Directions and possibilities of mathematical geology

This paper considers the present state of mathematical geology. Three directions are recognized: applied, theoretical, and mathematical. Applied mathematical geology includes formal use of mathematics to solve problems and computer processing of data. Success is achieved by a correspondence of mathematical methods used to the nature of geological data. This correspondence can be demonstrated by purely mathematical means. Theoretical mathematical geology uses mathematics as a language of geology; however, a number of methodological problems must be solved: formalization of initial geological concepts and creation of a strict conceptual basis, substantiation of initial principles of mathematical simulation, creation of theoretical geological models, problems of elementary and coincidence in geology, and methodological substantiations of possibilities of any mathematical model to approximate geological models. The essense and significance of these problems are considered. The main task of mathematical geology is to prove its correspondence to the nature of the geological objects studied, geological data obtained, and geological problems solvable. Finally, the main problems of mathematical geology are not so much mathematical as geological and methodological.     

The Stress–Strain State of Recent Structures in the Northeastern Sector of the Russian Arctic Region

Doklady Earth Sciences - Complex research to determine the stress–strain state of the Earth’s crust and the types of seismotectonic destruction for the northeastern sector of the...     

On the reoccurrence of site specific response

The period and amplitude variations of local peaks in the Fourier amplitude spectra of free-field strong ground motion recorded at five stations in San Fernando Valley of metropolitan Los Angeles, California, are described, searching for peaks that reoccur during different earthquakes. The data suggest that some local peaks reoccur (about 50% of the time), during shaking by small local earthquakes (peak ground velocities, v_max<10–20 cm/s). During large strong motion amplitudes (v_max>20 cm/s), these peaks are shifted towards longer periods (by nonlinear response of soils) or disappear. The data also suggest that densification and settlement of soil, minutes and hours following the strong shaking may contribute towards fluctuations in the effective stiffness of the shallow surface layers.     

The influence of particle composition on thorium scavenging in the NE Atlantic ocean (POMME experiment)

²³⁰Th, ²³²Th and ²³⁴Th were analyzed in sinking particles collected by moored and drifting sediment traps in the NE Atlantic Ocean (POMME experiment) in order to constrain the phase(s) carrying Th isotopes in the water column. It reveals a contrasted behaviour between ²³⁴Th and ²³⁰Th. ²³⁴Th is correlated to the particulate organic carbon suggesting that it is primarily scavenged by organic compounds in the surface waters. ²³⁰Th_xs is correlated with Mn, Ba and the lithogenic fraction that are enriched in small suspended particles and incorporated in the sinking particulate flux throughout the water column. The lack of correlation between ²³⁰Th_xs and CaCO₃ or biogenic silica (bSi) indicates that CaCO₃ and bSi are not responsible for ²³⁰Th scavenging in the deep waters of this oceanic region. ²³⁰Th is generally correlated with the lithogenic content of the trapped material but this correlation disappears in winter during strong atmospheric dust inputs suggesting that lithogenic matter is not directly responsible for ²³⁰Th scavenging in the deep waters or that sufficient time is required to achieve particle–solution equilibration. MnO₂ could be the prevalent ²³⁰Th_xs-bearing phase. The narrow range of K_{d_MnO2}^Th obtained for very contrasted oceanic environments supports a global control of ²³⁰Th_xs scavenging by MnO₂ and raises the possibility that the ²³⁰Th–²³¹Pa fractionation is controlled by the amount of colloidal MnO₂ in seawater.     

Benthic foraminifers in upper Quaternary sediments of the southern Bering Sea: Distribution and paleoceanographic interpretations

Composition and distribution of benthic foraminifers, being coupled with isotopic-geochemical data on Upper Pleistocene and Holocene sediments from the southern Bering Sea (Core GC-11; 53°31′ N, 178°51′E, water depth 3060 m), demonstrate variations in bottom water properties during the last 54 kyr. Their abundance increased to some extent during short periods corresponding to warm Dansgaard-Oeshger interstadials 14, 12, 8, and 2 of marine isotopic stages (MIS) 3 and 2. The first and second deglaciation phases separated by the Younger Dryas cooling episode are marked by significant abundance peaks of benthic foraminifers (an order magnitude higher than in the glacial period), although their share in community of benthic and planktonic foraminifers taken together decreases. Species typical of stable high-productivity areas gain the dominant position. A significant proportion of agglutinated species in the Holocene sediments is indicative of Ca ions deficiency that accelerates dissolution of carbonate tests up to their disappearance approximately 2.5–3 ka ago.     

