The use of the coda for determination of the earthquake source spectrum

1978 ◽  
Vol 68 (4) ◽  
pp. 923-948 ◽  
Author(s):  
T. G. Rautian ◽  
V. I. Khalturin
Keyword(s):  
Frequency Band ◽  
Epicentral Distance ◽  
Source Parameters ◽  
Seismic Energy ◽  
The Body ◽  
Corner Frequency ◽  
Source Spectrum ◽  
Time Interval ◽  
S Wave ◽  
Absolute Amplitude

abstract We studied the spectral content and variations in time of the coda of seismic oscillations following the body and surface waves of local earthquakes. Within narrow frequency bands, the form of the envelope of the coda is remarkably stable—independent of epicenter (and therefore epicentral distance), depth of focus, and all other parameters of the source. Only the absolute amplitude of the coda differs from event to event. Similarly, the forms of the coda at two stations from the same earthquake overlap one another, differing only in absolute amplitude by a factor that is the same for all events. Hence given the form of the coda, its amplitude in any frequency band may be parameterized by one number—the amplitude at a certain time. Therefore, the spectrum of the coda as a function of time can be described as the product of two factors—one, independent of time, is dependent only on the source, and the other, reflecting the effects of the medium and the same for all sources, gives the time dependence for each frequency band. Segments of the envelopes with time can be matched by simple theories of scattering. Using the theoretical relationships, estimates of Q can be made and show that for any time interval, Q increases with frequency, approximately proportional to the square root of frequency. As longer elapsed times are considered, the estimates of Q increase, suggesting greater penetration of seismic energy into the higher Q parts of the Earth. The spectra of different events can be compared directly by comparing the spectra of the codas at the same elapsed time. Such a comparison reveals a wide variety of different source spectra. By using empirical relations among coda spectra, observed S-wave spectra, and theoretical constraints, an estimate of the spectrum radiated by the source can be calculated from the coda spectrum. Source parameters (seismic moment, corner frequency of the radiated spectrum, calculated stress drop, etc.) can be determined from coda spectra of events with many different moments and in different regions, with the same station. The results show several interesting features dependent on the seismic moments and on the regions in which the earthquakes occurred.

Ground Motion From A Magnitude 3.5 Earthquake Near Massena, New York: Evidence For Poor Resolution of Corner Frequency For Small Events

1989 ◽  
Vol 60 (3) ◽  
pp. 95-100 ◽  
Author(s):  
S.E. Hough ◽  
K. Jacob ◽  
R. Busby ◽  
P.A. Friberg
Keyword(s):  
Earthquake Engineering ◽  
Epicentral Distance ◽  
Wave Spectrum ◽  
P Wave ◽  
Corner Frequency ◽  
Source Spectrum ◽  
Wave Spectra ◽  
S Wave ◽  
High Quality ◽  
Wide Range

Abstract We present analysis of a magnitude 3.5 event which occurred at 9 km epicentral distance from a digital strong motion instrument operated by the National Center for Earthquake Engineering Research. Although the size of this isolated event is such that it can scarcely be considered to be a significant earthquake, a careful analysis of this high quality recording does yield several interesting results: 1) the S-wave spectra can be interpreted in terms of a simple omega-squared source spectrum and frequency-independent attenuation, 2) there is the suggestion of a poorly-resolved resonance in the P-wave spectrum, and perhaps most importantly, 3) the apparently simple S-wave spectra can be fit almost equally well with a surprisingly wide range of seismic corner frequencies, from roughly 5 to 25 Hz. This uncertainty in corner frequency translates into uncertainties in inferred Q values of almost an order of magnitude, and into uncertainties in stress drop of two orders of magnitude. Given the high quality of the data and the short epicentral distance to the station, we consider it likely that resolution of spectral decay and corner frequency will be at least as poor for any other recording of earthquakes with comparable or smaller magnitudes.

