Analytical method for the effects of the asteroid belt on planetary orbits

Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant density asteroid belt. The derivations include extensions and adaptations of Plakhov's analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus.The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained using the analytic expressions and those obtained using numerical integration are discussed. The effects of the asteroid belt on the Earth based ranging to Mars are also demonstrated.     

Fracture flow and groundwater compartmentalization in the Rollins Sandstone, Lower Mesaverde Group, Colorado, USA

 This paper presents a site-specific conceptual model of groundwater flow in fractured damage zones associated with faulting in a package of sedimentary rocks. The model is based on the results of field and laboratory investigations. Groundwater and methane gas inflows from fault-fracture systems in the West Elk coal mine, Colorado, USA, have occurred with increasing severity. Inflows of 6, 160 and 500 L s⁻¹ discharged almost instantaneously from three separate faults encountered in mine workings about 460 m below ground level. The faults are about 600 m apart. The δ ²H and δ ¹⁸O compositions of the fault-related inflow waters and the hydrodynamic responses of each fault inflow indicate that the groundwaters discharge from hydraulically isolated systems. ¹⁴C data indicate that the groundwaters are as much as 10,500 years old. Discharge temperatures are geothermal (≈30°C), which could indicate upwelling from depth. However, calculations of geothermal gradients, analysis of solute compositions of groundwater in potential host reservoirs, geothermometer calculations, and results of packer testing indicate that the fractured groundwater reservoir is the Rollins Sandstone (120 m thick) directly beneath the coal seams. The packer test also demonstrates that the methane gas is contained in the coal seams. A geothermal gradient of 70–80°C km⁻¹, related to an underlying intrusion, is probably responsible for the slightly elevated discharge temperatures. Large discharge volumes, as great as 8.2×10⁵m³ from the 14 South East Headgate fault (14 SEHG), rapid declines in discharge rates, and vertical and horizontal permeability (matrix permeability generally <0.006 Darcy) indicate fracture flow. An in-mine pumping test demonstrates that the 14 SEHG fault has excellent hydraulic communication with fractures 50 m from the fault. Aeromagnetic data indicate that the faults are tectonically related to an igneous body that is several thousand meters below the coal seams. Exploratory drilling has confirmed a fourth fault, and two additional faults are projected, based on the aeromagnetic data. The conceptual model describes a series of parallel, hydraulically separate groundwater systems associated with fault-specific damage zones. The faults are about 600 m apart. Groundwater stored in fractured sandstone is confined above and below by clayey layers. Received March 1999 / Revised, November 1999 / Accepted, December 1999     

Fractal measures of drainage network to investigate surface deformation from remote sensing data: A paradigm from Hindukush (NE-Afghanistan)

This approach represents the relative susceptibility of the topography of the earth to active deformation by means of geometrical distinctiveness of the river networks. This investigation employs the fractal analysis of drainage system extracted from ASTER Global Digital Elevation Model (GDEM-30m resolution). The objective is to mark active structures and to pinpoint the areas robustly influenced by neotectonics. This approach was examined in the Hindukush, NE-Afghanistan. This region is frequently affected by deadly earthquakes and the modern fault activities and deformation are driven by the collision between the northward-moving Indian subcontinent and Eurasia. This attempt is based on the fact that drainage system is strained to linearize due to neotectonic deformation. Hence, the low fractal dimensions of the Kabul, Panjsher, Laghman, Andarab, Alingar and Kocha Rivers are credited to active tectonics. A comprehensive textural examination is conducted to probe the linearization, heterogeneity and connectivity of the drainage patterns. The aspects for these natural textures are computed by using the fractal dimension (FD), lacunarity (LA) and succolarity (SA) approach. All these methods are naturally interrelated, i.e. objects with similar FD can be further differentiated with LA and/or SA analysis. The maps of FD, LA and SA values are generated by using a sliding window of 50 arc seconds by 50 arc seconds (50" × 50"). Afterwards, the maps are interpreted in terms of regional susceptibility to neotectonics. This method is useful to pinpoint numerous zones where the drainage system is highly controlled by Hindukush active structures. In the North-Northeast of the Kabul block, we recognized active tectonic blocks. The region comprising, Kabul, Panjsher, Andrab, Alingar and Badakhshan is more susceptible to damaging events. This investigation concludes that the fractal analysis of the river networks is a bonus tool to localize areas vulnerable to deadly incidents influencing the Earth’s topography and consequently intimidate human lives.     

Experimental study of bed topography variations due to placement of a triad series of vertical piers at different positions in a 180° bend

In this study, scouring around piers perpendicular to flow (PPF) and piers toward the flow (PTF) under clear-water condition was examined by placing a set of triad cylindrical piers with a 5-cm diameter and a 15-cm center to center distance at the positions of 60, 90, and 120° of the bend at a constant flow rate of 70 l per second. Natural sand of uniform grain size and average diameter of 1 mm with a uniformity coefficient of 1.3 was used as bed material of the flume. According to the results of this study, the maximum scouring depth occurred in the PPF test situated at the position of 90° of the bend. In such a position, the maximum depth of scouring hole was equal to 1.1 times the depth of the flow at the beginning of the bend. Also, where the piers were positioned in PTF and PPF modes in a 60° angle, the maximum area of scouring hole was observed around piers and sediment piles at the downstream side of the piers. The maximum height of sedimentation occurred in the PPF test situated at the 90° position of the bend. Such a stack was as high as 0.7 times the flow depth at the beginning of the bend and was observed at the 156° position of the bend, at a 20% distance of the flume width from the inner bank. Further results as well as discussion and analysis are among other points presented in the article.     

