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Brune model

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Journal Article
Published: 04 January 2023
Bulletin of the Seismological Society of America (2023) 113 (2): 577–591.
...Meichen Liu; Yihe Huang; Jeroen Ritsema ABSTRACT Although 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...
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First thumbnail for: Characterizing Multisubevent Earthquakes Using the...
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Third thumbnail for: Characterizing Multisubevent Earthquakes Using the...
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Brune model fit of the median corrected displacement spectrum for event “38476711.” The black dots are the median of the corrected spectral amplitudes, and the black line is the Brune fit, with moment and corner frequency given by the values shown with the red dot. Contours show levels of constant misfit, and error bars are determined from bootstrapping. The color version of this figure is available only in the electronic edition.
Published: 09 January 2025
Figure 7. Brune model fit of the median corrected displacement spectrum for event “38476711.” The black dots are the median of the corrected spectral amplitudes, and the black line is the Brune fit, with moment and corner frequency given by the values shown with the red dot. Contours show levels
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The main limitations of the Brune model approach for stress‐drop estimation, demonstrated with results from two different rupture models: MGK2018, McGuire and Kaneko (2018), light and dark blue; Kurzon et al. (2021), orange to red colors. (a) Source radii as a function of corner frequencies—radii are calculated by applying a circular source approximation, and corner frequencies are measured in spectral domain. The Brune model curves are calculated using the different parameters of each of the models (constant K‐values and shear‐wave velocities). The source radii do not fit the Brune model curves, and for similar source sizes there is a wide range of possible corner frequencies. (b) Seismic moment as a function of frequency for some similar corner frequency simulations: 1.25 Hz for MGK2018 simulations; 11 Hz for Kurzon et al. (2021) simulations; 0.137 and 0.0305 Hz for several events from the Allman and Shearer (2009)M0–fc catalog. All, further emphasize that sources with even more than one order of magnitude difference in seismic moments, may show similar corner frequencies. The color version of this figure is available only in the electronic edition.
Published: 31 December 2024
Figure 1. The main limitations of the Brune model approach for stress‐drop estimation, demonstrated with results from two different rupture models: MGK2018, McGuire and Kaneko (2018) , light and dark blue; Kurzon et al. (2021) , orange to red colors. (a) Source radii as a function of corner
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Examples spectrum from NOLF inverted for fc using (a) Brune model, which results in significantly lower fc values than models adopting the κ0 operator. Models adopting the (b) κ0=0.030 and (c) κ0=0.034 provide a better fit at lower magnitudes. The color version of this figure is available only in the electronic edition.
Published: 28 April 2020
Figure 10. Examples spectrum from NOLF inverted for f c using (a) Brune model, which results in significantly lower f c values than models adopting the κ 0 operator. Models adopting the (b)  κ 0 = 0.030 and (c)  κ 0 = 0.034 provide a better fit
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Brune model fit for complete data case. (a) Observed seismogram and maximum‐likelihood (ML) fit. (b) Detail of 3 s of the seismogram. (c) Comparison of the fitted parametric spectrum with the discrete Fourier transform (DFT) of the seismogram. (d) Slices of the log‐likelihood function, the white cross pinpoints the ML estimate.
Published: 03 January 2017
Figure 3. Brune model fit for complete data case. (a) Observed seismogram and maximum‐likelihood (ML) fit. (b) Detail of 3 s of the seismogram. (c) Comparison of the fitted parametric spectrum with the discrete Fourier transform (DFT) of the seismogram. (d) Slices of the log‐likelihood function
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Brune model fit for incomplete data case. (a) Observed seismogram, unobserved seismogram, and time‐domain fit. (b) Detail of three seconds of the seismogram. (c) Comparison of the fitted parametric spectrum with Fourier transform of the complete seismogram and maximum a posteriori (MAP) estimate of the spectrum from observed (incomplete) seismogram. (d) Slices of the log‐likelihood function, the white cross and the white dot pinpoint the ML estimate for the complete and incomplete data case, respectively.
Published: 03 January 2017
Figure 7. Brune model fit for incomplete data case. (a) Observed seismogram, unobserved seismogram, and time‐domain fit. (b) Detail of three seconds of the seismogram. (c) Comparison of the fitted parametric spectrum with Fourier transform of the complete seismogram and maximum a posteriori
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Variation of stress drop against focal depth for (a) Brune model and (b) Madariaga model.
Published: 01 February 2013
Figure 5. Variation of stress drop against focal depth for (a) Brune model and (b) Madariaga model.
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Source spectra obtained from the direct method, compared to Brune model spectra. Brune model parameters (moment magnitude, stress drop, and κ) as shown. Frequency range for the direct method is generally 0.5–15 Hz. (a) 8 December 1991: M 3.7; stress = 80 bars; κ = 0.0. (b) 24 September 1996: M 2.4; stress > 8 bars. (c) 9 March 1989: M 3.6; stress = 42 bars; κ = 0.0. (d) 11 March 1989: M 3.6; stress = 21 bars; κ = 0.0. (e) 7 August 1993: M 2.5; stress > 10 bars. (f) 22 November 1989: M 2.9; stress = 1 bar; κ = 0.0. (g) 21 October 1990: M 2.8; stress = 27 bars. (h) 7 June 1996: M 2.6; stress > 12 bars.
Published: 01 December 2001
Figure 4. Source spectra obtained from the direct method, compared to Brune model spectra. Brune model parameters (moment magnitude, stress drop, and κ ) as shown. Frequency range for the direct method is generally 0.5–15 Hz. (a) 8 December 1991: M 3.7; stress = 80 bars; κ = 0.0. (b) 24
Journal Article
Published: 01 October 2001
Bulletin of the Seismological Society of America (2001) 91 (5): 1190–1198.
