Competitive exclusion in a two-especies chemotasis model

We consider a mathematical model for the spatio-temporal evolution of two biological species in a competitive situation. Besides diffusing, both species move toward higher concentrations of a chemical substance which is produced by themselves. The resulting system consists of two parabolic equations with Lotka–Volterra-type kinetic terms and chemotactic cross-diffusion, along with an elliptic equation describing the behavior of the chemical. We study the question in how far the phenomenon of competitive exclusion occurs in such a context. We identify parameter regimes for which indeed one of the species dies out asymptotically, whereas the other reaches its carrying capacity in the large time limit.

Sistema de adquisición de datos para una aplicación de detección del ruido de reversa en tiempo real

Entre todas las fuentes de ruido, la activación de la propulsión en reversa de un avión después de aterrizar es conocida por las autoridades del aeropuerto como una causa importante de impacto acústico, molestias y quejas en las proximidades vecinas de los aeropuertos. Por ello, muchos de los aeropuertos de todo el mundo han establecido restricciones en el uso de la reversa, especialmente en las horas de la noche. Una forma de reducir el impacto acústico en las actividades aeroportuarias es implementar herramientas eficaces para la detección de ruido en reversa en los aeropuertos. Para este proyecto de fin de carrera, aplicando la metodología TREND (Thrust Reverser Noise Detection), se pretende desarrollar un sistema software capaz de determinar que una aeronave que aterrice en la pista active el frenado en reversa en tiempo real. Para el diseño de la aplicación se plantea un modelo software, que se compone de dos módulos:  El módulo de adquisición de señales acústicas, simula un sistema de captación por señales de audio. Éste módulo obtiene muestra de señales estéreo de ficheros de audio de formato “.WAV” o del sistema de captación, para acondicionar las muestras de audio y enviarlas al siguiente módulo. El sistema de captación (array de micrófonos), se encuentra situado en una localización cercana a la pista de aterrizaje.  El módulo de procesado busca los eventos de detección aplicando la metodología TREND con las muestras acústicas que recibe del módulo de adquisición. La metodología TREND describe la búsqueda de dos eventos sonoros llamados evento 1 (EV1) y evento 2 (EV2); el primero de ellos, es el evento que se activa cuando una aeronave aterriza discriminando otros eventos sonoros como despegues de aviones y otros sonidos de fondo, mientras que el segundo, se producirá después del evento 1, sólo cuando la aeronave utilice la reversa para frenar. Para determinar la detección del evento 1, es necesario discriminar las señales ajenas al aterrizaje aplicando un filtrado en la señal capturada, después, se aplicará un detector de umbral del nivel de presión sonora y por último, se determina la procedencia de la fuente de sonido con respecto al sistema de captación. En el caso de la detección del evento 2, está basada en la implementación de umbrales en la evolución temporal del nivel de potencia acústica aplicando el modelo de propagación inversa, con ayuda del cálculo de la estimación de la distancia en cada instante de tiempo mientras el avión recorre la pista de aterrizaje. Con cada aterrizaje detectado se realiza una grabación que se archiva en una carpeta específica y todos los datos adquiridos, son registrados por la aplicación software en un fichero de texto. ABSTRACT. Among all noise sources, the activation of reverse thrust to slow the aircraft after landing is considered as an important cause of noise pollution by the airport authorities, as well as complaints and annoyance in the airport´s nearby locations. Therefore, many airports around the globe have restricted the use of reverse thrust, especially during the evening hours. One way to reduce noise impact on airport activities is the implementation of effective tools that deal with reverse noise detection. This Final Project aims to the development of a software system capable of detecting if an aircraft landing on the runway activates reverse thrust on real time, using the TREND (Thrust Reverser Noise Detection) methodology. To design this application, a two modules model is proposed: • The acoustic signals obtainment module, which simulates an audio waves based catchment system. This module obtains stereo signal samples from “.WAV” audio files or the catchment system in order to prepare these audio samples and send them to the next module. The catchment system (a microphone array) is located on a place near the landing runway. • The processing module, which looks for detection events among the acoustic samples received from the other module, using the TREND methodology. The TREND methodology describes the search of two sounds events named event 1 (EV1) and event 2 (EV2). The first is the event activated by a landing plane, discriminating other sound events such as background noises or taking off planes; the second one will occur after event one only when the aircraft uses reverse to slow down. To determine event 1 detection, signals outside the landing must be discriminated using a filter on the catched signal. A pressure level´s threshold detector will be used on the signal afterwards. Finally, the origin of the sound source is determined regarding the catchment system. The detection of event 2 is based on threshold implementations in the temporal evolution of the acoustic power´s level by using the inverse propagation model and calculating the distance estimation at each time step while the plane goes on the landing runway. A recording is made every time a landing is detected, which is stored in a folder. All acquired data are registered by the software application on a text file.

