El problema isostático inverso de Vening Meinesz. Teoría y desarrollo. Aplicación práctica para la determinación de la profundidad de la discontinuidad de Mohorovičić en la Península Ibérica

La discontinuidad de Mohorovičić, más conocida simplemente como “Moho” constituye la superficie de separación entre los materiales rocosos menos densos de la corteza y los materiales rocosos más densos del manto, suponiendo estas capas de densidad constante del orden de 2.67 y 3.27 g/cm3, y es un contorno básico para cualquier estudio geofísico de la corteza terrestre. Los estudios sísmicos y gravimétricos realizados demuestran que la profundidad del Moho es del orden de 30-40 km por debajo de la Península Ibérica y 5-15 km bajo las zonas marinas. Además las distintas técnicas existentes muestran gran correlación en los resultados. Haciendo la suposición de que el campo de gravedad de la Península Ibérica (como le ocurre al 90% de la Tierra) está isostáticamente compensado por la variable profundidad del Moho, suponiendo un contraste de densidad constante entre la corteza y el manto y siguiendo el modelo isostático de Vening Meinesz (1931), se formula el problema isostático inverso para obtener tal profundidad a partir de la anomalía Bouguer de la gravedad calculada gracias a la gravedad observada en la superficie terrestre. La particularidad de este modelo es la compensación isostática regional de la que parte la teoría, que se asemeja a la realidad en mayor medida que otros modelos existentes, como el de Airy-Heiskanen, que ha sido históricamente el más utilizado en trabajos semejantes. Además, su solución está relacionada con el campo de gravedad global para toda la Tierra, por lo que los actuales modelos gravitacionales, la mayoría derivados de observaciones satelitales, deberían ser importantes fuentes de información para nuestra solución. El objetivo de esta tesis es el estudio con detalle de este método, desarrollado por Helmut Moritz en 1990, que desde entonces ha tenido poca evolución y seguidores y que nunca se ha puesto en práctica en la Península Ibérica. Después de tratar su teoría, desarrollo y aspectos computacionales, se está en posición de obtener un modelo digital del Moho para esta zona a fin de poder utilizarse para el estudio de la distribución de masas bajo la superficie terrestre. A partir de los datos del Moho obtenidos por métodos alternativos se hará una comparación. La precisión de ninguno de estos métodos es extremadamente alta (+5 km aproximadamente). No obstante, en aquellas zonas donde exista una discrepancia de datos significaría un área descompensada, con posibles movimientos tectónicos o alto grado de riesgo sísmico, lo que le da a este estudio un valor añadido. ABSTRACT The Mohorovičić discontinuity, simply known as “Moho” constitutes the division between the rocky and less thick materials of the mantle and the heavier ones in the crust, assuming densities of the orders of 2.67 y 3.27 g/cm3 respectively. It is also a basic contour for every geophysical kind of studies about the terrestrial crust. The seismic and previous gravimetric observations done in the study area show that the Moho depth is of the order of 30-40 km beneath the ground and 5-15 km under the ocean basin. Besides, the different techniques show a good correlation in their results. Assuming that the Iberian Peninsula gravity field (as it happens for the 90% of the Earth) is isostatically compensated according to the variable Moho depth, supposing a constant density contrast between crust and mantle, and following the isostatic Vening Meinesz model (1931), the inverse isostatic problem can be formulated from Bouguer gravity anomaly data obtained thanks to the observed gravity at the surface of the Earth. The main difference between this model and other existing ones, such as Airy- Heiskanen’s (pure local compensation and mostly used in these kinds of works) is the approaching to a regional isostatic compensation, much more in accordance with reality. Besides, its solution is related to the global gravity field, and the current gravitational models -mostly satellite derived- should be important data sources in such solution. The aim of this thesis is to study with detail this method, developed by Helmut Moritz in 1990, which hardly ever has it put into practice. Moreover, it has never been used in Iberia. After studying its theory, development and computational aspects, we are able to get a Digital Moho Model of the Iberian Peninsula, in order to study the masses distribution beneath the Earth’s surface. With the depth Moho information obtained from alternative methods, a comparison will be done. Both methods give results with the same order of accuracy, which is not quite high (+ 5 km approximately). Nevertheless, the areas in which a higher difference is observed would mean a disturbance of the compensation, which could show an unbalanced area with possible tectonic movements or potential seismic risk. It will give us an important additive value, which could be used in, at first, non related fields, such as density discrepancies or natural disasters contingency plans.

