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Amicable T-matrices and applicationsGholamiangonabadi, Hamed January 2012 (has links)
Our main aim in this thesis is to produce new T-matrices from the set of existing
T-matrices. In Theorem 4.3 a multiplication method is introduced to generate new
T-matrices of order st, provided that there are some specially structured T-matrices
of orders s and t. A class of properly amicable and double disjoint T-matrices are
introduced. A number of properly amicable T-matrices are constructed which includes
2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 18, 22.
To keep the new matrices disjoint an extra condition is imposed on one set of
T-matrices and named double disjoint T-matrices. It is shown that there are some
T-matrices that are both double disjoint and properly amicable. Using these matrices
an infinite family of new T-matrices are constructed.
We then turn our attention to the application of T-matrices to construct orthogonal
designs and complex Hadamard matrices.
Using T-matrices some orthogonal designs constructed from 16 circulant matrices
are constructed. It is known that having T-matrices of order t and orthogonal designs
constructible from 16 circulant matrices lead to an infinite family of orthogonal designs.
Using amicable T-matrices some complex Hadamard matrices are shown to exist. / iii, 49 leaves ; 29 cm
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A T-Matrix Approach to Heavy Quark Interaction with Thermal Gluons in a Quark Gluon PlasmaHuggins, Kyle 2012 August 1900 (has links)
The interactions of heavy quarks within the Quark Gluon Plasma (QGP) are interpreted utilizing an elastic, thermodynamic, 2-body T-matrix in order to calculate drag coefficients of heavy-quark systems derived from a Fokker-Planck equation. A spacelike momentum constraint is employed and produces an effective, color dependent potential with the addition of relativistic factors motivated by the appropriate Feynman diagrams. Hard Thermal Loop (HTL) corrections are interpreted in the context of a finite temperature quark-gluon system, allowing a non-perturbative determination of the gluon's contribution to the drag coefficient. An enhancement of the relaxation rate of ~2 is observed at low momenta, leading to an enhancement of the overall relaxation rate of 20%, while the high-p limit approaches a perturbative level. The importance of a nonperturbative treatment of the QGP to reproduce the dynamical drag coefficient is illustrated.
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Electromagnetic detection of buried dielectric targets /Schneider, John Brand. January 1991 (has links)
Thesis (Ph. D.)--University of Washington, 1991. / Vita. Includes bibliographical references (leaves [154]-167).
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Inferência de hidrometeoros a partir de um radar meteorológico de dupla polarização banda X / Inference of hydrometeors from a X-band dual polarization meteorological radar.Ramirez, Yusvelis Maribel Barzaga 12 July 2018 (has links)
Este estudo apresentou uma metodologia para inferir hidrometeoros a partir de medidas polarimétricas de um radar meteorológico de dupla polarização banda X. A metodologia consiste em uma abordagem teórica baseada em simulações numéricas com um modelo de espalhamento Mie (T M atrix e M ueller) e uma experimental pautada na aplicação de um algoritmo de classificação de hidrometeoros (Dolan and Rutledge [2009]). As si- mulações teóricas foram utilizadas para estudar os efeitos da distribuição de tamanho de gotas, temperatura dos hidrometeoros, ângulo de elevação e mistura de hidrometeoros a partir do fator de refletividade do radar (Z), refletividade diferencial (Z DR ), fase diferen- cial especifica (K DP ) e coeficiente de correlação( HV ). Os valores de Z DR são 0.5 dBZ maior para a frequência de banda X do que para um banda S. A partir de Z maior que 45 dBZ K DP começa a ficar maior que 0. Já HV começa a diminuir quando Z é maior que 25 dBZ. Não se observa variações significativas para o graupel, porém para granizo K DP é maior que 0 quando Z é maior que 15 dBZ, entretanto, para água, os valores são consideravelmente menores. Os efeitos de temperatura só são notados quando Z é maior que 60 dBZ. Ao analisar o efeito da elevação, observa-se que Z DR diminui com o aumento da elevação, sendo mais sensível para Z maiores, o mesmo efeito é observado para K DP e HV . Estas variações são mais sensíveis para água e granizo do que para o