A theoretical study of the radiation from small strikeslip earthquakes at close distances

1983 ◽  
Vol 73 (1) ◽  
pp. 83-96 ◽  
Author(s):  
Michel Campillo ◽  
Michel Bouchon
Keyword(s):  
Ground Motion ◽  
Epicentral Distance ◽  
Homogeneous Medium ◽  
Source Model ◽  
Strike Slip ◽  
Peak Ground Velocity ◽  
Corner Frequency ◽  
Crack Model ◽  
Sharp Change ◽  
S Wave

abstract We present a study of the seismic radiation of a physically realistic source model—the circular crack model of Madariaga—at close distance range and for vertically heterogeneous crustal structures. We use this model to represent the source of small strike-slip earthquakes. We show that the characteristics of the radiated seismic spectra, like the corner frequency, are strongly affected by the presence of the free surface and by crustal layering, and that they can be considerably different from the ones of the homogeneous-medium far-field solution. The vertical and radial displacement spectra are the most strongly affected. We use this source model to calculate the decay of peak ground velocity with epicentral distance and source depth for small strike-slip earthquakes in California. For distances between 10 and 80 km, the peak horizontal velocity decay is of the form r−1.25 for a 4-km hypocentral depth and r−1.65 for deeper sources. The predominance of supercritically reflected arrivals beyond epicentral distances of 70 to 80 km produces a sharp change in the rate of decay of the ground motion. For most of the cases considered, the peak ground velocity increases between 80 and 100 km. We also show that the S-wave velocity in the source layer is the lower limit of phase velocities associated with significant ground motion.

Stress Drop Derived from Spectral Analysis Considering the Hypocentral Depth in the Attenuation Model: Application to the Ridgecrest Region, California

2021 ◽  
Author(s):  
Dino Bindi ◽  
Hoby N. T. Razafindrakoto ◽  
Matteo Picozzi ◽  
Adrien Oth
Keyword(s):  
Stress Drop ◽  
Spectral Decomposition ◽  
Epicentral Distance ◽  
Source Parameters ◽  
S Wave ◽  
Qualitative Comparison ◽  
Ground Shaking ◽  
Attenuation Model ◽  
Hypocentral Distance ◽  
The Impact

ABSTRACT We investigate the impact of considering a depth-dependent attenuation model on source parameters assessed through a spectral decomposition. In particular, we evaluate the effect of considering the hypocentral depth as an additional variable for the attenuation model, using as the target the tendency of the average stress drop to increase with depth, as observed in recent studies. We analyze the Fourier spectra of S-wave windows for about 1900 earthquakes with a magnitude above 2.5 recorded in the Ridgecrest region, southern California. Two different parameterizations of the attenuation term are implemented in the spectral decomposition, either as a function of the hypocentral distance alone or as a function of both epicentral distance and depth. The comparison of the spectral attenuation curves shows that, although the hypocentral model describes, on average, the range of values spanned by the attenuation curve for different depths, systematic differences with distance, depth, and frequency are observed. These differences are transferred to the source spectra and, in turn, to the source parameters extracted from the best-fitting ω−2 models. In particular, stress drops for events deeper than 7 km are, on average, almost double even when depth is introduced explicitly in the attenuation model. The increase of stress drop with depth is confirmed also after accounting for the increase of the shear velocity with depth, which absorbs about 30%–40% of the total increase. Moreover, a qualitative comparison with a model for the gradient of the effective normal stress confirms the reliability of the observed trend. Finally, the coherent spatial patterns shown by a simplified 2D tomographic representation of the spectral residuals highlights the impact on ground-shaking variability of the lateral variability of the crustal attenuation properties in the region.

