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# Introduction

Normal mode methods have been used for many years in underwater acoustics. One of the earliest papers was published in 1948 by Pekeris [1] who developed the theory for a simple two-layer model (ocean and sediment) with constant sound speed in each layer. Progress in the development of normal-mode methods is represented in an excellent summary given by Williams[2] and published in 1970. Today, there are many models available that are based on normal modes [3--12]. With respect to Pekeris's original work, these models allow for a more detailed description of both the ocean and sediment sound-speed profiles.

Work on KRAKEN was begun in 1980 as part of the author's dissertation with the objective of developing a normal mode model which was more robust, accurate and efficient[13,14]. The basic algorithm was then extended to treat a more sophisticated ocean model in which the elastic properties of the ocean bottom are included[15]. At the time, elastic normal mode codes were widely used by seismologists but not very familiar to the ocean-acoustics community. Additional work was done to include the effects of shear flows (e.g. ocean currents) [16].

The KRAKEN model was initially developed as a research code to evaluate new algorithms. As such it required numerous modifications to be usable as a production code. This work was begun at the Naval Ocean Systems Center and continued at the Naval Research Laboratory in support of the research on matched-field processing.

Figure: Cachet engraving of a KRAKEN (from the Canadian Illustrated News, October 27, 1877).

The extension to three-dimensional environments [17] was also done at NRL. That work led to the program FIELD3D which formed the nucleus of the Wide-Area Rapid Acoustic Prediction (WRAP) system. WRAP has been extended by a number of people and now includes options for noise modeling[18] and can include this information to predict array performance in complex 3-D environments with different kinds of signal processing schemes. This report documents only the KRAKEN model, not the complete WRAP system.

When the original KRAKEN work was done the algorithm was incorporated into the very popular SNAP model at SACLANTCEN and subsequently renamed to SUPERSNAP. Since 1984 SUPERSNAP has become the standard and is now simply referred to as SNAP. As a result the current version of SNAP and KRAKEN provide identical results when run on the same problem. The execution time is also identical.

In essence, the difference between the two models is that KRAKEN provides a large number of extensions and options, whose presence is an advantage to a sophisticated user and a disadvantage to the uninitiated. At SACLANTCEN, both models are being maintained: KRAKEN is recommended for more experienced modelers or for those requiring 3-D capability and SNAP recommended for those interested simply in transmission loss calculations. Amongst the features of KRAKEN are:

• efficient eigenvalue finding techniques guaranteed to converge

• stable eigenfunction calculation even with multiple ducts

• ability to handle multilayered environments

• inclusion of stratified elastic layers

• inclusion of interfacial roughness

• tabulated surface and bottom reflection coefficients

• choice of perturbational or exact treatment of loss

• calculation of leaky modes

• free, rigid, and homogenous half-space options for boundary conditions

• adiabatic or coupled mode options for range-dependent problems

• tilted and displaced array calculations

• high-accuracy via extrapolation

• extension to 3-dimensionally varying problems

This report is organized as follows. Chapter 2 provides a fairly technical description of the mathematical basis for normal modes. This material is intended as a tutorial on normal modes and makes limited reference to the specifics of the KRAKEN model. Chapter 3 discusses the numerical treatment of the modal equation and Chap. 4 provides information on running the program. In Chap. 5 we present a number of test problems which exercise different parts of the code. These problems are not particularly physical but they do provide a means of verifying the model on a new installation. In addition, they illustrate the set-up of the input file for different types of environmental scenarios.

Next: Mathematical Formulation Up: The KRAKEN Normal Mode Previous: Contents

Michael B. Porter
Tue Oct 28 13:27:38 PST 1997