graupel. Comparando as distribuições exponencial e gama para considerar os efeitos da distribuição do tamanho de gotas para o caso da chuva, nota-se que a distribuição exponenciais é maior que a gama quando as gotas aumentam seu tamanho e diminui sua concentração, devido que na simulação teórica foi utilizado N 0 fixo.Ao analisar os efeitos da co-existência de água e graupel, temos que as gotas de água dominam o sinal de Z quando Z for maior que 30 dBZ, já K DP será positivo(negativo) quando Z for maior(menor) que 35 dBZ da água, desde que Z do graupel seja menor que 10 dBZ, já HV tende a ficar próximo de 1 quanto mais graupel é observado. Para a mistura de granizo e água, Z da água domina o do granizo quando Z é maior que 45 dBZ, K DP é maior(menor) que zero quando Z for maior (menor) que 25 dBZ desde que Z do granizo seja menor que 10 dBZ, já Z DR da água(granizo) domina o do granizo(água) quando Z for maior(menor) que 45 dBZ. Na parte experimental, dois casos observados durante o experimento de campo do Projeto CHUVA no Vale do Paraíba em 8 de Fevereiro e 22 de Março de 2012 foram utilizados. A classificação de hidrometeoros segundo Dolan and Rutledge [2009] indicaram a presença de chuva próximo da superfície proveniente de graupel e granizo. Acima dos 5 km foram identificados a presença de graupel,granizo e cristais de gelo. Ao examinar as regiões classificadas como granizo e graupel dentro da região de 0 e 15 C com os resultados teóricos, é possível explicar a presença concomitante de água e granizo e água e graupel nestas regiões. / This study presents a methodology for inferring hydrometeors from polarimetric mea- surements of a X band double polarization meteorological radar. The methodology consists of a theoretical approach based on numerical simulations with a Mie scattering model (T-Matrix and Mueller) and an experimental approach based on the application of a classification algorithm of hydrometeors (Dolan and Rutledge [2009]). The theoretical simulations were used to study the effects of droplet size distribution, hydrometeor tem- perature, elevation angle and mixture of hydrometeors from radar reflectivity factor (Z), differential reflectivity (Z DR ), specific differential phase (K DP ) and correlation coefficient ( HV ). The values of Z DR are 0.5 dBZ higher for the X band frequency than for the S band frequency. From Z greater than 45 dBZ, K DP starts to get higher than 0. When Z is greater than 25 dBZ, HV starts to decrease. No significant variations are observed for the graupel, however for hail, K DP is greater than 0 when Z is greater than 15 dBZ, but these values were much lower than for water. Temperature effects are only noticed when Z is greater than 60 dBZ. When analyzing the effect of elevation, it is observed that Z DR decreases with increasing elevation, being more sensitive to Z larger; the same effect is observed for K DP and HV . These variations are more sensitive to water and hail than to the graupel. Comparing the exponential and gamma distributions to consider the effects of droplet size distribution in the case of rain, it is noted that the exponential distribution is larger than the gamma when the droplets increase in size and decrease in concentration, due to the fact that in the simulation was used N 0 fixed. When analyzing the effects of co-existence of water and graupel, we have that the water droplets dominate the Z signal when Z is greater than 30 dBZ, K DP will be positive (negative) when Z is greater (lower) than 35 dBZ of water, since Z of the graupel is less than 10 dBZ and HV tends to be close to 1 when more graupel is observed. For the mixture of hail and water, Z of water dominates that of hail when Z is greater than 45 dBZ, K DP is larger (smaller) than zero when Z is larger (smaller) than 25 dBZ since Z of hail is less than 10 dBZ and Z DR of water (hail) dominates hail (water) when Z is greater (lower) than 45 dBZ. In the experimental part, two cases observed during the field experiment of the RAIN Project in Vale do Paraíba on February 8 and March 22, 2012 were used. The classification of hydrometeors according to Dolan and Rutledge [2009] indicated the presence of rain near the surface coming of graupel and hail. Above 5 km were identified the presence of graupel, hail and ice crystals. When examining the regions classified as hail and graupel within the region of 0 and 15 C with the theoretical results, it is possible to explain the concomitant presence of water and hail and water and graupel in these regions.
