Tests of Remote Dynamic Aftershock Triggering by Small Mainshocks Using Taiwan’s Earthquake Catalog

2021 ◽  
Author(s):  
Wei Peng ◽  
Shinji Toda
Keyword(s):  
Power Law ◽  
Dynamic Stress ◽  
Geothermal Gradient ◽  
Active Volcano ◽  
Stress Change ◽  
Small Scale ◽  
Earthquake Catalog ◽  
Earthquake Triggering ◽  
Power Law Decay ◽  
Dynamic Stress Change

Abstract To understand earthquake interaction and forecast time-dependent seismic hazard, it is essential to determine which static or dynamic stress change due to a mainshock plays a major role in triggering its aftershocks and subsequent mainshocks. Using small mainshocks (2≤M<3) and their aftershocks, Felzer and Brodsky (2006) argued that mainshock induced dynamic stress change is responsible for earthquake triggering in a form of power-law decay within 50 km. Richards-Dinger et al. (2010), however, studied the foreshock decay and claimed that mainshock had no effect at distances outside its static stress triggering range, which required an alternative explanation. We tested these hypotheses using Taiwan’s earthquake catalog by taking advantage of its lack of large events and the absence of active volcano and associated significant seismic swarm. In examining earthquakes occurring in 1994–2010, following Felzer and Brodsky’s method, we found a linear aftershock density with a power-law decay of −1.12±0.38 that is very similar to the one seen in Felzer and Brodsky (2006). None of the mainshock–aftershock pairs were associated with an M 7 rupture event or M 6 event. We further demonstrated that the density decay in a short time period is more likely a randomized behavior than mainshock–aftershock triggering. These pairs were located mostly in high geothermal gradient areas, which are probably triggered by a small-scale aseismic process.

scholarly journals Power spectra of random heterogeneities in the solid earth

Solid Earth ◽  
2019 ◽  
Vol 10 (1) ◽  
pp. 275-292 ◽  
Author(s):  
Haruo Sato
Keyword(s):  
Solid Earth ◽  
Power Law ◽  
Upper Mantle ◽  
Spectral Envelope ◽  
Small Scale ◽  
Mean Square ◽  
Statistical Characterization ◽  
The Earth ◽  
Power Law Decay ◽  
Wide Range

Abstract. Recent seismological observations focusing on the collapse of an impulsive wavelet revealed the existence of small-scale random heterogeneities in the earth medium. The radiative transfer theory (RTT) is often used for the study of the propagation and scattering of wavelet intensities, the mean square amplitude envelopes through random media. For the statistical characterization of the power spectral density function (PSDF) of the random fractional fluctuation of velocity inhomogeneities in a 3-D space, we use an isotropic von Kármán-type function characterized by three parameters: the root mean square (RMS) fractional velocity fluctuation, the characteristic length, and the order of the modified Bessel function of the second kind, which leads to the power-law decay of the PSDF at wavenumbers higher than the corner. We compile reported statistical parameters of the lithosphere and the mantle based on various types of measurements for a wide range of wavenumbers: photo-scan data of rock samples; acoustic well-log data; and envelope analyses of cross-hole experiment seismograms, regional seismograms, and teleseismic waves based on the RTT. Reported exponents of wavenumber are distributed between −3 and −4, where many of them are close to −3. Reported RMS fractional fluctuations are on the order of 0.01–0.1 in the crust and the upper mantle. Reported characteristic lengths distribute very widely; however, each one seems to be restricted by the dimension of the measurement system or the sample length. In order to grasp the spectral characteristics, eliminating strong heterogeneity data and the lower mantle data, we have plotted all the reported PSDFs of the crust and the upper mantle against wavenumber for a wide range (10−3–108 km−1). We find that the spectral envelope of those PSDFs is well approximated by the inverse cube of wavenumber. It suggests that the earth-medium randomness has a broad spectrum. In theory, we need to re-examine the applicable range of the Born approximation in the RTT when the wavenumber of a wavelet is much higher than the corner. In observation, we will have to carefully measure the PSDF on both sides of the corner. We may consider the obtained power-law decay spectral envelope as a reference for studying the regional differences. It is interesting to study what kinds of geophysical processes created the observed power-law spectral envelope at different scales and in different geological environments in the solid earth medium.

scholarly journals Power Spectra of Random Heterogeneities of the Solid Earth

2018 ◽  
Author(s):  
Haruo Sato
Keyword(s):  
Solid Earth ◽  
Power Law ◽  
Upper Mantle ◽  
Spectral Envelope ◽  
Small Scale ◽  
Mean Square ◽  
Statistical Characterization ◽  
The Earth ◽  
Power Law Decay ◽  
Wide Range

Abstract. Recent seismological observations focusing on the collapse of an impulsive wavelet revealed the existence of small-scale random heterogeneities in the earth medium. The radiative transfer theory (RTT) is often used for the study of the propagation and scattering of wavelet intensities, the mean square amplitude envelopes. For the statistical characterization of the power spectral density function (PSDF) of the random fractional fluctuation of velocity inhomogeneities in a 3D space, we use von Karman type with three parameters: the root mean square (RMS) fractional velocity fluctuation, the characteristic length, and the order of the modified Bessel function of the second kind, which leads to the power-law decay of PSDF at wavenumbers higher than the corner. We compile reported statistical parameters of the lithosphere and the mantle based on various types of measurements for a wide range of wavenumbers: photo scan data of rock samples, acoustic well log data, and envelope analyses of cross-hole experiment seismograms, regional seismograms and tele-seismic waves based on the RTT. Reported exponents of wavenumber are distributed between −3 and −4, where many of them are close to −3. Reported RMS fractional fluctuations are of the order of 0.01 ~ 0.1 in the crust and the upper mantle. Reported characteristic lengths distribute very widely, however, each one seems to be restricted by the dimension of the measurement system or the sample length. In order to grasp the spectral characteristics, eliminating strong heterogeneity data and the lower mantle data, we have plotted all the reported PSDFs of the crust and the upper mantle against wavenumber for a wide range 10−3 ∼ 108 km−1. We find that the envelope of those PSDFs is well approximated by the −3rd power of wavenumber. It suggests that the earth medium randomness has a broad spectrum. In theory, we need to re-examine the applicable range of the Born approximation in the RTT when the wavenumber of a wavelet is much higher than the corner. In observation, we will have to measure carefully the PSDF on both sides of the corner. We may consider the obtained power-law decay spectral envelope as a reference for studying the regional differences. It is interesting to study what kinds of geophysical processes created the observed power-law spectral envelope in different scales and in different portions of the solid earth medium.

