Generalized Laplace coefficients and Newcomb derivatives

It is shown how the generalized Laplace coefficients can be employed to deduce explicit formulas for ordinary and Newcomb derivatives of the Laplace coefficients.      

Spatial Relations between Classes as Integrity Constraints

The quality and integrity of spatial data is very important to support interoperability among different systems. To reach this aim integrity rules defined by the application play an important role (for example, constraints between object classes). In this article, we propose a methodology to define integrity constraints using user level spatial relations between classes of individuals. We will also provide mapping rules from user level relations to geometric level operators to allow the computation of relations. As a case study, we will define the constraints for the class of rivers and some of its specializations.     

Higher-order corrections to the relativistic perihelion advance and the mass of binary pulsars

We study the general relativistic orbital equation and using a straightforward perturbation method and a mathematical device first introduced by d’Alembert, we work out approximate expressions of a bound planetary orbit in the form of trigonometrical polynomials and the first three terms of the power series development of the perihelion advance. The results are applied to a more precise determination of the total mass of the double pulsar J0737-3039.     

Relationship between tilt changes and effusive-explosive episodes at an andesitic volcano: the 2004–2005 eruption at Volcán de Colima,México

Continuous tilt changes during the 2004–2005 effusive-explosive episodes at Volcán de Colima (México) were recorded simultaneously by two tiltmeters installed on opposite sides of the volcano at elevations of 2200 m and 3060 m above sea level. Data indicate that the 2004 lava extrusion was preceded by an inflation accompanied by a deflation. The 2005 explosion sequences were associated with a deflationary–inflationary tilt. The period between the 2004 extrusion and the 2005 explosions was characterized by an inflationary tilt during a 3 month period. Two deformation sources were located. The first was situated at a depth between 300 m and 1800 m beneath the crater at the northern flank of the volcano and was responsible for volcano deformation during the preliminary September 2004 stage, the October 2004 extrusion, and the initial stage of the transition period and the March 2005 explosion sequence. The second source was located at a depth between 1800 m and 2800 m beneath the crater at the southern flank of the volcano and was responsible for volcano deformation during the final stage of the transition period and the May–June 2005 explosion sequence.     

Facies Recognition Using Multifractal Hurst Analysis: Applications to Well-Log Data

Well-log (radioactivity, density and resistivity) analysis constitutes a standard approach for inferring lithology from wells. However, due to inherent complexity of the signals (such as highly heterogeneous deep-water sedimentary sequences) lithology recognition is not straightforward. We used a rescaled range analysis, calibrated with cores, to recognize lithological patterns from signal recorded along wireline logs. The detected intervals coincide with zones of visual electro-facies associations proposed by geologist well-log interpreters. In addition, we propose a rescaled range multifractal analysis to identify ranges of well-log signal complexities, which could be related to sedimentary process variations at specific stratigraphic order cycles.     

Homological relations: A methodology for the certification of irregular tessellations

In GIS, spatial analysis is based on the use of spatial operations such as testing the spatial relations between features. Often, such tests are invalidated by errors in datasets. It is a very common experience that two bordering regions which should obey the topological relation “meet” fall instead in the “overlap” category. The situation is exacerbated when applying topological operators to regions that come from different datasets, where resolution and error sources are different. Despite the problem being quite common, up to now no standard approach has been defined to deal with spatial relations affected by errors of various origins. Referring to topological relations, we define a model to extend the eight Egenhofer relations between two simple regions: we call them homological relations (H‐relations). We discuss how exact topological relations can be extracted from observed relations and discuss the case of irregular tessellations, where errors have the most impact on vector data. In the proposed case study within the domain of geographic crowdsourced data, we propose algorithms for identifying homological regions and obtaining a corrected tessellation. This methodology can be considered as a step for quality control and the certification of irregular tessellations.     

The relativistic precession of the orbits

The relativistic precession can be quickly inferred from the nonlinear polar orbit equation without actually solving it.     

Quaternary drainage network reorganization in the Colombian Eastern Cordillera plateau

Dramatic drainage reorganization from initial longitudinal to transversal domains has occurred in the Eastern Cordillera of Colombia. We perform a regional analysis of drainage basin geometry and transformed river profiles based on the integral form of the slope-area scaling, to investigate the dynamic state of drainage networks and to predict the degree of drainage reorganization in this region. We propose a new model of drainage rearrangement for the Eastern Cordillera, based on the analyses of knickpoint distribution, normalized river profiles, landforms characteristic of river capture, erosion rates and palaeodrainage data. We establish that the oldest longitudinal basin captured by the Magdalena River network was the Suárez Basin at ≈409 ka, inferring the timing of abandonment of a river terrace using in situ produced cosmogenic beryllium-10 (¹⁰Be) depth profiles and providing a first estimation of incision rate of 0.07 mm/yr. We integrate published geochronologic data and interpret the last capture of the Sabana de Bogotá, providing a minimum age of the basin opening to the Magdalena drainage at ≈38 ka. Our results suggest that the Magdalena basin Increased its drainage area by integrating the closed basins from the western flank of the Eastern Cordillera. Our study also suggests that the Magdalena basin is an aggressor compared to the basins located in the eastern flank of the orogen and provides a framework for examining drainage reorganization within the Eastern Cordillera and in similar orogenic settings. The results improve our understanding of headward integration of closed basins across orogenic plateaux. © 2020 John Wiley & Sons, Ltd.     

Sequence of thrusting and syntectonic sedimentation in the eastern Sub-Atlas thrust belt (Dadès and Mgoun valleys,Morocco)

A series of balanced cross-sections across the Sub-Atlas thrust belt and the northern Ouarzazate basin are used to illustrate the structural geometry and the timing of deformation at the southern front of the High Atlas Mountains of Morocco. The selected area is among the best sedimentary records of mountain building of the entire orogenic system. The study of the relationships between thrusts and synorogenic continental formations enables the unraveling of kinematic sequences and the proposal of a relative chronology of deformation. Active thrusting in the area occurred in a rather continuous fashion from the Oligocene to the Pliocene, punctuated by a major erosional phase imprecisely placed in late Oligocene to early Miocene times. Detrital sedimentary facies indicate that uplift in the hinterland of the High Atlas, to the north of the Sub-Atlas belt, was taking place already by mid Eocene times, although it might have commenced locally even earlier. Within the Sub-Atlas zone, the exposed faults did not propagate in a simple piggy-back fashion but show evidence of a complex, synchronous sequence with events of fault reactivation and out-of-sequence thrusting.