RADON DEPTH MIGRATION1

A depth migration method is presented that uses Radon-transformed common-source seismograms as input. It is shown that the Radon depth migration method can be extended to spatially varying velocity depth models by using asymptotic ray theory (ART) to construct wavefield continuation operators. These operators downward continue an incident receiver-array plane wave and an assumed point-source wavefield into the subsurface. The migration velocity model is constrained to have longer characteristic wavelengths than the dominant source wavelength such that the ART approximations for the continuation operators are valid. This method is used successfully to migrate two synthetic data examples:

• 1 a point diffractor, and
• 2 a dipping layer and syncline interface model.

It is shown that the Radon migration method has a computational advantage over the standard Kirchhoff migration method in that fewer rays are computed in a main memory implementation.     

Cesstibtantite—a geologic introduction to the inverse pyrochlores

Summary The crystal structure of cesstibtantite has been solved from diffractometer data collected on samples from Leshaia, Russia and the Tanco pegmatite, Manitoba. Cesstibtantite from the Leshaia pegmatite (type locality) hasa 10.515(2) Å, space groupFd3m, composition Cs_0.31(Sb_0.57Na_0.31Pb_0.02Bi_0.01)_O.91(Ta_1.88Nb_0.12)₂(O_5.69[OH, F]_0.31)₆(OH, F)_0.69, Z 8; its structure was refined toR 3.8,wR 4.3% using 96 observed (F > 3[F]) reflections (MoK). Cesstibtantite from the Tanco pegmatite hasa 10.496(1) Å, space groupFd3m, composition (Cs_0.22K_0.01)_0.23(Na_0.45Sb_0.39Pb_0.14· Ca_0.06Bi_0.02)_1.06(Ta_1.95Nb_0.05)₂(O_5.78[OH,F]_0.22)₆(OH,F)_0.55,Z 8; its structure was refined toR 3.9w R 3.7% using 104 observed reflections. Cesstibtantite differs from the normal pyrochlores in that it contains significant amounts of very large cations such as Cs. As these cations are too large (^VIII[r] > 1.60 Å) for the conventional [8]-coordinated A site, they occupy the [18]-coordinated site, which normally contains monovalent anions. Natural cesstibtantite samples are non-ideal in that both Cs and monovalent anions occur at the site; thus cesstibtantite is intermediate to thenormal pyrochlores (with only monovalent anions at the site) and theinverse pyrochlores (with only large cations at the site).

---

Cesstibtantit—eine geologische Einfiihrung in die inversen Pyrochlore

Zusammenfassung Die Kristallstruktur von Cesstibtantit wurde auf der Basis von Diffraktometerdaten von Proben von Leshaia, Russland and dem Tanco Pegmatit, Manitoba, gelöst. Cesstibtantit aus dem Leshaia Pegmatit (Typlokalität) hat a 10.515(2) Å, RaumgruppeFd3m, die Zusammensetzung CS_0.31(Sb_0.57Na_0.31Pb_0.02Bi_0.01)_0.91(Ta_1.88Nb_0.12)₂· (O_5.69OH, F_0.31)₆(OH, F)_0.69 Z 8; die Struktur wurde aufR 3.8,wR 4.3% verfeinert unter Benützung von 96 beobachteten Reflexen. Cesstibtantit vom Tanco Pegmatit hat a 10.496(1) Å, RaumgruppeFd3m, die Zusammensetzung (Cs_0.22K_0.01)_0.23(Na_0.45· Sb_0.39Pb_0.14Ca_0.06Bi_0.02)_1.06(Ta_1.95Nb_0.05)₂(O_5.78OH,F_0.22)₆(OH,F)_0.55,Z 8; seine Struktur wurde aufR 3.9wR 3.7% auf der Basis von 104 beobachteten Rettexen verfeinert. Cesstibtantit unterscheidet sich von normalen Pyrochloren insofern, als er signifikante Mengen von sehr großen Kationen, wie z.B. Cs enthält. Da these Kationen zu groß sind (^VIII r 1.60 Å) für eine konventionelle [8]-koordinierteA Stelle, nehmen she die [18]-koordinierten Positionen ein, welche normalerweise monovalente Anionen enthalten. Natürliche Cesstibtantitproben sind nicht ideal insofern als sowohl Cs als auch monovalente Anionen in der Position vorkommen. Somit ist Cesstibtantit intermediär zu den normalen Pyrochloren (mit nur monovalenten Anionen auf der Position) and den inversen Pyrochloren (mit ausschließlichen großen Kationen an der Position).

