Limitations Of The Tangent Plane Approximation For Wide-field Imaging Using The Mauritius Radio Telescope

The Mauritius Radio Telescope (MRT) is a Fourier synthesis, non-coplanar T array. The primary objective of the telescope is to survey the southern sky at 151.5 MHz in the declination range -70^° to -10^°. Due to non-coplanarity, wide-field imaging and deconvolution of wide field images made using MRT are challenging problems in applications of radio interferometric techniques. This paper discusses the usefulness and limitations of the tangent plane approximation in transforming the measured visibilities to wide field images and in estimating the point spread function (PSF) required for the deconvolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

The KC method: Numerical investigation of a new analysis method for reinforced soil walls

Reinforced soil walls commonly include facing elements which affect the mechanical behavior of the system. However, the design procedures involved in the existing codes and manuals (e.g. FHWA, BS8006, AASHTO, etc.) do not consider the structural contribution of the facing to the wall stability. Recently, a new computer based method for the analysis of reinforced soil walls which takes into account the interaction between the facing and the soil reinforcement layers was presented [Klar A and Sas T. Rational approach for the analysis of segmental reinforced soil walls based on kinematic constraints. Geotextiles and Geomembranes 2009;27:332-340]. This method demands full compatibility between the reinforcement layers and the deforming wall, and is solved as an optimization problem on this constraint. This kinematic compatibility (KC) method entails several assumptions regarding the interaction between the three components of the system (soil, wall, and reinforcement). This paper compares the KC method to a more rigorous continuum analysis. Results show that the KC method is capable of replicating the behavior of the more rigorous system, with a good agreement on both the value of maximum tensile forces in the reinforcement and shear and bending moment distributions along the wall. The KC method has a certain advantage over continuum methods, such as finite element or finite difference, since it requires limited input data that can easily be obtained from field tests.     

Transformation of coordinates using piecewise conformal mapping

A multiresolution-like algorithm for piecewise conformal mapping is presented. The algorithm is based on partitioning the complex plane into convex polygons, defining appropriate window functions for these polygons, and finding a conformal mapping for each polygon. The window functions are used to glue the pieces together into a single mapping. An application of this algorithm to determine a transformation from the Estonian coordinate system of L-EST92 into the respective system L-EST97, is presentedAcknowledgments.This work has been supported by Estonian Science Foundation grant nr. 5037. The author also thanks the Estonian Land Board, especially U. Mets and L. Tamme for their help in preparing the data, and the reviewers for valuable suggestions.     

A note on the statistics of ordered peaks in stationary stochastic processes

Numerical simulation experiments have been carried out to evaluate the relative performance of three approximate formulations owing to Amini and Trifunac,[1] Gupta and Trifunac[2] and Basu et al.[3] for probability distributions of ordered peaks in stationary stochastic processes. The first two formulations are based on the assumption that the unordered peaks are statistically independent; whereas the formulation of Basu et al.[3] considers the dependence via Markov transition probability. In the formulation of Gupta and Trifunac,[2] the probability distribution of nth order peak is inherently conditioned by the fact that at most (n−1) peaks can occur with higher amplitudes and, thus, the ordered peaks are necessarily dependent. In this paper, ensembles of stationary time-histories are generated for three PSDFs representing a narrow-band, a broad-band and a band-limited white noise type of processes. Comparison of the results for the expected value and standard deviation for various orders of peaks, obtained by averaging over these ensembles, with the corresponding results obtained from the above mentioned three approximations, defined in terms of the moments of the PSDFs, has shown that the formulation of Gupta and Trifunac[2] describes the data well.     

Indentation of a continent with a built-in thickness change: experiment and nature

Orogens oblique to the direction of plate convergence are currently attributed to obliquity between the margins of one or both of the sutured continents to their direction convergence. We use a single analogue experiment and natural examples to illustrate a potential additional factor: variations in strength of the indented continent at a high angle to the convergence direction. The wavelengths of structures in laterally shortened lithosphere depend on the strength of the most competent layers. Lateral variations in crustal thickness must therefore lead to structures oblique to any applied lateral compression.

