Application of the extreme value approaches to the apparent magnitude distribution of the earthquakes

The apparent magnitude of an earthquakey is defined as the observed magnitude value and differs from the true magnitudem because of the experimental noisen. Iff(m) is the density distribution of the magnitudem, and ifg(n) is the density distribution of the errorn, then the density distribution ofy is simply computed by convolvingf andg, i.e.h(y)=f*g.If the distinction betweeny andm is not realized, any statistical analysis based on the frequency-magnitude relation of the earthquake is bound to produce questionable results. In this paper we investigate the impact of the apparent magnitude idea on the statistical methods that study the earthquake distribution by taking into account only the largest (or extremal) earthquakes. We use two approaches: the Gumbel method based on Gumbel theory (Gumbel, 1958), and the Poisson method introduced byEpstein andLomnitz (1966). Both methods are concerned with the asymptotic properties of the magnitude distributions. Therefore, we study and compare the asymptotic behaviour of the distributionsh(y) andf(m) under suitable hypotheses on the nature of the experimental noise. We investigate in detail two dinstinct cases: first, the two-side limited symmetrical noise, i.e. the noise that is bound to assume values inside a limited region, and second, the normal noise, i.e. the noise that is distributed according to a normal symmetric distribution.We further show that disregarding the noise generally leads to biased results and that, in the framework of the apparent magnitude, the Poisson approach preserves its usefulness, while the Gumbel method gives rise to a curious paradox.     

P in the shadow zone of the earth's core—Part I

Summary Regional variations have been indicated in the slope of theP travel-time curve in the shadow zone of the earth's core. Further study is needed since the uncertainties of the slope are large, especially for the observations from North American stations. There is no significant difference between themean slope of theP travel-time curve in the 95°102.9 range and those obtained byJeffreys, andJeffreys andBullen. However, there is a significant difference between themean slope in the 103° to 135° range as obtained in this study, and those obtained byJeffreys andBullen, and in a later revision byJeffreys. Themean travel-time curve ofP in the shadow zone of the earth's core should be lowered. A trial travel-time table is given with amean slope of 4.41 sec/deg. This table is in close agreement with the times obtained byGutenberg andRichter, and with the trial travel-times ofLehmann. Under the assumption of diffraction the longitudinal wave velocity has been determined to be 13.7 km/sec at the core-mantle boundary.This paper was presented at the Annual Meeting of the Seismological Society of America Reno, Nevada, 1966.     

Comparison of techniques that use the single scattering model to compute the quality factorQ from coda waves

Using simulated coda waves, the resolution of the single-scattering model to extract codaQ (Q _c ) and its power law frequency dependence was tested. The back-scattering model ofAki andChouet (1975) and the single isotropic-scattering model ofSato (1977) were examined. The results indicate that: (1) The inputQ _c models are reasonably well approximated by the two methods; (2) almost equalQ _c values are recovered when the techniques sample the same coda windows; (3) lowQ _c models are well estimated in the frequency domain from the early and late part of the coda; and (4) models with highQ _c values are more accurately extracted from late code measurements.     

The electrostatic force between a charged conducting sphere and a charged dielectric sphere in an arbitrarily oriented external electric field

Summary The electrostatic force between a charged conducting sphere and a charged dielectric sphere in a uniform, arbitrarily oriented external electric field is obtained and presented in terms of force coefficients which depend only on the relative geometry of the two spheres and the dielectric constants of the dielectric sphere and the medium. When the dielectric constant of the dielectric sphere is allowed to approach infinity, the resulting computed force agrees with that ofDavis (1964) for two conducting spheres, and when the external field and the charge on the dielectric sphere are set to zero, the resulting force agrees with that ofHall andBeard (1975) for a charged conducting sphere near an uncharged dielectric sphere.     

