AbstractsEngineering

Geophysical applications often require finding an appropriate solution to an ill-posed inverse problem. An example application is interpolating irregular or sparse data to a regular grid. This data regularization problem must be addressed appropriately before many data processing techniques can begin. In this thesis, I investigate plane-wave shaping in two and three dimensions as a data regularization algorithm, which can be used for the interpolation of seismic data and images. I use plane-wave shaping to interpolate several synthetic and field datasets and test its accuracy in image reconstruction. Because plane-wave shaping adheres to the direction of the local slopes of an image, the image-guided interpolation scheme attempts to preserve information of geologic structures. I apply several alternative interpolation schemes - formulated as an inverse problem with a convolutional operator to constrain the model space - namely: plane-wave destruction, plane-wave construction, and prediction-error filters. Investigating their iterative convergence rates, I find that plane-wave shaping converges to a solution in fewer iterations than the alternative techniques. I find that the only required parameter for this method, the smoothing radius, is best chosen to be approximately the same size as the holes for missing-data problems. The optional parameter for edge padding is best selected as approximately half of the smoothing radius. Applications of this research project include potential applications in well-log interpolation, seismic tomography, and 5-D seismic data interpolation. Advisors/Committee Members: Fomel, Sergey B. (advisor), Spikes, Kyle (committee member), Ghattas, Omar (committee member).