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# SEGREGATING P AND S CROSSTALK

Signals can be contaminated by other signals, and images can be contaminated by other images. This contamination is called crosstalk." An everyday example in seismology is the mixing of pressure waves and shear waves. When waves come straight up, vertical detectors record their pressure-wave component, and horizontal detectors record their shear-wave component. Often, however, waves do not come exactly straight up. In these cases, the simple idealization is contaminated and there is crosstalk. Here we study a simplified form of this signal-corruption problem, as given by the equations
 (1) (2)
where and represent vertical and horizontal observations of earth motion, and represent theoretical pressure and shear waves, and represent noises, and and are the cross-coupling parameters. You can think of , , , , and as collections of numbers that can be arranged into a signal or into an image. Mathematically, they are abstract vectors. In our notation, boldface represents the vector as a whole, and italic v represents any single component in it. (Traditionally, a component is denoted by vi.)

Next: Two univariate problems Up: Univariate problems Previous: INSIDE AN ABSTRACT VECTOR
Stanford Exploration Project
10/21/1998