Asymptotic Representation of Low-Degree, Higher-Order p-Modes

Abstract

A second-order asymptotic representation of p-modes belonging to low degrees and higher radial orders is developed on the basis of a fourth-order system of differential equations for the divergence and the radial component of the Lagrangian displacement. The interval [0, R] is divided into three subintervals: a subinterval distant from the singular boundary points r = 0 and r = R, a subinterval near the singular boundary point r = 0, and a subinterval near the singular boundary point r = R. In the first subinterval, two-variable expansions are used; in the two other intervals, boundary-layer theory is applied. Second-order asymptotic approximations for the eigenfrequencies are determined. Moreover, asymptotic representations of the eigenfunctions are constructed that are uniformly valid, one from the boundary point r = 0, the other one from the boundary point r = R.