scholarly journals Earthquake magnitude, intensity, energy, and acceleration

1956 ◽  
Vol 46 (2) ◽  
pp. 105-145 ◽  
Author(s):  
B. Gutenberg ◽  
C. F. Richter
Keyword(s):  
Surface Waves ◽  
Additional Data ◽  
Earthquake Magnitude ◽  
Body Waves ◽  
Magnitude Scale ◽  
Energy Relation ◽  
Local Earthquakes ◽  
Average Factor

Abstract This supersedes Paper 1 (Gutenberg and Richter, 1942). Additional data are presented. Revisions involving intensity and acceleration are minor. The equation log a = I/3 − 1/2 is retained. The magnitude-energy relation is revised as follows: (20) log ⁡ E = 9.4 + 2.14 M − 0.054 M 2 A numerical equivalent, for M from 1 to 8.6, is (21) log ⁡ E = 9.1 + 1.75 M + log ⁡ ( 9 − M ) Equation (20) is based on (7) log ⁡ ( A 0 / T 0 ) = − 0.76 + 0.91 M − 0.027 M 2 applying at an assumed point epicenter. Eq. (7) is derived empirically from readings of torsion seismometers and USCGS accelerographs. Amplitudes at the USCGS locations have been divided by an average factor of 2 1/2 to compensate for difference in ground; previously this correction was neglected, and log E was overestimated by 0.8. The terms M2 are due partly to the response of the torsion seismometers as affected by increase of ground period with M, partly to the use of surface waves to determine M. If MS results from surface waves, MB from body waves, approximately (27) M S − M B = 0.4 ( M S − 7 ) It appears that MB corresponds more closely to the magnitude scale determined for local earthquakes. A complete revision of the magnitude scale, with appropriate tables and charts, is in preparation. This will probably be based on A/T rather than amplitudes.

A magnitude scale for local earthquakes in South Australia

1975 ◽  
Vol 65 (5) ◽  
pp. 1267-1285
Author(s):  
Ian C. F. Stewart
Keyword(s):  
Epicentral Distance ◽  
South Australia ◽  
Magnitude Scale ◽  
Source Spectrum ◽  
S Waves ◽  
Scale Parameters ◽  
Local Earthquakes ◽  
Dependent Absorption ◽  
Relationship Of ◽  
The Relationship

Abstract To minimize dispersion in local magnitude estimates due to different instrumental bandwidths, a scale has been established to allow for the average source spectrum, geometrical attenuation, and frequency-dependent absorption. The data used to derive the scale parameters were from S waves recorded in South Australia from 1967 through 1970, in the frequency range 1 to 10 Hz, and for epicentral distances up to 5°. The magnitudes were mainly in the range 1.5 to 3.5. The local scale MN is given by M N = 4.85 + log A g + 0.84 log Δ + 0.0003 f Δ / 2.3 − 2.89 log f + 2.45 ( log f ) 2 + c where Ag mm is the ground amplitude at f Hz at Δ km epicentral distance, and c is a station correction. The dispersion in observations of magnitude has probably been reduced by use of the scale to near the theoretical limits, allowing for possible source radiation patterns. The relationship of the scale to other measures of magnitude is uncertain, but MN may be approximately equivalent to the local Richter magnitude ML for the magnitude range (1.5 < ML < 3.5) commonly observed in South Australia. The scle is limited in use to data in the ranges given above, for local earthquakes in South Australia. Modification is necessary before such a magnitude scale can be applied elsewhere or to different data ranges.

Azimuthal multiple signal classification of dispersive and aliased surface waves recorded in 3D seismic acquisition

Geophysics ◽  
2021 ◽  
pp. 1-84
Author(s):  
Chunying Yang ◽  
Wenchuang Wang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Body Waves ◽  
Signal Classification ◽  
Dispersion Pattern ◽  
Velocity Spectrum ◽  
Low Velocity ◽  
Surface Wave Dispersion ◽  
Multiple Signal Classification ◽  
Multiple Signal