Self-organizing thermal fluid flow in fractured crystalline rock: a geochemical and theoretical approach to evaluating fluid flow in the southern Idaho batholith,USA

Thermal springs in the Idaho batholith (USA) discharge at discrete locations along a 50+ km reach of the Middle Fork of the Boise River (MFBR). Recharge water flows through Basin and Range extension fractures where it is heated by the geothermal gradient and ultimately discharges from the damage zone of the trans-Challis faults located near the bottom of the MFBR. Stable isotopes of water, ¹⁴C groundwater ages, fracture and fault orientations, fracture volume changes due to chemical evolution, and recharge area calculations suggest that the thermal springs issue from individual hydrothermal systems and that they are self-organizing. Water evolves chemically along flow paths, dissolving feldspars and precipitating secondary minerals. Secondary minerals accumulate in less-efficient fractures and are flushed from the more efficient ones. Flow-area calculations using heat-flow, exponential decay-of-porosity, and curve-intersection methods show that many of the thermal systems extend beyond their immediate topographic watershed, and that some capture water from adjacent watersheds. Geochemical/flow feedback loops that provide a mechanism for self-organization are modeled using PHREEQC, and positive and negative fracture volume changes are calculated. Criteria for identifying self-organizing granitoid thermal groundwater systems are suggested.     

The role of interbasin groundwater transfers in geologically complex terranes,demonstrated by the Great Basin in the western United States

In the Great Basin, USA, bedrock interbasin flow is conceptualized as the mechanism by which large groundwater fluxes flow through multiple basins and intervening mountains. Interbasin flow is propounded based on: (1) water budget imbalances, (2) potential differences between basins, (3) stable isotope evidence, and (4) modeling studies. However, water budgets are too imprecise to discern interbasin transfers and potential differences may exist with or without interbasin fluxes. Potentiometric maps are dependent on conceptual underpinnings, leading to possible false inferences regarding interbasin transfers. Isotopic evidence is prone to non-unique interpretation and may be confounded by the effects of climate change. Structural and stratigraphic considerations in a geologically complex region like the Great Basin should produce compartmentalization, where increasing aquifer size increases the odds of segmentation along a given flow path. Initial conceptual hypotheses should explain flow with local recharge and short flow paths. Where bedrock interbasin flow is suspected, it is most likely controlled by diversion of water into the damage zones of normal faults, where fault cores act as barriers. Large-scale bedrock interbasin flow where fluxes must transect multiple basins, ranges, and faults at high angles should be the conceptual model of last resort.     

Ion acoustic solitary waves in electron-positron-ion magneto-rotating Lorentzian plasmas

Nonlinear ion acoustic solitary wave structures in electron-positron-ion (e-p-i) magnetized rotating plasmas is studied. The electron and positron species are assumed to be nonthermal and follow the kappa distribution function. The Korteweg de Vries (kdV) equation is derived by employing the reductive perturbation technique for solitary wave in the nonlinear regime. The variation in the amplitude and width of the solitary wave are discussed with the effects of positron concentration, temperature ratio of kappa distributed electrons to positrons, spectral index of the positrons, direction of propagation of the wave with magnetic field and effective gyrofrequency of the rotating nonthermal plasmas. The numerical results are also presented for illustration.     

A semi-analytical model for estimating seismic behavior of buried steel pipes at bend point under propagating waves

A buried pipe extends over long distances and passes through soils with different properties. In the event of an earthquake, the same pipe experiences a variable ground motion along its length. At bends, geometrically a more complicated problem exists where seismic waves propagating in a certain direction affect pipe before and after bend differently. Studying these different effects is the subject of this paper. Two variants for modeling of pipe, a beam model and a beam-shell hybrid model are examined. The surrounding soil is modeled with the conventional springs in both models. A suitable boundary condition is introduced at the ends of the system to simulate the far field. Effects of angle of incidence in the horizontal and vertical planes, angle of pipe bend, soil type, diameter to thickness ratio, and burial depth ratio on pipe strains at bend are examined thoroughly. It is concluded that extensional strains are highest at bends and these strains increase with the angle of incidence with the vertical axis. The pipe strains attain their peaks when pipe bend is around $135^{\circ }$ and exceed the elastic limit in certain cases especially in stiffer soils, but remain below the rupture limit. Then equations for predicting the seismic response of the buried pipe at bend are developed using the analytical data calculated above and regression analysis. It is shown that these semi-analytical equations predict the response with very good accuracy saving much time and effort.