scholarly journals Scaling law between corner frequency and seismic moment of microearthquakes: Is the breakdown of the cube law a nature of earthquakes?

2002 ◽  
Vol 29 (8) ◽  
pp. 52-1-52-4 ◽  
Author(s):  
Yoshihiro Hiramatsu ◽  
Hiroshi Yamanaka ◽  
Keiichi Tadokoro ◽  
Kin′ya Nishigami ◽  
Shiro Ohmi
Keyword(s):  
Seismic Moment ◽  
Scaling Law ◽  
Corner Frequency

The relations between the corner frequency, seismic moment and source dynamic parameters derived from the spontaneous rupture of a circular fault

2021 ◽  
Vol 228 (1) ◽  
pp. 134-146
Author(s):  
Jian Wen ◽  
Jiankuan Xu ◽  
Xiaofei Chen
Keyword(s):  
Stress Drop ◽  
Seismic Moment ◽  
Dynamic Models ◽  
Scaling Law ◽  
Boundary Integral ◽  
Corner Frequency ◽  
Dynamic Parameters ◽  
Zone Size ◽  
Dynamic Rupture ◽  
Scaling Relationships

SUMMARY The stress drop is an important dynamic source parameter for understanding the physics of source processes. The estimation of stress drops for moderate and small earthquakes is based on measurements of the corner frequency ${f_c}$, the seismic moment ${M_0}$ and a specific theoretical model of rupture behaviour. To date, several theoretical rupture models have been used. However, different models cause considerable differences in the estimated stress drop, even in an idealized scenario of circular earthquake rupture. Moreover, most of these models are either kinematic or quasi-dynamic models. Compared with previous models, we use the boundary integral equation method to simulate spontaneous dynamic rupture in a homogeneous elastic full space and then investigate the relations between the corner frequency, seismic moment and source dynamic parameters. Spontaneous ruptures include two states: runaway ruptures, in which the rupture does not stop without a barrier, and self-arresting ruptures, in which the rupture can stop itself after nucleation. The scaling relationships between ${f_c}$, ${M_0}$ and the dynamic parameters for runaway ruptures are different from those for self-arresting ruptures. There are obvious boundaries in those scaling relations that distinguish runaway ruptures from self-arresting ruptures. Because the stress drop varies during the rupture and the rupture shape is not circular, Eshelby's analytical solution may be inaccurate for spontaneous dynamic ruptures. For runaway ruptures, the relations between the corner frequency and dynamic parameters coincide with those in the previous kinematic or quasi-dynamic models. For self-arresting ruptures, the scaling relationships are opposite to those for runaway ruptures. Moreover, the relation between ${f_c}$ and ${M_0}$ for a spontaneous dynamic rupture depends on three factors: the dynamic rupture state, the background stress and the nucleation zone size. The scaling between ${f_c}$ and ${M_0}$ is ${f_c} \propto {M_0^{ - n}}$, where n is larger than 0. Earthquakes with the same dimensionless dynamic parameters but different nucleation zone sizes are self-similar and follow a ${f_c} \propto {M_0^{ - 1/3}}$ scaling law. However, if the nucleation zone size does not change, the relation between ${f_c}$ and ${M_0}$ shows a clear departure from self-similarity due to the rupture state or background stress.

The use of duration as a measure of seismic moment and magnitude

1975 ◽  
Vol 65 (4) ◽  
pp. 899-913
Author(s):  
Robert B. Herrmann
Keyword(s):  
United States ◽  
Linear Relationship ◽  
Linear Dependence ◽  
Seismic Moment ◽  
Instrumental Response ◽  
Limited Range ◽  
Corner Frequency ◽  
Source Spectrum ◽  
Duration Magnitude ◽  
Central United States

Abstract The observed relationship between magnitude and duration is shown to be a result of the particular shape of the signal coda as a function of time. If the envelope of the coda follows a t−q relationship with increasing time, then the magnitude, mτ, based on a duration τ is consequently of the form m τ = q log ⁡ 10 τ + r . A study of the duration-magnitude and duration-moment relationships for a set of central United States earthquakes indicates that the linear relationship between mτ and log10τ is valid only over a limited range. The departure from the simple linear dependence is explained in terms of instrumental response and the shift of the source-spectrum corner frequency with increasing event size.