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Inferência de hidrometeoros a partir de um radar meteorológico de dupla polarização banda X / Inference of hydrometeors from a X-band dual polarization meteorological radar.Yusvelis Maribel Barzaga Ramirez 12 July 2018 (has links)
Este estudo apresentou uma metodologia para inferir hidrometeoros a partir de medidas polarimétricas de um radar meteorológico de dupla polarização banda X. A metodologia consiste em uma abordagem teórica baseada em simulações numéricas com um modelo de espalhamento Mie (T M atrix e M ueller) e uma experimental pautada na aplicação de um algoritmo de classificação de hidrometeoros (Dolan and Rutledge [2009]). As si- mulações teóricas foram utilizadas para estudar os efeitos da distribuição de tamanho de gotas, temperatura dos hidrometeoros, ângulo de elevação e mistura de hidrometeoros a partir do fator de refletividade do radar (Z), refletividade diferencial (Z DR ), fase diferen- cial especifica (K DP ) e coeficiente de correlação( HV ). Os valores de Z DR são 0.5 dBZ maior para a frequência de banda X do que para um banda S. A partir de Z maior que 45 dBZ K DP começa a ficar maior que 0. Já HV começa a diminuir quando Z é maior que 25 dBZ. Não se observa variações significativas para o graupel, porém para granizo K DP é maior que 0 quando Z é maior que 15 dBZ, entretanto, para água, os valores são consideravelmente menores. Os efeitos de temperatura só são notados quando Z é maior que 60 dBZ. Ao analisar o efeito da elevação, observa-se que Z DR diminui com o aumento da elevação, sendo mais sensível para Z maiores, o mesmo efeito é observado para K DP e HV . Estas variações são mais sensíveis para água e granizo do que para o graupel. Comparando as distribuições exponencial e gama para considerar os efeitos da distribuição do tamanho de gotas para o caso da chuva, nota-se que a distribuição exponenciais é maior que a gama quando as gotas aumentam seu tamanho e diminui sua concentração, devido que na simulação teórica foi utilizado N 0 fixo.Ao analisar os efeitos da co-existência de água e graupel, temos que as gotas de água dominam o sinal de Z quando Z for maior que 30 dBZ, já K DP será positivo(negativo) quando Z for maior(menor) que 35 dBZ da água, desde que Z do graupel seja menor que 10 dBZ, já HV tende a ficar próximo de 1 quanto mais graupel é observado. Para a mistura de granizo e água, Z da água domina o do granizo quando Z é maior que 45 dBZ, K DP é maior(menor) que zero quando Z for maior (menor) que 25 dBZ desde que Z do granizo seja menor que 10 dBZ, já Z DR da água(granizo) domina o do granizo(água) quando Z for maior(menor) que 45 dBZ. Na parte experimental, dois casos observados durante o experimento de campo do Projeto CHUVA no Vale do Paraíba em 8 de Fevereiro e 22 de Março de 2012 foram utilizados. A classificação de hidrometeoros segundo Dolan and Rutledge [2009] indicaram a presença de chuva próximo da superfície proveniente de graupel e granizo. Acima dos 5 km foram identificados a presença de graupel,granizo e cristais de gelo. Ao examinar as regiões classificadas como granizo e graupel dentro da região de 0 e 15 C com os resultados teóricos, é possível explicar a presença concomitante de água e granizo e água e graupel nestas regiões. / This study presents a methodology for inferring hydrometeors from polarimetric mea- surements of a X band double polarization meteorological radar. The methodology consists of a theoretical approach based on numerical simulations with a Mie scattering model (T-Matrix and Mueller) and an experimental approach based on the application of a classification algorithm of hydrometeors (Dolan and Rutledge [2009]). The theoretical simulations were used to study the effects of droplet size distribution, hydrometeor tem- perature, elevation angle and mixture of hydrometeors from radar reflectivity factor (Z), differential reflectivity (Z DR ), specific differential phase (K DP ) and correlation coefficient ( HV ). The values of Z DR are 0.5 dBZ higher for the X band frequency than for the S band frequency. From Z greater than 45 dBZ, K DP starts to get higher than 0. When Z is greater than 25 dBZ, HV starts to decrease. No significant variations are observed for the graupel, however for hail, K DP is greater than 0 when Z is greater than 15 dBZ, but these values were much lower than for water. Temperature effects are only noticed when Z is greater than 60 dBZ. When analyzing the effect of elevation, it is observed that Z DR decreases with increasing elevation, being more sensitive to Z larger; the same effect is observed for K DP and HV . These variations are more sensitive to water and hail than to the graupel. Comparing the exponential and gamma distributions to consider the effects of droplet size distribution in the case of rain, it is noted that the exponential