Datos de precisión en la evaluación del ruido transmitido al interior de una habitación según el Real Decreto 1367/2007

El objetivo del presente trabajo es realizar una evaluación realista de la incertidumbre en los ensayos de ruido transmitido al interior de una sala según el Anexo IV del Real Decreto 1367/2007, contemplando todas las posibles causas que intervienen en la incertidumbre de forma que las imprecisiones observadas en los ejercicios de intercomparación se cubran con un único ensayo. Otra parte fundamental del trabajo es cuantificar la fuente de incertidumbre generada en la elección del punto de medición. En primer lugar se realiza la medición del nivel continuo equivalente ponderado A en habitaciones de distinto tamaño, a la que llegan los distintos tipos de ruido emitido desde el exterior de las mismas. El siguiente paso es realizar un análisis de los niveles medidos, tanto en su distribución espacial como en su evolución temporal, incidiendo en los valores máximos, LAeq,5s. A continuación se comprueba si la distribución de los niveles medidos se ajusta a una distribución normal mediante el software de análisis estadístico STATGRAPHICS. Determinando, en base al tamaño de las muestras escogidas, por medio de análisis estadísticos, la aportación a la incertidumbre generada en la elección del punto de medida, cuantificando su valor. Por último se realiza una medición del ruido de actividades según el Real Decreto 1367/2007, aportando una evaluación de la incertidumbre, teniendo en cuenta todas las fuentes que la generan, mediante el enfoque clásico de la GUM. ABSTRACT. The objective of this work is to carry out a realistic assessment of the uncertainty in the trials of noise transmitted into the interior of a room according to Annex IV of the Royal Decree 136772997, considering all of the causes involved in uncertainty in such a way that the inaccuracies observed in intercomparison exercises are covered with a single trial. Another fundamental part of the work is to quantify the source of uncertainty in the choice of the point of measurement. First is the weighted equivalent of the continuous level measurement in rooms of different sizes, which reach different types of noise emitted from outside of them. The next step is to perform an analysis of the measured levels, both in their spatial distribution and their temporal evolution, influencing the maximum values, LAeq,5s. Then it is checked to see whether the distribution of the measured levels conforms to a normal distribution using the STATGRAPHICS statistical analysis software. Determining therefore, based on the size of the selected samples, through statistical analysis, the contribution to the uncertainty generated in the choice of the measurement point, quantifying its value. At last is the measure of the noise of activities according to the Royal Decree 1367/2007, providing an assessment of the uncertainty, taking into account all sources that generate it, using the classical approach to the GUM.

Coupled Nonlinear Ginzburg-Landau and Mechanics Model for Martensitic Transformations in Polycrystals

Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedades destacables como alta resistencia mecánica, memoria de forma, efectos de superelasticidad o funcionalidades ferroicas como la piezoelectricidad, electro y magneto-estricción etc. Varios modelos/teorías se han desarrollado en sinergia con el desarrollo de la física del estado sólido para entender por qué las MT generan microstructuras muy variadas y ricas que muestran propiedades muy interesantes. Entre las teorías mejor aceptadas se encuentra la Teoría Fenomenológica de la Cristalografía Martensítica (PTMC, por sus siglas en inglés) que predice el plano de hábito y las relaciones de orientación entre la austenita y la martensita. La reinterpretación de la teoría PTMC en un entorno de mecánica del continuo (CM-PTMC) explica la formación de los dominios de estructuras multivariantes, mientras que la teoría de Landau con dinámica de inercia desentraña los mecanismos físicos de los precursores y otros comportamientos dinámicos. La dinámica de red cristalina desvela la reducción de la dureza acústica de las ondas de tensión de red que da lugar a transformaciones débiles de primer orden en el desplazamiento. A pesar de las diferencias entre las teorías estáticas y dinámicas dado su origen en diversas ramas de la física (por ejemplo mecánica continua o dinámica de la red cristalina), estas teorías deben estar inherentemente conectadas entre sí y mostrar ciertos elementos en común en una perspectiva unificada de la física. No obstante las conexiones físicas y diferencias entre las teorías/modelos no se han tratado hasta la fecha, aun siendo de importancia crítica para la mejora de modelos de MT y para el desarrollo integrado de modelos de transformaciones acopladas de desplazamiento-difusión. Por lo tanto, esta tesis comenzó con dos objetivos claros. El primero fue encontrar las conexiones físicas y las diferencias entre los modelos de MT mediante un análisis teórico detallado y simulaciones numéricas. El segundo objetivo fue expandir el modelo de Landau para ser capaz de estudiar MT en policristales, en el caso de transformaciones acopladas de desplazamiento-difusión, y en presencia de dislocaciones. Comenzando con un resumen de los antecedente, en este trabajo se presentan las bases físicas de los modelos actuales de MT. Su capacidad para predecir MT se clarifica mediante el ansis teórico y las simulaciones de la evolución microstructural de MT de cúbicoatetragonal y cúbicoatrigonal en 3D. Este análisis revela que el modelo de Landau con representación irreducible de la deformación transformada es equivalente a la teoría CM-PTMC y al modelo de microelasticidad para predecir los rasgos estáticos durante la MT, pero proporciona una mejor interpretación de los comportamientos dinámicos. Sin embargo, las aplicaciones del modelo de Landau en materiales estructurales están limitadas por su complejidad. Por tanto, el primer resultado de esta tesis es el desarrollo del modelo de Landau nolineal con representación irreducible de deformaciones y de la dinámica de inercia para policristales. La simulación demuestra que el modelo propuesto es consistente fcamente con el CM-PTMC en la descripción estática, y también permite una predicción del diagrama de fases con la clásica forma ’en C’ de los modos de nucleación martensítica activados por la combinación de temperaturas de enfriamiento y las condiciones de tensión aplicada correlacionadas con la transformación de energía de Landau. Posteriomente, el modelo de Landau de MT es integrado con un modelo de transformación de difusión cuantitativa para elucidar la relajación atómica y la difusión de corto alcance de los elementos durante la MT en acero. El modelo de transformaciones de desplazamiento y difusión incluye los efectos de la relajación en borde de grano para la nucleación heterogenea y la evolución espacio-temporal de potenciales de difusión y movilidades químicas mediante el acoplamiento de herramientas de cálculo y bases de datos termo-cinéticos de tipo CALPHAD. El modelo se aplica para estudiar la evolución microstructural de aceros al carbono policristalinos procesados por enfriamiento y partición (Q&P) en 2D. La microstructura y la composición obtenida mediante la simulación se comparan con los datos experimentales disponibles. Los resultados muestran el importante papel jugado por las diferencias en movilidad de difusión entre la fase austenita y martensita en la distibución de carbono en las aceros. Finalmente, un modelo multi-campo es propuesto mediante la incorporación del modelo de dislocación en grano-grueso al modelo desarrollado de Landau para incluir las diferencias morfológicas entre aceros y aleaciones con memoria de forma con la misma ruptura de simetría. La nucleación de dislocaciones, la formación de la martensita ’butterfly’, y la redistribución del carbono después del revenido son bien representadas en las simulaciones 2D del estudio de la evolución de la microstructura en aceros representativos. Con dicha simulación demostramos que incluyendo las dislocaciones obtenemos para dichos aceros, una buena comparación frente a los datos experimentales de la morfología de los bordes de macla, la existencia de austenita retenida dentro de la martensita, etc. Por tanto, basado en un modelo integral y en el desarrollo de códigos durante esta tesis, se ha creado una herramienta de modelización multiescala y multi-campo. Dicha herramienta acopla la termodinámica y la mecánica del continuo en la macroescala con la cinética de difusión y los modelos de campo de fase/Landau en la mesoescala, y también incluye