An experimental and theoretical approach to correct for the scattered radiation in an X-ray computer tomography system for industrial applications

The main problem connected to cone beam computed tomography (CT) systems for industrial applications employing 450 kV X-ray tubes is the high amount of scattered radiation which is added to the primary radiation (signal). This stray radiation leads to a significant degradation of the image quality. A better understanding of the scattering and methods to reduce its effects are therefore necessary to improve the image quality. Several studies have been carried out in the medical field at lower energies, whereas studies in industrial CT, especially for energies up to 450 kV, are lacking. Moreover, the studies reported in literature do not consider the scattered radiation generated by the CT system structure and the walls of the X-ray room (environmental scatter). In order to investigate the scattering on CT projections a GEANT4-based Monte Carlo (MC) model was developed. The model, which has been validated against experimental data, has enabled the calculation of the scattering including the environmental scatter, the optimization of an anti-scatter grid suitable for the CT system, and the optimization of the hardware components of the CT system. The investigation of multiple scattering in the CT projections showed that its contribution is 2.3 times the one of primary radiation for certain objects. The results of the environmental scatter showed that it is the major component of the scattering for aluminum box objects of front size 70 x 70 mm2 and that it strongly depends on the thickness of the object and therefore on the projection. For that reason, its correction is one of the key factors for achieving high quality images. The anti-scatter grid optimized by means of the developed MC model was found to reduce the scatter-toprimary ratio in the reconstructed images by 20 %. The object and environmental scatter calculated by means of the simulation were used to improve the scatter correction algorithm which could be patented by Empa. The results showed that the cupping effect in the corrected image is strongly reduced. The developed CT simulation is a powerful tool to optimize the design of the CT system and to evaluate the contribution of the scattered radiation to the image. Besides, it has offered a basis for a new scatter correction approach by which it has been possible to achieve images with the same spatial resolution as state-of-the-art well collimated fan-beam CT with a gain in the reconstruction time of a factor 10. This result has a high economic impact in non-destructive testing and evaluation, and reverse engineering.

Multiresolution spherical wavelet analysis in global seismic tomography

Every seismic event produces seismic waves which travel throughout the Earth. Seismology is the science of interpreting measurements to derive information about the structure of the Earth. Seismic tomography is the most powerful tool for determination of 3D structure of deep Earth's interiors. Tomographic models obtained at the global and regional scales are an underlying tool for determination of geodynamical state of the Earth, showing evident correlation with other geophysical and geological characteristics. The global tomographic images of the Earth can be written as a linear combinations of basis functions from a specifically chosen set, defining the model parameterization. A number of different parameterizations are commonly seen in literature: seismic velocities in the Earth have been expressed, for example, as combinations of spherical harmonics or by means of the simpler characteristic functions of discrete cells. With this work we are interested to focus our attention on this aspect, evaluating a new type of parameterization, performed by means of wavelet functions. It is known from the classical Fourier theory that a signal can be expressed as the sum of a, possibly infinite, series of sines and cosines. This sum is often referred as a Fourier expansion. The big disadvantage of a Fourier expansion is that it has only frequency resolution and no time resolution. The Wavelet Analysis (or Wavelet Transform) is probably the most recent solution to overcome the shortcomings of Fourier analysis. The fundamental idea behind this innovative analysis is to study signal according to scale. Wavelets, in fact, are mathematical functions that cut up data into different frequency components, and then study each component with resolution matched to its scale, so they are especially useful in the analysis of non stationary process that contains multi-scale features, discontinuities and sharp strike. Wavelets are essentially used in two ways when they are applied in geophysical process or signals studies: 1) as a basis for representation or characterization of process; 2) as an integration kernel for analysis to extract information about the process. These two types of applications of wavelets in geophysical field, are object of study of this work. At the beginning we use the wavelets as basis to represent and resolve the Tomographic Inverse Problem. After a briefly introduction to seismic tomography theory, we assess the power of wavelet analysis in the representation of two different type of synthetic models; then we apply it to real data, obtaining surface wave phase velocity maps and evaluating its abilities by means of comparison with an other type of parametrization (i.e., block parametrization). For the second type of wavelet application we analyze the ability of Continuous Wavelet Transform in the spectral analysis, starting again with some synthetic tests to evaluate its sensibility and capability and then apply the same analysis to real data to obtain Local Correlation Maps between different model at same depth or between different profiles of the same model.