     

Paleohydrology and paleoclimate records in a saline prairie lake core: mineral,isotope and organic indicators

This pilot study examines the potential of obtaining a sedimentary record of paleoenvironmental/climatic/hydrologic conditions for saline Redberry Lake in southern Saskatchewan, Canada. The tools are mineralogy, stable isotopes and pigments. The upper meter of an offshore sediment core contains 10 to 20% by weight aragonite (CaCO₃), which apparently precipitated in the water column. The ¹⁸O and ¹³C of the bulk aragonite (corrected for content of detrital calcite) vary by 4 to 5. Enrichment in ¹⁸O in aragonite is significantly correlated with pigment concentrations (chlorophyll a, phaeophytin). The ¹⁸O and pigment data provide evidence for relatively dry and/or warm conditions and high limnetic productivity for the period 2500 to 1500 yrs B.P. After 1500 B.P., the climate was apparently similar to the present, with two episodes of relatively enhanced productivity, dryness and/or warmth, at around 1000 to 900 and 500 to 200 B.P. During the past century, Redberry Lake has decreased approximately 8 m in depth and its salinity has doubled. No clear sedimentary signal was observed in response to these recent hydrologic trends. These changes have not been associated with a significant climate trend in the region, but may have been induced by land use changes in the catchment.This publication is the third of a series of papers presented at the Conference on Sedimentary and Paleolimnological Records of Saline Lakes. This Conference was held August 13–16, 1991 at the University of Saskatchewan, Saskatoon, Canada. Dr. Evans is serving as Guest Editor for this series.     

Origin of the hydrocarbon component of carbonaceous chondrites: the star-meteorite connection

We report the results of an experiment that produced a residue which closely matches the hydrocarbon component of the Murchison carbonaceous chondrite. This experiment suggests that the parent material of the meteoritic component originated as polycyclic aromatic hydrocarbon species in carbon stars during their later stages of evolution. The experiments also indicate that the pathway from those formation sites to eventual incorporation into the meteorite parent body involved hydrogenation in a plasma in the solar nebula or in H II regions prior to the solar nebula. This model is consistent with what is known about the meteoritic hydrocarbon component including deuterium abundance, the observation of cosmic infrared emission bands best attributed to polycyclic aromatic hydrocarbon molecules, and the inherent stability of these molecules that allows their formation in stars and subsequent survival in the interstellar medium.     

Radiation pressure effects in the oscillations of compressible rotating homogeneous spheroids

Earlier models of compressible, rotating, and homogeneous ellipsoids with gas pressure are generalized to include the presence of radiation pressure. Under the assumptions of a linear velocity field of the fluid and a bounded ellipsoidal surface, the dynamical behaviour of these models can be described by ordinary differential equations. These equations are used to study the finite oscillations of massive radiative models with masses 10M and 30M in which the effects of radiation pressure are expected to be important.Models with two different degrees of equilibrium are chosen: an equilibrium (i.e., dynamically stable) model with an initial asymmetric inward velocity, and a nonequilibrium model with a nonequilibrium central temperature and which falls inwards from rest. For each of these two degrees of equilibrium, two initial configurations are considered: rotating spheroidal and nonrotating spherical models.From the numerical integration of the differential equations for these models, we obtain the time evolution of their principal semi-diametersa ₁ anda ₃, and of their central temperatures, which are graphically displayed by making plots of the trajectories in the (a ₁,a ₃) phase space, and of botha ₁ and the total central pressureP _c against time.It is found that in all the equilibrium radiative models (in which radiation pressure is taken into account), the periods of the oscillations of botha ₁ andP _c are longer than those of the corresponding nonradiative models, while the reverse is true for the nonequilibrium radiative models. The envelopes of thea ₁ oscillations of the equilibrium radiative models also have much longer periods; this result also holds for the nonequilibrium models whenever the envelope is well defined. Further, as compared to the nonradiative models, almost all the radiative models collapse to smaller volumes before rebouncing, with the more massive model undergoing a larger collapse and attaining a correspondingly larger peakP _c.When the mass is increased, the dynamical behavior of the radiative model generally becomes more nonperiodic. The ratio of the central radiation pressure to the central gas pressure, which is small for low mass models, increases with mass, and at the center of the more massive model, the radiation pressure can be comparable in magnitude to the gas pressure. In all the radiative models, the average periods as well as the average amplitudes of both thea ₁ andP _c oscillations also increase with mass.When either rotation or radiation pressure effects or both are included in the equilibrium nonradiative model, the period of the envelope of thea ₁ oscillations is increased. The presence of rotation in the equilibrium radiative model, however, decreases this period.Some astrophysical implications of this work are briefly discussed.     