The partition of radiated energy between P and S waves

1984 ◽  
Vol 74 (2) ◽  
pp. 361-376
Author(s):  
John Boatwright ◽  
Jon B. Fletcher
Keyword(s):  
Wave Energy ◽  
Body Wave ◽  
Focal Mechanisms ◽  
The Body ◽  
Body Waves ◽  
P Wave ◽  
Corner Frequency ◽  
S Wave ◽  
S Waves ◽  
Radiated Energy

Abstract Seventy-three digitally recorded body waves from nine multiply recorded small earthquakes in Monticello, South Carolina, are analyzed to estimate the energy radiated in P and S waves. Assuming Qα = Qβ = 300, the body-wave spectra are corrected for attenuation in the frequency domain, and the velocity power spectra are integrated over frequency to estimate the radiated energy flux. Focal mechanisms determined for the events by fitting the observed displacement pulse areas are used to correct for the radiation patterns. Averaging the results from the nine events gives 27.3 ± 3.3 for the ratio of the S-wave energy to the P-wave energy using 0.5 〈Fi〉 as a lower bound for the radiation pattern corrections, and 23.7 ± 3.0 using no correction for the focal mechanisms. The average shift between the P-wave corner frequency and the S-wave corner frequency, 1.24 ± 0.22, gives the ratio 13.7 ± 7.3. The substantially higher values obtained from the integral technique implies that the P waves in this data set are depleted in energy relative to the S waves. Cursory inspection of the body-wave arrivals suggests that this enervation results from an anomalous site response at two of the stations. Using the ratio of the P-wave moments to the S-wave moments to correct the two integral estimates gives 16.7 and 14.4 for the ratio of the S-wave energy to the P-wave energy.

SEISMOLOGICAL AND ENGINEERING PARAMETERS OF 24 and 26 SEPTEMBER, 2019 MARMARA SEA EARTHQUAKES

2020 ◽  
Author(s):  
Eser Çakti ◽  
Fatma Sevil Malcioğlu ◽  
Hakan Süleyman
Keyword(s):  
Earthquake Engineering ◽  
Prediction Models ◽  
Source Parameters ◽  
Strong Motion ◽  
P Wave ◽  
Corner Frequency ◽  
Marmara Sea ◽  
S Wave ◽  
Data Set ◽  
The North

<p>On 24<sup>th</sup> and 26<sup>th</sup>  September 2019, two earthquakes of M<sub>w</sub>=4.5 and M<sub>w</sub>=5.6 respectively took place in the Marmara Sea. They were associated with the Central Marmara segment of the North Anatolian Fault Zone, which is pinpointed by several investigators as the most likely segment to rupture in the near future giving way to an earthquake larger than M7.0. Both events were felt widely in the region. The M<sub>w</sub>=5.6 event, in particular, led to a number of building damages in Istanbul, which were larger than expected in number and severity. There are several strong motion networks in operation in and around Istanbul. We have compiled a data set of recordings obtained at the stations of the Istanbul Earthquake Rapid Response and Early Warning operated by the Department of Earthquake Engineering of Bogazici University and of the National Strong Motion Network operated by AFAD. It consists of 148 three component recordings, in total.  444 records in the data set, after correction, were analyzed to estimate the source parameters of these events, such as corner frequency, source duration, radius and rupture area, average source dislocation and stress drop. Duration characteristics of two earthquakes were analyzed first by considering P-wave and S-wave onsets and then, focusing on S-wave and significant durations. PGAs, PGVs and SAs were calculated and compared with three commonly used ground motion prediction models (i.e  Boore et al., 2014; Akkar et al., 2014 and Kale et al., 2015). Finally frequency-dependent Q models were estimated using the data set and their validity was dicussed by comparing with previously developed models.</p>

Simultaneous inversion for Q and source parameters of microearthquakes accompanying hydraulic fracturing in granitic rock

1991 ◽  
Vol 81 (2) ◽  
pp. 553-575 ◽  
Author(s):  
Michael Fehler ◽  
W. Scott Phillips
Keyword(s):  
Hydraulic Fracturing ◽  
Stress Drop ◽  
Source Parameters ◽  
Low Frequency ◽  
Seismic Energy ◽  
P Wave ◽  
Corner Frequency ◽  
Spectral Amplitude ◽  
Seismic Zone ◽  
Stress Drops

