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The fractal dimension estimate for two-variable fractional Brownian motion using the maximum likelihood estimate (MLE) is developed. We formulate a model to describe the two-variable fractional Brownian motion, then derive the likelihood function for that model and estimate the fractal dimension by maximizing the likelihood function. We then compare the MLE with the box-dimension estimation method.

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The modern seismic acquisition produces a large data volume that significantly increases the cost of storage and transmission. Therefore, it is desirable to reduce the cost by compressing the seismic data. In this work, we propose a model-based compression scheme to deal with the large data volume. First, each seismic trace is modeled as a superposition of multiple exponential decaying sinusoidal waves (EDSWs). Each EDSW represents a model component and is determined by a set of parameters. Secondly, a single component parameter estimation algorithm is proposed accordingly using the particle swarm optimization (PSO) technique. We extend the algorithm for multiple model components by sequentially estimating the parameter set wave by wave. A suitable number of model components for each trace is selected according to the level of the energy of residuals. Next, the residuals are encoded using quantization coding techniques to improve the reconstruction quality. Comparison of PSO, genetic algorithm (GA), and simulated annealing (SA) is presented where the proposed model estimation technique outperforms the comparative models. The proposed model-based compression scheme is experimentally compared with the discrete cosine transform (DCT) on a real seismic dataset. The performance of the proposed model-based exhibits superiority to that of the DCT.