Organic matter of the North Atlantic

The areas that we studied in the North Atlantic (53 and 60°N) and in the Labrador Sea in the summer were characterized by a wide variability of the concentrations of dissolved and particulate organic matter and its elemental composition both in the surface and in the deep waters. The concentrations of dissolved and particulate C_org varied within 69–360 μM and 0.7–25.6 μM, respectively; the N_org and P_org contents varied within 1.4–22.2 μM and 0.02–0.86 μM, respectively. The maximal concentrations were registered in the photic layer and in the zones of mixing between the waters of different genesis. The particulate matter contribution to the total organic matter (OM) content varied from 0.5 to 15.4%. The waters of the photic layer contained more particulate C_org than those of the near-bottom layer. The values of the C/N molar ratios from the surface to the bottom over the entire aquatic area surveyed varied 5-to 6-fold; at that, the values of the C/P molar ratios varied more than tenfold. In the most productive waters, the values of the C/N ratios were close to the Redfield ratios (6–10). The values of the C/P molar ratios varied from 160 in the photic layer to 4831 in the deep waters. The pronounced non-uniformity in the spatial distribution of the OM and its elemental composition is caused not only by the penetration of the waters of different origins but also by the changes in the microplankton metabolism under mixing of these waters.     

Spectral analysis of the “Koshava” wind

Summary “Koshava” is a gusty wind of changeable intensity, blowing from a south-easterly direction, over Serbia, Romania and Bulgaria. It is caused by the interaction between the synoptic circulation and the orography of the Carpathian and the Balkan mountains. This paper analyzes wind data measured at the Belgrade-Observatory during the longest period of consecutive days of “Koshava” which occurred from 14 January to 13 February 1972. Mean hourly wind speed data has been examined using spectral analysis. The power spectra are calculated using autocorrelation spectral analysis, the multi-taper method and wavelet transform. The maximum of which is about 122 h (5 days) corresponds to the time span of synoptic processes.     

Response of detrital zircon and monazite,and their U–Pb isotopic systems,to regional metamorphism and host‐rock partial melting,Cooma Complex,southeastern Australia

Progressive Early Silurian low‐pressure greenschist to granulite facies regional metamorphism of Ordovician flysch at Cooma, southeastern Australia, had different effects on detrital zircon and monazite and their U–Pb isotopic systems. Monazite began to dissolve at lower amphibolite facies, virtually disappearing by upper amphibolite facies, above which it began to regrow, becoming most coarsely grained in migmatite leucosome and the anatectic Cooma Granodiorite. Detrital monazite U–Pb ages survived through mid‐amphibolite facies, but not to higher grade. Monazite in the migmatite and granodiorite records only metamorphism and granite genesis at 432.8 ± 3.5 Ma. Detrital zircon was unaffected by metamorphism until the inception of partial melting, when platelets of new zircon precipitated in preferred orientations on the surface of the grains. These amalgamated to wholly enclose the grains in new growth, characterised by the development of {211} crystal faces, in the migmatite and granodiorite. New growth, although maximum in the leucosome, was best dated in the granodiorite at 435.2 ± 6.3 Ma. The combined best estimate for the age of metamorphism and granite genesis is 433.4 ± 3.1 Ma. Detrital zircon U–Pb ages were preserved unmodified throughout metamorphism and magma genesis and indicate derivation of the Cooma Granodiorite from Lower Palaeozoic source rocks with the same protolith as the Ordovician sediments, not Precambrian basement. Cooling of the metamorphic complex was relatively slow (average ～12°C/10⁶y from ～730 to ～170°C), more consistent with the unroofing of a regional thermal high than cooling of an igneous intrusion. The ages of detrital zircon and monazite from the Ordovician flysch (dominantly composite populations 600–500 Ma and 1.2–0.9 Ga old) indicate its derivation from a source remote from the Australian craton.     

Assessment of the impact of the planetary scale on the decay of blocking and the use of phase diagrams and enstrophy as a diagnostic

It was shown that abrupt changes in the large-scale structure of atmospheric flows may lead to the rapid decay of blocking. Analysis of phase diagrams made it possible to identify when sharp changes occurred in the dynamics of the system. The connection of these changes to the decay of blocking was estimated for three blocking events in the Southern Hemisphere. In addition to phase diagrams, enstrophy was used as a diagnostic tool for the analysis of blocking events. From the results of this analysis, four scenarios for the decay mechanisms were determined: (i) decay with a lack of synoptic-scale support, (ii) decay with an active role for synoptic processes, and (iii–iv) either of these mechanisms in the interaction with an abrupt change in the character of the planetary-scale flow.