To achieve seismic exploration goals, conventional seismic data processing methods need subsurface information (for example velocity distribution and earth structure), which is generally inaccessible for geologically complex regions. Seismic algorithms derived from inverse scattering series (ISS) do not require subsurface information, but they directly invert seismic data (with a reference medium) order by order for achieving seismic processing objectives.

The ISS internal multiple attenuator (IMA) is data-driven and uses a constant reference velocity (water speed for marine cases, and p-wave and s-wave velocities for land cases) to accurately predict all leading order internal multiples' arrival time. However, in the land application of ISS IMA, it is hard to choose a simple constant elastic medium as the reference, due to the heterogeneous and complicated properties in near surface layer. This dissertation presents research on the ISS IMA’s sensitivity to the reference velocity in land cases. An analytical calculation of the ISS IMA is performed for a 1D layered earth with multi-component PP, PS, SP and SS (P denotes compressional wave, and S denotes shear wave) data at both normal and non-normal incidence. The computation demonstrates that the prediction of 1D ISS IMA is independent of the chosen P and S reference velocities. Numerical tests on the 1D ISS IMA algorithm are done for different types of media to demonstrate its value for land applications.

The leading order imaging subseries (LOIS) and higher order imaging subseries (HOIS) methods for the one-parameter (velocity variation only) case can fail for an acoustic medium with both velocity and density variation. Hence, a multi-parameter LOIS imaging algorithm is derived and tested in this dissertation to extend the one-parameter imaging algorithms to a 1D two-parameter (velocity and density) acoustic medium, and to a more complete earth model, eventually. The calculation of the ISS third order term for a 1D acoustic medium leads to the identification of the two-parameter LOIS algorithm, and justifies the multi-parameter LOIS and HOIS imaging conjectures. Analytical and synthetic tests are done for the two-parameter LOIS and HOIS algorithms to demonstrate their different imaging capability: HOIS is better than LOIS in locating subsurface interfaces for an acoustic medium with larger contrast and error duration in velocity and density. The multi-parameter LOIS and HOIS imaging algorithms are capable of outputting subsurface structure without using a velocity model.