scholarly journals Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory

2021 ◽  
Vol 10 (3) ◽  
pp. 157
Author(s):  
Paul-Mark DiFrancesco ◽  
David A. Bonneau ◽  
D. Jean Hutchinson
Keyword(s):  
Computational Geometry ◽  
Surface Reconstruction ◽  
Power Law ◽  
Point Cloud ◽  
Point Clouds ◽  
Volume Estimation ◽  
Estimation Methods ◽  
Small Scale ◽  
Reconstruction Methods ◽  
3D Volume

Key to the quantification of rockfall hazard is an understanding of its magnitude-frequency behaviour. Remote sensing has allowed for the accurate observation of rockfall activity, with methods being developed for digitally assembling the monitored occurrences into a rockfall database. A prevalent challenge is the quantification of rockfall volume, whilst fully considering the 3D information stored in each of the extracted rockfall point clouds. Surface reconstruction is utilized to construct a 3D digital surface representation, allowing for an estimation of the volume of space that a point cloud occupies. Given various point cloud imperfections, it is difficult for methods to generate digital surface representations of rockfall with detailed geometry and correct topology. In this study, we tested four different computational geometry-based surface reconstruction methods on a database comprised of 3668 rockfalls. The database was derived from a 5-year LiDAR monitoring campaign of an active rock slope in interior British Columbia, Canada. Each method resulted in a different magnitude-frequency distribution of rockfall. The implications of 3D volume estimation were demonstrated utilizing surface mesh visualization, cumulative magnitude-frequency plots, power-law fitting, and projected annual frequencies of rockfall occurrence. The 3D volume estimation methods caused a notable shift in the magnitude-frequency relations, while the power-law scaling parameters remained relatively similar. We determined that the optimal 3D volume calculation approach is a hybrid methodology comprised of the Power Crust reconstruction and the Alpha Solid reconstruction. The Alpha Solid approach is to be used on small-scale point clouds, characterized with high curvatures relative to their sampling density, which challenge the Power Crust sampling assumptions.

scholarly journals When an oscillating center in an open system undergoes power law decay

2018 ◽  
Vol 57 (3) ◽  
pp. 750-768 ◽  
Author(s):  
Sandip Saha ◽  
Gautam Gangopadhyay
Keyword(s):  
Power Law ◽  
Open System ◽  
Power Law Decay

scholarly journals Transient brightenings in the quiet Sun detected by ALMA at 3 mm

2020 ◽  
Vol 638 ◽  
pp. A62 ◽  
Author(s):  
A. Nindos ◽  
C. E. Alissandrakis ◽  
S. Patsourakos ◽  
T. S. Bastian
Keyword(s):  
Solar Atmosphere ◽  
Power Law ◽  
Small Scale ◽  
Solar Chromosphere ◽  
Average Intensity ◽  
Quiet Sun ◽  
Brightness Temperatures ◽  
Weak Preference ◽  
Thermal Origin ◽  
First Time

Aims. We investigate transient brightenings, that is, weak, small-scale episodes of energy release, in the quiet solar chromosphere; these episodes can provide insights into the heating mechanism of the outer layers of the solar atmosphere. Methods. Using Atacama Large Millimeter/submillimeter Array (ALMA) observations, we performed the first systematic survey for quiet Sun transient brightenings at 3 mm. Our dataset included images of six 87″ × 87″ fields of view of the quiet Sun obtained with angular resolution of a few arcsec at a cadence of 2 s. The transient brightenings were detected as weak enhancements above the average intensity after we removed the effect of the p-mode oscillations. A similar analysis, over the same fields of view, was performed for simultaneous 304 and 1600 Å data obtained with the Atmospheric Imaging Assembly. Results. We detected 184 3 mm transient brightening events with brightness temperatures from 70 K to more than 500 K above backgrounds of ∼7200 − 7450 K. All events showed light curves with a gradual rise and fall, strongly suggesting a thermal origin. Their mean duration and maximum area were 51.1 s and 12.3 Mm2, respectively, with a weak preference of appearing at network boundaries rather than in cell interiors. Both parameters exhibited power-law behavior with indices of 2.35 and 2.71, respectively. Only a small fraction of ALMA events had either 304 or 1600 Å counterparts but the properties of these events were not significantly different from those of the general population except that they lacked their low-end energy values. The total thermal energies of the ALMA transient brightenings were between 1.5 × 1024 and 9.9 × 1025 erg and their frequency distribution versus energy was a power law with an index of 1.67 ± 0.05. We found that the power per unit area provided by the ALMA events could account for only 1% of the chromospheric radiative losses (10% of the coronal ones). Conclusions. We were able to detect, for the first time, a significant number of weak 3 mm quiet Sun transient brightenings. However, their energy budget falls short of meeting the requirements for the heating of the upper layers of the solar atmosphere and this conclusion does not change even if we use the least restrictive criteria possible for the detection of transient brightenings.

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