Rays, traveltimes and amplitudes in an underwater sound channel described by the Munk’s formula

Abstract

Summary Recently, the Munk’s formula has been used as a velocity model for numerically analyzing the influence of the underwater sound channel on both of the seismic data and the migrated-image. Since numerical analysis can give mode-dependent results only, the conclusions drawn from the results are model-dependent as well. Thus, they should be used with care for general cases. To resolve the model-dependence, we first expand the depth-dependent terms in the Munk’s formula into a Taylor series with respect to a parameter called the “normalized depth”, and then truncate the series at its first term and linearize the term with respect to the depth. Next, we insert the linearized and the original form of the first term into the Munk’s formula and derive two approximations to the Munk’s formula. By applying the approximate velocity formulas in the corresponding integrals and formulas, respectively, we obtain approximate formulas for both the rays and the traveltimes along the rays, and for the amplitude factors as well. Using all of these approximate formulas, finally, we establish the formulas for the deviations of the ray endpoints and the wavefields at the endpoints from those in a homogeneous seawater layer by building the corresponding differences and ratios.