Irregular acquisition geometry causes discontinuities in the appearance of surface wave events, and a large offset causes seismic records to appear as aliased surface waves. The conventional method of sampling data affects the accuracy of the dispersion spectrum and reduces the resolution of surface waves. At the same time, ”mode kissing” of the low-velocity layer and inhomogeneous scatterers requires a high-resolution method for calculating surface wave dispersion. This study tested the use of the multiple signal classification (MUSIC) algorithm in 3D multichannel and aliased wavefield separation. Azimuthal MUSIC is a useful method to estimate the phase velocity spectrum of aliased surface wave data, and it represent the dispersion spectra of low-velocity and inhomogeneous models. The results of this study demonstrate that mode-kissing affects dispersion imaging, and inhomogeneous scatterers change the direction of surface-wave propagation. Surface waves generated from the new propagation directions are also dispersive. The scattered surface wave has a new dispersion pattern different to that of the entire record. Diagonal loading was introduced to improve the robustness of azimuthal MUSIC, and numerical experiments demonstrate the resultant effectiveness of imaging aliasing surface waves. A phase-matched filter was applied to the results of azimuthal MUSIC, and phase iterations were unwrapped in a fast and stable manner. Aliased surface waves and body waves were separated during this process. Overall, field data demonstrate that azimuthal MUSIC and phase-matched filters can successfully separate aliased surface waves.

The rupture process and aftershock distribution of the 6 April 1992 MS 6.8 earthquake, Offshore British Columbia

1995 ◽  
Vol 85 (3) ◽  
pp. 716-735 ◽  
Author(s):  
John F. Cassidy ◽  
Garry C. Rogers
Keyword(s):  
Surface Waves ◽  
Triple Junction ◽  
Rupture Process ◽  
Body Waves ◽  
Ocean Bottom Seismometer ◽  
Strain Accumulation ◽  
Transform Fault ◽  
Junction Region ◽  
Long Period ◽  
Initial Rupture

Abstract On 6 April 1992, a magnitude 6.8 (MS) earthquake occurred in the triple-junction region at the northern end of the Cascadia subduction zone. This was the largest earthquake in at least 75 yr to occur along the 110-km-long Revere-Dellwood-Wilson (RDW) transform fault and the first large earthquake in this region recorded by modern broadband digital seismic networks. It thus provides an opportunity to examine the rupture process along a young (<2 Ma) oceanic transform fault and to gain better insight into the tectonics of this triple-junction region. We have investigated the source parameters and the rupture process of this earthquake by modeling broadband body waves and long-period surface waves and by accurately locating the mainshock and the first 10 days of aftershocks using a well-located “calibration” event recorded during an ocean-bottom seismometer survey. Analysis of P and SH waveforms reveals that this was a complex rupture sequence consisting of three strike-slip subevents in 12 sec. The initial rupture occurred 5 to 6 km to the SW of the seafloor trace of the RDW fault at 50.55° N, 130.46° W. The dominant subevent occurred 2 to 3 sec later and 4.3 km beneath the seafloor trace of the RDW fault, and a third subevent occurred 5 sec later, 18 km to the NNW, suggesting a northwestward propagating rupture. The aftershock sequence extended along a 60- to 70-km-long segment of the RDW fault, with the bulk of the activity concentrated ∼30 to 40 km to the NNW of the epicenter, consistent with this interpretation. The well-constrained mechanism of the initial rupture (strike/dip/slip 339°/90°/−168°) and of the largest aftershock (165°/80°/170°) are rotated 15° to 20° clockwise relative to the seafloor trace of the RDW fault but are parallel to the Pacific/North America relative plate motion vector. In contrast, the mechanisms of the dominant subevent (326°/87°/−172°), and the long-period solution derived from surface waves aligns with the RDW fault. This suggests that small earthquakes (M < 6) in this area occur along faults that are optimally aligned with respect to the regional stress field, whereas large earthquakes, involving tens of kilometers of rupture, activate the RDW fault. For the mainshock, we estimate a seismic moment (from surface waves) of 1.0 × 1026 dyne-cm, a stress drop of 60 bars, and an average slip of 1.2 m. This represents only 21 yr of strain accumulation, implying that there is either a significant amount of aseismic slip along the RDW fault or that much of the strain accumulation manifests itself as deformation within the Dellwood and Winona blocks or along the continental margin.