An analogue experiment was performed to explore this phenomenon. A two-layer ‘indented continent’ was modelled by a brittle upper crust of sand above a lower crust of high-viscosity polymer floating on a single layer of low-viscosity syrup representing the mantle. The well-known strike-slip structures allowing lateral escape to distant weak boundaries were hindered by lateral boundaries in front of the indenter. This allowed us to focus on the effects of a thickness change built into the ‘indented continent’ along a zone parallel to the direction in which a vertical rigid wall advancing at a steady rate represented the indenter. Vertical escape led to an ‘orogenic belt’ oblique to the advancing wall; this obliquity influences subsequent lateral escape. Model scaling and interpretations are based on Extended Thin Sheet Approximation (ETSA) and standard theories of faulting.

Four sectors of the Alpine–Himalayan orogen (Iran, Tunisia, the Eastern Alps and the Himalaya) are oblique to the continental convergence direction, and we point to thickness changes at high angles to the suture that may account for this geometry. As crustal thicknesses north of oblique sectors of the Himalayas are not yet known, we speculate on them.

We infer from the main difference between our experiment and all our examples chosen from nature that vertical orogenic escape was oblique to our model suture but can be parallel to natural sutures.     

各向异性介质中的AVO

分析了横向各向同性和方位各向异性介质的本构关系,由此讨论弹性波在两种各向异性介质中的传播特点,提出可表征这两种介质各向异性程度的广义参数．以此为基础讨论了两种各向异性介质中存在水平界面时的反射系数近似式,将Dely等人推导的横向各向同性介质中的反射系数公式推广到方位各向异性介质的主轴方向上．根据算例讨论修正的Banik和Thomsen的近似式,着重分析两种各向异性介质中的AVO关系及其对实际勘探的影响和指导意义．     

Comparison of Methods Used to Estimate Conventional Undiscovered Petroleum Resources: World Examples

Various methods for assessing undiscovered oil, natural gas, and natural gas liquid resources were compared in support of the USGS World Petroleum Assessment 2000. Discovery process, linear fractal, parabolic fractal, engineering estimates, PETRIMES, Delphi, and the USGS 2000 methods were compared. Three comparisons of these methods were made in: (1) the Neuquen Basin province, Argentina (different assessors, same input data); (2) provinces in North Africa, Oman, and Yemen (same assessors, different methods); and (3) the Arabian Peninsula, Arabian (Persian) Gulf, and North Sea (different assessors, different methods). A fourth comparison (same assessors, same assessment methods but different geologic models), between results from structural and stratigraphic assessment units in the North Sea used only the USGS 2000 method, and hence compared the type of assessment unit rather than the method. In comparing methods, differences arise from inherent differences in assumptions regarding: (1) the underlying distribution of the parent field population (all fields, discovered and undiscovered), (2) the population of fields being estimated; that is, the entire parent distribution or the undiscovered resource distribution, (3) inclusion or exclusion of large outlier fields; (4) inclusion or exclusion of field (reserve) growth, (5) deterministic or probabilistic models, (6) data requirements, and (7) scale and time frame of the assessment. Discovery process, Delphi subjective consensus, and the USGS 2000 method yield comparable results because similar procedures are employed. In mature areas such as the Neuquen Basin province in Argentina, the linear and parabolic fractal and engineering methods were conservative compared to the other five methods and relative to new reserve additions there since 1995. The PETRIMES method gave the most optimistic estimates in the Neuquen Basin. In less mature areas, the linear fractal method yielded larger estimates relative to other methods. A geologically based model, such as one using the total petroleum system approach, is preferred in that it combines the elements of petroleum source, reservoir, trap and seal with the tectono-stratigraphic history of basin evolution with petroleum resource potential. Care must be taken to demonstrate that homogeneous populations in terms of geology, geologic risk, exploration, and discovery processes are used in the assessment process. The USGS 2000 method (7th Approximation Model, EMC computational program) is robust; that is, it can be used in both mature and immature areas, and provides comparable results when using different geologic models (e.g. stratigraphic or structural) with differing amounts of subdivisions, assessment units, within the total petroleum system.