The problem of fitting a material property of the earth to a certain model by analysing a returned seismic signal is investigated here. Analysis proceeds with methods taken from the theory of inverse problems. Seismic wave inversion is tack- led by minimisation of the objective function with respect to the model parameters. Absorbing boundary conditions are implemented using an exponentially decaying ansatz. / Physics / Ph. D. (Physics)

Nowadays, many environmental and climatic factors such as weathering actions, temperature variation, chemical attacks, abrasion and other degradation processes can cause near surface damage (0.0 m to 0.5 m) to most concrete structures exposed to severe environmental conditions. As such, the spread of such damage and, subsequently, the loss of mechanical properties of materials are very progressive in long term. The main purpose of Multichannel Analysis of Surface Waves (MASW) method is to 1) characterize near surface damage in concrete structures as a nondestructive testing procedure, 2) estimate the thickness of superficial layers and determine shear-wave velocity (V[subscript S]) profiles. The originality of this research is the application of MASW as a non-destructive method for the evaluation of near surface damage in concrete structures. Indeed, major applications of this method are concerning geotechnical applications. Experiments have been conducted on two concrete slabs (0.80 m, 3 m et 3.50 m) at IREQ with different typical simulated near surface pathologies in order to test the accuracy of MASW method. The results demonstrate that the MASW method has a potential to identify the homogeneity of concrete and estimate the thickness of superficial layers in concrete structures.

Middle and Upper Ordovician strata in the southernmost Appalachians document initial collision along the southeastern margin of Laurentia during the Blountian orogeny, an early phase of the Taconic orogeny. Coeval drowning and exposure of different parts of the former platform and variations in stratal architecture have been attributed to tectonic and depositional loading along the collisional margin. Stratigraphic correlations, using a bentonite-graptoliteconodont time framework, a palinspastic map, and a map of subsurface basement structures, suggest that basement-fault reactivation, flexural subsidence, and eustasy variously controlled uplift, subsidence, and deposition at different sites within the peripheral foreland basin. This dissertation documents how pre-existing structures in the continental margin and interior affected subsidence, deposition, diagenesis, and composition of foreland strata, and deformation in tectonic loads. Stratigraphic correlations document an early episode of basementfault inversion in the distal foreland, and heterogeneous subsidence and provenance patterns in the middle and proximal foreland. Abrupt variations in depth of erosion of passive-margin strata and in thickness of distal foreland deposits coincide with the boundaries of the intraplate Birmingham graben. Inversion of the former graben increased the magnitude of erosion on inverted upthrown blocks; increased tectonic subsidence in adjacent blocks; supplied chert and quartz detritus to shallow-marine carbonate depocenters; and facilitated influx of meteoric water to aquifers in shallow-marine limestones. Tectonic subsidence of middle and proximal foreland deposits reflects local irregularities in the foreland subsidence and different rates of migration of the flexural wave along strike. Differential subsidence between embayments and promontories may have caused reactivation of transverse basement faults. Relief produced by reactivation of transverse basement faults and flexural normal reactivation of basement faults may provide sources for local conglomerates interbedded with deep-water shales. Differences in orogenicbelt deformation are reflected in provenance analyses that suggest exposure of dominantly feldspar-bearing basement rocks in the orogenic belt adjacent to the promontory and exposure of basement rocks and sedimentary cover in the orogenic belt adjacent to the embayment. Results of this study reveal the importance of considering the effects of pre-existing structures in the interpretation of along- and across-strike variations of foreland strata. Therefore, geodynamic modeling of the Blountian foreland basin needs to consider along-strike variations in the geometry of tectonic loads and reactivation of different basement structures.

In this thesis, we investigate two expressions for symmetric group characters: Kerov?s universal character polynomials and Stanley?s character polynomials. We give a new explicit form for Kerov?s polynomials, which exactly evaluate the characters of the symmetric group scaled by degree and a constant. We use this explicit expression to obtain specific information about Kerov polynomials, including partial answers to positivity questions. We then use the expression obtained for Kerov?s polynomials to obtain results about Stanley?s character polynomials.

