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105
Theoretical basis of some empirical relations in seismology
 Bull. Seismol. Soc. Am
, 1975
"... Empirical relations involving seismic moment Mo, magnitude Ms, energy Es and fault dimension L (or area S) are discussed on the basis of an extensive set of earthquake data (M s> = 6) and simple crack and dynamic dislocation models. The relation between log S and log M o is remarkably linear (s ..."
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Cited by 313 (6 self)
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Empirical relations involving seismic moment Mo, magnitude Ms, energy Es and fault dimension L (or area S) are discussed on the basis of an extensive set of earthquake data (M s> = 6) and simple crack and dynamic dislocation models. The relation between log S and log M o is remarkably linear (slope ~ 2/3) indicating a constant stress drop Aa; Atr = 30, 100 and 60 bars are obtained for interplate, intraplate and "average " earthquakes, respectively. Except for very large earthquakes, the relation M s ~ (2/3) log M o ~ 2 log L is established by the data. This is consistent with the dynamic dislocation model for point dislocation rise times and rupture times of most earthquakes. For very large earthquakes M s ~ (1/3) log M o,, ~ log L ~ (1/3) log E s. For very small earthquakes M s ~ log M o, ~ 3 log L ~ log E s. Scaling rules are assumed and justified. This model predicts log E s ~ 1.5 M s, ~ 3 log L which is consistent with the GutenbergRichter elation. Since the static energy is proportional to 0L 3, where ~ is the average stress, this relation suggests a constant apparent stress ~/¢i where r / is the efficiency. The earthquake data suggest r/0 ~ Atr. These relations lead to log S,, ~ M s consistent with the empirical relation. This relation together with a simple geometrical argument explains the magnitudefrequency relation log N N Ms.
Scaling relations for earthquake source parameters and magnitudes
, 1976
"... A data set of 41 moderate and large earthquakes has been used to derive scaling rules for kinematic fault parameters. If effective stress and static stress drop are equal, then fault rise time, z, and fault area, S, are related by z = 16S1/2/(7~3/2~8), where,8 is shear velocity. Fault length (parall ..."
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Cited by 58 (1 self)
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A data set of 41 moderate and large earthquakes has been used to derive scaling rules for kinematic fault parameters. If effective stress and static stress drop are equal, then fault rise time, z, and fault area, S, are related by z = 16S1/2/(7~3/2~8), where,8 is shear velocity. Fault length (parallel to strike) and width (parallel to dip) are empirically related by L = 2W. Scatter for both scaling rules is about a factor of two. These scaling laws combine to give width and rise time in terms of fault length. Length is then used as the sole free parameter ina Haskell type fault model to derive scaling laws relating seismic moment o Ms (20sec surfacewave magnitude), Ms to S and mh (1sec bodywave magnitude) to M s. Observed ata agree well with the predicted scaling relation. The "source spectrum " depends on both azimuth and apparent velocity of the phase or mode, so there is a different "source spectrum " for each mode, rather than a single spectrum for all modes. Furthermore, fault width (i.e., the two dimensionality of faults) must not be neglected. Inclusion of width leads to different average source spectra for surface waves and body waves. These
Magnitude and energy of earthquakes
 Annals of Geophysics
, 2010
"... Discrepancies arise among magnitudes as derived from local earthquake data (ML), body waves (MB) and surface waves (MS). The relation of ML to the others is as yet not definitive; but MS – mB = a (MS – b). The latest revision gives a = 0.37, b = 6.76. Pending further research it is recommended that ..."
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Cited by 44 (0 self)
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Discrepancies arise among magnitudes as derived from local earthquake data (ML), body waves (MB) and surface waves (MS). The relation of ML to the others is as yet not definitive; but MS – mB = a (MS – b). The latest revision gives a = 0.37, b = 6.76. Pending further research it is recommended that ML continue to be used as heretofore, but MS (and ultimately ML) should be referred to mB as a general standard, called the unified magnitude and denoted by m. Tentatively log E = 5.8 + 2.4 m (E in ergs). Revised tables and charts for determining m are given. This paper is in continuation of previous investigations [Gutenberg and Richter 1942, 1956]. The earthquake magnitude has statistical and other uses independent of the relation between magnitude and energy. Indeed, it is possible that there is no complete onetoone correlation between magnitude and energy for large and
PRELIMINARY ANALYSIS OF THE PEAKS OF STRONG EARTHQUAKE GROUND MOTIONDEPENDENCE OF PEAKS ON EARTHQUAKE MAGNITUDE, EPICENTRAL DISTANCE, AND RECORDING SITE CONDITIONS
"... Analyses of peak amplitudes of strong earthquake ground motion have been carried out with the emphasis on their dependence on earthquake magnitude, epicentral distance, and geological conditions at the recording site. Approximate empirical scaling functions have been developed which, for a selected ..."
