Seweryn J. Duda

Some aspects of global seismicity

Abstract An earlier catalogue of major earthquakes for the period 1897–1964 is continued for the period 1965–1977. The total material, now including about 80 years and being fairly homogeneous, is evaluated with regard to some of its statistical properties, such as relations of frequency and energy to magnitude and time.

Gutenberg's surface-wave magnitude calibrating function: Theoretical basis from synthetic seismograms

The surface-wave magnitude, as originally defined by Gutenberg (1945), appears to be the most stable quantity rating the strengths of seismic sources. It is based on the ground displacement produced by a nearly monochromatic wave train. The calibrating function underlying the magnitude definition was obtained from observations of the amplitudes as a function of epicentral distance for a wealth of earthquakes. No distinction was made as to focal depths. Thus, the calibrating function depends on one parameter—the epicentral distance-only. Subsequent attempts to introduce a focal depth correction were not successful in practice, and one and the same calibrating function continues to be applied to events with focal depths ranging from 0 to about 70 km. Assuming a strike-slip point source located inside a standard Earth model, synthetic seismograms of the fundamental mode SH-(Love-) wave are computed for a range of focal depths and azimuths. Amplitude-distance curves are obtained, and averaged over the azimuths. The curves are the basis for improved calibrating functions. Average depth corrections are obtained and applied to some populations of seismic events. The corrected surface-wave magnitudes are internally more consistent than the uncorrected ones usually published. Applying the depth correction to published surface wave magnitudes and considering themb-Ms relation for a sample of earthquakes and explosions, it has been established that, for a given intensity of short-periodic radiation, the 20-s radiation intensity can vary by orders of magnitude. While it is known that the 20-s radiation intensity is generally lower for explosions than for earthquakes, it turns out to be even lower if the depth correction is applied, yielding a clearer separation between both classes of seismic events.

Determination of spectral properties of earthquakes from their magnitudes

Abstract Following the recommendation of the “IASPEI Commission on Magnitudes” from 1967, P-wave magnitudes of distant earthquakes are being computed with the aid of the calibration functions of Gutenberg and Richter (1956). With the development of the instrumental seismology, especially in view of the availability of broad-band recordings, the question arises whether the functions are still adequate. In this investigation new calibration functions for P- and S-waves are presented, which are not only dependent on epicentral distance and focal depth, but also on the period of the spectral component of the wave. The determination of calibration functions is based on the currently most plausible global models for the velocity and anelasticity distribution. Taking into account the effective bandwidth of the instruments employed, eventually leads to the so-called spectral magnitudes. From the spectral magnitudes m ( T ) , the energy density spectrum E ( T ) of the respective wave can readily be computed. The corresponding formula is E ( T ) = 10 2m(T)− 1.4 , with E ( T ) in joules per hertz.

Crustal structure in the Svalbard region from seismic measurements

Abstract Seismic refraction measurements along three profiles with lengths ranging from 160 km to 270 km were made in 1976 and 1978 as part of a multinational effort to study the Earths crust and upper mantle in the Svalbard region. The crustal tliickness is about 26 km along the west coast of Spitsbergen, and faulting and a strong eastwardly dip of the Moho increase the; crustal thickness to 40 km beneath the Tertiary Fold Belt on West Spitsbergen. Further to the east, Pn arrivals indicate a transitional nature of the Moho in the area beneath the Central Spitsbergen Basin. Evidence suggests the presence of major N-S trending faults dividing the Spitsbergen crust into blocks. A down-faulted sedimentary basin, containing about 3 km of sediments and presumably of Cenozoic age is observed in the Forlandsundet area. The maximum thickness of the Cenozoic and Mesozoic rock sequences on Central Spitsbergen is estimated to be about 5 km.

Strain release in relation to focal depth

SummaryThe world-wide strain release in relation to focal depth has been calculated for all shocks with magnitude 7 and over for the interval 1918–1952. The strain exhibits a strong maximum in the uppermost 75 km of the earth; it decreases exponentially with depth between 75 and 400 km, with an unimportant minimum corresponding to the asthenosphere low-velocity layer and another minimum at 275 km; after a pronounced minimum between 400 and 475 km it increases again approximately exponentially between 475 and 650 km, after which it drops rapidly to zero. The shape of the strain-depth curve is interpreted in terms of the physical conditions and the intensity of strain accumulation. In particular, the increase between 475 and 650 km is ascribed to a combined effect of temperature and pressure variation with depth with related phase changes and possible changes in composition. The depth curve for the number of shocks is nearly parallel to the strain-depth curve, and the average strain per earthquake shows only an insignificant decrease with depth.ZusammenfassungEs wird die Tiefenabhängigkeit der Deformationsauslösung in allen Erdbeben mit Magnitude 7 und darüber, im Zeitraum 1918–1952 untersucht. Die Deformationsauslösung hat ein ausgesprochenes Maximum in den obersten 75 km. Sie nimmt im Tiefenbereich zwischen 75 und 400 km exponential mit der Tiefe ab, wobei sich ein Minimum, das der Schicht mit niedriger Wellengeschwindigkeit entspricht, schwach andeutet, und ein zweites Minimum bei 275 km liegt. Nach einem ausgeprägten Minimum zwischen 400 und 475 km Tiefe, steigt die Deformationsauslösung erneut, etwa exponential, im Tiefenbereich zwischen 475 und 650 km an, und nimmt danach schnell ab. Der Verlauf der Deformationsauslösung in Abhängigkeit von der Tiefe wird an Hand der physikalischen Verhältnisse im Erdkörper, sowie der Intensität der Deformationsaufspeicherung gedeutet. Insbesondere wird der Anstieg zwischen 475 und 650 km einer Änderung der Temperatur und des Druckes mit der Tiefe, bei Phasensprung und möglicher Änderung in der Zusammensetzung des Materials zugeschrieben. Die Tiefenabhängigkeit der Anzahl der Beben und der Deformationsauslösung verlaufen annähernd parallel; die mittlere Deformationsauslösung pro Erdbeben zeigt lediglich eine unbedeutende Abnahme mit der Tiefe.