Carbonatites from Eastern Paraguay and genetic relationships with potassic magmatism: C, O, Sr and Nd Isotopes

Summary Geochemical characteristics were systematically determined for Early Cretaceous samples of carbonatitic rocks from Eastern Paraguay (Rio Apa, Amambay and Central Provinces). The data show that all the occurrences have an enriched isotopic signature and that the carbonatites have negligible or absent crustal signature. A petrogenetic model (parent liquids, fractional crystallization, hydrothermal interactions and weathering) is proposed as a function of incompatible trace element, stable (O-C) and radiogenic (Sr-Nd) isotope variations with the aim to test the significance of carbonatitic complexes as a marker of the metasomatized subcontinental lithospheric mantle. The results indicate that the carbonatites and primary carbonates from eastern Paraguay, and those from the north eastern Paraná Basin (SE Brazil), were affected by metasomatic events distinct in time and composition.

---

Karbonatite aus Ost-Paraguay und ihre genetische Beziehung zu Kalium-Magmatismus: C O, Sr und Nd isotope

Zusammenfassung Die geochemischen Charakteristika von frühkretazischen Karbonatitproben aus Ostparaguay (Rio Alpa, Amambay und Zentrale Provinzen) wurden untersucht. Die Daten belegen, daß alle Vorkommen eine isotopische Anreicherungssignatur zeigen und daß ihnen eine entsprechende Krustensignatur fehlt. Ein Petrologisches Modell (Ausgangsschmelze, fraktionierte Kristallisation, hydrothermale Interaktion und Verwitterung) wird auf Grund der Verteilung der inkompatiblen Spurenelemente, der stabilen (C-O) und radiogenen (Sr-Nd) Isotope vorgeschlagen. Es versucht die Bedeutung der Karbonatitkomplexe als Markerhorizonte des metasomatischen subkontinentalen Mantels zu überprüfen. Die Ergebnisse zeigen, daß die Karbonatite und die primären Karbonate in Ostparaguay, und jene aus dem Paraná Becken SüdostBrasiliens durch zeitlich und zusammensetzungsmäßig unterschiedliche metasomatische Prozesse erfaßt wurden.

---

---

With 10 Figures     

Compressibility and crystal structure of sillimanite, Al2SiO5, at high pressure

The unit-cell dimensions and crystal structure of sillimanite at various pressures up to 5.29 GPa have been refined from single-crystal X-ray diffraction data. As pressure increases, a and b decrease linearly, whereas c decreases nonlinearly with a slightly positive curvature. The axial compression ratios at room pressure are β_a:β_b:β_c=1.22:1.63:1.00. Sillimanite exhibits the least compressibility along c, but the least thermal expansivity along a (Skinner et al. 1961; Winter and Ghose 1979). The bulk modulus of sillimanite is 171(1) GPa with K′=4 (3), larger than that of andalusite (151 GPa), but smaller than that of kyanite (193 GPa). The bulk moduli of the [Al1O₆], [Al2O₄], and [SiO₄] polyhedra are 162(8), 269(33), and 367(89) GPa, respectively. Comparison of high-pressure data for Al₂SiO₅ polymorphs reveals that the [SiO₄] tetrahedra are the most rigid units in all these polymorphic structures, whereas the [AlO₆] octahedra are most compressible. Furthermore, [AlO₆] octahedral compressibilities decrease from kyanite to sillimanite, to andalusite, the same order as their bulk moduli, suggesting that [AlO₆] octahedra control the compression of the Al₂SiO₅ polymorphs. The compression of the [Al1O₆] octahedron in sillimanite is anisotropic with the longest Al1-OD bond shortening by ～1.9% between room pressure and 5.29 GPa and the shortest Al1-OB bond by only 0.3%. The compression anisotropy of sillimanite is primarily a consequence of its topological anisotropy, coupled with the compression anisotropy of the Al-O bonds within the [Al1O₆] octahedron.     

