Stable, accurate and efficient computation of normal modes for horizontal stratified models

Abstract

We propose an adaptive root-determining strategy that is very usefulwhen dealingwith trapped modes or Stoneley modes whose energies become very insignificant on the free surface in the presence of low-velocity layers or fluid layers in the model. Loss of modes in these cases or inaccuracy in the calculation of these modes may then be easily avoided. Built upon the generalized reflection/transmission coefficients, the concept of 'family of secular functions' that we herein call 'adaptive mode observers' is thus naturally introduced to implement this strategy, the underlying idea of which has been distinctly noted for the first time and may be generalized to other applications such as free oscillations or applied to other methods in use when these cases are encountered. Additionally, we have made further improvements upon the generalized reflection/transmission coefficient method; mode observers associated with only the free surface and low-velocity layers (and the fluid/solid interface if the model contains fluid layers) are adequate to guarantee no loss and high precision at the same time of any physically existent modes without excessive calculations. Finally, the conventional definition of the fundamental mode is reconsidered, which is entailed in the cases under study. Some computational aspects are remarked on.With the additional help afforded by our superior rootsearching scheme and the possibility of speeding calculation using a less number of layers aided by the concept of 'turning point', our algorithm is remarkably efficient as well as stable and accurate and can be used as a powerful tool for widely related applications.