Estimation of uncertainties in eigenspectral estimates from decaying geophysical time series

Summary. The response of many dynamical systems to an impulse is a linear combination of decaying cosines. The frequencies of the cosines have generally been estimated in geophysics by periodogram analysis and little formal indication of uncertainty has been provided. This work presents an estimation procedure by the methods of complex demodulation and nonlinear regression that specifically incorporates in the basic model the decaying aspect of the cosines (periodogram analysis does not). The use of plots of the instantaneous phase as a function of time is shown to greatly enhance resolution. Expressions for the variances of eigenfrequencies, amplitudes, phases and damping constants Q are derived by non-linear least-squares. The results are illustrated, for the problem of the free oscillations of the Earth, by computations with the record made at Trieste of the Chilean earthquake of 1960 May 22. Sample values are periods and standard errors of 737.79 ± 0.13 s, 506.25 ± 0.13 s and 429.60 ± 0.14 s for ₀ T ₈, ₀ T ₁₃ and ₀ T ₁₆ with Q values and standard errors of 200 ± 14, 230 ± 28 and 215 ± 30, respectively.     

Distinguishing lower and upper crustal processes in magmas erupted during the buildup to the 7.7 ka climactic eruption of Mount Mazama, Crater Lake, Oregon, using 238U–230Th disequilibria

Uranium-series isotope ratios determined for 35 volcanic rocks and 4 glass separates erupted from ~36 to 4.8 ka at Mt. Mazama, Crater Lake, Oregon, identify both ²³⁰Th-excess and ²³⁸U-excess components. U–Th isotope compositions cover a wide range, exceeding those previously measured for the Cascade arc. Age-corrected (²³⁰Th/²³²Th) and (²³⁸U/²³²Th) activity ratios range from 1.113 to 1.464 and from 0.878 to 1.572 (44.4 % ²³⁰Th-excess to 8.8 % ²³⁸U-excess), respectively. The most distinctive aspect of the data set is the contrast in U–Th isotope ratios between low and high Sr (LSr, HSr) components that have been previously identified in products of the 7.7 ka caldera-forming climactic eruption and preclimactic rhyodacite lavas. The LSr component exclusively contains ²³⁸U-excess, but the HSr component, as well as more primitive lavas, are marked by ²³⁰Th-excess. ²³⁰Th-excesses such as those recorded at Mt. Mazama are commonly observed in the Cascades. Melting models suggest that high ²³⁰Th-excesses observed in the more primitive lavas evolved through mixing of a mantle melt with a partial melt of a mafic lower crustal composition that contained garnet in the residuum that was produced through dehydration melting of amphibolite that was initially garnet free. Dehydration melting in the lower crust offers a solution to the “hot-slab paradox” of the Cascades, where low volatile contents are predicted due to high slab temperatures, yet higher water contents than expected have been documented in erupted lavas. The ²³⁸U-excess observed at Mt. Mazama is rare in Cascade lavas, but occurs in more than half of the samples analyzed in this study. Traditionally, ²³⁸U-excess in arc magmas is interpreted to reflect slab fluid fluxing. Indeed, ²³⁸U-excess in arcs is common and likely masks ²³⁰Th-excess resulting from lower crustal interaction. Isotopic and trace element data, however, suggest a relatively minor role for slab fluid fluxing in the Cascades. We propose that ²³⁸U-excess reflects melting and assimilation of young, hydrothermally altered upper crust. The processes related to generating ²³⁸U-excess are likely important features at Mt. Mazama that accompanied development of a large-scale silicic magma chamber that led to the caldera-forming eruption.     

Relationship between stable isotope ratios and drop size distribution in tropical rainfall

We carried out simultaneous measurements of drop size distribution (DSD) and stable oxygen and hydrogen isotopic compositions (??¹⁸O and ??D) of rain at the National Atmospheric Research Laboratory (NARL), Gadanki (13.5°N, 79.2°E), southern India, during September?COctober 2006, with the aim of understanding microphysical processes leading to rain formation. The MST radar at NARL was operated continuously during rain events, while rain samples were collected at very short time intervals (<1?h), to capture small changes (>0.2?? and >2??) in their ??¹⁸O and ??D. The slope of the local meteoric water line (??D?C??¹⁸O line), was 8.07?±?0.47, similar to that of global meteoric water line, confirming that the precipitation occurred under isotopic equilibrium, and was unaffected by some anomalous process; further, the evaporation of rain drops at the cloud base was insignificant. Whenever the isotopic variations were larger during a rain event (>2??) there was a significant negative correlation between the ??¹⁸O and DSD. The possible explanation is that larger drops are mostly associated with convective rather than stratiform rain, and ¹⁸O (and D) depletion in convective rain is relatively more. Bin-resolved microphysical models incorporating water isotopologues could benefit by considering drop size spectra, which could improve the match with stable isotope observations of precipitation.     

