety of coal mine. To quantify the seismic source properties of micro-earthquakes and blasting events in coal mines, and further distinguish between micro-earthquakes and blasting events, the source parameters of micro-earthquakes and blasting events in coal mine were obtained, and the differences between micro-earthquakes and blasting events were investigated by comparing the characteristics of their respective source parameters. Firstly, the corner frequency f0, spectral level Ω0, seismic moment M0, source energy E, source radius R, stress drop △σ, apparent stress σa, and magnitude (Mw and ML) of micro-earthquakes and blasting events in Qianqiu coal mine were calculated using the Brune model and grid-search method; then, the relationship between seismic moment and the other source parameters was analysed, the differences between micro-earthquakes and blasting events were studied based on the above source parameters, and the automatic identification model of micro-seismic and blast signals thus established; finally, the local magnitude was calculated and the relationship between moment magnitude and local magnitude analysed. The magnitudes of micro-earthquakes and blasting events are determined based on the calculated Mw and ML. The above analysis can be used to determine and quantify the seismic source properties and scale of micro-earthquakes and blasting events, and further distinguish micro-earthquakes from blasting events effectively to ensure the accuracy of source location and allow implementation of effective control measures.

Reliability Assessment of the Hydraulic Fracturing Process in Coal Mine Based on the Analysis of Micro-Seismic Source Parameters

In a reliability assessment of hydraulic fracturing, the efficacy of hydraulic fracturing must be evaluated, and the source properties and magnitude of micro-earthquakes induced by hydraulic fracturing in a coal mine need to be quantified. Firstly, the changing trends of the number and energy of micro-seismic events induced by hydraulic fracturing with high-pressure water were examined, and the hydraulic fracturing effect was evaluated by micro-seismic location. Then, the source parameters (seismic moment M0, source radius R, corner frequency f0, radiated seismic energy E, stress drop △σ, and apparent stress σa) were calculated using the Brune model and the grid-search method, and the relationships between M0 and other source parameters were analyzed. Finally, the source parameters between micro-earthquakes induced by hydraulic fracturing and those induced by mining were compared, and the relationship between Mw (moment magnitude) and ML (local magnitude) of a micro-earthquake induced by hydraulic fracturing was ascertained. The results show that most micro-earthquakes occur in the initial stage of water pressure increase during hydraulic fracturing. In addition, the occurrence of several micro-earthquakes does not correspond strictly to the significant decrease of water pressure; the locations of micro-earthquakes can be used to evaluate the effect of hydraulic fracturing. The source parameters of micro-earthquakes induced by hydraulic fracturing in the Xieqiao coal mine can be obtained from the Brune model and the grid-search method. Corner frequency f0 decreases with increase in seismic moment M0, source parameters of R and E, as well as △σ increase with increase in seismic moment M0, but the apparent stress σa fluctuates around a certain value; the relationships between the other source parameters and M0 of micro-earthquake induced by hydraulic fracturing are consistent with that of a micro-earthquake induced by coal mining. Considering Mw, ML1 can be better used to calculate the magnitude of micro-earthquakes induced by hydraulic fracturing. Through Mw and ML1, the magnitude of a micro-earthquake induced by hydraulic fracturing can be evaluated. Our results improve the evaluation of the hydraulic fracturing effect, the understanding of source properties, and evaluation of the magnitude of micro-earthquakes induced by hydraulic fracturing. It is found that these micro-earthquakes are within the safe controllable range, and the hydraulic fracturing process of the Xieqiao coal mine is reliable and safe.

Study on the source parameters of the micro-earthquakes in Laohutai coal mine based on double difference relocation

Seismicity related to industrial mining activities needs to be understood and quantified in order to ensure safe mining operations. It is of great important to determine if the sources of such events follow the common models and theories, and determine the source rupture property and scale of such events. Moreover, the location of the source is very important to obtain the source parameters. For this purpose, we analyze 103 events recorded in the Laohutai coal mine that are related to fault structure and mining activities to determine their source properties based on relocation. Firstly, the 103 micro-earthquakes were relocated based on double difference algorithm. Then, the source parameters of seismic moment M0, source radius R, corner frequency f0, seismic attenuation Q, energy E, stress drop △σ and apparent stress σa are computed based on relocation, Brune model and grid-search method. The relationship between the other source parameters and seismic moment, the relationship between ML and Mw, and the influence of location on source parameters and magnitude are further analyzed. Finally, the difference of the source parameters between Laohutai coal mine, Qianqiu coal mine and natural earthquakes are analyzed. We find that the source location can be effectively corrected based on double difference algorithm; ω2 model is well suited to estimate source parameters of micro-earthquakes in the Laohutai coal mine. The source spectra show strong directivity effects. Stations in the rupture direction have higher corner frequencies, while stations away from rupture direction have lower corner frequencies. With the increase of M0, the source parameters of R, E and △σ basically show a linear increase, the source parameter f0 basically show a linear decrease and the apparent stress fluctuate up and down around a certain value as a whole. After relocation, the location of the source has a significant effect on the quality attenuation factor Q and has no obvious effect on other source parameters. The influence of relocation on moment magnitude and local magnitude is not obvious. The moment magnitude is linear with the local magnitude. Considering Mw, ML1 can relatively well be used to evaluate the magnitude of the earthquakes in Laohutai coal mine; For the micro-earthquakes with the same magnitude, the values of corner frequency, stress drop, apparent stress and energy in Qianqiu coal mine are greater than those in Laohutai coal mine, the value of source radius in Laohutai coal mine is greater than those in Qianqiu coal mine. For the events with the same magnitude, the corner frequency and the stress drop value of micro-earthquakes are smaller than those of natural earthquake. These indicate that the rupture properties and scales of micro-earthquakes in Laohutai coal mine are different from those of the micro-earthquakes in Qianqiu coal mine and natural earthquakes. The results help us to effectively evaluate the property and magnitude of microseismic source, and better understand causes and consequences of microseismicity in coal mine.

Towards a homogeneous moment magnitude determination for earthquakes in South Africa: Reduction of associated uncertainties

New MW–ML magnitude relations valid for the periods January 1971–March 1997, April 1997–September 2012 and October 2012–present are presented for South Africa. Three MW–ML relations were derived for the respective periods by applying a general orthogonal regression using 85 mining-related and tectonic events. Moment magnitudes (MW) were calculated using spectral analysis of the vertical component seismograms. A Brune model for source radiation was assumed. Attenuation functions previously derived from local seismic events were used. For each event, the final MW was computed by taking the average of the values determined at four or more stations. These MW values were used to compute new MW –ML regression equations for three previous ML relations that had been used to compile the South African earthquake catalogue. The new MW–ML relations were then compared with the MW determined from the Harvard Centroid Moment Tensor (CMT) project. The MW computed using the relation derived for the most recent period (October 2012–present) produces MW values that are similar to those reported by the Harvard CMT solutions. The relations can be used in the homogenization of the South African earthquake catalogue. Application of the new relations for the three periods will reduce uncertainty in the homogenized catalogues, which are important when calculating seismic hazard parameters (i.e. when estimating activity rates, b-values and Mmax).