Abstract An inversion that fits spectra of earthquake waveforms and gives robust estimates of corner frequency and low-frequency spectral amplitude has been used to determine source parameters of 223 microearthquakes induced by hydraulic fracturing in granodiorite. Assuming a ω−2 source model, the inversion fits the P-wave spectra of microearthquake waveforms to determine individual values of corner frequency and low-frequency spectral amplitude for each event and one average frequency-independent Q for all source-receiver paths. We also implemented a constraint that stress drops of all microearthquakes be similar but not equal and found that this constraint did not significantly degrade the quality of the fits to the spectra. The waveforms analyzed were recorded by a borehole seismometer. The P-wave Q was found to be 1070. For Q values as low as 600 and as high as 3000, the misfit between model and spectra increased by less than 5 per cent and the average corner frequency changed by less than 15 per cent from those obtained with a Q of 1070. Average stress drop was 3.7 bars. Seismic moments obtained from spectra ranged from 1013 to 1018 dyne-cm. The low stress drops are interpreted to result from underestimation of the actual stress drops because of a nonuniform distribution of stress drop and slip along the fault planes. Spatially varying stress drops and slips result from the strong rock heterogeneity due to the injection of fluid into the rock. Stress drops were found to be larger near the edges of the seismic zone, in regions that had not been seismically active during previous injections. The seismic moments determined from spectra were used to obtain a coda length-to-moment relation. Then, moments were estimated for 1149 events from measurements of coda lengths from events whose moments could not be measured from spectra because of saturation or a low signal-to-noise ratio. The constant of proportionality between cumulative number of events and seismic moment is higher than that found for tectonic regions. The slope is so high that the seismic energy release is dominated by the large number of small events. In the absence of information about the number of events smaller than we studied, we cannot estimate the total seismic energy released by the hydraulic injection.

scholarly journals Unravelling the links between seismo-acoustic signals and eruptive parameters: Etna lava fountain case study

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Mariangela Sciotto ◽  
Andrea Cannata ◽  
Michele Prestifilippo ◽  
Simona Scollo ◽  
David Fee ◽  
...  
Keyword(s):  
Time Series ◽  
Power Law ◽  
Seismic Velocity ◽  
Source Parameters ◽  
Seismic Energy ◽  
Power Laws ◽  
Geophysical Data ◽  
Time Interval ◽  
Lava Fountain ◽  
Eruptive Parameters

Abstract Deriving eruption source parameters from geophysical data is critical for volcano hazard mitigation, yet remains a challenging task in most volcanoes worldwide. In this work, we explored the temporal relationship between geophysical signals and eruptive parameters measured during six explosive episodes from the New South-East Crater of Mt. Etna (Italy). The quadratic reduced seismic velocity and pressure were calculated to track the temporal variation of volcanic elastic radiation, and the lava fountain height was estimated by thermal camera image processing. The temporal relationships between these geophysical and eruptive time series were studied. In particular, the first considered lava fountain exhibited a “clockwise hysteresis” pattern: higher seismic amplitude with respect to the fountain height during the waxing phase as compared to the waning phase. We also calculated the regression parameters for both linear and power laws, linking seismo-acoustic and eruptive time series. For the linear regressions, we found fairly constant values of the scaling factors in five out of six eruptive episodes, which can be considered as a promising step to derive eruption source parameters from geophysical data in real-time. Regarding power law regressions, a clear relationship was observed between the exponents determined for the power law linking quadratic reduced velocity and lava fountain height, and the time interval duration from the previous eruption. These results suggest that the condition of the uppermost part of the plumbing system (e.g. viscosity of residing magma and conduit conditions) play a key role in the seismic energy generation during the eruptions.

