Abstract
An initial study is performed in which dynamically focused Gaussian beams are investigated for seismic imaging. Focused Gaussian beams away from the source and receiver plane allow the narrowest and planar portions of the beams to occur at the depth of a specific target structure. To match the seismic data, quadratic phase corrections are required for the local slant stacks of the surface data. To provide additional control of the imaging process, dynamic focusing is investigated where all subsurface points are specified to have the same planar beam fronts. This gives the effect of using nondiffracting beams, but actually results from the use of multiple focusing depths for each Gaussian beam. However, now different local slant stacks must be performed depending on the position of the subsurface scattering point. To speed up the process, slant stacking of the local data windows is varied to match the focusing depths along individual beams when tracked back into the medium. The approach is tested with a simple model of 5-point scatterers which are then imaged with the data, and then to the imaging of a single dynamically focused beam for one shot gather computed from the Sigsbee2A model.
Highlights
Focused Gaussian beams are investigated for the seismic imaging of common-shot reflection data
The beam fronts at the beam waists are planar leading to more stable beam summations for imaging
The application of dynamically focused Gaussian beams has been initially investigated for seismic imaging and is an extension of the focused beam approach of Nowack [1]
Summary
Focused Gaussian beams are investigated for the seismic imaging of common-shot reflection data. In order to speed up the imaging process, the slant stacking of the data window is varied to match the focusing depths along individual beams when tracked back into the medium These focused slant stacks are matched to Gaussian beams with beam waists located at different subsurface locations. In order to test the dynamically focused Gaussian beam approach, a model is constructed with 5 small scatterers with depth in a vertically varying medium resulting in five diffracted arrivals each with different move-outs with distance. When summed over all angles and data windows, the scatterers are properly imaged This is tested for a single dynamically focused beam for one-shot gather computed from the Sigsbee2a model. A disadvantage is that multiple slant stacks are required for different points of the subsurface which increases the computational burden compared to a standard Gaussian beam algorithm or a beam algorithm with a single focus depth. This can in part be offset by precomputing the beam stacks at a set number of focusing depths and interpolating the results required at different subsurface points
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