Continuous surface representation and approximation: spatial analytical implications

Field-based continuous representation in a geographical information system (GIS) has long been important for describing complex spatially distributed phenomena, such as population, precipitation, air pollution, temperature elevation and land cover. Though theoretical knowledge and properties of continuous distributions can be employed, such surfaces are generally approximated or abstracted in practice due to a lack of complete information. That is, such surfaces are based on finite spatial samples, which is a practical necessity with regard to the infinite underlying attribute variability. These approximated surfaces are then used in various spatial analyses, yet impacts are not well understood. This article will examine theoretical properties and errors that result in practice when approximated continuous surfaces are relied on in spatial analysis.     

Multiplet-Multiplet Coupling Due to Lateral Heterogeneity: Asymptotic Effects On the Amplitude and Frequency of the Earth's Normal Modes

Summary. Starting with the first-order formulation of quasi-degenerate splitting theory for the normal modes of a laterally heterogeneous earth, we have obtained an asymptotic expression for the coupling terms corresponding to neighbouring multiplets along the same dispersion branch as the mode considered, valid to order 1/ℓ, where ℓ is the angular order of this mode (ℓ≥ 1).
We show that, to order zero, these coupling terms introduce a small shift in epicentral distance into the expression for the long period seismogram obtained by normal mode summation. This shift depends on the difference between the great circle and the minor arc averages of the local frequency. the coupling terms thus permit us to reconcile results obtained by normal-mode summation and by a propagating wave approach, as far as the dependence on structure of the phase of surface waves is concerned.
To order 1/ℓ, the coupling terms result in a perturbation in the amplitude of the mode considered, which depends on spatial derivatives of the local frequency and thus on the structure in the vicinity of the source station great circle path. We show that this term is equivalent to that which is found using ray perturbation methods for propagating surface waves. We compare and discuss the assumptions underlying both approaches and illustrate, by an example, the potential of the asymptotic normal-mode formulation for improved modelling of lateral heterogeneity in the earth.     

STAGES OF LATE HOLOCENE GULLY DEVELOPMENT IN THE CENTRAL RUSSIAN PLAIN

Two gullies located in the Protva River basin （central part of European Russia, 100 Ion southwest of Moscow） were studied to investigate the history of their development during Late Holocene. This case study included detailed topographic and geomorphologic surveys, geological cross-sections, and radiocarbon dating of organic matter in gully sediments. For both gullies, incision of the long profile occurred for most of the Holocene, as indicated by the limited presence of infill sediment. However, interruptions of incisions occurred in both gullies during the last -3.5 ka （the Chugunkin gully） or -2.0 ka （the Uzkiy gully）, as evident from stratigraphic interpretation of the sediment record. Periods of surface stabilization are represented by buried soil horizons, whereas relatively thick sediment layers suggest periods of predominant aggradation. Similarities and differences in discovered sequences of erosion and accumulation stages for the two gullies point out the importance of distinguishing between local and regional controls. Evidence of the role of internal system behavior and self-development in the gully long-term evolution is clear from asynchronous response of different parts of gullies. In recent times （-500 years）, active agricultural development of the study territory resulted in accelerated incisions, followed by deposition of catchment-derived material. The latter was limited to the upper parts of the gullies, while incisions have continued in the middle and lower parts. The impact of human activities （-500 years） has been very limited. This suggests that within the forest zone of the Russian Plain many gullies which were earlier attributed to anthropogenic factors are, in realitv, due to natural phenomena.     

End-point contributions to synthetic seismograms

Summary . Synthetic seismograms represented by integrals generally display signals associated with the limits of integration. Sometimes these 'end-point' contributions are spurious (e.g. in the WKBJ seismogram) and sometimes they are the main physical interest (e.g. the Kirchhoff integral for an edge). The end-point contributions may be asymptotically approximated using integration by parts or Laplace's method and it may then be possible to reduce them if desired. We describe examples in the WKBJ seism ogram for reflected or transmitted waves in homogeneous layers and for turning waves. We also study signals due to discontinuities in reflection coefficients, by partitioning the real slowness integral so that the discontinuities lie at end points. Examples are the head wave, which is a physically correct signal, and spurious diffractions caused by using plane-wave coefficients for grazing rays in the WKBJ seismogram.     

Mathematical modelling of an infilled RC frame structure based on the results of pseudo‐dynamic tests

In this paper, a technique is presented which employs the results of pseudo‐dynamic tests for the development of a mathematical model. This technique, described by means of the mathematical modelling of a three‐storey reinforced concrete frame building with infill in the bottom two storeys, which was tested at ELSA in Ispra, proved to be effective and to lead to a fairly accurate structural model. The results of analyses suggest that the global non‐linear seismic response of reinforced concrete frames with masonry infill can be adequately simulated by a relatively simple mathematical model, which combines beam elements with concentrated plasticity, simple connection elements, and equivalent strut elements representing the infill walls (provided that the infill does not fail out of plane and that no shear sliding failure occurs). Copyright © 2002 John Wiley & Sons, Ltd.     

