Dictionary:Fig A-15

FIG. A-15. Aplanatic surface. (a) The locus of reflection traveltimes from a given source to a receiver with constant velocity is an ellipse with the source and receiver as foci. Such a plot is called a bathtub chart. (b) To find the boundary between two media of different velocities where source and geophone are in different media, draw wavefronts about each and find intersections where the sum equals the traveltime (4.0 s for the heavy curve). The interface between the two media must be tangent to this curve. (c) Use of aplanatic surface in the 3-D problem of locating a salt-dome flank by shooting into a geophone in a borehole in the salt. The common tangent surface to the aplanatic paraboloids locates the interface. (From Gardner, 1949.)