los principios de la cristalografía y de la dinámica de red cristalina en la microescala. ABSTRACT Martensitic transformation (MT), in a narrow sense, is defined as the change of the crystal structure to form a coherent phase, or multi-variant domain structures out from a parent phase with the same composition, by small shuffles or co-operative movements of atoms. Over the past century, MTs have been discovered in different materials from steels to shape memory alloys, ceramics, and smart materials. They lead to remarkable properties such as high strength, shape memory/superelasticity effects or ferroic functionalities including piezoelectricity, electro- and magneto-striction, etc. Various theories/models have been developed, in synergy with development of solid state physics, to understand why MT can generate these rich microstructures and give rise to intriguing properties. Among the well-established theories, the Phenomenological Theory of Martensitic Crystallography (PTMC) is able to predict the habit plane and the orientation relationship between austenite and martensite. The re-interpretation of the PTMC theory within a continuum mechanics framework (CM-PTMC) explains the formation of the multivariant domain structures, while the Landau theory with inertial dynamics unravels the physical origins of precursors and other dynamic behaviors. The crystal lattice dynamics unveils the acoustic softening of the lattice strain waves leading to the weak first-order displacive transformation, etc. Though differing in statics or dynamics due to their origins in different branches of physics (e.g. continuum mechanics or crystal lattice dynamics), these theories should be inherently connected with each other and show certain elements in common within a unified perspective of physics. However, the physical connections and distinctions among the theories/models have not been addressed yet, although they are critical to further improving the models of MTs and to develop integrated models for more complex displacivediffusive coupled transformations. Therefore, this thesis started with two objectives. The first one was to reveal the physical connections and distinctions among the models of MT by means of detailed theoretical analyses and numerical simulations. The second objective was to expand the Landau model to be able to study MTs in polycrystals, in the case of displacive-diffusive coupled transformations, and in the presence of the dislocations. Starting with a comprehensive review, the physical kernels of the current models of MTs are presented. Their ability to predict MTs is clarified by means of theoretical analyses and simulations of the microstructure evolution of cubic-to-tetragonal and cubic-to-trigonal MTs in 3D. This analysis reveals that the Landau model with irreducible representation of the transformed strain is equivalent to the CM-PTMC theory and microelasticity model to predict the static features during MTs but provides better interpretation of the dynamic behaviors. However, the applications of the Landau model in structural materials are limited due its the complexity. Thus, the first result of this thesis is the development of a nonlinear Landau model with irreducible representation of strains and the inertial dynamics for polycrystals. The simulation demonstrates that the updated model is physically consistent with the CM-PTMC in statics, and also permits a prediction of a classical ’C shaped’ phase diagram of martensitic nucleation modes activated by the combination of quenching temperature and applied stress conditions interplaying with Landau transformation energy. Next, the Landau model of MT is further integrated with a quantitative diffusional transformation model to elucidate atomic relaxation and short range diffusion of elements during the MT in steel. The model for displacive-diffusive transformations includes the effects of grain boundary relaxation for heterogeneous nucleation and the spatio-temporal evolution of diffusion potentials and chemical mobility by means of coupling with a CALPHAD-type thermo-kinetic calculation engine and database. The model is applied to study for the microstructure evolution of polycrystalline carbon steels processed by the Quenching and Partitioning (Q&P) process in 2D. The simulated mixed microstructure and composition distribution are compared with available experimental data. The results show that the important role played by the differences in diffusion mobility between austenite and martensite to the partitioning in carbon steels. Finally, a multi-field model is proposed by incorporating the coarse-grained dislocation model to the developed Landau model to account for the morphological difference between steels and shape memory alloys with same symmetry breaking. The dislocation nucleation, the formation of the ’butterfly’ martensite, and the redistribution of carbon after tempering are well represented in the 2D simulations for the microstructure evolution of the representative steels. With the simulation, we demonstrate that the dislocations account for the experimental observation of rough twin boundaries, retained austenite within martensite, etc. in steels. Thus, based on the integrated model and the in-house codes developed in thesis, a preliminary multi-field, multiscale modeling tool is built up. The new tool couples thermodynamics and continuum mechanics at the macroscale with diffusion kinetics and phase field/Landau model at the mesoscale, and also includes the essentials of crystallography and crystal lattice dynamics at microscale.