Monitoring changes of clouds

An analysis of the spatial and temporal scales of cloud variability and their coupling provided by the results from existing cloud observing systems allows us to reach the following conclusions about the necessary attributes of a cloud monitoring system. (1) Complete global coverage with uniform density is necessary to obtain an unbiased estimate of cloud change and an estimate of the reliability with which that change can be determined. (2) A spatial sampling interval of less than 50 km is required so that cloud cover distributions will generally be homogeneous, or statistically homogeneous, within a sample. (3) A sampling frequency of at least six times a day ensures not only that the diurnal and semi-diurnal cycles are not aliased into long term mean values, but also that changes in them can be monitored. (4) Since estimated climate changes are only evident on a decadal time-scale, unless cloud monitoring is continuous with a record length greater than 10 years and has very high precision ( 1%) instrument calibration with overlapping observations between each pair of instruments, it will not be possible either to detect or to diagnose the effects of cloud changes on the climate.     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.     

Crystallization processes in an artificial magma: variations in crystal shape,growth rate and composition with melt cooling history

A large (4.8 m³, 1.3x10⁷ g) artificial mafic melt with a bulk composition similar to that of a basalt (but with a high CaO content of 17 wt%) was generated during a demonstration of in situ vitrification and was allowed to cool naturally. During the melting process, convection was vigorous, resulting in a chemically and thermally homogeneous melt body. Once heating was complete, the cooling rate was rapid with the temperature dropping from 1500°C to 500°C in 6 days within the interior of the 3 m diameter, 1.5 m thick body. A 20 h period of constant temperature (1140°C) observed during colling was the result of latent heat released by widespread crystallization. The final crystalline assemblage consists of diopsidic to hedenbergitic pyroxene and anorthitic feldspar, with a subordinate amount of potassic feldspar, plus a small amount of evolved glass. The compositions and proportions of phases agree well with those predicted by the MELTS thermodynamic model. Thermal and textural evidence suggest that convection within the melt ceased coincident with formation of the first crystals. Textural investigation of core samples reveals large (up to 1 cm in length) acicular diopsidic pyroxenes in a matrix of smaller feldspar and zoned pyroxene crystals (500 m in length). Crystal shape and pyroxene composition vary as a function of position within the solidified body, as a function of cooling rate. Both crystal size and degree of crystallinity are highest in the central, most slowly-cooled parts of the rock. Crystal shape is characterized by tabular, equilibrium-growth forms in the slowly-cooled areas, grading to highly skeletal, dendritic forms at the rapidly-cooled edges of the body. The pyroxene crystals are dominantly homogeneous diopside, but crystals are characterized by thin Fe-rich hedenbergitic rims. These rims were deposited when Mg in the melt was depleted by diopside growth, and melt temperature had cooled sufficiently to allow Fe-rich pyroxene growth. Crystal growth rates can be calculated based on thermal behavior of the melt, reinforced by thermodynamic modelling, and are determined to be between 10^-7 and 10^-8 cm/s in the central part of the melt. These estimates agree well with growth rates in natural systems with similar cooling rates. Pyroxene crystals that formed at a higher cooling rates are characterized by higher Al and lower Mg contents relative to tabular equilibrium crystalline forms, presumably as a result of disequilibrium melt compositions at the crystal-melt interface.New Mexico Bureau of Mines and Mineral Resources, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA