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.

Tue Oct 28 13:27:38 PST 1997