Determinación de un modelo de geoide gravimétrico para Puerto Rico como sistema de referencia para las altitudes ortométricas

El geoide, definido como la superficie equipotencial que mejor se ajusta (en el sentido de los mínimos cuadrados) al nivel medio del mar en una determinada época, es la superficie que utilizamos como referencia para determinar las altitudes ortométricas. Si disponemos de una superficie equipotencial de referencia como dátum altimétrico preciso o geoide local, podemos entonces determinar las altitudes ortométricas de forma eficiente a partir de las altitudes elipsoidales proporcionadas por el Sistema Global de Navegación por Satélite (Global Navigation Satellite System, GNSS ). Como es sabido uno de los problemas no resueltos de la geodesia (quizás el más importante de los mismos en la actualidad) es la carencia de un dátum altimétrico global (Sjoberg, 2011) con las precisiones adecuadas. Al no existir un dátum altimétrico global que nos permita obtener los valores absolutos de la ondulación del geoide con la precisión requerida, es necesario emplear modelos geopotenciales como alternativa. Recientemente fue publicado el modelo EGM2008 en el que ha habido una notable mejoría de sus tres fuentes de datos, por lo que este modelo contiene coeficientes adicionales hasta el grado 2190 y orden 2159 y supone una sustancial mejora en la precisión (Pavlis et al., 2008). Cuando en una región determinada se dispone de valores de gravedad y Modelos Digitales del Terreno (MDT) de calidad, es posible obtener modelos de superficies geopotenciales más precisos y de mayor resolución que los modelos globales. Si bien es cierto que el Servicio Nacional Geodésico de los Estados Unidos de América (National Geodetic Survey, NGS) ha estado desarrollando modelos del geoide para la región de los Estados Unidos de América continentales y todos sus territorios desde la década de los noventa, también es cierto que las zonas de Puerto Rico y las Islas Vírgenes Estadounidenses han quedado un poco rezagadas al momento de poder aplicar y obtener resultados de mayor precisión con estos modelos regionales del geoide. En la actualidad, el modelo geopotencial regional vigente para la zona de Puerto Rico y las Islas Vírgenes Estadounidenses es el GEOID12A (Roman y Weston, 2012). Dada la necesidad y ante la incertidumbre de saber cuál sería el comportamiento de un modelo del geoide desarrollado única y exclusivamente con datos de gravedad locales, nos hemos dado a la tarea de desarrollar un modelo de geoide gravimétrico como sistema de referencia para las altitudes ortométricas. Para desarrollar un modelo del geoide gravimétrico en la isla de Puerto Rico, fue necesario implementar una metodología que nos permitiera analizar y validar los datos de gravedad terrestre existentes. Utilizando validación por altimetría con sistemas de información geográfica y validación matemática por colocación con el programa Gravsoft (Tscherning et al., 1994) en su modalidad en Python (Nielsen et al., 2012), fue posible validar 1673 datos de anomalías aire libre de un total de 1894 observaciones obtenidas de la base de datos del Bureau Gravimétrico Internacional (BGI). El aplicar estas metodologías nos permitió obtener una base de datos anomalías de la gravedad fiable la cual puede ser utilizada para una gran cantidad de aplicaciones en ciencia e ingeniería. Ante la poca densidad de datos de gravedad existentes, fue necesario emplear un método alternativo para densificar los valores de anomalías aire libre existentes. Empleando una metodología propuesta por Jekeli et al. (2009b) se procedió a determinar anomalías aire libre a partir de los datos de un MDT. Estas anomalías fueron ajustadas utilizando las anomalías aire libre validadas y tras aplicar un ajuste de mínimos cuadrados por zonas geográficas, fue posible obtener una malla de datos de anomalías aire libre uniforme a partir de un MDT. Tras realizar las correcciones topográficas, determinar el efecto indirecto de la topografía del terreno y la contribución del modelo geopotencial EGM2008, se obtuvo una malla de anomalías residuales. Estas anomalías residuales fueron utilizadas para determinar el geoide gravimétrico utilizando varias técnicas entre las que se encuentran la aproximación plana de la función de Stokes y las modificaciones al núcleo de Stokes, propuestas por Wong y Gore (1969), Vanicek y Kleusberg (1987) y Featherstone et al. (1998). Ya determinados los distintos modelos del geoide gravimétrico, fue necesario validar los mismos y para eso se utilizaron una serie de estaciones permanentes de la red de nivelación del Datum Vertical de Puerto Rico de 2002 (Puerto Rico Vertical Datum 2002, PRVD02 ), las cuales tenían publicados sus valores de altitud elipsoidal y elevación. Ante la ausencia de altitudes ortométricas en las estaciones permanentes de la red de nivelación, se utilizaron las elevaciones obtenidas a partir de nivelación de primer orden para determinar los valores de la ondulación del geoide geométrico (Roman et al., 2013). Tras establecer un total de 990 líneas base, se realizaron dos análisis para determinar la 'precisión' de los modelos del geoide. En el primer análisis, que consistió en analizar las diferencias entre los incrementos de la ondulación del geoide geométrico y los incrementos de la ondulación del geoide de los distintos modelos (modelos gravimétricos, EGM2008 y GEOID12A) en función de las distancias entre las estaciones de validación, se encontró que el modelo con la modificación del núcleo de Stokes propuesta por Wong y Gore presentó la mejor 'precisión' en un 91,1% de los tramos analizados. En un segundo análisis, en el que se consideraron las 990 líneas base, se determinaron las diferencias entre los incrementos de la ondulación del geoide geométrico y los incrementos de la ondulación del geoide de los distintos modelos (modelos gravimétricos, EGM2008 y GEOID12A), encontrando que el modelo que presenta la mayor 'precisión' también era el geoide con la modificación del núcleo de Stokes propuesta por Wong y Gore. En este análisis, el modelo del geoide gravimétrico de Wong y Gore presento una 'precisión' de 