Imaging and filtering by least-squares migration

New imaging and filtering methods are presented and applied to both synthetic and field data. The imaging method, denoted as least-squares migration, is developed to reduce the migration artifacts due to incomplete data. The filtering method, denoted as migration filtering, is developed to separate the signal and coherent noise components in the observed data.; These methods estimate the model parameters by calculating least-squares inverses to the modeling operators, rather than applying adjoint operators. Although the least-squares inverse operators are more computationally expensive than adjoint operators, they have better resolution and reconstruction capabilities.; In Chapter 1, the least-squares migration method is presented and applied to both synthetic and field data. The performances of the standard and the least-squares migration operators are compared for synthetic data recorded by a truncated recording aperture and/or with a large geophone spacing. Results show that least-squares migration eliminates many of the associated migration artifacts seen in the standard migration image. The method is also applied to a ground-penetrating radar data and a seismic reverse vertical seismic profiling (VSP) data, eliminating artifacts that complicate the interpretation of the migrated sections.; In Chapter 2, the migration filtering method is developed and tested on synthetic data. The method separates data arrivals according to their actual path of propagation, instead of according to a simple {dollar}x-t{dollar} moveout function. Synthetic examples for point scatterers demonstrate the strengths and the limitations of this new separation method.; In Chapter 3, the migration filtering method is applied to two field data sets: a crosswell common-shot point (CSP) gather to remove aliased tube waves and three dimensional (3-D) CSP data to attenuate the surface-related waves. Results show that the inversion method is capable of attenuating these coherent noise components. In general the migration filtering algorithm can easily be extended to a broad class of coherent noise filtering problems, including: (1) separation of primaries and multiples; (2) separation of reflections and surface waves, (3) separation of S waves and converted P-S waves; (4) separation of reflections and aliased tube waves; (5) separation of online and offline reflections in a 3-D survey; and (6) separation of multicomponent data.