Signal changes in the spinal cord of the rat after injection of formalin into the hindpaw: Characterization using functional magnetic resonance imaging

Changes in metabolism and local circulation occur in the spinal cord during peripheral noxious stimulation. Evidence is presented that this stimulation also causes signal intensity alterations in functional magnetic resonance images of the spinal cord during formalin-induced pain. These results indicate the potential of functional magnetic resonance imaging in assessing noninvasively the extent and intensity of spinal cord excitation in this well characterized pain model. Therefore, the aim of this study was to establish functional magnetic resonance imaging as a noninvasive method to characterize temporal changes in the spinal cord after a single injection of 50 μl of formalin subcutaneously into the hindpaw of the anesthetized rat. This challenge produced a biphasic licking activity in the freely moving conscious animal. Images of the spinal cord were acquired within 2 min, enabling monitoring of the site and the temporal evolution of the signal changes during the development of formalin-induced hyperalgesia without the need of any surgical procedure. The time course of changes in the spinal cord functional image in the isoflurane-anesthetized animal was similar to that obtained from behavioral experiments. Also, comparable physiological data, control experiments, and the inhibition of a response through application of the local anesthetic agent lidocaine indicate that the signal changes observed after formalin injection were specifically related to excitability changes in the relevant segments of the lumbar spinal cord. This approach could be useful to characterize different models of pain and hyperalgesia and, more importantly, to evaluate effects of analgesic drugs.

An approach to probe some neural systems interaction by functional MRI at neural time scale down to milliseconds

In this paper, we demonstrate an approach by which some evoked neuronal events can be probed by functional MRI (fMRI) signal with temporal resolution at the time scale of tens of milliseconds. The approach is based on the close relationship between neuronal electrical events and fMRI signal that is experimentally demonstrated in concurrent fMRI and electroencephalographic (EEG) studies conducted in a rat model with forepaw electrical stimulation. We observed a refractory period of neuronal origin in a two-stimuli paradigm: the first stimulation pulse suppressed the evoked activity in both EEG and fMRI signal responding to the subsequent stimulus for a period of several hundred milliseconds. When there was an apparent site–site interaction detected in the evoked EEG signal induced by two stimuli that were primarily targeted to activate two different sites in the brain, fMRI also displayed signal amplitude modulation because of the interactive event. With visual stimulation using two short pulses in the human brain, a similar refractory phenomenon was observed in activated fMRI signals in the primary visual cortex. In addition, for interstimulus intervals shorter than the known latency time of the evoked potential induced by the first stimulus (≈100 ms) in the primary visual cortex of the human brain, the suppression was not present. Thus, by controlling the temporal relation of input tasks, it is possible to study temporal evolution of certain neural events at the time scale of their evoked electrical activity by noninvasive fMRI methodology.

Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

The case for unification.

I investigate the issue of whether the various subclasses of radio-loud galaxies are intrinsically the same but have been classified differently mainly due to their being viewed from different directions. Evidence for the two key elements of this popular version of the "unified scheme (US)," relativistic jets and nuclear tori, is updated. The case for the torus opening angle increasing with the radio luminosity of the active galactic nucleus (AGN) is freshly argued. Radio-loud AGN are particularly suited for testing the US, since their structures and polarization properties on different scales, as well as their overall radio sizes, provide useful statistical indicators of the relative orientations of their various subclasses. I summarize recent attempts to bring under a single conceptual framework the USs developed for radio-moderate [Fanaroff-Riley type I (FRI)] and radio-powerful (FRII) AGN. By focusing on FRII radio sources, I critically examine the recent claims of conflict with the US, based on the statistics of radio-size measurements for large, presumably orientation-independent, samples with essentially complete optical identifications. Possible ways of reconciling these results, and also the ones based on very-long-baseline radio interferometry polarimetric observations, with the US are pointed out. By incorporating a highly plausible temporal evolution of radio source properties into the US, I outline a scenario that allows the median linear size of quasars to approach, or even exceed, that of radio galaxies, as samples with decreasing radio luminosity are observed. Thus, even though a number of issues remain to be fully resolved, the scope of unified models continues to expand.