0,027 metros en comparación con la 'precisión' del modelo EGM2008 que fue de 0,031 metros mientras que la 'precisión' del modelo regional GEOID12A fue de 0,057 metros. Finalmente podemos decir que la metodología aquí presentada es una adecuada ya que fue posible obtener un modelo del geoide gravimétrico que presenta una mayor 'precisión' que los modelos geopotenciales disponibles, incluso superando la precisión del modelo geopotencial global EGM2008. ABSTRACT The geoid, defined as the equipotential surface that best fits (in the least squares sense) to the mean sea level at a particular time, is the surface used as a reference to determine the orthometric heights. If we have an equipotential reference surface or a precise local geoid, we can then determine the orthometric heights efficiently from the ellipsoidal heights, provided by the Global Navigation Satellite System (GNSS). One of the most common and important an unsolved problem in geodesy is the lack of a global altimetric datum (Sjoberg, 2011)) with the appropriate precision. In the absence of one which allows us to obtain the absolute values of the geoid undulation with the required precision, it is necessary to use alternative geopotential models. The EGM2008 was recently published, in which there has been a marked improvement of its three data sources, so this model contains additional coefficients of degree up to 2190 and order 2159, and there is a substantial improvement in accuracy (Pavlis et al., 2008). When a given region has gravity values and high quality digital terrain models (DTM), it is possible to obtain more accurate regional geopotential models, with a higher resolution and precision, than global geopotential models. It is true that the National Geodetic Survey of the United States of America (NGS) has been developing geoid models for the region of the continental United States of America and its territories from the nineties, but which is also true is that areas such as Puerto Rico and the U.S. Virgin Islands have lagged behind when to apply and get more accurate results with these regional geopotential models. Right now, the available geopotential model for Puerto Rico and the U.S. Virgin Islands is the GEOID12A (Roman y Weston, 2012). Given this need and given the uncertainty of knowing the behavior of a regional geoid model developed exclusively with data from local gravity, we have taken on the task of developing a gravimetric geoid model to use as a reference system for orthometric heights. To develop a gravimetric geoid model in the island of Puerto Rico, implementing a methodology that allows us to analyze and validate the existing terrestrial gravity data is a must. Using altimetry validation with GIS and mathematical validation by collocation with the Gravsoft suite programs (Tscherning et al., 1994) in its Python version (Nielsen et al., 2012), it was possible to validate 1673 observations with gravity anomalies values out of a total of 1894 observations obtained from the International Bureau Gravimetric (BGI ) database. Applying these methodologies allowed us to obtain a database of reliable gravity anomalies, which can be used for many applications in science and engineering. Given the low density of existing gravity data, it was necessary to employ an alternative method for densifying the existing gravity anomalies set. Employing the methodology proposed by Jekeli et al. (2009b) we proceeded to determine gravity anomaly data from a DTM. These anomalies were adjusted by using the validated free-air gravity anomalies and, after that, applying the best fit in the least-square sense by geographical area, it was possible to obtain a uniform grid of free-air anomalies obtained from a DTM. After applying the topographic corrections, determining the indirect effect of topography and the contribution of the global geopotential model EGM2008, a grid of residual anomalies was obtained. These residual anomalies were used to determine the gravimetric geoid by using various techniques, among which are the planar approximation of the Stokes function and the modifications of the Stokes kernel, proposed by Wong y Gore (1969), Vanicek y Kleusberg (1987) and Featherstone et al. (1998). After determining the different gravimetric geoid models, it was necessary to validate them by using a series of stations of the Puerto Rico Vertical Datum of 2002 (PRVD02) leveling network. These stations had published its values of ellipsoidal height and elevation, and in the absence of orthometric heights, we use the elevations obtained from first - order leveling to determine the geometric geoid undulation (Roman et al., 2013). After determine a total of 990 baselines, two analyzes were performed to determine the ' accuracy ' of the geoid models. The first analysis was to analyze the differences between the increments of the geometric geoid undulation with the increments of the geoid undulation of the different geoid models (gravimetric models, EGM2008 and GEOID12A) in function of the distance between the validation stations. Through this analysis, it was determined that the model with the modified Stokes kernel given by Wong and Gore had the best 'accuracy' in 91,1% for the analyzed baselines. In the second analysis, in which we considered the 990 baselines, we analyze the differences between the increments of the geometric geoid undulation with the increments of the geoid undulation of the different geoid models (gravimetric models, EGM2008 and GEOID12A) finding that the model with the highest 'accuracy' was also the model with modifying Stokes kernel given by Wong and Gore. In this analysis, the Wong and Gore gravimetric geoid model presented an 'accuracy' of 0,027 meters in comparison with the 'accuracy' of global geopotential model EGM2008, which gave us an 'accuracy' of 0,031 meters, while the 'accuracy ' of the GEOID12A regional model was 0,057 meters. Finally we can say that the methodology presented here is adequate as it was possible to obtain a gravimetric geoid model that has a greater 'accuracy' than the geopotential models available, even surpassing the accuracy of global geopotential model EGM2008.