Stress Drops and Directivity of Induced Earthquakes in the Western Canada Sedimentary Basin

2019 ◽  
Vol 109 (5) ◽  
pp. 1635-1652 ◽  
Author(s):  
Joanna M. Holmgren ◽  
Gail M. Atkinson ◽  
Hadi Ghofrani
Keyword(s):  
Stress Drop ◽  
Sedimentary Basin ◽  
Source Parameters ◽  
Corner Frequency ◽  
Source Spectrum ◽  
Western Canada ◽  
Induced Earthquakes ◽  
Western Canada Sedimentary Basin ◽  
Stress Drops ◽  
Canada Sedimentary Basin

Abstract The Western Canada sedimentary basin (WCSB) has experienced an increase in seismicity during the last decade due primarily to hydraulic fracturing. Understanding the ground motions of these induced earthquakes is critical to characterize the increase in hazard. Stress drop is considered an important parameter in this context because it is a measure of the high‐frequency content of the shaking. We use the empirical Green’s function (EGF) method to determine S‐wave corner frequencies and stress drops of 87 earthquakes of moment magnitude (M) 2.3–4.4 in the WCSB. The EGF method is an effective technique to isolate earthquake source effects by dividing out the path and site components in the frequency domain, using a smaller collocated earthquake as an EGF. The corner frequency of the target event is determined for an assumed spectral ratio shape, from which the stress drop is computed. Assuming a fixed velocity, we find that the average stress drop for induced earthquakes in the WCSB for small‐to‐moderate events is 7.5±0.5  MPa, with a total range from 0.2 to 370 MPa. However, because of the dependence of stress drop on model conventions and constants, we consider the absolute stress‐drop value meaningful only for comparison with other results using the same underlying models. By contrast, corner frequency is a less‐ambiguous variable with which to characterize the source spectrum. The range of corner frequencies obtained in this study for events of M 4.0±0.5 is 1.1–5.8 Hz. Significant rupture directivity is observed for more than one‐third of the earthquakes, with station corner frequencies varying by about a factor of 4 with azimuth. This emphasizes the importance of having suitable station coverage to determine source parameters. We model directivity where evident using a Haskell source model and find that the rupture azimuths are primarily oriented approximately north–south throughout the region.

Preparation and In Vitro Evaluation of Resealed Erythrocytes as A New Trend in Treatment of Asthma

2016 ◽  
Vol 6 (3) ◽  
Author(s):  
Mohammed Ibrahim ◽  
Alaa Zaky ◽  
Mohsen Afouna ◽  
Ahmed Samy
Keyword(s):  
In Vitro Release ◽  
Human Erythrocytes ◽  
The Body ◽  
Blood Levels ◽  
Time Interval ◽  
Burst Release ◽  
Prolonged Release ◽  
Nocturnal Asthma ◽  
Carrier Erythrocytes

Carrier erythrocytes are emerging as one of the most promising biological drug delivery systems investigated in recent decades. Beside its biocompatibility, biodegradability and ability to circulate throughout the body, it has the ability to perform extended release system of the drug for a long period. The ultimate goal of this study is to introduce a new carrier system for Salbutamol, maintaining suitable blood levels for a long time, as atrial to resolve the problems of nocturnal asthma medication Therefore in this work we study the effect of time, temperature as well as concentration on the loading of salbutamol in human erythrocytes to be used as systemic sustained release delivery system for this drug. After the loading process is performed the carrier erythrocytes were physically and cellulary characterized. Also, the in vitro release of salbutamol from carrier erythrocytes was studied over time interval. From the results it was found that, human erythrocytes have been successfully loaded with salbutamol using endocytosis method either at 25 Co or at 37 Co . The highest loaded amount was 3.5 mg/ml and 6.5 mg/ml respectively. Moreover, the percent of cells recovery is 90.7± 1.64%. Hematological parameters and osmotic fragility behavior of salbutamol loaded erythrocytes were similar that of native erythrocytes. Scanning electron microscopy demonstrated that the salbutamol loaded cells has moderate change in the morphology. Salbutamol releasing from carrier cell was 43% after 36 hours in phosphate buffer saline. The releasing pattern of the drug from loaded erythrocytes showed initial burst release in the first hour followed by a very slow release, obeying zero order kinetics. It concluded that salbutamol is successfully entrapped into erythrocytes with acceptable loading parameters and moderate morphological changes, this suggesting that erythrocytes can be used as prolonged release carrier for salbutamol.

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.

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