... the accelerograms recorded at short distances from the fault traces. Applying Brune's model, we have determined important source parameters, such as rise time, stress drop, offset, and particle velocity. Generally, the earthquake is characterized as having had two distinct fault segments. The southern segment...
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First thumbnail for: Estimates of Source Parameters for the 1999 Chi-Ch...
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Journal Article
Journal: Geophysics
Published: 08 May 2014
Geophysics (2014) 79 (3): KS31–KS41.
... to be used in microseismic studies for characterizing the size of an event and calculating its moment magnitude. For non-double-couple sources, the proportional relationship between body-wave amplitude and seismic moment in the Brune model breaks down. So under such situations, the Brune model...
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First thumbnail for: The matter of size: On the moment magnitude of mic...
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Journal Article
Published: 27 November 2023
Bulletin of the Seismological Society of America (2024) 114 (2): 690–709.
... parameters. The source spectrum of the simulated rupture process using the hierarchical patch model generally follows the Brune model. However, the source spectrum underestimates the Brune model near the corner frequencies when the event size grows over M w 5.5. This spectral shape is consistent...
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First thumbnail for: Source Scaling of Simulated Dynamic Ruptures Using...
Second thumbnail for: Source Scaling of Simulated Dynamic Ruptures Using...
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Journal Article
Published: 01 August 2000
Bulletin of the Seismological Society of America (2000) 90 (4): 1028–1040.
... of the Georgia Strait earthquake is in good agreement with the Brune point-source model, with a stress drop of approximately 45 bars. The apparent source spectrum of the slightly larger Duvall earthquake is in reasonable agreement with the Brune model, with a stress drop of about 70 bars; however, for the Duvall...
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First thumbnail for: Integrated Use of Seismograph and Strong-Motion Da...
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Journal Article
Published: 21 April 2025
Bulletin of the Seismological Society of America (2025) 115 (3): 825–838.
... and larger magnitude dependence than the Brune model. Variance reduction threshold, frequency bandwidth, and time‐window length, if chosen within an appropriate parameter range, have limited influence on source parameter measurement. For both methods, wave type, attenuation correction, and spectral...
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First thumbnail for: Factors That Influence Variability in Stress‐Drop ...
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Third thumbnail for: Factors That Influence Variability in Stress‐Drop ...
Journal Article
Published: 18 June 2024
Bulletin of the Seismological Society of America (2024) 114 (5): 2310–2324.
... by Brune (1970) , a new method of estimating f c , based on the phase fitting of Fourier spectra of the Brune’s seismic pulse related to S ‐waves, called Fourier phase spectra fitting (FPS), is proposed and evaluated in this study. The method can be applied in cases in which Brune’s model may...
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First thumbnail for: Direct Estimation of the Source Corner Frequency o...
Second thumbnail for: Direct Estimation of the Source Corner Frequency o...
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Journal Article
Published: 01 October 1996
Bulletin of the Seismological Society of America (1996) 86 (5): 1300–1313.
... similarity. Observed characteristics of S -wave spectra in ENA are fully explained as simple consequences of directivity effects entailed by the classical crack rupture model (Kostrov, 1964; Madariaga, 1976), with “normal” effective stresses of the order of 100 bars and fractional stress drop (Brune, 1970...
Journal Article
Published: 17 December 2024
Bulletin of the Seismological Society of America (2025) 115 (3): 760–776.
..., methods that assumed a Boatwright model tended to have lower Ω 0 and somewhat higher f c compared to those assuming a Brune model, although resulting Δ σ estimates are similar. When compared to the overall validation study results, the fitting approach alone may account for between 5% and 90% (25...
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First thumbnail for: SCEC/USGS Community Stress‐Drop Validation Study: ...
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Journal Article
Published: 01 February 1997
Bulletin of the Seismological Society of America (1997) 87 (1): 97–113.
..., recorded at rupture distances from 1 to 200 km. Empirically derived source spectra for California earthquakes are generally inconsistent with the spectral shape implied by a Brune (“omega-squared”) point-source model. This is manifested by magnitude- and frequency-dependence of the Brune model parameters...
Journal Article
Published: 21 August 2024
Bulletin of the Seismological Society of America (2025) 115 (3): 1149–1161.
...—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...
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First thumbnail for: The Impact of Source Time Function Complexity on S...
Second thumbnail for: The Impact of Source Time Function Complexity on S...
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Estimated source parameters using Brune’s model. The circles and triangles denote events between mb 4–5 and 5–6, respectively. (a) Variation of stress drop with seismic moment. Higher stress drops, with averages close to 9.5 MPa (95 bars) and 16.0 MPa (160 bars) for mb 4–5 and 5–6, respectively, were found. The dashed lines represent constant corner frequencies of 1 and 7 Hz. (b) Variation of corner frequency with the seismic moment. The dashed lines represent constant stress drops of 0.4 and 140 MPa.
Published: 30 June 2015
Figure 10. Estimated source parameters using Brune’s model. The circles and triangles denote events between m b  4–5 and 5–6, respectively. (a) Variation of stress drop with seismic moment. Higher stress drops, with averages close to 9.5 MPa (95 bars) and 16.0 MPa (160 bars) for m b  4–5
Journal Article
Published: 27 May 2014
Bulletin of the Seismological Society of America (2014) 104 (3): 1458–1478.
... )=−1.72+0.43 M with a standard deviation of 0.19 in log10 units, based on the values obtained from the study earthquakes. The apparent source spectra of most M 6+ earthquakes can be modeled using a simple Brune point‐source model. For a few of the M 6+ earthquakes, notably those in California, we observed...
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