I develop a number of new methods for performing slant stacking and its variants suitable to the processing of ocean bottom seismograph (OBS) data. I develop two versions of the discrete Radon transform (DRT) pair, a generalization of slant stacking, which can handle data unevenly spaced in both offset (x) and ray parameter (p). The discrete Radon transform matrix consists of two parts: a scaling matrix and a phase shift matrix. The elements in the phase shift matrix determine the amounts of the shift of given frequencies for stacking. I develop an iterative approach to perform velocity stacking, a parabolic variant of slant stacking, in the time domain. Invertibility of the transform is secured by iteration over the residual energy. A better focused version of the velocity profile is achieved. I extend conventional slant stacking of single component data to multicomponent data by performing a "vector" slant stack. The vector slant stack is performed by first transforming each component of the data, then combining the components in the $\tau$-p. This transform produces a vector field in $\tau$ and p. A color scheme using RGB intensity respectively to represent the vertical, radial and transverse components in either the x-t or the $\tau$-p domain is developed for displaying three component seismic data. I develop a technique to separate P-wave and S-waves arriving at the receiver in the vector $\tau$-p domain. I have designed an algorithm to decompose a vector common-p trace into P, SV, and SH traces. The result will be three sections in the $\tau$-p domain which can be inverse transformed to the x-t domain. (Abstract shortened by UMI.
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