### ASA 124th Meeting New Orleans 1992 October

## 3aUW17. The maximal range step in parabolic wave propagation in
shallow-water acoustics.

**Vic Dannon
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*Ocean and Atmospheric Sci. Div. NRaD, San Diego, CA 92152-5000
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To quickly obtain the wave field in parabolic wave propagation, this study
sweeps the range in the largest possible range steps. Jensen and Krol
[Saclanten Memorandum-72, NATO-SACLANTEN, La Spezia, Italy (1975)] obtained the
truncation error of the parabolic equation that depends on the range step but
did not derive the appropriate range step. The derivation was completed and it
was implemented to a parabolic equation code. This study demonstrates that the
truncation error of the parabolic wave equation is inadequate for the purpose
of determining the maximal range step under acceptable wave-field error. This
led to an analysis based on the truncation error of the wave field. It is shown
that given a wave-field gain/loss of (gamma)=10 log[sub 10]|(eta)|dB, the
maximal range step (Delta)r allowed is given by a formula that relates it to
(eta) (that measures the wave-field truncation error), the gradients of the
refraction index n (with respect to range and height) and to the wave field and
its gradients. The formula had been tested successfully on the parabolic
equation code.