Two-parameter scaling of source spectra: Love waves from deep-focus Bonin Islands earthquakes

1977 ◽  
Vol 67 (2) ◽  
pp. 285-300
Author(s):  
R. James Brown
Keyword(s):  
Body Wave ◽  
Scaling Law ◽  
Spectral Ratio ◽  
Love Waves ◽  
Corner Frequency ◽  
Spectral Ratios ◽  
Bonin Islands ◽  
Deep Focus ◽  
Two Parameter ◽  
Fault Length

Abstract Starting with the one-parameter scaling law of Aki, a two-parameter expression is developed to model the source factor of the far-field spectrum from a dislocation fault source for both ω−2 and ω−3 high-frequency asymptotic types. Aki's assumption of similarity is relaxed in two respects: it is neither here assumed that wD0 ∞ L2 (L = fault length, w = fault width, D0 = average dislocation) nor that kT = v kL (kT−1 = correlation time, kL−1 = correlation length, v = velocity of rupture propagation), the latter being equivalent to allowing for Brune's fractional stress drop. From this two-parameter model a four-parameter model of spectral ratio is obtained and fitted to observed spectral ratios by computer optimization of the four parameters. Observed spectral ratios have been determined from the Love waves recorded at NORSAR from six deep-focus Bonin Islands earthquakes using a common-path method. From the optimal values of the four parameters, values are determined for corner frequency (f ≈ 0.2 Hz for m 6.0; f ≈ 0.3 Hz for m = 5.3; m = PDE body-wave magnitude), relative fault length, relative seismic moment (and magnitudes), and p, the slope of the corner-frequency locus. Values found for p are all greater than 3 and such p, in combination with an ω−3 scaling law, can yield a reasonable m:M relation, i.e., with no ceiling imposed on m. A slightly better fit is obtained by starting with an ω−3 model than with ω−2.

scholarly journals Analysis of strong-motion data of the 1990 Eastern Sicily earthquake

1995 ◽  
Vol 38 (2) ◽  
Author(s):  
M. Di Bona ◽  
M. Cocco ◽  
A. Rovelli ◽  
R. Berardi ◽  
E. Boschi
Keyword(s):  
Frequency Band ◽  
Stress Drop ◽  
Seismic Moment ◽  
Ground Motions ◽  
Broad Band ◽  
Strong Motion ◽  
Moment Magnitude ◽  
Corner Frequency ◽  
Local Magnitude ◽  
The Moment

The strong motion accelerograms recorded during the 1990 Eastern Sicily earthquake have been analyzed to investigate source and attenuation parameters. Peak ground motions (peak acceleration, velocity and displacement) overestimate the values predicted by the empirical scaling law proposed for other Italian earthquakes, suggesting that local site response and propagation path effects play an important role in interpreting the observed time histories. The local magnitude, computed from the strong motion accelerograms by synthesizing the Wood-Anderson response, is ML = 5.9, that is sensibly larger than the local magnitude estimated at regional distances from broad-band seismograms (ML = 5.4). The standard omega-square source spectral model seems to be inadequate to describe the observed spectra over the entire frequency band from 0.2 to 20 Hz. The seismic moment estimated from the strong motion accelerogram recorded at the closest rock site (Sortino) is Mo = 0.8 x 1024 dyne.cm, that is roughly 4.5 times lower than the value estimated at regional distances (Mo = 3.7 x 1024 dyne.cm) from broad-band seismograms. The corner frequency estimated from the accelera- tion spectra i.5 J; = 1.3 Hz, that is close to the inverse of the dUl.ation of displacement pulses at the two closest recording sites. This value of corner tì.equency and the two values of seismic moment yield a Brune stress drop larger than 500 bars. However, a corner frequency value off; = 0.6 Hz and the seismic moment resulting from regional data allows the acceleration spectra to be reproduced on the entire available frequency band yielding to a Brune stress drop of 210 bars. The ambiguity on the corner frequency value associated to this earthquake is due to the limited frequency bandwidth available on the strong motion recordil1gs. Assuming the seismic moment estimated at regional distances from broad-band data, the moment magnitude for this earthquake is 5.7. The higher local magnitude (5.9) compared with the moment magnitude (5.7) is due to the weak regional attenuation. Beside this, site amplifications due to surface geology have produced the highest peak ground motions among those observed at the strong motion sites.