Frictional heat generation and seismic radiation in a foam rubber model of earthquakes

Results from a study of stick-slip particle motion at the interface between two stressed foam rubber blocks indicate that normal vibrations and interface separation are an important part of the stick-slip process in foam rubber. The dimension of the dynamic slip pulse is small compared to the dimension of the model (approximately 10 cm vs. 200 cm) consistent with the abrupt-locking slip pulse model ofBrune (1970, 1976), andHeaton (1990). A comparison of frictional heat generation between stable-sliding and stick-slip foam rubber models indicates a linear relation between the temperature increase on the fault surface (for a given distance of slip) and the driving shear force for the stable-sliding model, while for the stick-slip model there is essentially no variation in frictional heat generation with an increase in shear stress. We performed experiments to investigate the ratio of normal motion to shear motion at different levels of normal stress in the stick-slip foam rubber model. Preliminary result indicate that the normal component of the particle motion increases more rapidly with increasing normal stress than the shear component. The phenomenon of interface separation and normal vibrations may thus explain some of the most frustrating problems in earthquake mechanics, e.g., the heat flow paradox, the long-term weakness of major active faults, and anomalousP-wave radiation.     

CodaQ as a combination of scattering and intrinsic attenuation: Numerical simulations with the boundary integral method

Numerical modelling ofSH wave seismograms in media whose material properties are prescribed by a random distribution of many perfectly elastic cavities and by intrinsic absorption of seismic energy (anelasticity) demonstrates that the main characteristics of the coda waves, namely amplitude decay and duration, are well described by singly scattered waves in anelastic media rather than by multiply scattered waves in either elastic or anelastic media. We use the Boundary Integral scheme developed byBenites et al. (1992) to compute the complete wave field and measure the values of the direct waveQ and coda wavesQ in a wide range of frequencies, determining the spatial decay of the direct wave log-amplitude relation and the temporal decay of the coda envelope, respectively. The effects of both intrinsic absorption and pure scattering on the overall attenuation can be quantified separately by computing theQ values for corresponding models with (anelastic) and without (elastic) absorption. For the models considered in this study, the values of codaQ ^–1 in anelastic media are in good agreement with the sum of the corresponding scatteringQ ^–1 and intrinsicQ ^–1 values, as established by the single-scattering model ofAki andChouet (1975). Also, for the same random model with intrinsic absorption it appears that the singly scattered waves propagate without significant loss of energy as compared with the multiply scattered waves, which are strongly affected by absorption, suggesting its dominant role in the attenuation of coda waves.     

Free and forced shallow-water oscillations in a rotating channel of parabolic cross-section

Free and forced oscillations of shallow water in an infinitely long rotating channel of parabolic cross-section are analyzed. The pure cross-channel oscillations ofChrystal (1905) and solutions for zero rotation first discussed byProudman (1925) andHidaka (1932) are special asymptotic solutions for the free modes of this model. However, for increasingly large, along-shore wave number, our solutions donot uniformly approach those ofReid (1958) andBall (1967) for a single shore-line and semi-infinite ocean. A method of computing eigen frequencies and eigen functions for the general problem is described, and a sufficient number of these are exhibited graphically to permit visualization of the transitions between the asymptotic regions.The forced problem consists of an incoming wave-train or surge generated at the center of the channel. Amplitude and transports near the shore are computed for a wide range of dimensionless incoming-wave frequencies and rotational frequencies.     

Focal mechanism study of South American earthquakes

Summary This study presents the focal mechanism solutions of four South American earth-quakes. These solutions have been determined using the sign of the initial motion ofP wave, and the polarization angle ofS wave. A regional study of the strike of the fault plane, the direction of motion, and the regional stress pattern has been made in which the focal mechanism solutions determined byStauder andBollinger were also used.     

