A robust and accurate interpolant for tabulated sound speed profiles

Abstract

An new interpolation algorithm that is a hybrid of the cubic spline and monotone piecewise cubic Hermite polynomial interpolants is introduced. The resulting algorithm has several properties that make it an attractive choice for the interpolation of sound speed profiles in acoustic propagation models. It has been shown that when interpolants do not have a continuous first and/or second derivative, the resulting acoustic model predictions can exhibit a variety of artifacts such as false or omitted caustics. The first derivative of our interpolant is continuous everywhere. Our interpolant also automatically respects the monotonicity of the underlying data in the sense that it will be monotone (increasing or decreasing) on any interval where the associated data is also monotone. This property avoids the oscillations between data points that can be a source of frustration when using some interpolants such as cubic splines. Finally, the interpolant will also possess a continuous second derivative everywhere, except at those data points where monotonicity considerations take priority. In some cases, the interpolant will coincide exactly with the cubic spline.An new interpolation algorithm that is a hybrid of the cubic spline and monotone piecewise cubic Hermite polynomial interpolants is introduced. The resulting algorithm has several properties that make it an attractive choice for the interpolation of sound speed profiles in acoustic propagation models. It has been shown that when interpolants do not have a continuous first and/or second derivative, the resulting acoustic model predictions can exhibit a variety of artifacts such as false or omitted caustics. The first derivative of our interpolant is continuous everywhere. Our interpolant also automatically respects the monotonicity of the underlying data in the sense that it will be monotone (increasing or decreasing) on any interval where the associated data is also monotone. This property avoids the oscillations between data points that can be a source of frustration when using some interpolants such as cubic splines. Finally, the interpolant will also possess a continuous second derivative everywhere, e...