Abstract
The equation of ray path in a linearly varying velocity field in one-dimensional (1-D) case corresponds to an equation of circle whose center is defined by the initial take-off angle and the constant parameters of the velocity field. The physical ray path can exist only on the half circle, where the velocity is positive. The initial take-off angle of a ray passing through the two specified points is derived, the expression of which assures an analytical two-point ray tracing. The linearly varying velocity field in two-dimensional (2-D) or three-dimensional (3-D) can be transformed to that in 1-D. This transformation reduces the equation of ray path in a linearly varying velocity field in 2-D or 3-D to one in 1-D in the transformed coordinates. The results can be implemented for two-point ray-tracing calculation as well as analytical ray path and travel time calculation, both in forward and inverse problems.
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