Principal horizontal stresses in Southern Africa

A review ofin situ stress measurements at eight regional localities in Africa south of the 15°S parallel shows that average directions of the horizontal pricipal stresses are N-S and E-W. These directions agree with principal stress orientations deduced from earthquake fault plane solutions. However, the maximum and minimum principal horizontal stresses are not consistently oriented parallel to either the N-S or E-W direction; they may vary within an individual region because of local geological structures and from region to region. At the sites within the Witwatersrand sediments (all at depths greater than 500 m) the maximum stress tends to lie NW-SE but at three of the four sites outside the Witwatersrand sediments (all at depths less than 500 m) this stress is oriented approximately N-S.The data reported here are compared with horizontal stresses predicted for Southern Africa bySolomon, Sleep andRichardson (1975) from various plate tectonic driving force models. The agreement between orientations is fair for all sites but only the deép sites in the Witwatersrand sediments have comparable stress magnitudes.     

Simultaneous inversion of velocity structures and hypocentral locations: Application to the Friuli seismic area NE Italy

A layeredP- andS-wave velocity model is obtained for the Friuli seismic area using the arrival time data ofP- andS-waves from local earthquakes. A damped least-squares method is applied in the inversion.The data used are 994P-wave arrival times for 177 events which have epicenters in the region covered by the Friuli seismic network operated by Osservatorio Geofisico sperimentale (OGS) di Trieste, which are jointly inverted for the earthquake hypocenters andP-wave velocity model. TheS-wave velocity model is estimated on the basis of 978S-wave arrival times and the hypocenters obtained from theP-wave arrival time inversion. We also applied an approach thatP- andS-wave arrival time data are jointly used in the inversion (Roecker, 1982). The results show thatS-wave velocity structures obtained from the two methods are quite consistent, butP-wave velocity structures have obvious differences. This is apparent becauseP-waves are more sensitive to the hypocentral location thanS-waves, and the reading errors ofS-wave arrival times, which are much larger than those ofP-waves, bring large location errors in the joint inversion ofP- andS-wave arrival time. The synthetic data tests indicated that when the reading errors ofS-wave arrivals are larger than four times that ofP-wave arrivals, the method proposed in this paper seems more valid thanP- andS-wave data joint inversion. Most of the relocated events occurred in the depth range between 7 and 11 km, just above the biggest jump in velocity. This jump might be related to the detachment line hypothesized byCarulli et al. (1982). From the invertedP- andS-wave velocities, we obtain an average value 1.82 forV _p /V _s in the first 16 km depth.     

A new measure of seismicity

Summary In this paper an attempt has been made to analyse the World shallow focus earth-quakes by the method ofGutenberg andRichter. Frequency-magnitude analysis of various earthquakes indicate that in the relation logN=a–b M, the ratio (b/a)^–1 satisfies fairly well the seismicity of a region and it is felt that this ratio may be used as a measure of seismicity for a given region.     

Relazioni tra la velocità del vento e le caratteristiche del moto ondoso al largo e in costa

Summary The A. points out that the confirmation of the theory ofNeumann's significative waves, which differ from those ofSverdrup andMunk, would require observations of an accuracy not yet available. The existence of these waves would not change, anyhow,Sverdrup andMunk's conclusions out of the wind area.     

Quantitative estimates of interplate coupling inferred from outer rise earthquakes

