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.

Focal mechanism and source depth of earthquakes from body- and surface-wave data

1971 ◽  
Vol 61 (5) ◽  
pp. 1369-1379 ◽  
Author(s):  
Nezihi Canitez ◽  
M. Nafi Toksöz
Keyword(s):  
Surface Wave ◽  
Body Wave ◽  
Source Parameters ◽  
Focal Depth ◽  
Spectral Ratio ◽  
The Body ◽  
Spectral Ratios ◽  
Motion Data ◽  
Wave Data ◽  
Surface Wave Data

abstract The determination of focal depth and other source parameters by the use of first-motion data and surface-wave spectra is investigated. It is shown that the spectral ratio of Love to Rayleigh waves (L/R) is sensitive to all source parameters. The azimuthal variation of the L/R spectral ratios can be used to check the fault-plane solution as well as for focal depth determinations. Medium response, attenuation, and source finiteness seriously affect the absolute spectra and introduce uncertainty into the focal depth determinations. These effects are nearly canceled out when L/R amplitude ratios are used. Thus, the preferred procedure for source mechanism studies of shallow earthquakes is to use jointly the body-wave data, absolute spectra of surface waves, and the Love/Rayleigh spectral ratios. With this procedure, focal depths can be determined to an accuracy of a few kilometers.

Robust measurements of corner frequency, t* and site effect: the iterative cluster event method

2020 ◽  
Author(s):  
Pei-Ru Jian ◽  
Ban-Yuan Kuo
Keyword(s):  
Body Wave ◽  
Wave Spectrum ◽  
Chemical Properties ◽  
Spectral Ratio ◽  
Site Effect ◽  
Seismic Attenuation ◽  
Corner Frequency ◽  
P Waves ◽  
Robust Measurements ◽  
The Stability

<p>Seismic attenuation accompanying the velocity structures demonstrates the variations of the physical and chemical properties of the earth. The t* measurement using the seismic body wave spectrum, however, typically encounters the trade-off of corner frequency, t*, and site effect. Ko et al, [2012] proposed the cluster event method (CEM) that reduced the model parameter numbers by grouping the spatial-closed enough events for those traveling to each station along the adjacent paths and sharing one t*. Yet, the site effects among different stations collected in the same cluster bring the challenges on fitting all spectrum. We adapt the cluster strategy to group multiple nearby events recorded by one station only. Moreover, the new iterative CEM algorithm includes both the spectrum and spectral ratio data which provide constraints on seismic moments and corner frequencies of each earthquake inside the cluster, respectively. The final t* and corner frequencies are determined again by including the side effects which are averaging from spectrum residuals in the initial CEM stage. We applied the iterative CEM for earthquakes recorded at dense deployed F-net and Hi-net by NIED in the Tohoku area, Japan. The multitaper spectrums are retrieved from direct P waves with coda wavetrains tapered. Combining the spectral ratio and spectrum data with proper weightings, our new approach increases the stability of t* measurements contributed from better constrains on the corner frequency estimations.</p>

Investigation of crustal structure by the analysis of reverberation periodicities

1978 ◽  
Vol 68 (5) ◽  
pp. 1387-1397
Author(s):  
Roopa Gir ◽  
Shiv Mohan G. Subhash ◽  
Mansur A. Choudhury
Keyword(s):  
Crustal Structure ◽  
Magnetic Tape ◽  
Numerical Models ◽  
Spectral Ratio ◽  
Spectral Ratios ◽  
Crustal Model ◽  
Matching Technique ◽  
Deep Focus ◽  
Data Length ◽  
Ratio Matching

abstract The analysis of reverberation periodicities is shown to be a promising method to study local crustal structure. It is demonstrated with the help of numerical models, that for an average crust; a data length of only 8 to 12 sec is sufficient to derive a crustal model in contrast to about 40 sec or more needed in the Phinney's spectral ratio matching technique. Examples from numerical models of one- and two-layer crusts are presented. Analysis of five intermediate and deep focus earthquakes, recorded on magnetic tape at the Echery (ECH) observatory of the Institut de Physique du Globe of Strasbourg, shows that while the spectral ratios indicate little overall coherence, the periodicity corresponding to the total crustal thickness is evident in all cases. The possibility of deriving a detailed crustal model is also discussed with the help of results from one of the above events.

