Reservoir models are generally constructed from seismic, well logs and other related datasets using inversion methods and geostatistics. It has already been recognized by the geoscientists that such a process is prone to non-uniqueness. Practical methods for estimation of uncertainty still remain elusive. In my dissertation, I propose two new methods to estimate uncertainty in reservoir models from seismic, well logs and well production data. The first part of my research is aimed at estimating reservoir impedance models and their uncertainties from seismic data and well logs. This constitutes an inverse problem, and we recognize that multiple models can fit the measurements. A deterministic inversion based on minimization of the error between the observation and forward modeling only provides one of the best-fit models, which is usually band-limited. A complete solution should include both models and their uncertainties, which requires drawing samples from the posterior distribution. A global optimization method called very fast simulated annealing (VFSA) is commonly used to approximate posterior distribution with fast convergence. Here I address some of the limitations of VFSA by developing a new stochastic inference method, named Greedy Annealed Importance Sampling (GAIS). GAIS combines VFSA with greedy importance sampling (GIS), which uses a greedy search in the important regions located by VFSA to attain fast convergence and provide unbiased estimation. I demonstrate the performance of GAIS on post- and pre-stack data from real fields to estimate impedance models. The results indicate that GAIS can estimate both the expectation value and the uncertainties more accurately than using VFSA alone. Furthermore, principal component analysis (PCA) as an efficient parameterization method is employed together with GAIS to improve lateral continuity by simultaneous inversion of all traces. The second part of my research involves estimation of reservoir permeability models and their uncertainties using quantitative joint inversion of dynamic measurements, including synthetic production data and time-lapse seismic related data. Impacts from different objective functions or different data sets on the model uncertainty and model predictability are investigated as well. The results demonstrate that joint inversion of production data and time-lapse seismic related data (water saturation maps here) reduces model uncertainty, improves model predictability and shows superior performance than inversion using one type of data alone. / text

Pulsed neutron capture (PNC) logs are commonly used for formation evaluation behind casing and to assess time-lapse variations of hydrocarbon pore volume. Because conventional interpretation methods for sigma logs assume homogeneous formations, errors may arise, especially in thinly-bedded formations, when appraising petrophysical properties of hydrocarbon-bearing beds. There exist no quantitative interpretation methods to account for shoulder-bed effects on sigma logs acquired in sand-shale laminated reservoirs. Because of diffusion effects between dissimilar beds, sigma logs acquired in such formations do not obey mixing laws between the sigma responses of pure-sand and pure-shale end members of the sedimentary sequence. We introduce a new numerical method to simulate rapidly and accurately PNC logs. The method makes use of late-time, thermal-neutron flux sensitivity functions (FSFs) to describe the contribution of multi-layer formations toward the measured capture cross section. It includes a correction procedure based on 1D neutron diffusion theory that adapts the transport-equation-derived, base-case FSF of a homogeneous formation to simulate the response of vertically heterogeneous formations. Benchmarking exercises indicate that our simulation method yields average differences smaller than 2 c.u. within seconds of CPU time with respect to PNC logs simulated with rigorous Monte Carlo methods for a wide range of geometrical, petrophysical, and fluid properties. We develop an inversion method to reduce shoulder-bed effects on pulsed neutron capture (PNC) logs in the estimation of layer-by-layer capture cross sections, Σ. The method is based on the previously developed rapid approximation of PNC logs. Tests performed on synthetic examples that include a variety of lithology, saturating-fluid, and bed-thickness configurations confirm the efficiency, reliability, and stability of the inversion procedure. Inversion consistently improves the vertical resolution and Σ definition of PNC logs across beds thinner than 45 cm. Our fast, iterative algorithm inverts sigma logs in seconds of CPU time, and is therefore suitable for joint petrophysical interpretation with other open- and cased-hole logs. / text

Continuity along reflectors in seismic images is used via Curvelet representation to stabilize the convolution operator inversion. The Curvelet transform is a new multiscale transform that provides sparse representations for images that comprise smooth objects separated by piece-wise smooth discontinuities (e.g. seismic images). Our iterative Curvelet-regularized deconvolution algorithm combines conjugate gradient-based inversion with noise regularization performed using non-linear Curvelet coefficient thresholding. The thresholding operation enhances the sparsity of Curvelet representations. We show on a synthetic example that our algorithm provides improved resolution and continuity along reflectors as well as reduced ringing effect compared to the iterative Wiener-based deconvolution approach.

A non-linear singularity-preserving solution to the least-squares seismic imaging problem with sparseness and continuity constraints is proposed. The applied formalism explores curvelets as a directional frame that, by their sparsity on the image, and their invariance under the imaging operators, allows for a stable recovery of the amplitudes. Our method is based on the estimation of the normal operator in the form of an ’eigenvalue’ decomposition with curvelets as the ’eigenvectors’. Subsequently, we propose an inversion method that derives from estimation of the normal operator and is formulated as a convex optimization problem. Sparsity in the curvelet domain as well as continuity along the reflectors in the image domain are promoted as part of this optimization. Our method is tested with a reverse-time ’wave-equation’ migration code simulating the acoustic wave equation.