Dunes on Titan observed by Cassini Radar

Thousands of longitudinal dunes have recently been discovered by the Titan Radar Mapper on the surface of Titan. These are found mainly within ±30° of the equator in optically-, near-infrared-, and radar-dark regions, indicating a strong proportion of organics, and cover well over 5% of Titan's surface. Their longitudinal duneform, interactions with topography, and correlation with other aeolian forms indicate a single, dominant wind direction aligned with the dune axis plus lesser, off-axis or seasonally alternating winds. Global compilations of dune orientations reveal the mean wind direction is dominantly eastwards, with regional and local variations where winds are diverted around topographically high features, such as mountain blocks or broad landforms. Global winds may carry sediments from high latitude regions to equatorial regions, where relatively drier conditions prevail, and the particles are reworked into dunes, perhaps on timescales of thousands to tens of thousands of years. On Titan, adequate sediment supply, sufficient wind, and the absence of sediment carriage and trapping by fluids are the dominant factors in the presence of dunes.     

Heavy rare gases from Rabbit Lake (Canada) and the Oklo mine (Gabon): natural spontaneous chain reactions in old uranium deposits

Xenon isotopic studies confirm natural spontaneous chain reactions at the Oklo mine site (Republic of Gabon) with an integrated neutron flux of approximately 4 × 10²⁰n/cm² and a duration between 14,000 and 70,000 years. Similar studies for the Rabbit Lake deposit (Saskatchewan), a slightly younger site with some evidence of continued geologic activity, shows no evidence of self-supporting reactions.     

Bootstrapped discrete scale invariance analysis of geomagnetic dipole intensity

The technique of bootstrapped discrete scale invariance allows multiple time-series of different observables to be normalized in terms of observed and predicted characteristic timescales. A case study is presented using the SINT2000 time-series of virtual axial dipole moment, which spans the past 2 Myr. It is shown that this sequence not only bears a clear signature of a preferred timescale of about 55.6 Ka, but additionally predicts similar features (of shorter and longer duration) that are actually observed on the timescales of historical secular variation and dipole reversals, respectively. In turn, the latter two empirical sources both predict the characteristic timescale found in the dipole intensity sequence. These communal scaling characteristics suggest that a single underlying process could be driving dynamo fluctuations across all three observed timescales, from years to millions of years.     

Understanding the surface hydrology of the Lake Eyre Basin: Part 1—Rainfall

This is the first of two papers that describe the surface hydrology of the Lake Eyre Basin (LEB) (1,140,000 km²) in central Australia and compares some key characteristics with those observed from arid regions globally. This paper concentrates on annual rainfall, whereas the second paper is devoted to streamflow. The first part describes the LEB's climate (arid to semi-arid), which is dominated by a subtropical high pressure ridge stretching latitudinally across central Australia. Then follow major analyses that include the characteristics of rainfall, wet and dry spell lengths and cumulative surpluses and deficiencies, rainfall trends and intra- and inter-decadal fluctuations, and the relationship between rainfall and El Niño-Southern Oscillation (ENSO). The paper concludes with six conclusions, the key ones being: the variability of the annual rainfall (based on the coefficient of variation) in the LEB is approximately 60% greater than that found for stations located in arid regions in the rest of the world; there is a bias towards longer lengths of dry years than observed in the rest of Australia; and, there is a significant lag correlation between rainfall and ENSO, particularly in the east and in the latter part of a year.     

Oceanic versus island arc origin of ophiolites

The silica content of basaltic rocks is an unreliable variable with which to distinguish ultramafic-mafic complexes developed at ocean ridges from those potentially formed beneath volcanic island arcs. Data from Appalachian ophiolites supports the view that silica metasomatism is responsible for the high silica content of supposed calc-alkaline basaltic rocks found in ophiolites such as Troodos, and that the high-silica (70 wt.%) leucocratic rocks associated with ophiolites are of tholeiitic rather than calc-alkaline parentage. The use of titanium as a discriminant of tectonic environment is also suspect because the titanium content of basalts associated with Appalachian ophiolites as well as those recently recovered from the Atlantic ocean floor ranges from values even lower than those typical of island arc tholeiites to values typical of abyssal tholeiites. However, the internal stratigraphy of ophiolites in both the Appalachian and Tethyan systems can only be explained on the basis of the postulate that ophiolites originate at oceanic spreading centres rather than beneath island arcs.     

Urban settlement size trends in the former USSR: 1970-1989

"Based upon recently published data, this paper investigates urban settlement size trends in the former USSR and its republics during the intercensal periods of 1970-1979 and 1979-1989. Results indicate that although a trend toward largeness of the Soviet urban hierarchy continues, a slowing in this direction has occurred. Among republics, all had an increasing trend towards largeness on at least one and usually all three summary measures of urban settlement size structure. The RSFSR [Russia] and Armenia especially consistently evidenced a relatively high degree of largeness, while the former Baltic republics generally revealed a relative smallness."