distribution is larger than the gamma when the droplets increase in size and decrease in concentration, due to the fact that in the simulation was used N 0 fixed. When analyzing the effects of co-existence of water and graupel, we have that the water droplets dominate the Z signal when Z is greater than 30 dBZ, K DP will be positive (negative) when Z is greater (lower) than 35 dBZ of water, since Z of the graupel is less than 10 dBZ and HV tends to be close to 1 when more graupel is observed. For the mixture of hail and water, Z of water dominates that of hail when Z is greater than 45 dBZ, K DP is larger (smaller) than zero when Z is larger (smaller) than 25 dBZ since Z of hail is less than 10 dBZ and Z DR of water (hail) dominates hail (water) when Z is greater (lower) than 45 dBZ. In the experimental part, two cases observed during the field experiment of the RAIN Project in Vale do Paraíba on February 8 and March 22, 2012 were used. The classification of hydrometeors according to Dolan and Rutledge [2009] indicated the presence of rain near the surface coming of graupel and hail. Above 5 km were identified the presence of graupel, hail and ice crystals. When examining the regions classified as hail and graupel within the region of 0 and 15 C with the theoretical results, it is possible to explain the concomitant presence of water and hail and water and graupel in these regions.
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Multiple electromagnetic scattering by spheres using the T-matrix formulation / Elektromagnetisk multipelspridning från sfärer med T-matrismetodenWallin, Marina January 2015 (has links)
Low observable technology is used in order to prevent detection, or to delay detection. Radar cross section is an important parameter in aircraft survivability since it measures how detectable an object is with radar. To find the radar cross section Maxwell's equations are solved numerically in the time-domain using a finite difference scheme. This numerical method called Finite Difference Time Domain is very suitable for structures including complex materials. However, this numerical method needs to be verified for large scale simulations, due to numerical dispersion errors. Therefore it is desirable to verify the accuracy of the numerical simulations. In this project, the analytical solution to the multiple scattering by two spheres is implemented using the T-matrix formulation. The analytical solution to the scattering problem is first validated with the analytical Mie-series solution then compared to the Finite Difference Time Domain implementation. The results imply that the difference between the numerical and analytical solution is larger for higher frequencies and larger computational volumes. / Smygteknik används för att förhindra detektering, eller för att fördröja detektion av ett flygplan. Radarmålarea är en viktig parameter för skyddsprestanda hos flygplan eftersom den mäter hur detekterbar ett föremål är med radar. För att hitta radarmålarean löses Maxwells ekvationer numeriskt i tidsdomänen med hjälp av ett finit differensschema. Den numeriska metoden som kallas Finita differensmetoden i tidsdomän, är mycket lämplig för strukturer med komplexa material. Den numeriska metoden behöver valideras för storskaliga simuleringar eftersom det förekommer felaktigheter på grund av den numeriska dispersionen. Därför är det önskvärt att kontrollera riktigheten av de numeriska simuleringarna. I detta projekt, är den analytiska lösningen till multipelspridning av två sfärer implementerad med hjälp av T-matrismetoden. Den analytiska lösningen på spridningsproblemet valideras först mot den analytiska Mie-serielösningen och sedan jämförs den med resultatet av simuleringarna med Finita differensmetoden i tidsdomän. Resultaten antyder att skillnaden mellan den numeriska och analytiska lösningen är större för högre frekvenser och större beräkningsvolymer.
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Scattering Properties of Oriented Hexagonal Ice CrystalsZhang, Feng 14 January 2010 (has links)
To interpret the data from spaceborn lidar measurements, one must have a basic
understanding of the backscattering of oriented ice particles. The conventional raytracing
method is not applicable to the scattering of light by oriented particles. In this
study, the dipole approximation (DDA) method is employed to the scattering of light
on oriented hexagonal ice columns and plates with various tilting angles. It is found
that the oriented hexagonal ice particles tend to have strong backscattering intensity
with low depolarization ratios which are strongly dependant on the tilting angle of
oriented particles. The present results show that the e ffect of particle orientation
plays an important role in determining the optical properties of ice clouds consisting
of horizontally oriented ice crystals.
