Abstract
One method to estimate the validity of the leading term in the geometrical acoustics expansion is to calculate the second term in the expansion. This second term plays an essential role in the construction of the second term in Ludwig’s uniform smooth caustic ansatz and in the construction of the progressing wave smooth caustic ansatz. Therefore, the determination of this term is important in the assessment of each of these expansions. Expressions for this second term are derived valid for arbitrary index profiles near the source point and near a smooth caustic. Numerical examples are presented for the n2‐linear profile. These results show that near the source the second term is not singular, but near the caustic it is more singular than the leading order term.
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