On the application of the mode-acceleration method to structural engineering problems

Mode-superposition has been extensively used in computing the dynamic response of complex structures. Two versions of mode-superposition, namely the mode-displacement method and the mode-acceleration method, have been employed. The present paper summarizes the results of a systematic study comparing the accuracy of the mode-displacement and mode-acceleration methods when applied to structures with various levels of damping or various excitation frequencies. The paper also discusses several details concerning the implementation of the mode-acceleration method.     

Lower Eocene carbonate-cemented “chimney” structures (Varna, Bulgaria) — Control of seepage rates on their formation and stable isotopic signature

The genesis of Lower Eocene calcite-cemented columns, “pisoid”-covered structures and horizontal interbeds, clustered in dispersed outcrops in the Pobiti Kamani area (Varna, Bulgaria) is related to fossil processes of hydrocarbon migration. Field observations, petrography and stable isotope geochemistry of the cemented structures and associated early-diagenetic veins, revealed that varying seepage rates of a single, warm hydrocarbon-bearing fluid, probably ascending along active faults, controlled the type of structure formed and its geochemical signature. Slow seepage allowed methane to oxidize within the sediment under ambient seafloor conditions (δ¹⁸O = − 1 ± 0.5‰ V-PDB), explaining columns' depleted δ¹³C ratios of − 43‰. Increasing seepage rates caused methane to emanate into the water column (δ¹³C = − 8‰) and raised precipitation temperatures (δ¹⁸O = − 8‰). Calcite-cemented conduits formed and upward migrating fluids also affected interbed cementation. Even higher-energy fluid flow and temperatures likely controlled the formation of “pisoids”, whereby sediment was whirled up and cemented.     

Effect of sampling and linkage on fault length and length–displacement relationship

The power-law exponent (n) in the equation: D=cL ⁿ , with D = maximum displacement and L = fault length, would be affected by deviations of fault trace length. (1) Assuming n=1, numerical simulations on the effect of sampling and linkage on fault length and length–displacement relationship are done in this paper. The results show that: (a) uniform relative deviations, which means all faults within a dataset have the same relative deviation, do not affect the value of n; (b) deviations of the fault length due to unresolved fault tip decrease the values of n and the deviations of n increase with the increasing length deviations; (c) fault linkage and observed dimensions either increase or decrease the value of n depending on the distribution of deviations within a dataset; (d) mixed deviations of the fault lengths are either negative or positive and cause the values of n to either decrease or increase; (e) a dataset combined from two or more datasets with different values of c and orders of magnitude also cause the values of n to deviate. (2) Data including 19 datasets and spanning more than eight orders of fault length magnitudes (10⁻²–10⁵ m) collected from the published literature indicate that the values of n range from 0.55 to 1.5, the average value being 1.0813, and the peak value of n _d (double regression) is 1.0–1.1. Based on above results from the simulations and published data, we propose that the relationship between the maximum displacement and fault length in a single tectonic environment with uniform mechanical properties is linear, and the value of n deviated from 1 is mainly caused by the sampling and linkage effects.     

Petrology of ultramafic and mafic xenoliths in picrite of Kahoolawe Island,Hawaii

A picrite lava (22 wt% MgO; 35 vol.% ol) along the western shore of the1.3–1.4 Ma Kahoolawe tholeiitic shield, Hawaii, contains small xenoliths of harzburgite, lherzolite, norite, and wehrlite. The various rock types have textures where either orthopyroxene, clinopyroxene, or plagioclase is in a poikilitic relationship with olivine. The Mg#s of the olivine, orthopyroxene, and clinopyroxene in this xenolith suite range between 86 and 82; spinel Mg#s range from 60 to 49, and plagioclase is An_75–80. A ⁸⁷Sr/⁸⁶Sr ratio for one ol-norite xenolith is 0.70444. In comparison, the host picrite has olivine phenocrysts with an average Mg# of 86.2 (range 87.5–84.5), and a whole-rock ⁸⁷Sr/⁸⁶Sr ratio of 0.70426. Textural and isotopic information together with mineral compositions indicate that the xenoliths are related to Kahoolawe tholeiitic magmatism, but are not crystallization products of the magma represented by their host picrite. Rather, the xenoliths are crystalline products of earlier primitive liquids (FeO/MgO ranging 1 to 1.3) at 5–9 kbar in the cumulate environment of a magma reservoir or conduit system. The presence of ultramafic xenoliths in picrite but not in typical Kahoolawe tholeiitic lava (6–9 wt% MgO) is consistent with replenishment of reservoirs by dense Mg-rich magma emplaced beneath resident, less dense tholeiitic magma. Mg-rich magmas have proximity to reservoir cumulate zones and are therefore more likely than fractionated residual liquids to entrain fragments of cumulate rock.     

Oscillations of galactic cosmic rays and solar indices before the arrival of relativistic solar protons

Using modern wavelet analysis techniques, we have made an attempt to search for oscillations of intensity of galactic cosmic rays (GCR), sunspot numbers (SS) and magnitudes of coronal index (CI) implying that the time evolution of those oscillations may serve as a precursor of Ground Level Enhancements (GLEs) of solar cosmic rays (SCR). From total number of 70 GLEs registered in 1942–2006, the four large events — 23 February 1956, 14 July 2000, 28 October 2003, and 20 January 2005 — have been chosen for our study. By the results of our analysis, it was shown that a frequency of oscillations of GCR decreases as time approaches to the event day. We have also studied a behaviour of common periodicities of GCR and SCR within the time interval of individual GLE. The oscillations of GLE occurrence rate (OR) at different stages of the solar activity (SA) cycle is of special interest. We have found some common periodicities of SS and CI in the range of short (2.8, 5.2, 27 and 60 days), medium (0.3, 0.5, 0.7, 1.3, 1.8 and 3.2 years) and long (4.6 and 11.0 years) periods. Short and medium periodicities, in general, are rather concentrated around the maxima of solar cycles and display the complex phase relations. When comparing these results with the behaviour of OR oscillations we found that the period of 11 years is dominating (controlling); it is continuous over the entire time interval of 1942–2006, and during all this time it displays high synchronization and clear linear ratios between the phases of oscillations of η, SS and CI. It implies that SCR generation is not isolated stochastic phenomena characteristic exclusively for chromospheric and/or coronal structures. In fact, this process may have global features and involve large regions in the Sun’s atmosphere.