Crosshole seismics using vertical eigenstates

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Abstract
This paper introduces the concept of vertical eigenstates to crosshole data analysis. In surface seismics, plane waves have played a fundamental role in many applications. This paper points out that for crosshole seismics, vertical eigenstates play a similar role. The vertical eigenstates separate the wave equation, and thus in terms of vertical eigenstate expansion the solution is a linear combination of modes, each mode traveling sideways with a distinct phase velocity. As a result, the vertical eigenstates form a natural set of basis functions for solution and data expansion, with potential applications to modeling, migration, and inversion.

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