The amplitude spectra of P- and S-waves and the body-wave magnitude of earthquakes

Abstract Synthetic calibration functions for body-wave magnitudes are presented. They have been obtained from computations made under the assumption that the variation of amplitude spectra along the earths surface is due to radial velocity heterogeneity and radial changes of the dissipation factor Q inside the earth only. The new calibration functions depend on the epicentral distance and the focal depth of the earthquake, as well as on the period of the body-wave under consideration. No single calibration function exists which would produce magnitude figures identical for all Fourier components of a body-wave. Observations on several hundreds of strong earthquakes in recent years show that the P-wave magnitudes vary systematically with the period of the wave. With the application of the synthetic calibration function a general increase of the teleseismically determined P-wave magnitudes with frequency is observed. This fact reconciles acceleration response spectra from narrowband strong-motion analyzers in the near-field of an earthquake and spectral magnitudes determined from far-field observations by sensitive narrow-band seismographs. The strength of high-frequent spectral components generally exceeds the strength of low-frequent components determined in both cases.

Spectral magnitudes, magnitude spectra and earthquake quantification; the stability issue of the corner period and of the maximum magnitude for a given earthquake

Abstract P-wave magnitude spectra of a foreshock-mainshock-aftershock sequence on 7 and 8 May 1986 in the Aleutian Islands are determined using broad-band seismograms recorded at the GRF-array. The magnitude spectra are compared for different stations of the array. The maximum magnitude is stable with a standard deviation below 1%. The reliability of other source parameters (fault length, seismic moment and stress drop) derived from the magnitude spectrum m(f) depends on the determination of the corner period. Different methods to derive the corner period are compared. Best suited and most stable is the one based on the formula: T c = ∫ 0 ∞ E s (f) df ∫ 0 ∞ E s (f) f df where Es(f) = 102mf−14 is the energy density spectrum of the P-wave, and mf, the spectral P-wave magnitude of the earthquake at the respective period.

Spectral P-wave magnitudes, Aki's ω-square model and source parameters of earthquakes

Abstract The earthquake magnitude is a quantity sampling the spectrum of the far-field radiation. With a suit of properly defined magnitudes in a sufficiently broad range of frequencies, the radiated spectrum can be restored and analyzed. A method is proposed for the extraction of stress drop, fault length and seismic moment from magnitudes on a routine basis. Thereby, the theoretical spectrum as predicted by the ω-square model of Aki is utilized. In applying the method to earthquakes which occurred in several parts of Asia over a time-span of 3 years, it is shown that in most cases earthquakes in a given region are characterized by the same stress drop, varying however from region to region. In one region a change of the stress drop with time is found, eventually indicating a change in the state of stress in the particular region during the time interval investigated.

The anelasticity of the earth's mantle in the European area

Abstract The anelastic attenuation of seismic waves, as expressed by the Q -factor, is compared for two regions: between the Mid-Atlantic Ridge and the seismic station Hamburg F.R.G., and the Hindu Kush and the same station. Eight earthquakes in the distance range 44.7 ° to 59.1 ° were chosen. The spectral ratios of short-period ScS- and ScP-, as well as PcS- and PcP-phases were computed, and used to estimate the differential effect of attenuation on P- and S-waves. Assuming the ratio of Q -factors for P- and for S-waves to be Q α Q β = 1.75 , Q β -values of 161 for the western part and of 324 for the eastern part of Europe are found. The pronounced difference of the average Q -values for the earths mantle is interpreted as being related to a regional variation of the anelasticity in the lowermost mantle, below 2200 km. In the frequency band 0.1 to 0.6 Hz the Q -factors are likely to be frequency-independent.

Fracture mechanics rupture model of earthquakes and an estimate of ambient shear stress

Abstract A model of the earthquake rupture process has been proposed in the light of fracture mechanics. In this model, the earthquake dislocation is not the elastic displacement on the faulting surface, rather it is an inelastic displacement at the tip of the crack. Every point on the crack surface always undergoes a process of stress rise from a low initial value, i.e. ambient shear stress τ o to the higher value and finally to the yielding strength during rupture. At the instant of fracture, a main dislocation at the tip of the crack generates a strong elastic wave radiating from the tip of the crack. Therefore the earthquake dislocation should be related to inelastic displacement at the tip of the crack, but not be related to elastic displacement on the crack surface. Thus, the resulting earthquake dislocation D is proportional to ambient shear stress τ o 2 , not τ o . A set of relations between source parameters and τ o has been built. They are different from the equations usually used for estimating stress drop. Based on our rupture model and our scaling law model, two equations for estimating ambient shear stress from body wave magnitude m b , maximum spectral magnitude m f and seismic moment log( M o ) have been derived.