The ability to synthesize recordings from surface data as if they had come from subsurface sources has allowed geophysicists to estimate subsurface properties. Either in the form of classical seismic migration which creates structural maps of the subsurface, to the more recent seismic interferometry which turns seismic sources into receivers and vice-versa, this ability has provided a rich trove of methods with which to probe the Earth's interior. While powerful, both of these techniques suffer from well-known issues. Standard migration requires data without multiply-scattered waves (multiples). Seismic interferometry, on the other hand, can be applied to full recorded data (containing multiples and other wave types), but requires sources (receivers) to be physically placed at the location from (to) one wishes to estimate responses. The Marchenko method, developed recently for the seismic setting, circumvents both of these restrictions: it creates responses from virtual subsurface sources as if measured at the surface. It requires only single-sided surface data, and a smooth estimate of the subsurface velocities. Initially developed for acoustic media, this thesis contributes the first elastic formulation of the Marchenko method, providing a more suitable setting for applications for the solid Earth. In another development, this thesis shows how the obtained virtual recordings may be used for migration. With these two contributions, this thesis shows that for elastic surface seismic data, the main drawbacks of migration and interferometry can be overcome using the Marchenko method: multiples do not harm migrated images, and sources (receivers) need not be physically placed in the medium for their responses to be accessible. In addition to the above methods, generating images devoid of multiple-related artifacts can be achieved in several other different ways. Two approaches to this are the use of a post-imaging filter, and attenuation of internal multiples in the data itself. This thesis contributes one new method using each of these approaches. First, a form of Marchenko imaging is known to create spurious reflectors, as also occurs in standard reverse-time migration (RTM). However, these artifacts usually appear at different locations in RTM and this form of Marchenko imaging. Using this insight, this thesis presents a way to combine pairs of seismic images in such a way that their differences (e.g. artifacts) are attenuated, while similarities (e.g. true reflectors) are preserved. Applying this to RTM and Marchenko-derived images markedly improves image quality. Second, this thesis presents a method to estimate multiples in the data. Multiples can either be migrated on their own to aid in interpretation, or be adaptatively removed from the data to improve image quality. However, because of the nature of adaptive subtraction, this second method may harm primary energy. To avoid this problem, this thesis develops a final method to directly image using only primary energy in the recorded data using only a small number of virtual points. This method bypasses the need for multiple removal and the estimation of subsurface responses at every depth location. In addition, primaries from particular reflectors may be particularly selected such that they can be imaged individually. Overall this thesis provides several new ways to use surface seismic data in such a way that multiples do not hamper the end product of seismic data processing: the seismic image. It demonstrates this use on synthetic and real data, proving their effectiveness.

This thesis is about high–dimensional problems considered under the so{called Kolmogorov condition. Hence, we consider research questions related to random matrices with p rows (corresponding to the parameters) and n columns (corresponding to the sample size), where p &gt; n, assuming that the ratio <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%5Cfrac%7Bp%7D%7Bn%7D" /> converges when the number of parameters and the sample size increase. We focus on the eigenvalue distribution of the considered matrices, since it is a well–known information–carrying object. The spectral distribution with compact support is fully characterized by its moments, i.e., by the normalized expectation of the trace of powers of the matrices. Moreover, such an expectation can be seen as a free moment in the non–commutative space of random matrices of size p x p equipped with the functional <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20%5Cfrac%7B1%7D%7Bp%7DE%5BTr%5C%7B%5Ccdot%5C%7D%5D" />. Here, the connections with free probability theory arise. In the relation to that eld we investigate the closed form of the asymptotic spectral distribution for the sum of the quadratic forms. Moreover, we put a free cumulant–moment relation formula that is based on the summation over partitions of the number. This formula is an alternative to the free cumulant{moment relation given through non{crossing partitions ofthe set. Furthermore, we investigate the normalized <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20E%5B%5Cprod_%7Bi=1%7D%5Ek%20Tr%5C%7BW%5E%7Bm_i%7D%5C%7D%5D" /> and derive, using the dierentiation with respect to some symmetric matrix, a recursive formula for that expectation. That allows us to re–establish moments of the Marcenko–Pastur distribution, and hence the recursive relation for the Catalan numbers. In this thesis we also prove that the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20%5Cprod_%7Bi=1%7D%5Ek%20Tr%5C%7BW%5E%7Bm_i%7D%5C%7D" />, where <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20W%5Csim%5Cmathcal%7BW%7D_p(I_p,n)" />, is a consistent estimator of the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20E%5B%5Cprod_%7Bi=1%7D%5Ek%20Tr%5C%7BW%5E%7Bm_i%7D%5C%7D%5D" />. We consider <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20Y_t=%5Csqrt%7Bnp%7D%5Cbig(%5Cfrac%7B1%7D%7Bp%7DTr%5Cbig%5C%7B%5Cbig(%5Cfrac%7B1%7D%7Bn%7DW%5Cbig)%5Et%5Cbig%5C%7D-m%5E%7B(t)%7D_1%20(n,p)%5Cbig)," />, where <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20m%5E%7B(t)%7D_1%20(n,p)=E%5Cbig%5B%5Cfrac%7B1%7D%7Bp%7DTr%5Cbig%5C%7B%5Cbig(%5Cfrac%7B1%7D%7Bn%7DW%5Cbig)%5Et%5Cbig%5C%7D%5Cbig%5D" />, which is proven to be normally distributed. Moreover, we propose, based on these random variables, a test for the identity of the covariance matrix using a goodness{of{t approach. The test performs very well regarding the power of the test compared to some presented alternatives for both the high–dimensional data (p &gt; n) and the multivariate data (p ≤ n).