Acoustic emissions (AE) can provide information relating to the internal state of a deforming rock sample during laboratory testing and have been utilised to quantify damage progression for time-dependent failure modeling. However, the underlying physical mechanisms that produce AE in different materials and their evolution during the process of damage localisation are not fully understood, particularly in porous media. In order to investigate the sources of laboratory acoustic emissions, a moment tensor inversion was applied to data from triaxial compression experiments on Aue granite and Clashach sandstone. The moment tensor inversion was verified for granite, by comparison with results obtained using a more simplistic source analysis technique. In the non-porous Aue granite, AE sources exhibited a predominantly tensile behaviour in the early stages of AE activity. However, shear sources become dominant in the vicinity of the peak stress. In contrast, during deformation of the Clashach sandstone, which has a significant pre-existing porosity, AE sources are dominated by a collapse signature and generally involve a notable shear component. AE that have a predominantly shear mechanism are also a major contributor to the microscale deformation imaged by the technique, and dominate during shear localisation. A combination of correlation analysis and source analysis was used to elucidate the temporal and spatial evolution of the AE source mechanisms involved in the localisation process, as well as during a temporary hiatus in the progression to failure. The results support the concept that the cascade to failure requires the simultaneous involvement of a range of micromechanical behaviours to maintain the progression of localised damage, and eventual formation of a fault. Localisation of collapse mechanisms was not observed until the final approach to failure. Finally, AE sources produced during brittle deformation of the Clashach sandstone were characterised in detail and compared to microstructural observations representing the integrated effect of all times up to the end of the test, and including smaller structures that may have been formed insufficiently dynamically to produce AE. Equivalent focal mechanisms for these events are presented and the relative proportions of their volumetric and shear components considered. The results indicate that AE sources display a wide spectrum of micromechanical behaviour that is consistent with microstructural observations, indicating that AE mechanisms are representative of ongoing deformation processes within the sandstone. It is argued that moment tensor inversion of acoustic emissions is a powerful tool for elucidating the micromechanical evolution of damage, during the brittle deformation of rock.

Characterization of heterogeneous soil hydraulic parameters of deep vadose zones is often difficult and expensive, making it necessary to rely on other sources of information. Pedotransfer functions (PTFs) based on soil texture data constitute a simple alternative to inverse hydraulic parameter estimation, but their accuracy is often modest. Inverse modeling entails a compromise between detailed description of subsurface heterogeneity and the need to restrict the number of parameters. We propose two methods of parameterizing vadose zone hydraulic properties using a combination of k-means clustering of kriged soil texture data, PTFs, and model inversion. One approach entails homogeneous and the other heterogeneous clusters. Clusters may include subdomains of the computational grid that need not be contiguous in space. The first approach homogenizes within-cluster variability into initial hydraulic parameter estimates that are subsequently optimized by inversion. The second approach maintains heterogeneity through multiplication of each spatially varying initial hydraulic parameter by a scale factor, estimated a posteriori through inversion. This allows preserving heterogeneity without introducing a large number of adjustable parameters. We use each approach to simulate a 95 day infiltration experiment in unsaturated layered sediments at a semiarid site near Phoenix, Arizona, over an area of 50 x 50 m(2) down to a depth of 14.5 m. Results show that both clustering approaches improve simulated moisture contents considerably in comparison to those based solely on PTF estimates. Our calibrated models are validated against data from a subsequent 295 day infiltration experiment at the site.

This thesis consists of two parts. The first part (Chapters 2-4) focuses on the problem of inverting the signature of a path of bounded variation, and we present three results here. First, we give an explicit inversion formula for any axis path in terms of its signature. Second, we show that for relatively smooth paths, the derivative at the end point can be approximated arbitrarily closely by its signature sequence, and we provide explicit error estimates. As an application, we give an effective inversion procedure for piecewise linear paths. Finally, we prove a uniform estimate for the signatures of paths of bounded variations, and obtain a reconstruction theorem via that uniform estimate. Although this general reconstruction theorem is not computationally efficient, the techniques involved in deriving the uniform estimate are useful in other situations, and we also give an application in the case of expected signatures for Brownian motion. The second part (Chapter 5) deals with rough paths. After introducing proper backgrounds, we extend the uniform estimate above to the context of rough paths, and show how it can lead to simple proofs of distance bounds for Gaussian iterated integrals.