Seismic coda Q and scaling law of the source spectra at the Aeolian Islands, southern Italy

1983 ◽  
Vol 73 (1) ◽  
pp. 97-108
Author(s):  
E. Del Pezzo ◽  
F. Ferulano ◽  
A. Giarrusso ◽  
M. Martini
Keyword(s):  
Southern Italy ◽  
Scaling Law ◽  
Coda Wave ◽  
Corner Frequency ◽  
Volcanic Complex ◽  
Coda Q ◽  
Aeolian Islands ◽  
Scaling Properties ◽  
Linear Pattern ◽  
Seismic Coda

abstract The model developed by Aki and Chouet for the coda wave generation and propagation has been used to calculate the quality factor Q for the zone of the Aeolian Islands, southern Italy, in the frequency range of 1 to 12 Hz, and the scaling properties of the seismic spectrum in the magnitude range of 0.4 to 4.7. The Q found for the Aeolian area has a frequency dependence of the form Q = qfv. The absolute values of Q seem to be dependent on the station and location of the seismic events, confirming the strong lateral heterogeneities in the geological structure beneath the Aeolian Arc. A temporal variation has been noted in the Q calculated at Vulcano station (VPL) in a period of 3 weeks soon after the occurrence of a main shock of ML = 5.5 located near the station. The scaling behavior of this sequence is similar to that obtained in two areas of California and one portion of Japan, with a corner frequency that remains constant with an increasing seismic moment between magnitudes 1 and 4. It differs substantially from the scaling properties of the Hawaian earthquakes that show a linear pattern, without an increase of the stress drop with magnitude. The fact that Vulcano is an active volcano seems not to influence the scaling properties of the seismic sequence localized very near it. It probably indicates that the aftershocks used for calculating the scaling law are generated out of the volcanic complex Lipari-Vulcano, in a zone with a good capability of accumulating the stress.

On the heterogeneity of the earthquake rupture

2020 ◽  
Author(s):  
Luca Malagnini ◽  
Douglas S Dreger ◽  
Robert M Nadeau ◽  
Irene Munafò ◽  
Massimo Cocco
Keyword(s):  
Stress Drop ◽  
Seismic Moment ◽  
Corner Frequency ◽  
Self Similarity ◽  
Earthquake Parameters ◽  
Scaling Models ◽  
Elastic Rebound ◽  
Earthquake Size ◽  
Source Models ◽  
Slip Area

Summary The scaling of earthquake parameters with seismic moment and its interpretation in terms of self-similarity is still debated in the literature. We address this question by examining a worldwide compilation of corner frequency-based and elastic rebound theory (ERT)-based fault slip, area and stress drop values for earthquakes ranging in magnitude from -0.7 to 7.8. We find that corner frequency estimates of slip (and stress drop) scale differently than those inferred from the ERT approach, where the latter deviates from the generally accepted constant stress drop behavior of so-called self-similar scaling models. We also find that average slips from finite-source models are consistent with corner frequency scaling, whereas peak slip values are more consistent with the ERT scaling. The different scaling of corner frequency- and ERT-based estimates of slip and stress drop with earthquake size is interpreted in terms of heterogeneity of the rupture process. ERT-based estimates of stress drop decrease with seismic moment suggesting a self-affine behavior. Despite the inferred heterogeneity at all scales, we do not observe a clear effect on the Brune stress drop scaling with earthquake size.

scholarly journals On the scaling between precursory moment release and earthquake magnitude: Insights from the laboratory.

