Variation of seismic scalar moment–corner frequency relationship during development of a hydraulic fracture system

2019 ◽  
Vol 38 (2) ◽  
pp. 123-129
Author(s):  
Takashi Mizuno ◽  
Joel Le Calvez ◽  
Jim Rutledge
Keyword(s):  
Hydraulic Fracture ◽  
Stress Drop ◽  
Static Stress ◽  
Corner Frequency ◽  
Fracture System ◽  
Rupture Velocity ◽  
Static Stress Drop ◽  
Two Parameter ◽  
Parameter Relation ◽  
Scalar Moment

We propose to utilize the corner frequency and seismic scalar moment relation as a new approach to monitor temporal changes of static stress drop as well as rupture velocity during development of a hydraulic fracture system. We introduce a single parameter M1 to describe a two-parameter relation (scalar moment and corner frequency relation) and analyze temporal variation of this two-parameter relation. Because M1 relates rupture velocity and static stress drop, we can infer temporal variation of rupture velocity and stress drop quantitatively. The parameter M1 is calculated in two case studies. We document that two types of fracturing processes exist: (1) stable rupture velocity and static stress drop during the development of rupture and (2) increase of rupture velocity and/or static stress drop while the fracture system develops. In the latter case, one possible scenario is increase of permeability at each fracture plane during development of the fracture system.

Source physics interpretation of non-self-similar double-corner frequency source spectral model JA19_2S

2021 ◽  
Author(s):  
Chen Ji ◽  
Ralph Archuleta
Keyword(s):  
Aspect Ratio ◽  
Stress Drop ◽  
Dynamic Stress ◽  
Static Stress ◽  
Corner Frequency ◽  
Rupture Velocity ◽  
Dynamic Stress Drop ◽  
Self Similar ◽  
Static Stress Drop ◽  
Frequency Source

<p>Source spectral models developed for strong ground motion simulations are phenomenological models that represent the average effect that the source processes have on near fault ground motion. Their parameters are directly regressed from the observations and often do not have clear meaning for the physics of the source process. We investigate the relation between the kinematic double-corner frequency (DCF) source spectral model JA19_2S (Ji and Archuleta, BSSA, 2020) and static fault geometry scaling relations proposed by Leonard (2010). We derive scaling relations for the low and high corner frequency in terms of static stress drop, dynamic stress drop, fault rupture velocity, fault aspect ratio, and relative hypocenter location. We find that the non-self-similar low corner frequency  scaling relation of JA19_2S model for 5.3<<strong>M</strong><6.9 earthquakes is well explained using the fault length scaling relation of Leonard’s model combined with a constant rupture velocity. Earthquakes following both models have constant average static stress drop and constant average dynamic stress drop. The high frequency source radiation is controlled by seismic moment, static stress drop and dynamic stress drop but strongly modulated by the fault aspect ratio and the hypocenter’s relative location. The mean, scaled energy  (or apparent stress) decreases with magnitude due to the magnitude dependence of the fault aspect ratio. Based on these two models, the commonly quoted average rupture velocity of 70-80% of shear wave speed implies predominantly unilateral rupture.</p>

A Source Physics Interpretation of Nonself-Similar Double-Corner-Frequency Source Spectral Model JA19_2S

2022 ◽  
Author(s):  
Chen Ji ◽  
Ralph J. Archuleta
Keyword(s):  
Stress Drop ◽  
Wave Speed ◽  
Dynamic Stress ◽  
Corner Frequency ◽  
Rupture Velocity ◽  
Scaling Relation ◽  
Shear Wave Speed ◽  
Dynamic Stress Drop ◽  
Static Stress Drop ◽  
Frequency Source

Abstract We investigate the relation between the kinematic double-corner-frequency source spectral model JA19_2S (Ji and Archuleta, 2020) and static fault geometry scaling relations proposed by Leonard (2010). We find that the nonself-similar low-corner-frequency scaling relation of JA19_2S model can be explained using the fault length scaling relation of Leonard’s model combined with an average rupture velocity ∼70% of shear-wave speed for earthquakes 5.3 < M< 6.9. Earthquakes consistent with both models have magnitude-independent average static stress drop and average dynamic stress drop around 3 MPa. Their scaled energy e˜ is not a constant. The decrease of e˜ with magnitude can be fully explained by the magnitude dependence of the fault aspect ratio. The high-frequency source radiation is generally controlled by seismic moment, static stress drop, and dynamic stress drop but is further modulated by the fault aspect ratio and the relative location of the hypocenter. Based on these two models, the commonly quoted average rupture velocity of 70%–80% of shear-wave speed implies predominantly unilateral rupture.