3D probability tomography: theoretical developments and applications to high-resolution geophysical prospecting

The theory of the 3D multipole probability tomography method (3D GPT) to image source poles, dipoles, quadrupoles and octopoles, of a geophysical vector or scalar field dataset is developed. A geophysical dataset is assumed to be the response of an aggregation of poles, dipoles, quadrupoles and octopoles. These physical sources are used to reconstruct without a priori assumptions the most probable position and shape of the true geophysical buried sources, by determining the location of their centres and critical points of their boundaries, as corners, wedges and vertices. This theory, then, is adapted to the geoelectrical, gravity and self potential methods. A few synthetic examples using simple geometries and three field examples are discussed in order to demonstrate the notably enhanced resolution power of the new approach. At first, the application to a field example related to a dipole–dipole geoelectrical survey carried out in the archaeological park of Pompei is presented. The survey was finalised to recognize remains of the ancient Roman urban network including roads, squares and buildings, which were buried under the thick pyroclastic cover fallen during the 79 AD Vesuvius eruption. The revealed anomaly structures are ascribed to wellpreserved remnants of some aligned walls of Roman edifices, buried and partially destroyed by the 79 AD Vesuvius pyroclastic fall. Then, a field example related to a gravity survey carried out in the volcanic area of Mount Etna (Sicily, Italy) is presented, aimed at imaging as accurately as possible the differential mass density structure within the first few km of depth inside the volcanic apparatus. An assemblage of vertical prismatic blocks appears to be the most probable gravity model of the Etna apparatus within the first 5 km of depth below sea level. Finally, an experimental SP dataset collected in the Mt. Somma-Vesuvius volcanic district (Naples, Italy) is elaborated in order to define location and shape of the sources of two SP anomalies of opposite sign detected in the northwestern sector of the surveyed area. The modelled sources are interpreted as the polarization state induced by an intense hydrothermal convective flow mechanism within the volcanic apparatus, from the free surface down to about 3 km of depth b.s.l..

Hepatobiliary diseases in small animals: a comparison of ultrasonography and multidetector-row computed tomography

Ultrasonography (US) is an essential imaging tool for identifying abnormalities of the liver parenchyma, biliary tract and vascular system. US has replaced radiography as the initial imaging procedure in screening for liver disease in small animals. There are few reports of the use of conventional and helical computed tomography (CT) to assess canine or feline parenchymal and neoplastic liver disease and biliary disorders. In human medicine the development of multidetector- row helical computed tomography (MDCT), with its superior spatial and temporal resolution, has resulted in improved detection and characterization of diffuse and focal liver lesions. The increased availability of MDCT in veterinary practice provides incentive to develop MDCT protocols for liver imaging in small animals. The purpose of this study is to assess the rule of MDCT in the characterization of hepatobiliary diseases in small animals; and to compare this method with conventional US. Candidates for this prospective study were 175 consecutive patients (dogs and cats) referred for evaluation of hepatobiliary disease. The patients underwent liver US and MDCT. Percutaneous needle biopsy was performed on all liver lesions or alterations encountered. As for gallbladder, histopatological evaluation was obtained from cholecystectomy specimens. Ultrasonographic findings in this study agreed well with those of previous reports. A protocol for dual-phase liver MDCT in small animals has been described. MDCT findings in parenchymal disorders of the liver, hepatic neoplasia and biliary disorders are here first described in dogs and cats and compared with the corresponding features in human medicine. The ability of MDCT in detection and characterization of hepatobiliary diseases in small animals is overall superior to conventional US. Ultrasonography and MDCT scanning, however, play complementary rules in the evaluation of these diseases. Many conditions have distinctive imaging features that may permit diagnosis. In most instances biopsy is required for definitive diagnosis.

