Modern sensing systems such as distributed acoustic sensing (DAS) can produce massive quantities of geophysical data, often in remote locations. This presents significant challenges with regards to data storage and performing efficient analysis. To address this, we have designed and implemented efficient algorithms for two commonly utilized techniques in geophysical imaging: cross-correlations, and multichannel analysis of surface waves (MASW). Our cross-correlation algorithms operate directly in the wavelet domain on compressed data without requiring a reconstruction of the original signal, reducing memory costs and improving scalabiliy. Meanwhile, our MASW implementations make use of MPI parallelism and GPUs, and present a novel problem for the GPU. / Master of Science / Modern sensor designs make it easier to collect large quantities of seismic vibration data. While this data can provide valuable insight, it is difficult to effectively store and perform analysis on such a high data volume. We propose a few new, general-purpose algorithms that enable speedy use of two common methods in geophysical modeling and data analytics: crosscorrelation, which provides a measure of similarity between signals; and multichannel analysis of surface waves, which is a seismic imaging technique. Our algorithms take advantage of hardware and software typically available on modern computers, and the mathematical properties of these two methods.

The motivation of this thesis is to provide a basic framework for treating long-range cross-correlated processes while keeping the methodology and as- sumptions as general as possible. Starting from the definition of long-range cross-correlated processes as jointly stationary processes with asymptotically power-law decaying cross-correlation function, we show that such definition implies a divergent at origin cross-power spectrum and power-law scaling of covariances of partial sums of the long-range cross-correlated processes. Chap- ter 2 describes these and other basic definitions and propositions together with necessary proofs. Chapter 3 then introduces several processes which possess long-range cross-correlated series properties. Apart from cases when the mem- ory parameter of the bivariate memory is a simple average of the parameters of the separate processes, we also introduce a new kind of process, which we call the mixed-correlated ARFIMA, which allows to control for both the bi- variate and univariate memory parameters. Chapter 4 deals with tests for a presence of long-range cross-correlations. We develop three new tests, and Monte-Carlo-simulation-based statistical power and size of the tests are com- pared. The newly introduced tests strongly surpass the already existing one. In Chapter 5,...

Foi realizado um estudo com dados físicos em superfície provenientes de implementação do modelo numérico POM e dados de clorofila a do sensor MODIS, no Atlântico Sul e Tropical, tendo como finalidade analisar as variações espaciais de suas correlações. O modelo hidrodinâmico foi submetido a uma validação com dados do Projeto PIRATA e do sensor MODIS, obtendo-se resultados satisfatórios, principalmente em superfície. A clorofila a apresenta altos valores de correlação com variáveis físicas em superfície, porém esses valores são influenciados pela presença dos sinais anual e semianual nas séries temporais. Consequentemente, as análises foram desenvolvidas após a remoção desses sinais das séries. As correlações cruzadas entre as variáveis físicas e clorofila a tiveram valores altos em módulo apresentando, de maneira geral, padrão espacial característico de correlações negativas no interior do Giro Subtropical e positivas nas demais regiões para temperatura e salinidade em superfície e elevação do nível do mar. Esse padrão espacial é mais evidente para elevação e temperatura em superfície, apresentando defasagem no tempo de resposta biológica de quase zero no interior do Giro Subtropical e Equador, com predomínio de atrasos nessa resposta nas demais regiões. A covariância cruzada foi calculada para alguns pontos ao longo do meridiano de 20ºW, para elevação de superfície e temperatura, verificando-se concordância com os resultados obtidos pela correlação cruzada. A análise espectral dessa covariância salientou a ocorrência de alguns sinais, dentre eles os sinais com períodos de 3,5 e 0,7 anos (que provavelmente estão associados aos fenômenos ENSO) e o período de 0,33 anos (que pode estar relacionado a ressonâncias do sinal anual). A assinatura desses sinais apresentou variabilidade latitudinal. / A study was performed with physical data at the surface produced by the implementation of the numerical model POM and chlorophyll a data from the MODIS sensor, in the Tropical and South Atlantic, with the aim of to analyze the spatial variations of their correlations. The hydrodynamic model was subjected to a validation with data of Project PIRATE and MODIS sensor, obtaining satisfactory results, especially at the surface. The chlorophyll a values have high correlation with physical variables at the surface, but these values are influenced by the presence of annual and semiannual signals in the time series. Then, the analyses were carried out after removal of these signals from the series. The cross-correlations between physical variables and chlorophyll a had high magnitudes showing, in general, characteristic spatial pattern of negative correlations within the Subtropical Gyre and positive in other regions, for surface temperature and salinity and sea surface level. This spatial pattern is most evident in surface elevation and temperature, presenting lag in the biological response time nearly zero within the Subtropical Gyre and Equator, with a predominance of delays of the responses in other regions. The cross-covariance is calculated for several points along the meridian of 20º W for surface elevation and surface temperature, verifying agreement with the results obtained by the cross correlation. Spectral analysis of this covariance shows the occurrence of some signals, including signals with periods of 3.5 and 0.7 years (which are probably associated with ENSO phenomena) and the period of 0.33 years (that can be related to resonances of the annual signal). The signature of these signals showed latitudinal variability.