2020 ◽  
Author(s):  
Mateo Acosta ◽  
Francois Passelègue ◽  
Alexandre Schubnel ◽  
Raúl Madariaga ◽  
Marie Violay
Keyword(s):  
Seismic Moment ◽  
Scaling Law ◽  
Fluid Pressure ◽  
Acoustic Emissions ◽  
Large Earthquake ◽  
Nucleation Theory ◽  
Stick Slip ◽  
Scaling Relationship ◽  
Precursory Slip ◽  
Large Earthquakes

<p>Recent seismological observations highlighted that both aseismic silent slip and/or foreshock sequences can precede large earthquake ruptures (Tohoku-Oki, 2011, Mw 9.0  (Kato et al., 2012); Iquique, 2014, Mw 8.1 (Ruiz et al, 2014; Socquet et al., 2017); Illapel, 2015, Mw 8.3 (Huang and Meng, 2018); Nicoya, 2012, Mw 7.6 (Voss et al., 2018)). However, the evolution of such precursory markers during earthquake nucleation remains poorly understood. Here, we report for the first time, experimental results regarding the nucleation of laboratory earthquakes (stick slip events) conducted on Westerly Granite saw-cut samples under both dry and fluid pressure conditions. Experiments were conducted under stress conditions representative of the upper continental crust, i.e confining pressures from 50 to 95 MPa; fluid pressures (water) ranging from 0 to 45 MPa.</p><p>At a given effective confining pressure, different precursory slip behaviors are observed. In dry conditions, we observe that slip evolves exponentially up to the main instability and is escorted by an exponential increase of acoustic emissions. With pressurized fluids, precursory slip evolves first exponentially then switches to a power law of time. There, precursory slip remains silent, independently of the fluid pressure level. The temporal evolution of precursory fault slip and seismicity are controlled by the fault’s environment, limiting its prognostic value. Nevertheless, we show that, independently of the fault conditions, the total precursory moment release scales with the co-seismic moment of the main instability. The relation follows a semi- empirical scaling relationship between precursory and co-seismic moment release by combining nucleation theory (Ida, 1972; Campillo and Ionescu, 1992) with the scaling between fracture energy and co-seismic slip which has been demonstrated experimentally (Nielsen et al., 2016; Passelègue et al., 2016), theoretically (Viesca and Garagash; 2015) and by natural observations (Abercrombie and Rice; 2005). We then compile data from natural earthquakes, and show that, over a range of Mw6.0 to Mw9.0 the proposed scaling law holds for natural observations. In summary, the amount of moment released prior to an earthquake is directly related to its magnitude, increasing therefore the detectability of large earthquakes. The scaling relationship between precursory and co-seismic moment should motivate detailed studies of precursory deformation of moderate to large earthquakes.</p>

scholarly journals SOURCE MECHANISM AND SIZE OF THE 24 APRIL 2002 ML 5.2 GNJILANE (KOSOVO) EARTHQUAKE

2017 ◽  
Vol 32 (1-2) ◽  
Author(s):  
Vera Čejkovska ◽  
Lazo Pekevski ◽  
Dragana Černih
Keyword(s):  
Seismic Moment ◽  
Main Shock ◽  
Amplitude Spectrum ◽  
Source Mechanism ◽  
Corner Frequency ◽  
Source Spectrum ◽  
Wave Group ◽  
Simple Method ◽  
Fault Surface ◽  
Lg Wave

A b s t r a c t: The 24 April 2002 ML 5.2 Gnjilane earthquake was studied first through inversion of the Sg – Lg wave group displacement amplitude spectrum and P-nodal planes determination. The seismic moment, source spectrum corner frequency and Brune equivalent circular fault surface for this shock were obtained, respectively, as M0 = 6.48·1016 N·m, f0 = 0.59 Hz and Σs,eq = 15.2 km2. The P-nodal planes for the four strongest aftershocks and the distribution of other aftershocks’ epicentres were determined, too, and used in identifying the actual source mechanism of the main shock by a simple method that included also the vertical projections on the Earth’s surface of the main shock Σs,eq with the two main shock P-nodal planes as possible fault planes. It was found that the main shock was caused by a normal right lateral faulting in a plane which struck with an azimuth of 238° and dipped toward NNW under an angle of 22°. This faulting was associated with the shear stressed fault structure along the Pliocene-Quarternary sinking valley of Binačka Morava, and it led to activations of other ruptures as sources of a significant number of aftershocks.