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Light Scattering Problem and its Application in Atmospheric ScienceMeng, Zhaokai 2010 December 1900 (has links)
The light scattering problem and its application in atmospheric science is studied
in this thesis. In the first part of this thesis, light scattering theory of single irregular
particles is investigated. We first introduce the basic concepts of the light scattering
problem. T-matrix ansatz, as well as the null-field technique, are introduced in the
following sections. Three geometries, including sphere, cylinder and hexagonal column,
are defined subsequently. Corresponding light scattering properties (i.e., T-matrix and
Mueller Matrix) of those models with arbitrary sizes are simulated via the T-matrix
method.
In order to improve the efficiency for the algorithms of single-light scattering, we
present a user-friendly database software package of the single-scattering properties of
individual dust-like aerosol particles. The second part of this thesis describes this
database in detail. Its application to radiative transfer calculations in a spectral region
from ultraviolet (UV) to far-infrared (far-IR) is introduced as well. To expand the degree
of morphological freedom of the commonly used spheroidal and spherical models, triaxial
ellipsoids were assumed to be the overall shape of dust-like aerosol particles. The
software package allows for the derivation of the bulk optical properties for a given distribution of particle microphysical parameters (i.e., refractive index, size parameter
and two aspect ratios). The array-oriented single-scattering property data sets are stored
in the NetCDF format.
The third part of this thesis examines the applicability of the tri-axial ellipsoidal
dust model. In this part, the newly built database is equipped in the study. The precomputed
optical properties of tri-axial models are imported to a polarized addingdoubling
radiative transfer (RT) model. The radiative transfer property of a well-defined
atmosphere layer is consequently simulated. Furthermore, several trial retrieval
procedures are taken based on a combination of intensity and polarization in the results of
RT simulation. The retrieval results show a high precision and indicate a further
application in realistic studies.
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Optical properties of mineral dust aerosol including analysis of particle size, composition, and shape effects, and the impact of physical and chemical processingAlexander, Jennifer Mary 01 July 2015 (has links)
Atmospheric mineral dust has a large impact on the earth’s radiation balance and climate. The radiative effects of mineral dust depend on factors including, particle size, shape, and composition which can all be extremely complex. Mineral dust particles are typically irregular in shape and can include sharp edges, voids, and fine scale surface roughness. Particle shape can also depend on the type of mineral and can vary as a function of particle size. In addition, atmospheric mineral dust is a complex mixture of different minerals as well as other, possibly organic, components that have been mixed in while these particles are suspended in the atmosphere. Aerosol optical properties are investigated in this work, including studies of the effect of particle size, shape, and composition on the infrared (IR) extinction and visible scattering properties in order to achieve more accurate modeling methods.
Studies of particle shape effects on dust optical properties for single component mineral samples of silicate clay and diatomaceous earth are carried out here first. Experimental measurements are modeled using T-matrix theory in a uniform spheroid approximation. Previous efforts to simulate the measured optical properties of silicate clay, using models that assumed particle shape was independent of particle size, have achieved only limited success. However, a model which accounts for a correlation between particle size and shape for the silicate clays offers a large improvement over earlier modeling approaches. Diatomaceous earth is also studied as an example of a single component mineral dust aerosol with extreme particle shapes. A particle shape distribution, determined by fitting the experimental IR extinction data, used as a basis for modeling the visible light scattering properties. While the visible simulations show only modestly good agreement with the scattering data, the fits are generally better than those obtained using more commonly invoked particle shape distributions.
The next goal of this work is to investigate if modeling methods developed in the studies of single mineral components can be generalized to predict the optical properties of more authentic aerosol samples which are complex mixtures of different minerals. Samples of Saharan sand, Iowa loess, and Arizona road dust are used here as test cases. T-matrix based simulations of the authentic samples, using measured particle size distributions, empirical mineralogies, and a priori particle shape models for each mineral component are directly compared with the measured IR extinction spectra and visible scattering profiles. This modeling approach offers a significant improvement over more commonly applied models that ignore variations in particle shape with size or mineralogy and include only a moderate range of shape parameters.