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

The purpose of Bayesian seismic inversion is to combine information derived from seismic data and prior geological knowledge to determine a posterior probability distribution over parameters describing the elastic and geological properties of the subsurface. Typically the subsurface is modelled by a cellular grid model containing thousands or millions of cells within which these parameters are to be determined. Thus such inversions are computationally expensive due to the size of the parameter space (being proportional to the number of grid cells) over which the posterior is to be determined. Therefore, in practice approximations to Bayesian seismic inversion must be considered. A particular, existing approximate workflow is described in this thesis: the so-called two-stage inversion method explicitly splits the inversion problem into elastic and geological inversion stages. These two stages sequentially estimate the elastic parameters given the seismic data, and then the geological parameters given the elastic parameter estimates, respectively. In this thesis a number of methodologies are developed which enhance the accuracy of this approximate workflow. To reduce computational cost, existing elastic inversion methods often incorporate only simplified prior information about the elastic parameters. Thus a method is introduced which transforms such results, obtained using prior information specified using only two-point geostatistics, into new estimates containing sophisticated multi-point geostatistical prior information. The method uses a so-called deep neural network, trained using only synthetic instances (or `examples') of these two estimates, to apply this transformation. The method is shown to improve the resolution and accuracy (by comparison to well measurements) of elastic parameter estimates determined for a real hydrocarbon reservoir. It has been shown previously that so-called mixture density network (MDN) inversion can be used to solve geological inversion analytically (and thus very rapidly and efficiently) but only under certain assumptions about the geological prior distribution. A so-called prior replacement operation is developed here, which can be used to relax these requirements. It permits the efficient MDN method to be incorporated into general stochastic geological inversion methods which are free from the restrictive assumptions. Such methods rely on the use of Markov-chain Monte-Carlo (MCMC) sampling, which estimate the posterior (over the geological parameters) by producing a correlated chain of samples from it. It is shown that this approach can yield biased estimates of the posterior. Thus an alternative method which obtains a set of non-correlated samples from the posterior is developed, avoiding the possibility of bias in the estimate. The new method was tested on a synthetic geological inversion problem; its results compared favourably to those of Gibbs sampling (a MCMC method) on the same problem, which exhibited very significant bias. The geological prior information used in seismic inversion can be derived from real images which bear similarity to the geology anticipated within the target region of the subsurface. Such so-called training images are not always available from which this information (in the form of geostatistics) may be extracted. In this case appropriate training images may be generated by geological experts. However, this process can be costly and difficult. Thus an elicitation method (based on a genetic algorithm) is developed here which obtains the appropriate geostatistics reliably and directly from a geological expert, without the need for training images. 12 experts were asked to use the algorithm (individually) to determine the appropriate geostatistics for a physical (target) geological image. The majority of the experts were able to obtain a set of geostatistics which were consistent with the true (measured) statistics of the target image.

This thesis develops and applies nonlinear Bayesian inversion methods for localization of bowhead whales and environmental characterization, with quantitative uncertainty estimation, based on acoustic measurements from a set of asynchronous single-channel recorders in the Chukchi Sea. Warping analysis is applied to estimate modal-dispersion data from airgun sources and whale calls. Whale locations and the water-column sound-speed profile (SSP) and seabed geoacoustic properties are estimated using reversible-jump Markov-chain Monte Carlo sampling in trans-dimensional inversions that account for uncertainty in the number of SSP nodes and subbottom layers. The estimated SSP and seafloor sound speed are in excellent agreement with independent estimates, and whale localization uncertainties decrease substantially when jointly-inverting data from multiple whale calls. Bowhead whales are also localized using a fixed-dimensional inversion of time-difference-of-arrival data derived using cross-correlation for the same recorders. The nonlinear localization uncertainty estimates are found to depend strongly on the source locations and receiver geometry. / Graduate