Li I enhancement during a long-duration stellar flare

We report the possible detection of a Li I λ6708 Å line enhancement during an unusual long-duration optical flare in the recently discovered, X-ray/EUV selected, chromospherically active binary 2RE J0743+224. The Li I equivalent width (EW) variations follow the temporal evolution of the flare and large changes are observed in the intensity of the line. The maximum Li I enhancement (40% in EW) occurs just after the maximum chromospheric emission observed in the flare. A significant increase of the Li^-6/Li^-7 isotopic ratio is also detected. No significant simultaneous variations are detected in other photospheric lines. Neither line blends nor starspots seem to be the primary cause of the observed Li I line variation. From all this we suggest that this Li I enhancement is produced by spallation reactions during the flare.

Simulation of the cold climate event 8200 years ago by meltwater outburst from Lake Agassiz

The cold climate anomaly about 8200 years ago is investigated with CLIMBER-2, a coupled atmosphere-ocean-biosphere model of intermediate complexity. This climate model simulates a cooling of about 3.6 K over the North Atlantic induced by a meltwater pulse from Lake Agassiz routed through the Hudson strait. The meltwater pulse is assumed to have a volume of 1.6 x 10^14 m^3 and a period of discharge of 2 years on the basis of glaciological modeling of the decay of the Laurentide Ice Sheet ( LIS). We present a possible mechanism which can explain the centennial duration of the 8.2 ka cold event. The mechanism is related to the existence of an additional equilibrium climate state with reduced North Atlantic Deep Water (NADW) formation and a southward shift of the NADW formation area. Hints at the additional climate state were obtained from the largely varying duration of the pulse-induced cold episode in response to overlaid random freshwater fluctuations in Monte Carlo simulations. The model equilibrium state was attained by releasing a weak multicentury freshwater flux through the St. Lawrence pathway completed by the meltwater pulse. The existence of such a climate mode appears essential for reproducing climate anomalies in close agreement with paleoclimatic reconstructions of the 8.2 ka event. The results furthermore suggest that the temporal evolution of the cold event was partly a matter of chance.

Advanced interpretation of subsidence in Murcia (SE Spain) using A-DInSAR data – modelling and validation

Subsidence is a natural hazard that affects wide areas in the world causing important economic costs annually. This phenomenon has occurred in the metropolitan area of Murcia City (SE Spain) as a result of groundwater overexploitation. In this work aquifer system subsidence is investigated using an advanced differential SAR interferometry remote sensing technique (A-DInSAR) called Stable Point Network (SPN). The SPN derived displacement results, mainly the velocity displacement maps and the time series of the displacement, reveal that in the period 2004–2008 the rate of subsidence in Murcia metropolitan area doubled with respect to the previous period from 1995 to 2005. The acceleration of the deformation phenomenon is explained by the drought period started in 2006. The comparison of the temporal evolution of the displacements measured with the extensometers and the SPN technique shows an average absolute error of 3.9±3.8 mm. Finally, results from a finite element model developed to simulate the recorded time history subsidence from known water table height changes compares well with the SPN displacement time series estimations. This result demonstrates the potential of A-DInSAR techniques to validate subsidence prediction models as an alternative to using instrumental ground based techniques for validation.

Forensic analysis of buildings affected by mining subsidence based on Differential Interferometry (Part III)

This work presents a forensic analysis of buildings affected by mining subsidence, which is based on deformation data obtained by Differential Interferometry (DInSAR). The proposed test site is La Union village (Murcia, SE Spain) where subsidence was triggered in an industrial area due to the collapse of abandoned underground mining labours occurred in 1998. In the first part of this work the study area was introduced, describing the spatial and temporal evolution of ground subsidence, through the elaboration of a cracks map on the buildings located within the affected area. In the second part, the evolution of the most significant cracks found in the most damaged buildings was monitored using biaxial extensometric units and inclinometers. This article describes the work performed in the third part, where DInSAR processing of satellite radar data, available between 1998 and 2008, has permitted to determine the spatial and temporal evolution of the deformation of all the buildings of the study area in a period when no continuous in situ instrumental data is available. Additionally, the comparison of these results with the forensic data gathered in the 2005–2008 period, reveal that there is a coincidence between damaged buildings, buildings where extensometers register significant movements of cracks, and buildings deformation estimated from radar data. As a result, it has been demonstrated that the integration of DInSAR data into forensic analysis methodologies contributes to improve significantly the assessment of the damages of buildings affected by mining subsidence.