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Cited by 28 (9 self)
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Analyses of peak amplitudes of strong earthquake ground motion have been carried out with the emphasis on their dependence on earthquake magnitude, epicentral distance, and geological conditions at the recording site. Approximate empirical scaling functions have been developed which, for a selected confidence level, yield an estimate of an upper bound of peak accelerations, velocities, and displacements. The parameters in these scaling functions have been computed by leastsquares fitting of the recorded data on peak amplitudes which are now available for a range of epicentral distances between about 20 and 200 km and are representative for the period from 1933 to 1971 in the Western United States. The possibility of extrapolating the derived scaling laws to small epicentral distances where no strongmotion data are currently available has been tested by comparing predicted peak amplitudes with related parameters at the earthquake source. These source parameters (average dislocation and stress drop) can be derived from other independent studies and do not contradict the inferences presented in this paper. It has been found that for an approximate 90 per cent confidence level the presently available data suggest that peak accelerations, velocities, and displacements at the fault and for the frequency band between 0.07 and 25 Hz probably do not exceed about 3 to 5 g, 400 to 700 cm/sec, and 200 to 400 cm, respectively. The logarithms of the peaks of strong ground motion seem to depend in a linear manner on earthquake magnitude only for small shocks. For large magnitudes this dependence disappears gradually and maximum amplitudes may be achieved for M ~ 7.5. The influence of geological conditions at the recording site appears to be insignificant for peak accelerations but becomes progressively more important for peaks of strongmotion velocity and displacement.
Observation of Growing Correlation Length as an Indicator for Critical Point Behavior Prior to Large Earthquakes
 J. Geophys. Res
, 2001
"... We test the critical point concept for earthquakes in terms of the spatial correlation length. A system near a critical point is associated with a diverging correlation length following a power law timetofailure relation. We estimate the correlation length directly from an earthquake catalog us ..."
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Cited by 14 (3 self)
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We test the critical point concept for earthquakes in terms of the spatial correlation length. A system near a critical point is associated with a diverging correlation length following a power law timetofailure relation. We estimate the correlation length directly from an earthquake catalog using singlelink cluster analysis. Therefore we assume that the distribution of moderate earthquakes reflects the state of the regional stress field. The parameters of the analysis are determined by an optimization procedure, and the results are tested against a Poisson process with realistic distributions of epicenters, magnitudes, and aftershocks. A systematic analysis of all earthquakes with M 6:5 in California since 1952 is conducted. In fact, we observe growing correlation lengths in most cases. The null hypothesis that this behavior can be found in random data is rejected with a confidence level of more than 99%. Furthermore, we find a scaling relation log R 0:7M (log h max i 0...
Neuronal Shot Noise and Brownian 1/f 2 Behavior in the Local Field Potential
"... We demonstrate that human electrophysiological recordings of the local field potential (LFP) from intracranial electrodes, acquired from a variety of cerebral regions, show a ubiquitous 1/f 2 scaling within the power spectrum. We develop a quantitative model that treats the generation of these field ..."
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Cited by 13 (1 self)
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We demonstrate that human electrophysiological recordings of the local field potential (LFP) from intracranial electrodes, acquired from a variety of cerebral regions, show a ubiquitous 1/f 2 scaling within the power spectrum. We develop a quantitative model that treats the generation of these fields in an analogous way to that of electronic shot noise, and use this model to specifically address the cause of this 1/f 2 Brownian noise. The model gives way to two analytically tractable solutions, both displaying Brownian noise: 1) uncorrelated cells that display sharp initial activity, whose extracellular fields slowly decay in time and 2) rapidly firing, temporally correlated cells that generate UPDOWN states.