Near-source effects on regional seismograms: An analysis of the NTS explosions PERA and QUESO

1991 ◽  
Vol 81 (6) ◽  
pp. 2371-2394
Author(s):  
Steven R. Taylor ◽  
John T. Rambo ◽  
Robert P. Swift
Keyword(s):  
Shock Wave ◽  
High Frequency ◽  
Spectral Characteristics ◽  
Low Frequency ◽  
Spectral Ratio ◽  
Corner Frequency ◽  
Burial Depth ◽  
Wave System ◽  
Spectral Ratios ◽  
Remarkable Similarity

Abstract A comparative analysis of two closely spaced Nevada Test Site explosions, PERA and QUESO, is made to study the effects of near-source phenomena on regional-wave excitation. Although the two explosions were of similar size, burial depth, and only separated by 4 km, the 1 to 2 and 6 to 8 Hz regional-wave spectral ratio for QUESO is anomalously low (a factor of 10 smaller than that of PERA). Examination of the regional and close-in spectra for each event shows a remarkable similarity and suggests that QUESO has less low-frequency and more high-frequency energy than PERA. These observations may be caused by a 564 m3, funnel-shaped region filled with unconsolidated sand and a possible void directly above the QUESO detonation point. Close-in observations suggest that this region may have partially decoupled the up-going energy from QUESO, resulting in a reduction of the low-frequency energy. The high-frequency enhancement for QUESO may be due to the rapid loss of energy to nonlinear effects such as greater pore collapse and fracturing in the anomalous region. This resulted in the radiation of more impulsive, shorter-duration waveforms producing a higher corner frequency and less-rapid high-frequency spectral decay for QUESO. For PERA, the loss of energy to a two-wave system occurred more slowly and over a larger volume, resulting in a broader source pulse typical of explosions in porous materials. Comparison of shock radius versus time data suggests that the shock wave was strongly affected in the anomalous zone a few meters above the QUESO device. One-dimensional finite-difference calculations with and without a partial decoupling region within 8 m of the device are consistent with the observations. Although spallation was reduced for QUESO, simulations using a finite spall model indicate that the spall spectral peak should be centered at about 3 to 7 Hz and probably did not significantly contribute to the reduced spectral ratio. The remarkable similarity of the PERA/QUESO spectral ratios taken at distances of 90 m and 400 km suggests that the spectral characteristics of explosions are established in close proximity to the source. Although depth-dependent effects of attenuation acting at small strains may enhance the differences in spectral ratios between NTS explosions and western U.S. earthquakes, these effects are probably secondary to the high-pressure, high strain-rate dynamic material response to the radiated explosion shock wave. These observations point out the importance of up-going energy on the generation of regional phases from explosions. Because of reduced overburden pressures above the detonation point, large nonlinear deformations predominate in this region and appear to affect all of the signals except perhaps the very initial part of the Pn waveform.

scholarly journals Attenuation of shear waves in the upper and lower mantle

1964 ◽  
Vol 54 (6A) ◽  
pp. 1855-1864 ◽  
Author(s):  
Robert L. Kovach ◽  
Don L. Anderson
Keyword(s):  
Lower Mantle ◽  
Seismic Waves ◽  
Wave Amplitude ◽  
Body Wave ◽  
Shear Waves ◽  
Normal Incidence ◽  
Frequency Range ◽  
Spectral Ratios ◽  
The Earth ◽  
Deep Focus

abstract The attenuation of seismic waves is a direct measure of the absorption due to nonelastic processes in the earth. The well known difficulties in obtaining body wave amplitude decrement data have been avoided by studying the spectral ratios of multiple ScS and sScS phases from two deep focus earthquakes recorded at near normal incidence. The average Q, for shear, in the mantle is about 600 for the frequency range 0.015 to 0.07 cps. Assuming that equal radiation occurs upwards and downwards from the source the average Q for the upper 600 km of the mantle is determined to be about 200 and about 2200 for the rest of the mantle. The value for Q at the base of the mantle is at least 5000 for shear waves.

Investigation of Relationship between the Response and Fourier Spectral Ratios Based on Statistical Analyses of Strong-Motion Records

2020 ◽  
pp. 2150008
Author(s):  
Haizhong Zhang ◽  
Yan-Gang Zhao
Keyword(s):  
Seismic Design ◽  
Site Effects ◽  
Epicentral Distance ◽  
Ground Motions ◽  
Scaling Law ◽  
Ground Surface ◽  
Strong Motion ◽  
Spectral Ratio ◽  
Spectral Ratios ◽  
Earthquake Scenario

In both seismic design and probabilistic seismic-hazard analyses, site effects are typically characterized as the ratio of the response spectral ordinate on the ground surface to that on the bedrock based on the scaling law borrowed from the Fourier spectral ordinate. Recent studies have shown that different from the Fourier spectral ratio (FSR), the response spectral ratio (RSR) does not purely reflect the site effects but also depends on the earthquake scenario even for linear analysis. However, previous studies are limited to theoretical analysis. This study statistically compares the two spectral ratios by analyzing many actual seismic ground motions recorded at nearby soil and rock sites. It is observed that the average RSR and FSR have similar overall shapes, and their maximum values occur at approximately the same period; however, the values around the peak are clearly different with FSRs consistently exceeding the RSRs. The RSR–FSR relationship depends on the earthquake scenario and the oscillator damping; their difference at periods longer than the site’s fundamental period decreases as the magnitude and epicentral distance increase, and the RSRs generally approach the FSRs as the oscillator damping decreases.

