Modes to replace transitional asymptotic ray fields in a vertically inhomogeneous earth model

Summary. Asymptotic ray theory (ART) fails in transition regions near critically reflected, bottom glancing or caustic‐forming rays in a vertically inhomogeneous layered earth. These deficiencies are repaired here by replacing the transitional ray fields with guided modes plus truncation remainders. Exact ray‐mode equivalences and their high‐frequency asymptotic approximations are formulated, and their validity and efficiency are verified by numerical comparisons for SH motion in a two‐layer earth model comprised of an inhomogeneous sediment above an homogeneous semi‐infinite bedrock.