Indications For A Successively Triggered Rupture Growth . . .
 JOURNAL OF GEOPHYSICAL RESEARCH
, 2002
"... The characteristics of earthquake swarms can neither be described by simple laws nor are the underlying mechanisms presently understood. Swarm activity is often assumed to be caused by an intrusion of fluids into the seismogenic zone. We have studied the earthquake catalog of the large earthquake ..."
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Cited by 12 (5 self)
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The characteristics of earthquake swarms can neither be described by simple laws nor are the underlying mechanisms presently understood. Swarm activity is often assumed to be caused by an intrusion of fluids into the seismogenic zone. We have studied the earthquake catalog of the large earthquake swarm which occurred in the year 2000 in Vogtland, SEGermany and NWBohemia, an area wellknown for its episodic swarm generation. We observe a significant decrease of the GutenbergRichter bvalue during the swarm evolution as well as a fractal temporal clustering of the earthquakes. The spatial spreading of the swarm's activity, which is approximately confined to one plane, cannot simply be explained by a process of fluid diffusion. Instead, we
The Richter scale: its development and use for determining earthquake source parameters, Tectonophysics 166
, 1989
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Correlation of Peak Acceleration, Velocity and Displacement with Earthquake Magnitude
 Distance and Site Conditions, Earthquake Engineering and Structural Dynamics
, 1976
"... A brief review of proposed correlations between peak accelerations and earthquake magnitude and distance has been presented. It has been found that most investigators agree favourably on what should be the amplitude of peak accelerations for the distance range between about 20 and 200 km. For distan ..."
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Cited by 9 (1 self)
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A brief review of proposed correlations between peak accelerations and earthquake magnitude and distance has been presented. It has been found that most investigators agree favourably on what should be the amplitude of peak accelerations for the distance range between about 20 and 200 km. For distances less than 20 km, there is significant disagreement in the predicted peak amplitudes, reflecting the lack of data there and the uncertainties associated with the extrapolation. Correlations of peak accelerations, peak velocities and peak displacements with earthquake magnitude, epicentral distance and the geologic conditions of the recording sites have been presented for 187 accelerograms recorded during 57 earthquakes. This data set describes strong earthquake ground motion in the Western United States during the period from 1933 to 1971. For large earthquakes, dependence of peak acceleration, velocity and displacement amplitudes on earthquake magnitude seems to be lost. This suggests that the amplitudes of strong ground motion close to a fault are scaled primarily by the maximum dislocation amplitudes and the stress drop, rather than the overall `size ' of an earthquake as measured by magnitude. The influence of geologic conditions at the recording station seems to be of minor importance for scaling peak accelerations, but it becomes noticeable for the peaks of velocity and even more apparent for the peaks of displacement.
Earthquake monitoring in southern california for seventyseven years (19322008
 doi: 10.1785/0120090130. URL http: //www.bssaonline.org/cgi/content/abstract/100/2/423. L. Knopoff and
"... SCSN earthquake catalog from 1932 to the present, a period of more than 77 yrs. This catalog consists of phase picks, hypocenters, and magnitudes. We present the history of the SCSN and the evolution of the catalog, to facilitate user understanding of its limitations and strengths. Hypocenters and m ..."
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Cited by 7 (0 self)
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SCSN earthquake catalog from 1932 to the present, a period of more than 77 yrs. This catalog consists of phase picks, hypocenters, and magnitudes. We present the history of the SCSN and the evolution of the catalog, to facilitate user understanding of its limitations and strengths. Hypocenters and magnitudes have improved in quality with time, as the number of stations has increased gradually from 7 to ∼400 and the data acquisition and measuring procedures have become more sophisticated. The magnitude of completeness (Mc) of the network has improved from Mc ∼3:25 in the early years toMc ∼1:8 at present, or better in the most densely instrumented areas. Mainshock–aftershock and swarm sequences and scattered individual background earthquakes characterize the seismicity of more than 470,000 events. The earthquake frequencysize distribution has an average bvalue of ∼1:0, with M ≥6:0 events occurring approximately every 3 yrs. The three largest earthquakes recorded were