THE HYPERBOLIC INCREASE OF DEPTH WITH TIME

The geometric description of wave fronts and ray paths has previously always started from the velocity distribution which has been chosen as simple as possible in order to be able to solve the integrals occurring in the basic equations. As the velocity is derived from the measured values of path and time, it is preferable to start from the path‐time function. There are exponential, parabolic and hyperbolic path‐time functions; the first and the second case correspond to the known linear and parabolic velocity functions. The hyperbolic case, on the other hand, has not yet been covered in literature. In the first two cases, two parameters–a and vo–can be chosen arbitrarily. In the hyperbolic case, we have 3 parameters (a, b and v)o at our disposal; this makes for a better approximation to actual conditions. A special advantage is seen also in the fact that the velocity does not become infinite with increasing depth but approaches a finite limit.