The acoustic wave equation is considered using a combination of finite integral transforms and finite differences in the solution method. This approach is known as the pseudo - spectral method or Alekseev - Mikhailenko Method (AMM) after the Russian researchers who spent decades pursuing this avenue of solution which has resulted in numerous dozens of related papers in the literature. One aspect of this solution method that is often referred to but has received little attention in the literature is the introduction of absorbing boundaries. Using the simple acoustic wave equation in this solution type, the algorithm developed by Clayton and Engquist (1977) is incorporated into the transformed wave equation to produce a manner of introducing an absorbing at the model bottom.
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