scholarly journals ANALISIS PARAMETER SUMBER SPEKTRAL GEMPABUMI VTA (VULKANO TEKTONIK-A) TERHADAP AKTIVITAS VULKANIK GUNUNG SINABUNG

2019 ◽  
Vol 5 (1) ◽  
pp. 18-23
Author(s):  
Tri Kusmita ◽  
Kirbani Brotopuspito ◽  
Hetty Triastuty
Keyword(s):  
Stress Drop ◽  
Seismic Moment ◽  
Source Parameters ◽  
Radiation Energy ◽  
Angular Frequency ◽  
Moment Magnitude ◽  
Corner Frequency ◽  
Volcanic Earthquake ◽  
Seismic Volumes ◽  
The Relationship

The source parameters describe the different physical properties of seismic volumes under the volcanoes. Source parameters that can be used to distinguish seismic events that are generated by different types of volcanoes activities. Temporary changes of the spectral source parameters provided a description of the main events during the eruption process.  Source parameters are calculated by correlating the relationship between source frequency at spectral displacement (corner frequency) and source parameters based on spectral sources of the Brune model (1970). The angular frequency obtained by applying the FFT algorithm to the VTA spectral displacement. The source parameters analyzed from this VTA earthquake are the spectral slope, seismic moment, stress drop, length of rupture, moment magnitude and radiation energy. Based on the obtained corner frequency (12 Hz-13 Hz), seismic moment, moment magnitude and energy radiation respectively were at 0.2 -1.9 x 1012 Nm, 0.7 - 2 Mw, and 0.1 - 9.5 x 1015 erg. The length of rupture were from 144.2 to 243.1 m, the spectra slope has 2.1 - 7.8 dB/cm, and stress drop are 0.1 - 7,6 bar. From the results of this study, it can be concluded that the changes of spectra characteristic and fluctuate of source patrameters value of VTA earthquakes was asosiated with the different  volcanic activity of Sinabung. Keywords: spectral, VTA, source parameter, volcanic earthquake

Source characteristics of small to moderate earthquakes in the Kanto region, Japan: application of a new definition of the S-wave time window length

1996 ◽  
Vol 86 (5) ◽  
pp. 1284-1291
Author(s):  
Kazutoshi Watanabe ◽  
Haruo Sato ◽  
Shigeo Kinoshita ◽  
Masakazu Ohtake
Keyword(s):  
Wave Energy ◽  
Seismic Moment ◽  
Time Window ◽  
P Wave ◽  
Corner Frequency ◽  
Window Length ◽  
S Wave ◽  
S Waves ◽  
Source Characteristics ◽  
Kanto Region

Abstract The S wave from a local earthquake generally consists of several pulses, in contrast to a simple pulse of P wave. This results in a large uncertainty in the estimation of seismic moment and wave energy when the window length for S-wave analysis is not chosen properly. In this study, we propose a new method to define objectively an appropriate time window length of the S wave for estimation of source characteristics based on the S-wave to P-wave energy ratio for a point shear dislocation source. Analyzing waveform data of 97 local earthquakes in the Kanto region, Japan, whose magnitudes M range from 3.3 to 6.0, we obtained simple equations for predicting the time window length of the S-wave TS as a function of earthquake magnitude or pulse width of P-wave TP; we got TS ≈ 1.8 TP for the relation between TP and TS. Applying the S-wave window thus defined, we estimated seismic energy E, seismic moment M0, and corner frequency fc for both P and S waves. Regression analysis of those parameters revealed (1) our method to define TS is confirmed by the fact that the seismic moment determined from P and S waves are consistent; (2) in the range of 1014 < M0 < 1018 (N·m), M0 is almost proportional to f−3c both for P and S waves; (3) the value of E/M0 is 2.7 ∼ 4.0 × 10−5; and (4) breakdown of the scaling relation is seen at M ≦ 4.

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