Application of the Maslov Seismogram Method in Three Dimensions

Asymptotic methods provide an efficient way to compute seismograms in heterogeneous media. However, zeroth-order ray theory, the simplest of the asymptotic methods, often fails because of the presence of caustics. Maslov theory is an extension of zeroth-order ray theory, which gives a uniformly valid expression of the wavefield everywhere, including the caustics. This result is given in terms of an integral of ray data over one or two ray parameters. It is shown in this paper how geometrical arrivals are constructed in the one and two-parameter Maslov integrals.In practice Maslov seismograms have been computed using only one ray parameter. However, in three-dimensional media two parameters are needed to uniquely define a ray. In this paper we present an efficient algorithm to compute two-parameter Maslov integrals. The Maslov integral is evaluated by computing the frequency-to-time Fourier transform prior to integration over the ray parameters. The wavefield is then discretized by smoothing with a boxcar function. The resulting expression, which only requires the results of ordinary kinematic and dynamic ray tracing, cen be computed efficiently and robustly. A numerical example is given that illustrates the use of this algorithm.     

The palaeo‐valley infilling glaciogenic Sarah Formation,an example from Rahal Dhab palaeo‐valley,Saudi Arabia

The Sarah Formation is a glaciogenic sedimentary unit deposited along the Gondwana margin during the latest Ordovician ice age and represents a major hydrocarbon reservoir in northern Saudi Arabia. Large‐scale glacial palaeo‐valleys cut into the Qasim Formation and were infilled by the Sarah Formation. Post‐glacial transgression in the earliest Silurian resulted in the deposition of the Qusaiba Shale Member and associated organic‐rich basal source rocks, which cap the Sarah Formation infilled palaeo‐valleys. This unique setting makes the Sarah Formation an important emerging exploration target in Saudi Arabia. This study focuses on the facies and depositional architecture in seismic‐scale outcrops of the Sarah Formation in north‐western Saudi Arabia. The Rahal Dhab palaeo‐valley provides a 100 km long dip‐oriented cross‐section which has been covered by 24 vertical sections, sedimentary architectural analyses at metre to kilometre scale and by three cored shallow boreholes. In the Rahal Dhab palaeo‐valley, the Sarah Formation was deposited in a proglacial setting that ranged from marginal marine to offshore prodelta and is made up of three units: (i) the Sarah Sandstone; (ii) the Sarah Shale; and (iii) the Uqlah Member. This study shows the relationships between these three units and architectural controls on reservoir quality in this system. This paper contributes to the regional understanding of the Sarah Formation, and the new depositional model of the Rahal Dhab palaeo‐valley provides an outcrop‐reservoir analogue for hydrocarbon exploration in adjacent areas.     

Nonlinear pushover analysis of infilled concrete frames

Six reinforced concrete frames with or without masonry infills were constructed and tested under horizontal cyclic loads. All six frames had identical details in which the transverse reinforcement in columns was provided by rectangular hoops that did not meet current ACI specifications for ductile frames. For comparison purposes, the columns in three of these frames were jacketed by carbon-fiber-reinforced-polymer （CFRP） sheets to avoid possible shear failure. A nonlinear pushover analysis, in which the force-deformation relationships of individual elements were developed based on ACI 318, FEMA 356, and Chen＇s model, was carried out for these frames and compared to test results. Both the failure mechanisms and impact of infills on the behaviors of these frames were examined in the study. Conclusions from the present analysis provide structural engineers with valuable information for evaluation and design of infilled concrete frame building structures.     

Low‐seismic damage strategies for infilled RC frames: shake‐table tests

Unreinforced masonry (URM) infill panels are widely used as partitions in RC frames and typically considered as non‐structural elements in the design process. However, observations from recent major earthquakes have shown that under seismic excitation, the structural interaction between columns and infill walls can significantly alter the structural behaviour, thus causing catastrophic consequences. The purpose of this research was to propose and test an innovative low seismic damage detailing method, which isolates the infill panel from bounding columns with finite width vertical gaps during the infill panel construction phase and deploys steel wire connections in mortar layers anchored to columns. Taking into account the similitude requirements, a total of six one‐third scale, single‐storey single‐bay RC frames with different infill configurations and flexible connection details were carefully designed and tested on a shake‐table. Three real earthquake records were selected and scaled to ascending intensity levels and used as input signals. A series of thorough investigations including dynamic characteristics, hysteretic behaviour, failure mechanisms, out‐of‐plane vulnerabilities and the effect of different gap filling materials and load transfer mechanisms were rigorously studied. The experimental results indicate that the undesirable interaction between infill panels and bounding frame is significantly reduced using the proposed low seismic damage detailing concept. Direct shear failure of columns at an early stage is prevented, and structural redundancy at high levels of excitation can be provided. In general, the structural stability and integrity, and displacement ductility of infilled RC frames can remarkably be improved. Copyright © 2017 John Wiley & Sons, Ltd.