Probabilistic tomography of atmospheric parameters from GNSS data

The objective of the work is the evaluation of the potential capabilities of navigation satellite signals to retrieve basic atmospheric parameters. A capillary study have been performed on the assumptions more or less explicitly contained in the common processing steps of navigation signals. A probabilistic procedure has been designed for measuring vertical discretised profiles of pressure, temperature and water vapour and their associated errors. Numerical experiments on a synthetic dataset have been performed with the main objective of quantifying the information that could be gained from such approach, using entropy and relative entropy as testing parameters. A simulator of phase delay and bending of a GNSS signal travelling across the atmosphere has been developed to this aim.

Spectral-Element and Adjoint 3D Full-Wave Tomography for the Lithosphere of Central Italy

The primary objective of this thesis is to obtain a better understanding of the 3D velocity structure of the lithosphere in central Italy. To this end, I adopted the Spectral-Element Method to perform accurate numerical simulations of the complex wavefields generated by the 2009 Mw 6.3 L’Aquila event and by its foreshocks and aftershocks together with some additional events within our target region. For the mainshock, the source was represented by a finite fault and different models for central Italy, both 1D and 3D, were tested. Surface topography, attenuation and Moho discontinuity were also accounted for. Three-component synthetic waveforms were compared to the corresponding recorded data. The results of these analyses show that 3D models, including all the known structural heterogeneities in the region, are essential to accurately reproduce waveform propagation. They allow to capture features of the seismograms, mainly related to topography or to low wavespeed areas, and, combined with a finite fault model, result into a favorable match between data and synthetics for frequencies up to ~0.5 Hz. We also obtained peak ground velocity maps, that provide valuable information for seismic hazard assessment. The remaining differences between data and synthetics led us to take advantage of SEM combined with an adjoint method to iteratively improve the available 3D structure model for central Italy. A total of 63 events and 52 stations in the region were considered. We performed five iterations of the tomographic inversion, by calculating the misfit function gradient - necessary for the model update - from adjoint sensitivity kernels, constructed using only two simulations for each event. Our last updated model features a reduced traveltime misfit function and improved agreement between data and synthetics, although further iterations, as well as refined source solutions, are necessary to obtain a new reference 3D model for central Italy tomography.

Deep geometry of subduction below the Andean belt of Colombia as revealed by seismic tomography

In this study new tomographic models of Colombia were calculated. I used the seismicity recorded by the Colombian seismic network during the period 2006-2009. In this time period, the improvement of the seismic network yields more stable hypocentral results with respect to older data set and allows to compute new 3D Vp and Vp/Vs models. The final dataset consists of 10813 P- and 8614 S-arrival times associated to 1405 earthquakes. Tests with synthetic data and resolution analysis indicate that velocity models are well constrained in central, western and southwestern Colombia to a depth of 160 km; the resolution is poor in the northern Colombia and close to Venezuela due to a lack of seismic stations and seismicity. The tomographic models and the relocated seismicity indicate the existence of E-SE subducting Nazca lithosphere beneath central and southern Colombia. The North-South changes in Wadati-Benioff zone, Vp & Vp/Vs pattern and volcanism, show that the downgoing plate is segmented by slab tears E-W directed, suggesting the presence of three sectors. Earthquakes in the northernmost sector represent most of the Colombian seimicity and concentrated on 100-170 km depth interval, beneath the Eastern Cordillera. Here a massive dehydration is inferred, resulting from a delay in the eclogitization of a thickened oceanic crust in a flat-subduction geometry. In this sector a cluster of intermediate-depth seismicity (Bucaramanga Nest) is present beneath the elbow of the Eastern Cordillera, interpreted as the result of massive and highly localized dehydration phenomenon caused by a hyper-hydrous oceanic crust. The central and southern sectors, although different in Vp pattern show, conversely, a continuous, steep and more homogeneous Wadati-Benioff zone with overlying volcanic areas. Here a "normalthickened" oceanic crust is inferred, allowing for a gradual and continuous metamorphic reactions to take place with depth, enabling the fluid migration towards the mantle wedge.

