Geoscience is the scientific study of the planet earth and its many different natural geologic systems. It has been widely used in geology, archaeology, mineral, oil and energy exploration, oceanography, and engineering. In geoscience methods, statistical signal processing, modeling, and machine learning techniques are of great importance. In this thesis, by exploiting the correlation structure from the geophysical data, we propose novel methods for signal processing, modeling and classification and apply them to three different geophysical data acquisition systems. For hyperspectral imaging and reconstruction system in the presence of spectral noise and additive noise, we propose a novel denoising and reconstruction optimization framework by joining low rank (from correlated slices), total variation and sparsity based regularization together. Using parallel proximal algorithm (PPXA) and alternating direction method of multipliers (ADMM) as solvers, our framework improves the reconstruction SNR by 1db to 8db, compared to the state of the art. For ultrasonic data online compression and imaging system, we exploit the high correlation among successively acquired signals through cosine similarities as measurements, and model the signal as sum of complex exponentials (SOE). We propose a new method called angle based basis grouping (ABBG), which represents a group of correlated waveforms sharing the same basis but different amplitudes. ABBG generates better compression results compared to SOE-MP, SOC-CSD and SOG-SAGE methods in terms of speed, compression ratio and reconstruction accuracy. It also achieves near lossless imaging performances in parallel scanning and borehole imaging by retaining only 43% of the original data. For borehole acoustic array data classification problem in well integrity diagnosis system, we exploit the cross correlation in each depth frame, and apply slowness time coherence (STC) processing and band pass filtering to extract new features. To further exploit the correlation in and across different channels from the feature maps, we discuss several deep learning models such as Convolutional Auto Encoder, Alex net, VGG, GoogLeNet, Inception V2, Residual net, and XCeption, and show the classification accuracy gain by 3--5 % in validation and test sets. To increase the prediction accuracy on field data set, we propose a new ensemble learning framework by feeding 6 types of features from 2 modalities into a stacked model composed of 10 classifiers. The proposed method generates consistent and convincing results visually, which have been validated by the prior knowledge and experts.