Interplate coupling plays an important role in the seismogenesis of great interplate earthquakes at subduction zones. The spatial and temporal variations of such coupling control the patterns of subduction zone seismicity. We calculate stresses in the outer rise based on a model of oceanic plate bending and coupling at the interplate contact, to quantitatively estimate the degree of interplate coupling for the Tonga, New Hebrides, Kurile, Kamchatka, and Marianas subduction zones. Depths and focal mechanisms of outer rise earthquakes are used to constrain the stress models. We perform waveform modeling of body waves from the GDSN network to obtain reliable focal depth estimates for 24 outer rise earthquakes. A propagator matrix technique is used to calculate outer rise stresses in a bending 2-D elastic plate floating on a weak mantle. The modeling of normal and tangential loads simulates the total vertical and shear forces acting on the subducting plate. We estimate the interplate coupling by searching for an optimal tangential load at the plate interface that causes the corresponding stress regime within the plate to best fit the earthquake mechanisms in depth and location.We find the estimated mean tangential load over 125–200 km width ranging between 166 and 671 bars for Tonga, the New Hebrides, the Kuriles, and Kamchatka. This magnitude of the coupling stress is generally compatible with the predicted shear stress at the plate contact from thermal-mechanical plate models byMolnar andEngland (1990), andVan den Buekel andWortel (1988). The estimated tectonic coupling,F _tc , is on the order of 10¹²–10¹³ N/m for all the subduction zones.F _tc for Tonga and New Hebrides is about twice as high as in the Kurile and Kamchatka arcs. The corresponding earthquake coupling forceF _ec appears to be 1–10% of the tectonic coupling from our estimates. There seems to be no definitive correlation of the degree of seismic coupling with the estimated tectonic coupling. We find that outer rise earthquakes in the Marianas can be modeled using zero tangential load.     

Zur Bestimmung einer rotenOscillatoria— ein Beitrag zur Variabilität vonOscillatoria rubescens D.C.

Summary For the purpose of determination a redOscillatoria species was after isolation cultivated and compared withO. rubescens (clones 51,Staub). Increase of trichoms and dry matter, length and diametre of trichoms and length of cells were measured; total volume of gas vacuoles and spectral absorption of the algal suspension between 380–730 nm were determined. The algae under discussion were attached to the speciesO. rubescens. Differences and accordances between the species studied andO. rubescens andO. prolifica as well, heterogeneity ofO. rubescens and variability of the characteristics ofO. rubescens are discussed.      

Intraplate seismicity of the Pacific Basin, 1913–1988

We establish here a comprehensive database of intraplate seismicity in the Pacific Basin. Relocation and analysis of 894 earthquakes yield 403 reliable intraplate earthquakes during 1913–1988. These numbers do not include earthquake swarms, which account for another 838 events. Most of the remainder (304 events) are actually plate boundary earthquakes that have been erroneously located in intraplate regions. A significant number occur in recent years when location capabilities should have guarded against this situation. Relocations involve a careful linear inversion ofP andS arrivals, accompanied by a Monte Carlo statistical analysis. We have also attentively removed the high number of clerical errors and nuclear tests that exist in epicenter bulletins.A geographical examination of the relocated epicenters reveals several striking features. There are three NW-SE lineaments north of the Fiji Plateau and in Micronesia; diffuse seismicity and incompatible focal mechanisms argue against the southernmost, discussed byOkal et al. (1986) andKroenke andWalker (1986), as the simple relocation of the Solomon trench to the North. Besides another striking lineament, along the 130°W meridian, there is also a strong correlation between seismicity and bathymetry in certain parts of the Basin. In the Eastcentral Pacific and Nazca plates there are many epicenters on fracture zones and fossil spreading ridges, and hot spot traces like the Louisville, Nazca and Cocos Ridges also display seismicity.     

L in Potsdam,Seddin and Niemegk

Summary This paper deals with the deriving ofL based on the observations in Potsdam, Seddin and Niemegk. The calculation uses the investigations on finestructure ofSq published in previous papers. Two sunspot cycles were used, a quiet one and a disturbed one. The influence of the solar activity is clearly marked. The results are in good conformity with those ofS. Chapman andAd. Schmidt, but there are remarkable deviations in the results caused by using hourly values and not hourly mean values. These results are discussed, especially their mean deviations.Communication No. 173 of the Central Earth Physics Institute of the German Academy of Sciences at Berlin, GDR-15 Potsdam, Telegrafenberg.-This paper was presented at the XV General Assembly of IUGG, held in Moscow in August 1971.     

