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Previous: Spatially bandlimited sources
Up: Wave equations and reciprocity
Previous Page: Spatially bandlimited sources
Next Page: How can it be used?
Recording multicomponent seismic is most often carried out over a surface. The medium under investigation is parameterized by properties such as stiffness and density of the medium. Not knowing the medium completely, experiments are designed to give us the best information. Seismic data realistically are recorded at very sparse locations within the medium itself, never ``at every point'' in the medium. Thus the complete Green's tensor with complete spatial coverage is surely impossible to obtain and will always be bandlimited.
For an elastic medium, the collected data will only approximate
the Green's tensor, even if data are collected in a manner that spans
the source and receiver component space.
For an ideal experiment with multi-component sources and receivers,
we should
use at least 3 linearly independent source directions and 3
linearly independent receiver
directions. Under ideal conditions then we record the full bandlimited
Green's tensor at a given source-receiver pair.
Using fewer components might lead to ill-conditioned inversion and imaging results. Types of such incomplete experiments: p source into 3 component receivers (missing other two wave types) or vertical source into horizontal geophones. One is lucky if there are near-source wave-type conversions such that significant amounts of the ``originally missing'' source-wave types are generated. However, the experiment is not orthogonal, but rather a superposition of those wave type experiments.