Radar interferometry techniques for the study of ground subsidence phenomena: a review of practical issues through cases in Spain

Subsidence related to multiple natural and human-induced processes affects an increasing number of areas worldwide. Although this phenomenon may involve surface deformation with 3D displacement components, negative vertical movement, either progressive or episodic, tends to dominate. Over the last decades, differential SAR interferometry (DInSAR) has become a very useful remote sensing tool for accurately measuring the spatial and temporal evolution of surface displacements over broad areas. This work discusses the main advantages and limitations of addressing active subsidence phenomena by means of DInSAR techniques from an end-user point of view. Special attention is paid to the spatial and temporal resolution, the precision of the measurements, and the usefulness of the data. The presented analysis is focused on DInSAR results exploitation of various ground subsidence phenomena (groundwater withdrawal, soil compaction, mining subsidence, evaporite dissolution subsidence, and volcanic deformation) with different displacement patterns in a selection of subsidence areas in Spain. Finally, a cost comparative study is performed for the different techniques applied.

A quasi-elastic aquifer deformational behavior: Madrid aquifer case study

The purpose of this paper is to analyze the quasi-elastic deformational behavior that has been induced by groundwater withdrawal of the Tertiary detrital aquifer of Madrid (Spain). The spatial and temporal evolution of ground surface displacement was estimated by processing two datasets of radar satellite images (SAR) using Persistent Scatterer Interferometry (PSI). The first SAR dataset was acquired between April 1992 and November 2000 by ERS-1 and ERS-2 satellites, and the second one by the ENVISAT satellite between August 2002 and September 2010. The spatial distribution of PSI measurements reveals that the magnitude of the displacement increases gradually towards the center of the well field area, where approximately 80 mm of maximum cumulated displacement is registered. The correlation analysis made between displacement and piezometric time series provides a correlation coefficient greater than 85% for all the wells. The elastic and inelastic components of measured displacements were separated, observing that the elastic component is, on average, more than 4 times the inelastic component for the studied period. Moreover, the hysteresis loops on the stress–strain plots indicate that the response is in the elastic range. These results demonstrate the quasi-elastic behavior of the aquifer. During the aquifer recovery phase ground surface uplift almost recovers from the subsidence experienced during the preceding extraction phase. Taking into account this unique aquifer system, a one dimensional elastic model was calibrated in the period 1997–2000. Subsequently, the model was used to predict the ground surface movements during the period 1992–2010. Modeled displacements were validated with PSI displacement measurements, exhibiting an error of 13% on average, related with the inelastic component of deformation occurring as a long-term trend in low permeability fine-grained units. This result further demonstrates the quasi-elastic deformational behavior of this unique aquifer system.

Regional subsidence modelling in Murcia city (SE Spain) using 1-D vertical finite element analysis and 2-D interpolation of ground surface displacements

Subsidence is a hazard that may have natural or anthropogenic origin causing important economic losses. The area of Murcia city (SE Spain) has been affected by subsidence due to groundwater overexploitation since the year 1992. The main observed historical piezometric level declines occurred in the periods 1982–1984, 1992–1995 and 2004–2008 and showed a close correlation with the temporal evolution of ground displacements. Since 2008, the pressure recovery in the aquifer has led to an uplift of the ground surface that has been detected by the extensometers. In the present work an elastic hydro-mechanical finite element code has been used to compute the subsidence time series for 24 geotechnical boreholes, prescribing the measured groundwater table evolution. The achieved results have been compared with the displacements estimated through an advanced DInSAR technique and measured by the extensometers. These spatio-temporal comparisons have showed that, in spite of the limited geomechanical data available, the model has turned out to satisfactorily reproduce the subsidence phenomenon affecting Murcia City. The model will allow the prediction of future induced deformations and the consequences of any piezometric level variation in the study area.