Offshore stereo measurements of gravity waves: classical epipolar and novel variational techniques

Stereo video techniques are effective for estimating the space-time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. Classical epipolar techniques and modern variational methods are reviewed to reconstruct the sea surface from the stereo pairs sequentially in time. Current improvements of the variational methods are presented.

Ground maritime structure interaction. Recent failures in inner gravity constructions on the Spanish Coastline

A maritime construction is usually a slender line in the ocean.It is usual to see just its narrow surface strip and not analyse the large amount of submerged material the latter is supporting.Without doubt,it is the ground to which a notable load is transmitted in an environment subjected to periodic,alternating stresses,dynamic forces which the sea's media constitute. Both an outer and inner maritime construction works in a complex fashion.A granular solid(breakwater)breathes with the incident wave flow,dissipating part of the wave energy between its gaps.The backflow tries to extract the different items from the solid block,setting a balance between effective and neutral tensions that follow Terzaghui's principle. On some occasions,fluidification of the armour layer has caused the breakwater to collapse(Sines,Portugal,February 1978).On others,siphoning or liquefaction of sand supporting monoliths(vertical breakwaters)lead them to destruction or collapse(New Barcelona Harbour Mouth,Spain,November 2001). This is why the ground-force-structure interaction is a complicated analysis with joint design tools still in an incipient state. The purpose of this article is to describe two singular failures in inner maritime constructions in Spain deriving from ground problems(Malaga,July 2004and Barcelona,January 2007).They occurred recently and the causes are the subject of reflection and analysis.

Fluid physics under reduced gravity : an overview

Problems related to several fluid physics experiments the case of two experiemnts to be performed under reduced gravity, onboard Space- temperatures,lab (1st Mission), are discussed. Special attention is placed on parallel and preparatory work on erth, wich could throw some light on the opportunity, present interest and limitations of these experiments. The need for strong supporting fundamental research and, in particular, a more precise determination of the paremeters involved, is stressed.

Parametric analysis of gravity offshore structures: Part 1

The objective of this paper is to analyse the influence of the variation of some parameters used in the analysis of the dynamic response of offshore structures under the action of wind generated waves. The structural response has been obtained by stochastic methods using two discretization models. One with lumped parameters, using translational degrees of freedom (d.o.f.) and the other with one-dimensional finite elements. Using each of these methods the problem has been solved with several d.o.f., analysing the influence of the number of d.o.f. on the results.

An ecological approach to anomaly detection: the EIA Model.

The presented work proposes a new approach for anomaly detection. This approach is based on changes in a population of evolving agents under stress. If conditions are appropriate, changes in the population (modeled by the bioindicators) are representative of the alterations to the environment. This approach, based on an ecological view, improves functionally traditional approaches to the detection of anomalies. To verify this assertion, experiments based on Network Intrussion Detection Systems are presented. The results are compared with the behaviour of other bioinspired approaches and machine learning techniques.