We present a new method to stabilize the three-term AVO inversion using Curvelet and Wavelet transforms. Curvelets are basis functions that effectively represent otherwise smooth objects having discontinuities along smooth curves. The applied formalism explores them to make the most of the continuity along reflectors in seismic images. Combined with Wavelets, Curvelets are used to denoise the data by penalizing high frequencies and small contributions in the AVO-cube. This approach is based on the idea that rapid amplitude changes along the ray-parameter axis are most likely due to noise. The AVO-inverse problem is linearized, formulated and solved for all (x, z) at once. Using densities and velocities of the Marmousi model to define the fluctuations in the elastic properties, the performance of the proposed method is studied and compared with the smoothing along the ray-parameter direction only. We show that our method better approximates the true data after the denoising step, especially when noise level increases.

The ability to process and respond to environmental cues requires the transformation of a sensory stimulus into an appropriate motor response, a process known as a sensorimotor transformation. The anti-saccade task can be used to investigate the ability of a subject to suppress a reflexive saccade towards a visual stimulus (pro-saccade) and generate a voluntary saccade 180° away from it. Additional steps are involved in the anti-saccade sensorimotor transformation that do not occur in the pro-saccade, which may produce performance differences between pro- and anti-saccade metrics. We were interested in exploring these differences to gain insight on the mechanism of the sensorimotor transformation of the anti-saccade and to uncover any directional biases in saccadic performance. Two experiments were performed, one in which stimuli were presented at 20 angular positions with a constant eccentricity of 12°, and another using 18 possible eccentricities along the horizontal. Pro-saccades had faster SRTs and velocities, larger amplitudes, higher accuracy and less variation in their trajectories than anti-saccades. Pro- and anti-saccade performance was shown to exhibit a similar dependence on both saccade goal direction and eccentricity. Differences manifested as a generalized reduction in anti-saccade performance that can be described as a scalar multiple of pro-saccade performance at all locations. Possible causes of this reduced performance were speculated to be i) the involvement of higher cortical structures, ii) errors in the internal representation of the stimulus, iii) sensorimotor coordinate transformation inaccuracy, and iv) online updating of the motor plan and the speed accuracy trade off inherent to saccades. The results of this study are comparable to previous monkey and human studies however certain differences were found that require further investigation. Further investigation is also required to determine the validity of the possible causes of performance reduction in the anti-saccade task and their specific contributions. / Thesis (Master, Neuroscience Studies) -- Queen's University, 2011-09-08 16:31:18.398

There are numerous different white spotting patterns in the horse, including two of particular interest tobiano and sabino. In the mouse, genetic variation in the gene KIT causes many white spotting patterns. Due to the phenotypic similarity among white spotting patterns in horses and mice, KIT was investigated as the cause of the tobiano and sabino spotting patterns in horses. Initially, the KIT cDNA sequences from horses with several spotting patterns were compared. Three single nucleotide polymorphisms (SNPs) were identified, though none were associated with a spotting pattern. Three novel splicing variants were also observed: exon 17 skipping, exon 18 skipping and alternative splicing of exon 3. Families segregating for a sabino spotting pattern (designated Sabino 1) and exon 17 skipping were discovered. Sequencing revealed a SNP (KI16+1037) within intron 16 that was completely associated with skipping of exon 17. Using a PCR-RFLP for KI16+1037, linkage was discovered for sabino spotting (LOD=9.02 for =0) and presence of the Sabino 1 allele detected in seven breeds. While all horses with this SNP exhibited the Sabino 1 phenotype, some horses with a sabino phenotype did not possess the SNP. This is most likely due to genetic heterogeneity of the phenotype. Fluorescent in situ hybridization (FISH) was used to investigate the possibility of chromosome inversion in the region of KIT. A chromosomal inversion was discovered spanning ECA3q13 to 3q21 using BAC clones containing KIT and other genes in the same region. The ECA3q inversion was completely associated with Tobiano in the eight horses tested by FISH. This inversion may disrupt regulatory sequences of the KIT gene and thereby cause tobiano spotting. Spotting patterns are important to horse breeders for aesthetic as well as economic reasons. Spotting patterns in the horse may also be an interesting scientific model. The two genetic variants discovered in this work are good examples of genetic diversity due to mechanisms other than SNPs. Study of these variants may be valuable for examining the effects of the KIT gene on health traits. In particular, the KIT gene directs many functions of the mast cell, a cell that is involved in the etiology of inflammation.

Bibliography: leaves 238-257. / ix, 257 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Develops a tomographic seismic inversion scheme that makes use of first arrivals and later arrivals simultaneously ; is easier to analyse in terms of convergence, stability and uniqueness of solutions; and is a proper non-linear inversion scheme. / Thesis (Ph.D.)--University of Adelaide, Dept. of Geology and Geophysics, 1998?

Th. doct.--Géophys. interne--Paris 7, 1996. / 1996 d'après la déclaration de dépôt légal. Bibliogr. p. 399-413. Index. Résumé en français et en anglais.

Thesis (M.S. in Physical Oceanography and Meteorology)--Naval Postgraduate School, Dec. 2004. / Thesis Advisor(s): Ching-Sang Chiu. Includes bibliographical references (p. 33). Also available online.