Approximate expression for the hilbert transform of a certain class of functions and their application to the ray theory of seismic waves

Summary Approximate expressions for the Hilbert transform of the functionf(t)=exp(- ₀ ² t ²/²) cos( ₀ t+v) are determined. This function, given a suitable choice of the three parameters ₀, and v, approximates a wide class of seismic signals very well. The approximate expressions for the Hilbert transform enable very simple formulae to be given for the elementary seismograms of the individual seismic body waves (in the zero approximation of the ray theory). This accelerates the computation of ray theoretical seismograms considerably.     

Vital and mortal staining of algae in the presence of chlorine-produced oxidants

Evans blue and neutral red were tested as mortal and vital stains respectively for eight estuarine algal species which had been exposed to chlorine-produced oxidants in a continuous-flow system. The effect of CPO on staining with Evans blue was negligible. High concentrations of CPO affected staining with neutral red in several instances; this is probably due to CPO-induced mortality of test organisms during the exposure or staining period. Neutral red leached fromSkeletonema costatum andOlisthodiscus luteus before the end of the staining period. Staining ofDunaliella tertiolecta with neutral red proceeded more slowly. Evens blue, which was incorporated quickly and remained in the cells, is recommended for live-dead determinations for all species examined exceptNitzschia closterium, for which neutral red should be used. Neither stain was effective onMychonastes ruminatus (Simpson and Van Valkenburg 1978).     

“Spectral ω2 model” and variable absorption coefficient

Summary Aki's spectral ² model[1] is used to estimate the amplitude field at epicentral distances up to 1000 km in the case of an absorption coefficient of seismic waves which varies with distance. Velocity spectra, the periods of the maximum of these spectra and the maximum velocity amplitudes are obtained. The results are compared with[2] and it is shown that the divergence of the amplitude field decreases if a variable absorption coefficient is used. The theoretical results, obtained in this case, approach the results seen in practice. The possibility of determining the limits of epicentral distances, at which the amplitude field may be considered as linear, is given.     

Dynamic loading of the boundaries in the finite-difference study of diffraction

Summary The finite-difference method can be used for obtaining the theoretical seismic response of a block structure to an incident plane wave. Computer time is saved by solving an equivalent problem of dynamic loading of the boundary of the block structure. The loading is performed by means of a set of discrete body forces, replacing the incident wave at the interface.     

Note on the seismicity of northeastern Italy (Friuli area)

The kinematics and mechanics of the seismicity of the Friuli area in northeastern Italy are discussed, especially the focal mechanism of the catastrophic earthquake of May 6, 1976. Alternative solutions are analyzed. A N-S section, down to 60 km below sea-level, across the Alps from the Bavarian foreland to the Adriatic Sea illustrates these possibilities.     

Age and isotopic studies of some Pan-African granites from North-Central Nigeria

Twenty-nine Rb-Sr whole-rock isotopic analyses and three U-Pb zircon analyses on foliated granites and largely unfoliated charnockitic rocks indicate that the central part of the Pan-African belt in west Africa was characterised by intense orogenic plutonism. These data and Rb-Sr analyses on muscovite books from late cross-cutting pegmatites indicate that the peak of magmatic activity occurred 610 ± 10 m.y. ago.Initial ⁸⁷Sr/⁸⁶Sr ratios for the granitic and charnockitic rocks are in the range 0.7065–0.7125, and indicate a significantly older crustal component in the magmas.     

The assemblage stilpnomelane–chlorite–phengitic mica: a geothermobarometer for blueschist and associated greenschist terranes

Two anhydrous equilibria can be written among the components of stilpnomelane, chlorite, white mica and quartz, namely 89 daphnite+131 Fe-celadonite+190 quartz=96 stilpnomelane+71 muscovite, and amesite+Mg-celadonite=muscovite+clinochlore. We assume that the free energy change of reaction, ΔG=ΔG^o+ΣRT lna_i^j, is approximated by ΔG=A?BT +C(P?1)+ΣRT lna_i^j, where ΔG^o is the free energy change of the end-member components at temperature T and pressure P, a_i is the activity of component i whose coefficient in the equilibrium is j, and A, B and C are constants to be determined. Values of C can be approximated by the change in volume on reaction, namely C=406.517 J/bar for the first reaction and C=0.613 J/bar for the second reaction. Constants A and B were determined by using six occurrences of the assemblage stilpnomelane–chlorite–white mica for which P–T have been otherwise estimated. Using solution models from the literature, linear regression gives for the first equation A=?6118.269 kJ, B=?4584.09 J/K, and for the second equation A=19.397 kJ, B=66.72 J/K. These values predict P–T within 0.5 kbar and 25 K for all occurrences, and appear reasonably robust relative to probable analytical errors. P–T are determined by intersection of the curves generated by given compositions in P–T space. Fine-grained and/or zoned chlorite and white mica make application of the geothermobarometer difficult in some instances, but our work in the Bathurst region of New Brunswick suggests that, with patience and care, useful analyses can be obtained, and the database for the geothermobarometer greatly expanded.     

Characterization of the lithological contact in the shergottite EETA79001—A record of igneous differentiation processes on Mars

Abstract— Elephant Moraine (EET) A79001 is the only Martian meteorite that consists of both an olivine‐phyric shergottite (lithology A) and a basaltic shergottite (lithology B). The presence of these lithologies in one rock has previously been ascribed to mixing processes (either magmatic or impact‐induced). Here we present data regarding phase changes across the contact between the lithologies. These data show that the contact is gradational and suggest that it is a primary igneous feature consistent with crystallization of a single cooling magma. We present a model to establish a petrogenetic connection between an olivine‐phyric and a basaltic shergottite through differentiation. The model involves the shallow or surface emplacement of a magma that contained pre‐eruptive solids (phenocrysts and minor xenocrysts). Subsequent differentiation via crystal settling and in situ crystallization (Langmuir 1989) resulted in a layered sequence of lithology A overlain by lithology B, with gradations in modal abundance of maskelynite (increasing from A to B) and pigeonite/maskelynite (decreasing from A to B), and a gradational change in pattern of pyroxene zonation (zones of magnesian augite separating magnesian and ferroan pigeonite appear and thicken into B) across the contact. A pigeonite phenocryst‐bearing zone near the contact in lithology B appears to be intermediate between lithology A and the bulk of lithology B (which resembles basaltic shergottite Queen Alexandra Range [QUE] 94201). Re‐examination of Sr isotopic compositions in lithology A and across the contact is required to test and constrain the model.