Mineral dust samples processed with organic acids and humic material are also studied in order to explore how the optical properties of dust can change after being aged in the atmosphere. Processed samples include quartz mixed with humic material, and calcite reacted with acetic and oxalic acid. Clear differences in the light scattering properties are observed for all three processed mineral dust samples when compared to the unprocessed mineral dust or organic salt products. These interactions result in both internal and external mixtures depending on the sample. In addition, the presence of these organic materials can alter the mineral dust particle shape. Overall, however, these results demonstrate the need to account for the effects of atmospheric aging of mineral dust on aerosol optical properties.
Particle shape can also affect the aerodynamic properties of mineral dust aerosol. In order to account for these effects, the dynamic shape factor is used to give a measure of particle asphericity. Dynamic shape factors of quartz are measured by mass and mobility selecting particles and measuring their vacuum aerodynamic diameter. From this, dynamic shape factors in both the transition and vacuum regime can be derived. The measured dynamic shape factors of quartz agree quite well with the spheroidal shape distributions derived through studies of the optical properties.
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[en] ROCK PHYSICS MODELING EVALUATION FOR CARBONATE RESERVOIRS / [pt] AVALIAÇÃO DE MODELOS DE FÍSICA DE ROCHAS PARA RESERVATÓRIOS CARBONÁTICOSJONATAN DE OLIVEIRA DIAS 06 February 2019 (has links)
[pt] Desde a década de 80, abordagens data-driven têm sido utilizadas para identificação de fluidos e caracterização de reservatórios carbonáticos e siliciclásticos principalmente em relação à análise das amplitudes sísmicas. No entanto, técnicas aplicadas com sucesso para rochas siliciclásticas, como por exemplo: Análise AVO, inversões sísmicas e IDH (Indicadores Diretos de Hidrocarbonetos) revelaram não obter o mesmo êxito para reservatórios carbonáticos heterogêneos. Em contrapartida, diversos artigos
mostram que fluxos de caracterização de reservatórios com modelos de física de rochas incorporados têm alcançado grande sucesso para obtenção de propriedades petrofísicas e atributos elásticos de ambas as rochas, utilizando sísmicas e well logs, em uma abordagem model-driven, focada nas características microestruturais do reservatório. Dessa forma, levando em consideração a importância de se utilizar modelos de física de rochas no escopo da caracterização de reservatórios, dois modelos de física de rochas - Xu e Payne e T-Matrix - foram aplicados, comparados e seus parâmetros foram estocasticamente avaliados e otimizados em um arcabouço Bayesiano. Através dessa abordagem, foi possível estimar, de uma forma confiável, os atributos elásticos de um reservatório carbonático (coquinas) levando em
consideração diversos tipos de incertezas. Além disso, após a calibração e validação de ambos os modelos de física de rochas para diferentes poços, análises de sensibilidade foram realizadas para compreensão de forma quantitativa do comportamento dos atributos elásticos das coquinas em relação às alterações do conteúdo mineralógico, tipos de poro e fluidos desse reservatório. / [en] Since the 80 s, data-driven approaches have been used for fluids identification and reservoir characterization of siliciclastic and carbonate rocks mainly regarding seismic amplitudes analyses. However, techniques successfully applied for siliciclastic rocks, such as: AVO analysis, seismic inversions and DHI (Direct Hydrocarbon Indicators) ranking revealed not have achieved the same outstanding and reliable results for heterogeneous carbonate rocks. On the other hand, several articles demonstrate that
reservoir characterization workflows with rock physics models embedded have been reaching a robust success in order to obtain petrophysical properties and elastic attributes of both rocks, from the seismic and well logs, in a model-driven approach focused on the reservoirs microstructural information. In this way, taking into account the importance of applying rock physics models in the scope of reservoir characterization, two rock physics models - Xu and Payne and T-Matrix - were applied, compared
and their parameters were stochastically evaluated and optimized in a Bayesian framework. Through this approach, it was possible to estimate, in a reliable manner, the elastic attributes of a carbonate reservoir (coquinas) taking into consideration different kinds of uncertainties. Furthermore, after the calibration in the well location and validation of both rock physics models for other wells, sensitivity analyses were conducted in order to quantitatively understand how the coquinas elastic attributes behave regarding the variations in the reservoir mineralogical content, pore shapes and fluids.
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