Onset of energy equipartition among surface and body waves

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200775
Author(s):  
L. Borcea ◽  
J. Garnier ◽  
K. Sølna
Keyword(s):  
Radiative Transfer ◽  
Thin Layer ◽  
Surface Waves ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Body Waves ◽  
Homogeneous Layer ◽  
Power Exchange ◽  
Energy Equipartition ◽  
The Mean

We derive a radiative transfer equation that accounts for coupling from surface waves to body waves and the other way around. The model is the acoustic wave equation in a two-dimensional waveguide with reflecting boundary. The waveguide has a thin, weakly randomly heterogeneous layer near the top surface, and a thick homogeneous layer beneath it. There are two types of modes that propagate along the axis of the waveguide: those that are almost trapped in the thin layer, and thus model surface waves, and those that penetrate deep in the waveguide, and thus model body waves. The remaining modes are evanescent waves. We introduce a mathematical theory of mode coupling induced by scattering in the thin layer, and derive a radiative transfer equation which quantifies the mean mode power exchange. We study the solution of this equation in the asymptotic limit of infinite width of the waveguide. The main result is a quantification of the rate of convergence of the mean mode powers toward equipartition.

Short-period seismic noise

1967 ◽  
Vol 57 (1) ◽  
pp. 55-81
Author(s):  
E. J. Douze
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Seismic Noise ◽  
Body Waves ◽  
Deep Hole ◽  
Period Range ◽  
Short Period ◽  
The Subject ◽  
Hole Arrays

abstract This report consists of a summary of the studies conducted on the subject of short-period (6.0-0.3 sec period) noise over a period of approximately three years. Information from deep-hole and surface arrays was used in an attempt to determine the types of waves of which the noise is composed. The theoretical behavior of higher-mode Rayleigh waves and of body waves as measured by surface and deep-hole arrays is described. Both surface and body waves are shown to exist in the noise. Surface waves generally predominate at the longer periods (of the period range discussed) while body waves appear at the shorter periods at quiet sites. Not all the data could be interpreted to define the wave types present.

scholarly journals Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180382
Author(s):  
Tianshi Liu ◽  
Haiming Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Surface Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Body Waves ◽  
Spherically Symmetric ◽  
Travel Times ◽  
Cross Correlations ◽  
The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

Tracking of velocity variations at depth in the presence of surface velocity fluctuations

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. U1-U8 ◽  
Author(s):  
Benoit de Cacqueray ◽  
Philippe Roux ◽  
Michel Campillo ◽  
Stefan Catheline
Keyword(s):  
Surface Waves ◽  
Body Waves ◽  
Surface Velocity ◽  
Small Scale ◽  
Beam Forming ◽  
Near Surface ◽  
Velocity Fluctuations ◽  
Wave Separation ◽  
Double Beam ◽  
Velocity Variations

We tested a small-scale experiment that is dedicated to the study of the wave separation algorithm and to the velocity variations monitoring problem itself. It handles the case in which velocity variations at depth are hidden by near-surface velocity fluctuations. Using an acquisition system that combines an array of sources and an array of receivers, coupled with controlled velocity variations, we tested the ability of beam-forming techniques to track velocity variations separately for body waves and surface waves. After wave separation through double beam forming, the arrival time variations of the different waves were measured through the phase difference between the extracted wavelets. Finally, a method was tested to estimate near-surface velocity variations using surface waves or shallow reflection and compute a correction to isolate target velocity variations at depth.

Observations of Loma Prieta aftershocks from a dense array in Sunnyvale, California

1991 ◽  
Vol 81 (5) ◽  
pp. 1900-1922
Author(s):  
Arthur Frankel ◽  
Susan Hough ◽  
Paul Friberg ◽  
Robert Busby
Keyword(s):  
Surface Waves ◽  
Body Waves ◽  
Love Waves ◽  
Apparent Velocity ◽  
Dense Array ◽  
S Wave ◽  
Small Aperture ◽  
Long Period ◽  
Santa Clara Valley ◽  
Loma Prieta