Novel Gravity Distortion Evaluation on Large Antenna Array for Deep Space Communication

This paper presents a simple gravity evaluation model for large reflector antennas and the experimental example for a case study of one uplink array of 4x35-m antennas at X and Ka band. This model can be used to evaluate the gain reduction as a function of the maximum gravity distortion, and also to specify this at system designer level. The case study consists of one array of 35-m antennas for deep space missions. Main issues due to the gravity effect have been explored with Monte Carlo based simulation analysis.

Similarities between ion waves in plasmas and gravity waves in incompressible fluids

Some similarities between ion waves in plasmas and gravity waves in incompressible fluids are investigated. It is shown that for zero ion temperature the ion-wave dispersion relation is similar to that of gravity waves in a stratified liquid between rigid, horizontal walls; for large wavelength the ion waves behave as the surface gravity waves of shallow-water theory. The general character of the pattern of ion waves arising in steady plasma flows is analyzed for arbitrary ion temperature, wavelength, and acoustic mach number (which is based on the ion-acoustic speed), and is compared to the pattern of surface gravity waves in steady water flows when surface tension is taken into account.

PUE attack detection in CWSNs using anomaly detection techniques

Cognitive wireless sensor network (CWSN) is a new paradigm, integrating cognitive features in traditional wireless sensor networks (WSNs) to mitigate important problems such as spectrum occupancy. Security in cognitive wireless sensor networks is an important problem since these kinds of networks manage critical applications and data. The specific constraints of WSN make the problem even more critical, and effective solutions have not yet been implemented. Primary user emulation (PUE) attack is the most studied specific attack deriving from new cognitive features. This work discusses a new approach, based on anomaly behavior detection and collaboration, to detect the primary user emulation attack in CWSN scenarios. Two non-parametric algorithms, suitable for low-resource networks like CWSNs, have been used in this work: the cumulative sum and data clustering algorithms. The comparison is based on some characteristics such as detection delay, learning time, scalability, resources, and scenario dependency. The algorithms have been tested using a cognitive simulator that provides important results in this area. Both algorithms have shown to be valid in order to detect PUE attacks, reaching a detection rate of 99% and less than 1% of false positives using collaboration.

Offshore stereo measurements of gravity waves

Stereo video techniques are effective for estimating the space-time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. To prove this, we consider an application of the Wave Acquisition Stereo System (WASS) for the analysis of offshore video measurements of gravity waves in the Northern Adriatic Sea. In particular, we deployed WASS at the oceanographic platform Acqua Alta, off the Venice coast, Italy. Three experimental studies were performed, and the overlapping field of view of the acquired stereo images covered an area of approximately 1100 m2. Analysis of the WASS measurements show that the sea surface can be accurately estimated in space and time together, yielding associated directional spectra and wave statistics that agree well with theoretical models. From the observed wavenumber-frequency spectrum one can also predict the vertical profile of the current flow underneath the wave surface. Finally, future improvements of WASS and applications are discussed.

A large displacement structural analysis of a pipeline subjected to gravity and buoyancy forces

A nonlinear analysis of an elastic tube subjected to gravity forces and buoyancy pressure is carried out. An update lagrangian formulation is used. The structural analysis efficiency in terms of computer time and accuracy, has been improved when load stiffness matrices have been introduced. In this way the follower forces characteristics such as their intensity and direction changes can be well represented. A sensitivity study of different involved variables on the final deformed pipeline shape is carried out.

Anomaly detection on cup anemometers

The performances of two rotor-damaged commercial anemometers (Vector Instruments A100 LK) were studied. The calibration results (i.e. the transfer function) were very linear, the aerodynamic behavior being more efficient than the one shown by both anemometers equipped with undamaged rotors. No detection of the anomaly (the rotors'damage) was possible based on the calibration results. However, the Fourier analysis clearly revealed this anomaly.

Anomaly Detection Using Remote Sensing for the Archaeological Heritage Registration

The aim of this work is an approach using multisensor remote sensing techniques to recognize the potential remains and recreate the original landscape of three archaeological sites. We investigate the spectral characteristics of the reflectance parameter and emissivity in the pattern recognition of archaeological materials in several hyperspectral scenes of the prehispanic site in Palmar Sur (Costa Rica), the Jarama Valley site and the celtiberian city of Segeda in Spain. Spectral ranges of the visible-near infrared (VNIR), shortwave infrared (SWIR) and thermal infrared (TIR) from hyperspectral data cubes of HyMAP, AHS, MASTER and ATM have been used. Several experiments on natural scenarios of Costa Rica and Spain of different complexity, have been designed. Spectral patterns and thermal anomalies have been calculated as evidences of buried remains and change detection. First results, land cover change analyses and their consequences in the digital heritage registration are discussed.