Retrieval of source-extent parameters and the interpretation of corner frequency

1983 ◽  
Vol 73 (6A) ◽  
pp. 1499-1511
Author(s):  
Paul Silver
Keyword(s):  
Body Wave ◽  
Amplitude Spectrum ◽  
Low Frequency ◽  
P Wave ◽  
Corner Frequency ◽  
S Wave ◽  
Dislocation Source ◽  
Statistical Measures ◽  
Dislocation Models ◽  
Planar Dislocation

Abstract A method is proposed for retrieving source-extent parameters from far-field body-wave data. At low frequency, the normalized P- or S-wave displacement amplitude spectrum can be approximated by |Ω^(r^,ω)| = 1 − τ2(r^)ω2/2 where r^ specifies a point on the focal sphere. For planar dislocation sources, τ2(r^) is linearly related to statistical measures of source dimension, source duration, and directivity. τ2(r^) can be measured as the curvature of |Ω^(r^,ω)| at ω = 0 or the variance of the pulse Ω^(r^,t). The quantity ωc=2τ−1(r^) is contrasted with the traditional corner frequency ω0, defined as the frequency at the intersection of the low- and high-frequency trends of |Ω^(r^,ω)|. For dislocation models without directivity, ωc(P) ≧ ωc(S) for any r^. A mean corner frequency defined by averaging τ2(r^) over the focal sphere, ω¯c=2<τ2(r^)>−1/2, satisfies ωc(P) > ωc(S) for any dislocation source. This behavior is not shared by ω0. It is shown that ω0 is most sensitive to critical times in the rupture history of the source, whereas ωc is determined by the basic parameters of source extent. Evidence is presented that ωc is the corner frequency measured on actual seismograms. Thus, the commonly observed corner frequency shift (P-wave corner greater than the S-wave corner), now viewed as a shift in ωc is simply a result of spatial finiteness and is expected to be a property of any dislocation source. As a result, the shift cannot be used as a criterion for rejecting particular dislocation models.

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.

scholarly journals Source parameters of earthquakes, and discrimination between earthquakes and nuclear explosions

1968 ◽  
Vol 58 (5) ◽  
pp. 1503-1517
Author(s):  
John B. Davies ◽  
Stewart W. Smith
Keyword(s):  
Fault Plane ◽  
Source Parameters ◽  
Spectral Ratio ◽  
Shallow Earthquake ◽  
Compressional Waves ◽  
Nuclear Explosions ◽  
Deep Earthquakes ◽  
Fracture Velocity ◽  
Fault Length

Abstract The first part of this study describes a technique by which the source parameters of an earthquake can be obtained from the spectrum of compressional waves. The source parameters defined are fault length, fracture velocity, and fault plane attitude. Two large, deep earthquakes are examined using this technique. The source parameters determined compare favorably with those obtained previously using different techniques. In the second section a method is proposed for discrimination between underground explosions and earthquakes. The technique utilizes the ratio of the spectrums of the two classes of events where the path of propagation is common to both. On the basis of the analysis of the SHOAL event and a nearby shallow earthquake it appears that the duration as determined from the spectral ratio is almost 10 times smaller for an explosion than it is for a comparable earthquake.

scholarly journals Analysis of Tsunami Inundation due in Pangandaran Tsunami Earthquake in South Java Area Based on Finite Faults Solutions Model

2020 ◽  
Vol 10 (2) ◽  
pp. 114
Author(s):  
Ramadhan Priadi ◽  
Dede Yunus ◽  
Berlian Yonanda ◽  
Relly Margiono
Keyword(s):  
Fault Plane ◽  
Body Wave ◽  
Scaling Law ◽  
Source Mechanism ◽  
Inversion Method ◽  
Tsunami Modeling ◽  
Residential Areas ◽  
North West ◽  
Wave Inversion ◽  
Run Up

On July 17, 2006 an earthquake with a magnitude of  7.7 triggered a tsunami that struck 500 km of the coast in the south of the island of Java. The tsunami generated is classified as an earthquake tsunami because the waves generated were quite large compared to the strength of the earthquake. The difference in the strength of the earthquake and the resulting tsunami requires a tsunami modeling study with an estimated fault area in addition to using aftershock and scaling law. The purpose of this study is to validate tsunamis that occur based on the estimation of the source mechanism and the area of earthquake faults. Determination of earthquake source mechanism parameters using the Teleseismic Body-Wave Inversion method that uses teleseismic waveforms with the distance recorded waveform from the source between  Whereas, tsunami modeling is carried out using the Community Model Interface for Tsunami (commit) method. Fault plane parameters that obtained were strike , dip , and rake  with dominant slip pointing up to north-north-west with a maximum value of 1.7 m. The fault plane is estimated to have a length of 280 km in the strike direction and a width of 102 km in the dip direction. From the results of the tsunami modeling, the maximum inundation area is 0.32 km2 in residential areas flanked by Pangandaran bays and the maximum run-up of 380.96 cm in Pasir Putih beach area. The tsunami modeling results in much smaller inundation and run-up from field observations, it was assumed that the fault plane segmentation had occurred due to the greater energy released than the one from the fault area, causing waves much larger than the modeling results.

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