Foi realizado um estudo com dados físicos em superfície provenientes de implementação do modelo numérico POM e dados de clorofila a do sensor MODIS, no Atlântico Sul e Tropical, tendo como finalidade analisar as variações espaciais de suas correlações. O modelo hidrodinâmico foi submetido a uma validação com dados do Projeto PIRATA e do sensor MODIS, obtendo-se resultados satisfatórios, principalmente em superfície. A clorofila a apresenta altos valores de correlação com variáveis físicas em superfície, porém esses valores são influenciados pela presença dos sinais anual e semianual nas séries temporais. Consequentemente, as análises foram desenvolvidas após a remoção desses sinais das séries. As correlações cruzadas entre as variáveis físicas e clorofila a tiveram valores altos em módulo apresentando, de maneira geral, padrão espacial característico de correlações negativas no interior do Giro Subtropical e positivas nas demais regiões para temperatura e salinidade em superfície e elevação do nível do mar. Esse padrão espacial é mais evidente para elevação e temperatura em superfície, apresentando defasagem no tempo de resposta biológica de quase zero no interior do Giro Subtropical e Equador, com predomínio de atrasos nessa resposta nas demais regiões. A covariância cruzada foi calculada para alguns pontos ao longo do meridiano de 20ºW, para elevação de superfície e temperatura, verificando-se concordância com os resultados obtidos pela correlação cruzada. A análise espectral dessa covariância salientou a ocorrência de alguns sinais, dentre eles os sinais com períodos de 3,5 e 0,7 anos (que provavelmente estão associados aos fenômenos ENSO) e o período de 0,33 anos (que pode estar relacionado a ressonâncias do sinal anual). A assinatura desses sinais apresentou variabilidade latitudinal. / A study was performed with physical data at the surface produced by the implementation of the numerical model POM and chlorophyll a data from the MODIS sensor, in the Tropical and South Atlantic, with the aim of to analyze the spatial variations of their correlations. The hydrodynamic model was subjected to a validation with data of Project PIRATE and MODIS sensor, obtaining satisfactory results, especially at the surface. The chlorophyll a values have high correlation with physical variables at the surface, but these values are influenced by the presence of annual and semiannual signals in the time series. Then, the analyses were carried out after removal of these signals from the series. The cross-correlations between physical variables and chlorophyll a had high magnitudes showing, in general, characteristic spatial pattern of negative correlations within the Subtropical Gyre and positive in other regions, for surface temperature and salinity and sea surface level. This spatial pattern is most evident in surface elevation and temperature, presenting lag in the biological response time nearly zero within the Subtropical Gyre and Equator, with a predominance of delays of the responses in other regions. The cross-covariance is calculated for several points along the meridian of 20º W for surface elevation and surface temperature, verifying agreement with the results obtained by the cross correlation. Spectral analysis of this covariance shows the occurrence of some signals, including signals with periods of 3.5 and 0.7 years (which are probably associated with ENSO phenomena) and the period of 0.33 years (that can be related to resonances of the annual signal). The signature of these signals showed latitudinal variability.