Characterization of inclusions and their distribution in natural and artificial samples by synchrotron cryo-micro-tomography (SCXRT)

Zur geometrischen Vermessung und Beschreibung von Einschlüssen in natürlichen sowie im Labor geschaffenen Eispartikeln wurde ein neuartiger Versuchaufbau an der Tomographie-Endstation der Material Science Beam Line an der Swiss Light Source (SLS, Paul Scherrer Institut, Villigen, Schweiz) entwickelt. Dieser besteht aus einer Plexiglas-Tasse und einem doppelwandigen Kaptonfolien-Käfig, der wiederum auf die Düse eines CryojetXL (Oxford Instruments) montiert wurde. Abgesehen von dem hohen Maß an Flexibilit¨at bez¨uglich der Installation erlaubt es dieser Aufbau, die Temperatur des Experiments mit einer Genauigkeit von ± 1 K über einen Bereich von 271 K bis 220 K zu regeln. In den hier beschriebenen Experimenten wurde eine räumliche Auflösung von 1.4 µm erzielt.

Localized potentials in electrical impedance tomography

In this work we study localized electric potentials that have an arbitrarily high energy on some given subset of a domain and low energy on another. We show that such potentials exist for general L-infinity-conductivities (with positive infima) in almost arbitrarily shaped subregions of a domain, as long as these regions are connected to the boundary and a unique continuation principle is satisfied. From this we deduce a simple, but new, theoretical identifiability result for the famous Calderon problem with partial data. We also show how to construct such potentials numerically and use a connection with the factorization method to derive a new non-iterative algorithm for the detection of inclusions in electrical impedance tomography.

Local Earthquake Tomography by trans-dimensional Monte Carlo Sampling

In this study a new, fully non-linear, approach to Local Earthquake Tomography is presented. Local Earthquakes Tomography (LET) is a non-linear inversion problem that allows the joint determination of earthquakes parameters and velocity structure from arrival times of waves generated by local sources. Since the early developments of seismic tomography several inversion methods have been developed to solve this problem in a linearized way. In the framework of Monte Carlo sampling, we developed a new code based on the Reversible Jump Markov Chain Monte Carlo sampling method (Rj-McMc). It is a trans-dimensional approach in which the number of unknowns, and thus the model parameterization, is treated as one of the unknowns. I show that our new code allows overcoming major limitations of linearized tomography, opening a new perspective in seismic imaging. Synthetic tests demonstrate that our algorithm is able to produce a robust and reliable tomography without the need to make subjective a-priori assumptions about starting models and parameterization. Moreover it provides a more accurate estimate of uncertainties about the model parameters. Therefore, it is very suitable for investigating the velocity structure in regions that lack of accurate a-priori information. Synthetic tests also reveal that the lack of any regularization constraints allows extracting more information from the observed data and that the velocity structure can be detected also in regions where the density of rays is low and standard linearized codes fails. I also present high-resolution Vp and Vp/Vs models in two widespread investigated regions: the Parkfield segment of the San Andreas Fault (California, USA) and the area around the Alto Tiberina fault (Umbria-Marche, Italy). In both the cases, the models obtained with our code show a substantial improvement in the data fit, if compared with the models obtained from the same data set with the linearized inversion codes.

Factorization method and irregular inclusions in electrical impedance tomography

In electrical impedance tomography, one tries to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many practically important situations, the investigated object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. Earlier, it has been shown that under suitable regularity conditions positive (or negative) inhomogeneities can be characterized by the factorization technique if the conductivity or one of its higher normal derivatives jumps on the boundaries of the inclusions. In this work, we use a monotonicity argument to generalize these results: We show that the factorization method provides a characterization of an open inclusion (modulo its boundary) if each point inside the inhomogeneity has an open neighbourhood where the perturbation of the conductivity is strictly positive (or negative) definite. In particular, we do not assume any regularity of the inclusion boundary or set any conditions on the behaviour of the perturbed conductivity at the inclusion boundary. Our theoretical findings are verified by two-dimensional numerical experiments.