Abstract A small aperture (≈300 m), four-station array was deployed in Sunnyvale, California for 5 days to record aftershocks of the Loma Prieta earthquake of October 1989. The purpose of the array was to study the seismic response of the alluvium-filled Santa Clara Valley and the role of surface waves in the seismic shaking of sedimentary basins. Strong-motion records of the Loma Prieta mainshock indicate that surface waves produced the peak velocities and displacements at some sites in the Santa Clara Valley. We use the recordings from the dense array to determine the apparent velocity and azimuth of propagation for various arrivals in the seismograms of four aftershocks with magnitudes between 3.6 and 4.4. Apparent velocities are generally observed to decrease with increasing time after the S wave in the seismograms. Phases arriving less than about 8 sec after the S wave have apparent velocities comparable to the S wave and appear to be body waves multiply reflected under the receiver site or reflected by crustal interfaces. For times 10 to 30 sec after the direct S wave, we observe long-period (1 to 6 sec) arrivals with apparent velocities decreasing from 2.5 to 0.8 km / sec. We interpret these arrivals to be surface waves and conclude that these surface waves produce the long duration of shaking observed on the aftershock records. Much of the energy in the 40 sec after the S-wave is coming approximately from the direction of the source, although some arrivals have backazimuths as much as 60° different from the backazimuths to the epicenters. Two of the aftershocks show arrivals coming from 30 to 40° more easterly than the epicenters. This energy may have been scattered from outcrops along the southeastern edge of the basin. In contrast, the deepest aftershock studied (d = 17 km) displays later arrivals with backazimuths 30 to 40° more westerly than the epicenter. A distinct arrival for one of the aftershocks propagates from the southwest, possibly scattered from the western edge of the basin. Synthetic seismograms derived from a plane-layered crustal model do not produce the long-period Love waves observed in the waveforms of the ML 4.4 aftershock. These Love waves may be generated by the conversion of incident S waves or Rayleigh waves near the edge of the basin.

Statistical properties of Rayleigh waves due to scattering by topography

1967 ◽  
Vol 57 (1) ◽  
pp. 83-90
Author(s):  
J. A. Hudson ◽  
L. Knopoff
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Seismic Noise ◽  
Forward Scattering ◽  
Statistical Properties ◽  
Body Waves ◽  
Simplified Model ◽  
Two Dimensional ◽  
Especial Reference ◽  
The Earth

abstract The two-dimensional problems of the scattering of harmonic body waves and Rayleigh waves by topographic irregularities in the surface of a simplified model of the earth are considered with especial reference to the processes of P-R, SV-R and R-R scattering. The topography is assumed to have certain statistical properties; the scattered surface waves also have describable statistical properties. The results obtained show that the maximum scattered seismic noise is in the range of wavelengths of the order of the lateral dimensions of the topography. The process SV-R is maximized over a broader band of wavelengths than the process P-R and thus the former may be more difficult to remove by selective filtering. An investigation of the process R-R shows that backscattering is much more important than forward scattering and hence topography beyond the array must be taken into account.

A model study of elastic waves in a layered sphere

1967 ◽  
Vol 57 (5) ◽  
pp. 959-981
Author(s):  
Victor Gregson
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Elastic Waves ◽  
Wave Dispersion ◽  
Flat Space ◽  
Dispersion Curves ◽  
Body Waves ◽  
Surface Wave Dispersion ◽  
Steel Sphere ◽  
Long Wave

abstract Elastic waves produced by an impact were recorded at the surface of a solid 12.0 inch diameter steel sphere coated with a 0.3 inch copper layer. Conventional modeling techniques employing both compressional and shear piezoelectric transducers were used to record elastic waves for one millisecond at various points around the great circle of the sphere. Body, PL, and surface waves were observed. Density, layer thickness, compressional and shear-wave velocities were measured so that accurate surface-wave dispersion curves could be computed. Surface-wave dispersion was measured as well as computed. Measured PL mode dispersion compared favorably with theoretical computations. In addition, dispersion curves for Rayleigh, Stoneley, and Love modes were computed. Measured surface-wave dispersion showed Rayleigh and Love modes were observed but not Stoneley modes. Measured dispersion compared favorably with theoretical computations. The curvature correction applied to dispersion calculations in a flat space has been estimated to correct dispersion values at long-wave lengths to about one per cent of correct dispersion in a spherical model. Measured dispersion compared with such flat space dispersion corrected for curvature proved accurate within one per cent at long wave lengths. Two sets of surface waves were observed. One set was associated with body waves radiating outward from impact. The other set was associated with body waves reflecting at the pole opposite impact. For each set of surface waves, measured dispersion compared favorably with computed dispersion.

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