Source dimensions and stress drops of small earthquakes near Parkfield, California

1984 ◽  
Vol 74 (1) ◽  
pp. 27-40
Author(s):  
M. E. O'Neill
Keyword(s):  
Stress Drop ◽  
Small Region ◽  
Static Stress ◽  
Depth Range ◽  
Zero Crossing ◽  
Source Dimensions ◽  
Duration Magnitude ◽  
Short Period ◽  
Static Stress Drop ◽  
Stress Drops

Abstract Source dimensions and stress drops of 30 small Parkfield, California, earthquakes with coda duration magnitudes between 1.2 and 3.9 have been estimated from measurements on short-period velocity-transducer seismograms. Times from the initial onset to the first zero crossing, corrected for attenuation and instrument response, have been interpreted in terms of a circular source model in which rupture expands radially outward from a point until it stops abruptly at radius a. For each earthquake, duration magnitude MD gave an estimate of seismic moment MO and MO and a together gave an estimate of static stress drop. All 30 earthquakes are located on a 6-km-long segment of the San Andreas fault at a depth range of about 8 to 13 km. Source radius systemically increases with magnitude from about 70 m for events near MD 1.4 to about 600 m for an event of MD 3.9. Static stress drop ranges from about 2 to 30 bars and is not strongly correlated with magnitude. Static stress drop does appear to be spatially dependent; the earthquakes with stress drops greater than 20 bars are concentrated in a small region close to the hypocenter of the magnitude 512 1966 Parkfield earthquake.

Rupture analysis of the 2020 Petrinja earthquake based on seismological observations

2021 ◽  
Author(s):  
Mathieu Causse
Keyword(s):  
Spectral Analysis ◽  
Stress Drop ◽  
Kinematic Model ◽  
Source Model ◽  
Corner Frequency ◽  
Rupture Propagation ◽  
Rupture Velocity ◽  
Geophysical Research ◽  
Apparent Source ◽  
Rupture Duration

<p>Here, I use seismological observations (~70 broadband stations at distances between 100 and 400 km from the source) to characterize the rupture properties of the Petrinja mainshock (Mw 6.4). First, I perform a spectral analysis of the P-waves to compute the corner frequency. In order to remove the wave propagation effects and isolate the source properties, I use the largest foreshocks and aftershocks (Mw>4) as empirical Green’s functions (EGFs). Assuming a Brune’s source model, the obtained stress drop is ~20 MPa. This rather large value is in agreement with the short rupture length of ~8 km inferred by InSAR data (Ganas et al. 2021). In addition, the weak azimuthal variations of the corner frequencies indicates a bilateral rupture, that is a rupture nucleating close to the fault center. Second, I compute the apparent source time functions (i.e. the source time functions “seen” from any station) using an EGF deconvolution approach. The results indicate an average rupture duration of 5-6 s with weak azimuthal variation of the apparent rupture duration, in agreement with the spectral analysis. Finally, I perform a Bayesian inversion of the apparent source function, in order to obtain a kinematic model of the rupture propagation (slip distribution, rupture velocity). The preliminary results reveal a slow velocity of the rupture propagation. Such a slow rupture velocity associated with a large stress drop has been observed on other faults with slow slip rates (e.g. Causse et al. 2017). This work provides insight on the rupture process of this major event on a poorly documented fault. I am fully open for collaborations to further develop and enrich this study.</p><p><br><strong>References</strong><br>Causse, M., G. Cultrera, L. Moreau, A. Herrero, E. Schiapappietra and F. Courboulex. Bayesian rupture imaging in a complex medium. The 29 May 2012 Emilia, Northern Italy, earthquake (2017), Geophysical Research Letters, DOI : 10.1002/2017GL074698.<br>Ganas, A., Elias, P., Valkaniotis, S., Tsironi, V., Karasante, I., Briole, P., 2021, Petrinja earthquake moved crust 10 feet, Temblor, http://doi.org/10.32858/temblor.156</p>

scholarly journals Static stress drop as determined from geodetic strain rates and statistical seismicity

2011 ◽  
Vol 116 (B2) ◽  
Author(s):  
Alessandro Caporali ◽  
Salvatore Barba ◽  
Michele M. C. Carafa ◽  
Roberto Devoti ◽  
Grazia Pietrantonio ◽  
...  
Keyword(s):  
Stress Drop ◽  
Static Stress ◽  
Strain Rates ◽  
Static Stress Drop ◽  
Geodetic Strain
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