A new tool for the study of periodic orbits

We present the generalization of the method of rational Fourier-series approximations for nonlinear ordinary differential equations in galactic dynamics. In previous papers we presented the formulae which describe simple families of periodic orbits with very good accuracy. In this Letter we generalize our formulae to describe periodic orbits of any resonancem:n.     

Correction: Guidelines and pitfalls of refraction microtremor surveys

Journal of Seismology -     

Late Quaternary sedimentation on the Leidy Creek fan, Nevada–California: geomorphic responses to climate change

Well-dated surface and subsurface deposits in semiarid Fish Lake Valley, Nevada and California, demonstrate that alluvial-fan deposition is strongly associated with the warm dry climate of the last two interglacial intervals, and that fans were stable and (or) incised during the last glaciation. Fan deposition was probably triggered by a change from relatively moist to arid conditions causing a decrease in vegetation cover and increases in flash floods and sediment yield. We think that this scenario applies to most of the other valleys in the southern Basin and Range. Radiocarbon, tephra, and a few thermoluminescence and cosmogenic ages from outcrops throughout Fish Lake Valley and from cores on the Leidy Creek fan yield ages of >100–50 ka and 11–0 ka for the last two periods of alluvial-fan deposition. Mapping, coring and shallow seismic profiling indicate that these periods were synchronous throughout the valley and on the proximal and distal parts of the fans. From 50 to 11 ka, fan deposition ceased, a soil formed on the older alluvium and the axial drainage became active as runoff and stream competence increased. Slow deposition due to sheet flow or aeolian processes locally continued during this interval, producing cumulic soil profiles. The soil was buried by debris-flow sediment beginning at about 11 ka, coincident with the onset of relatively dry and warm conditions in the region. However, ground-water discharge maintained a large freshwater marsh on the valley floor throughout the Holocene. Pulses of deposition during the Holocene are recorded in the marsh and fan deposits; some pulses coincided with periods of or transitions to warm, dry climate indicated by proxy climate records, whereas others may reflect local disturbances associated with volcanism and fires. Within the marsh deposits, much of the clastic material is probably desert loess. In addition, the deposition of coppice dunes within the fan deposits coincides with two dry periods during the late Holocene.     

The glacilacustrine sedimentary environment of Bowser Lake in the northern Coast Mountains of British Columbia, Canada

Bowser Lake, a fiord lake in the northern Coast Mountains of British Columbia, contains a thick Holocene fill consisting mainly of silt and clay varves. These sediments were carried into the lake by proglacial Bowser River which drains a high-energy, heavily glacierized basin. Sedimentation in the lake is controlled by seasonal snow and ice melt, by autumn rainstorms, and by rare, but very large jökulhlaups from glacier-dammed lakes in the upper Bowser River basin which complicate environmental inferences from the sedimentary record. Sediment is dispersed through the deep western part of the lake by energetic turbidity currents. The turbidity currents apparently do not overtop a sill that separates the western basin from much shallower areas to the east. Large amounts of silt and clay are deposited from suspension in the eastern part of the lake, but sediment accumulation rates there are much lower than to the west. Several strong acoustic reflectors punctuate the varved fill in the western basin; these may be thick or relatively coarse beds deposited during jökulhlaups or exceptionally large storms. The contemporary sediment yield to Bowser Lake, estimated from sediments in the lake, is about 360 t km^-2a^-1. This is a relatively high value, but it is less than yields insome other, similar montane basins with extensive snow and ice cover.The most likely explanation for the difference is that large amounts of sediment have been, and continue to be, stored on the Bowser delta andin small proglacial lakes.     

Late Tertiary paleoclimatic interpretation from lacustrine rhythmites in the Gray Fossil Site,northeastern Tennessee,USA

The Gray Fossil Site (GFS) includes a small (<2 ha) paleosinkhole lake fill with an exceptionally well-preserved record of sedimentation and fossils from the latest Miocene to earliest Pliocene. The uppermost lacustrine stratigraphy is characterized by rhythmites that regularly alternate between coarse-grained and organic-rich (A) laminae and fine-grained, silty clay (B) laminae. Both the A and B components are almost exclusively comprised of exogenic sediment (including organic matter). Periodicities of 24 and 4.4 are recorded within a continuous 96 interpreted year sequence of rhythmite sediment. In a small lake with a poorly oxygenated bottom, the presence of laterally continuous laminated sediment that includes well-known periodicities in rhythmite thickness is interpreted as representing annually generated varves that correspond to seasonal variations in sedimentation. The distinctly larger fraction of medium sand-size quartz grains present within the A laminae, as well as the abrupt transitions between A and B components suggest that the rhythmites represent deposition during alternating high-energy and lower-energy seasons, which is consistent with a monsoonal precipitation pattern. The seasonal climate may relate to changes in the ocean circulation pattern prior to 4.6 Ma that resulted in an increased temperature and atmospheric pressure gradient between the east coast of North America and the Atlantic Ocean, but this climate phase seems to be only a temporary condition, as underlying and overlying sediment are both consistent with drier conditions. The periodicity at 24 interpreted years is consistent with the well-known Hale solar cycle. The 4.4 interpreted-year periodicity occurs within the ENSO frequency band, and if this documentation of ENSO-like interannual climate change is correct, then it suggests that ENSO operated at times during the warm Earth conditions characterizing the late Tertiary.     

Knowledge-Driven Prospectivity Mapping for Granite-Related Polymetallic Sn–F–(REE) mineralization,Bushveld Igneous Complex,South Africa

This paper presents mineral prospectivity mapping to identify potential new exploration ground for polymetallic Sn–F–REE mineralization associated with the Bushveld granites of the Bushveld Igneous Complex, South Africa. The Lebowa Granite Suite, commonly known as the Bushveld granites, is host to a continuum of polymetallic mineralization with a wide range of metal assemblages (Sn–Mo–W–Cu–Pb–Zn–As–Au–Ag–Fe–F–U–REE), ranging from a high-temperature to a low-temperature magmatic hydrothermal mineralizing environment. The prospectivity map was generated by fuzzy logic modeling and a selection of targeting criteria (or spatial proxies) based on a conceptual mineral system highlighting critical processes responsible for the formation of the polymetallic mineralization. The spatial proxies include proximity to differentiated granites (as heat and metal-rich fluid sources), Rb geochemical map (fluid-focusing mechanism such as fractionation process), principal component maps (PC 4 Y–Th and PC 14 Sn–W, fluid pathways for both high- and low-temperature mineralization) and proximity to roof rocks (traps for fluids). Logarithmic functions were used to rescale rasterized evidential maps into continuous fuzzy membership scores in a range of [0, 1]. The evidential maps were combined in two-staged integration matrix using fuzzy AND, OR and gamma operators to produce the granite-related polymetallic Sn–F–(REE) prospectivity map. The conceptual mineral system model and corresponding prospectivity model developed in this study yielded an encouraging result by delineating the known mineral deposits and occurrences of Sn–F–(REE) mineralization that were not used to assign weights to the evidential maps. The prospectivity model predicted, on average, 77% of the known mineral occurrences in the BIC (i.e., 56 of 73 Sn occurrences, 12 of 15 F occurrences and 6 of 8 REE occurrences). Based on this validation, 13 new targets were outlined in this study.