This thesis is about high–dimensional problems considered under the so{called Kolmogorov condition. Hence, we consider research questions related to random matrices with p rows (corresponding to the parameters) and n columns (corresponding to the sample size), where p &gt; n, assuming that the ratio <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%5Cfrac%7Bp%7D%7Bn%7D" /> converges when the number of parameters and the sample size increase. We focus on the eigenvalue distribution of the considered matrices, since it is a well–known information–carrying object. The spectral distribution with compact support is fully characterized by its moments, i.e., by the normalized expectation of the trace of powers of the matrices. Moreover, such an expectation can be seen as a free moment in the non–commutative space of random matrices of size p x p equipped with the functional <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20%5Cfrac%7B1%7D%7Bp%7DE%5BTr%5C%7B%5Ccdot%5C%7D%5D" />. Here, the connections with free probability theory arise. In the relation to that eld we investigate the closed form of the asymptotic spectral distribution for the sum of the quadratic forms. Moreover, we put a free cumulant–moment relation formula that is based on the summation over partitions of the number. This formula is an alternative to the free cumulant{moment relation given through non{crossing partitions ofthe set. Furthermore, we investigate the normalized <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20E%5B%5Cprod_%7Bi=1%7D%5Ek%20Tr%5C%7BW%5E%7Bm_i%7D%5C%7D%5D" /> and derive, using the dierentiation with respect to some symmetric matrix, a recursive formula for that expectation. That allows us to re–establish moments of the Marcenko–Pastur distribution, and hence the recursive relation for the Catalan numbers. In this thesis we also prove that the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20%5Cprod_%7Bi=1%7D%5Ek%20Tr%5C%7BW%5E%7Bm_i%7D%5C%7D" />, where <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20W%5Csim%5Cmathcal%7BW%7D_p(I_p,n)" />, is a consistent estimator of the <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20E%5B%5Cprod_%7Bi=1%7D%5Ek%20Tr%5C%7BW%5E%7Bm_i%7D%5C%7D%5D" />. We consider <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20Y_t=%5Csqrt%7Bnp%7D%5Cbig(%5Cfrac%7B1%7D%7Bp%7DTr%5Cbig%5C%7B%5Cbig(%5Cfrac%7B1%7D%7Bn%7DW%5Cbig)%5Et%5Cbig%5C%7D-m%5E%7B(t)%7D_1%20(n,p)%5Cbig)," />, where <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Csmall%20m%5E%7B(t)%7D_1%20(n,p)=E%5Cbig%5B%5Cfrac%7B1%7D%7Bp%7DTr%5Cbig%5C%7B%5Cbig(%5Cfrac%7B1%7D%7Bn%7DW%5Cbig)%5Et%5Cbig%5C%7D%5Cbig%5D" />, which is proven to be normally distributed. Moreover, we propose, based on these random variables, a test for the identity of the covariance matrix using a goodness{of{t approach. The test performs very well regarding the power of the test compared to some presented alternatives for both the high–dimensional data (p &gt; n) and the multivariate data (p ≤ n).

Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-03-28T19:29:10Z No. of bitstreams: 1 HaulissonJodyBatistaDaCosta_TESE.pdf: 2105364 bytes, checksum: 02ce6394c65e4f1c777677345eac66c6 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-03-29T18:57:57Z (GMT) No. of bitstreams: 1 HaulissonJodyBatistaDaCosta_TESE.pdf: 2105364 bytes, checksum: 02ce6394c65e4f1c777677345eac66c6 (MD5) / Made available in DSpace on 2017-03-29T18:57:57Z (GMT). No. of bitstreams: 1 HaulissonJodyBatistaDaCosta_TESE.pdf: 2105364 bytes, checksum: 02ce6394c65e4f1c777677345eac66c6 (MD5) Previous issue date: 2016-08-22 / A evolu??o da comunica??o sem fio traz suporte a m?ltiplos dispositivos que, simultaneamente, transmitem altas taxas de dados. T?cnicas emergentes de comunica??o LSMIMO permitem explorar o aumento da capacidade para a moderniza??o dos sistemas de transmiss?o. Apesar da pr?pria caracter?stica do canal de multipercurso proporcionar efici?ncia espectral, a complexidade computacional dos m?todos de detec??o LS-MIMO tornam-se proibitivos em sistemas com elevada quantidades de antenas. Procurando aumentar a quantidade de antenas empregadas na detec??o MIMO, este trabalho prop?e adaptar o m?todo iterativo de Richardson ao conceito de matrizes aleat?rias estabelecido por Marchenko-Pastur e ao conceito de execu??o paralela de modo a adequ?-lo ? aplica??o em sistema LS-MIMO. O m?todo iterativo de Richardson exige condi??es para resolu??o linear que restringem sua ampla aplica??o. Contudo, a compreens?o do canal permite estabelecer adapta??es que suprem as exig?ncias do m?todo. Os efeitos do canal conceituados por Marchenko-Pastur permitem modificar o m?todo, atrelando a estabilidade ? quantidade de antenas de maneira que o aumento dessa propor??o contribui tanto para a melhoria da converg?ncia quanto para a redu??o relativa das itera??es. Adicionalmente, a execu??o compartilhada com o m?todo de decodifica??o proporciona uma divis?o de carga de trabalho, de modo a permitir uma taxa de transfer?ncia que supera outros m?todos. Os resultados levantados a partir das an?lises comparativas entre outras propostas de execu??o paralela mostraram de forma in?dita a capacidade de detec??o em larga escala. Ainda, a proposta mostrou um n?vel de adaptabilidade que permite variar a rela??o entre taxa de transfer?ncia de dados e complexidade. Nesse sentido, o m?todo mostrou que com taxas de transmiss?o equipar?veis com outras propostas permite aumentar seu desempenho em 150% abdicando 1,75 dB da rela??o sinal ru?do. Baseando-se nessa abordagem, o sistema mostra um desempenho superior as outras estrat?gias executadas em GPU que apontam um incremento significativo na capacidade de transmiss?o paralela. A proposta, tamb?m, mostra aspectos escal?veis que permitem alcan?ar um desempenho na ordem de Gb=s pela inser??o de outros dispositivos (GPUs) operando paralelamente no sistema. / The evolution of wireless communications must support multiples devices and maintain high-speed data transmission. The emerging Large-Scale MIMO techniques allows improving the capacity for the next generations of communications systems. Although the benefit of multipath involves the spectral efficiency, the computational complexity of LS-MIMO detection becomes prohibitive in large systems. Seeking to overcome it, we propose to adapt the Richardson iterative method to the LS-MIMO with random matrices theory by concepts of Marchenko-Pastur and parallel executions. This method requires restricted conditions for the linear resolution that limits its applications. However, the channel knowledge allows establishing adaptations that supply the requirements of the method. The channel effect explained by Marchenko-Pastur allows associating the stability of the process with an increase in the numbers of antennas that contributed to improved the convergence and reduction the iterations. Furthermore, the shared execution with decoding blocks provide a workload distribution that surpasses the throughput of others detections. The results achieved from the comparative analysis of other proposals showed an unprecedented way to increase capability on the large scale detection and provides an efficient parallel processing. Also, the proposal demonstrated a level of adaptability that allows diversifying the association between transmission rate and complexity. Therefore, the implementation of Richardson detection establishes that the transmission rate is comparable with other projects and the increasing of 1.74dB SNR improve 150% at throughput. Based on this approach, the execution shows a significant increase in parallel transmission capacity when implemented on GPU. Also, the implementation shows scalable aspects that allow increasing the performance to Gb/s by insertion of others parallels devices (GPUs) in the system.