Die Sonnenstrahlung und ihre Messung

Summary History and results of a 41/2-years-expedition to Argentine. A determination of the sun's «temperature» can only be given by the laws ofBoltzmann-Stefan andWien, because the temperature of the different layers is different. In the measurements of the sun's radiation the law ofBoltzmann-Stefan was introduced (T ⁴, where is a constant, andT the Kelvin-Temperature) while in the passed 100 years the difference between the sun's and the instruments radiation was taken as radiation, although this difference was arbitrariously variable with the instruments temperature. The effect of the vertical exchange of airmasses, on the radiation of the sun and the radiation of the air between the sun and the instrument was cleared. With these corrections one can not receive more as the difference between the so called solar constant and the albedo of the atmosphere. If the highest values are used (smallest albedo) the approximated value of the solar constant becomes 2.4, corresponding well to the value, derived from the supposed temperature of the sun.     

Die sogenannte «Moorschnecke»Leptobasis goesingense Palikein Pilzkonidium

Zusammenfassung Bau, Entwicklungsgeschichte (in Reinkulturen!) und ?kologie zeigen:Steinekkes ?Moorschnecke?, seineHelicosporium-Konidien,Leptobasis goesingense Palik undFortiea spirulina f. goesingense (Palik) Poljanskij geh?ren zusammen und stellen das Konidium einerHelicoonart dar. Es besteht keine Beziehung zuFortiea spirulina (Steinecke)J. De Toni.

---

Summary Morphology, development (in pure cultures) and ecology show thatSteinecke’s ‘Moorschnecke’, hisHelicosporiumconidium,Leptobasis goesingense Palik andFortiea spirulina f.goesingense (Palik) Poljanskij belong together and represent the conidium of a species ofHelicoon. There is no connection to theFortiea spirulina (Steinecke)J. De Toni.

     

The amplitude ratioPcP/P and the core-mantle boundary

Summary Using the Haskell matrix formulation, theoretical reflection coefficient curves have been calculated for a multi-layered core-mantle boundary for comparison with observational data. Two cases are considered, first when the shear velocity in the core is equal to zero and second when the core has a finite rigidity. If the velocity contrast is large between the imbedded layer and the mantle, the reflection coefficient curves for the multi-layered medium are irregular in shape as compared to those for two half-spaces, representing the core and the mantle, respectively. The reflection coefficient curves show an oscillatory character if the imbedded layer is thick and has a high velocity contrast.The observational data consist of short-period vertical-component seismograph records ofP andPcP from nuclear explosions in the Aleutian chain, Nevada, Novaya Zemlya, Kazakh and Sahara. Attenuation and geometrical spreading are taken into consideration. Four different models for the quality factorQ are applied to the observational data. The data are found to be much affected by theQ-model used for the corrections.Based on proposedQ-values, a model for the core-mantle boundary is found, characterized by two low-velocity layers at the bottom of the mantle. The thicknesses are 16.10 km (outer layer) and 19.96 km (inner layer), the compressional wave velocities 12.17 km/sec and 10.94 km/sec and the shear wave velocities are 6.29 km/sec and 5.33 km/sec, respectively. A better fit to this model is found when in addition the shear velocity in the outer core is 2.20 km/sec and the density ratio at the core-mantle boundary is 1.07. In other words, the observations favour a layer of finite rigidity in the outer core rather than a fluid one.     

Travel times ofP-waves for the Swedish-Finnish seismograph network

Summary About 360 seismic events from almost all directions recorded at 13 seismological observatories in Sweden and Finland have been investigated. The depths of these events vary from the surface to 650 km and the epicentral distances from 9° to 119° with fairly even coverage. The two most separated stations in this array are about 15° apart (Karlskrona in Sweden and Kevo in Finland). Comparison of observed travel-time curves and their slope with those ofJeffreys-Bullen andHerrin are made. Generally, the observed travel times are earlier than theJeffreys-Bullen times and later than theHerrin ones. Path and depth effects on residuals with respect to the two given tables are studied, and station corrections and source corrections are estimated. Global and regional travel-time tables of theP-wave have been constructed for this network of stations.On leave from Geophysical Institute, Tehran University, Tehran, Iran