9.4 The REVMOD model - a specific example

The reverberation spectrum model (REVMOD), originally developed by C.L. Ackerman and R.L. Kesser at the Applied Research Laboratory, The Pennsylvania State University, has been expanded and further documented by Hodgkiss (1980, 1984). REVMOD is a set of computer programs that models surface, bottom and volume reverberations. It is based on the cell-scattering approach.

REVMOD considers the effects of motion of the sonar platform, transmit signal windowing, transmit and receive beam patterns, scatterer velocity distributions and sound absorption. Model constraints include specification of a constant sound-speed profile and nonreflection of sound at the surface and bottom boundaries.

Geometrically, REVMOD divides the ensonified volume of the ocean into cells and evaluates scatterer motion relative to the sonar platform for a measure of the spectral shifting and spreading due to the environment. Acoustically, REVMOD determines the backscattering level for each cell. The contributions from each cell are then summed to compute the total reverberation power spectra received at the sonar.

REVMOD is composed of three major software modules:

1 RVMDS - computes the scattering function resulting from the combined effects of the environment, vehicle dynamics, and transmit and receive beam patterns.

2 RVMDT - convolves the scattering function with the transmit-signal energy spectrum to yield the reverberation power spectrum.

3 RVMDR - convolves the reverberation power spectrum with the receiver-impulse response-energy spectrum.

Module RVMDS computes the scattering function for reverberation and describes the effects of the ocean medium on a transmit signal with carrier frequency &>c. Module RVMDT completes the reverberation model by combining a detailed description of the transmit signal (pulse length, envelope shape and source level) with the environmental characterization provided by module RVMDS. Module RVMDR creates a model of a receiver operating in a reverberant ocean environment. A matched filter envelope detector uses the reverberation spectra generated by module RVMDT. Optional software can also be included to model a matched filter envelope detection receiver appropriate for post-processing the reverberation spectra. Thus, the effects of utilizing a receiver impulse response window, which differs from that of the transmitter waveform, can be investigated.

A mathematical description of the scattering function (RVMDS) will be provided here. Calculations of the reverberation power spectrum (RVMDT) and subsequent convolution with the receiver impulse response energy spectrum (RVMDR) were discussed by Hodgkiss (1980, 1984). REVMOD generates a scattering-function description of the ocean medium that does not require a detailed description of the transmit signal. Thus, the model is appropriate for investigations of the influence of the medium on various transmit-signal types.

Acoustic backscatter can be modeled as the passage of a transmit waveform through a linear, time-varying filter:

where sr (t) is the received backscattered signal, Et the transmit-signal energy, f (t — X) the transmit waveform, t the time, X the time delay and b(t — X/2, X) the time-varying impulse function of the filter.

The basic geometry of REVMOD consists of a spherical shell representing that portion of the ocean medium ensonified by the signal wavefront corresponding to a range (R) after transmittance (refer to Figure 9.3). The shell thickness is governed by the variables Ds, DB and AR for surface, bottom and volume scattering, respectively. The spherical shell is further subdivided into a grid of cells, each of which contributes to surface, bottom or volume backscatter. The location of each cell is specified in terms of an azimuth-elevation angle pair (Oj, 4>i). Using this geometry, REVMOD calculates the scattering functions corresponding to the surface, bottom and volume backscatter of a transmit waveform at specified ranges of interest. Specifically, the normalized attenuation (Ai,j) of the transmitted signal (including propagation and beampattern effects) is calculated for each surface, bottom

and volume grid cell as follows:

Surface scattering

10logic (Ai,D = 10logic Ds(RA0)] + Ss - 40log10(R) - (2aR)

Volume scattering

10logj0 (Aij) = 10log1Q[AR(RAO)(RA0)]+SV - 40log!Q(R) - (2aR) + 10log™ [PT(0j,0i)pR(Oj,0i)] + 10log10[c/2AR)]

Bottom scattering

10 log™ (Aij) = 10log1Q[DB(RA0)]+SB - 40 log™ (R) - (2aR)

where A ij is the scattering level (normalized to 1 s in range) from the (i, j)-th grid cell (s-1), Ds the lateral dimension of surface-scattering patch (m), Db the lateral dimension of bottom-scattering patch (m), R the range (m), AR the increment in range over which scattering is averaged (m), A0 the angular grid cell width in azimuth (rad), A0 the angular grid cell height in elevation (rad), Ss the surface-scattering coefficient (dBm-2), Sv the volume-scattering

coefficient (dBm ), Sb the bottom-scattering coefficient (dBm ), a the sound absorption coefficient (dBm-1), pT(0j,0i) the transmit beam pattern (normalized to 1 at 0j = 0t and 0i = 0t), pR(0j, 0i) the receive beam pattern (normalized to 1 at 0j = 0r and 0i = 0r), 0j the azimuth to center of jth grid column (rad), 0i the elevation to center of ith grid row (rad), (0t, 0t) the transmit beam vector, (0r, 0r) the receive beam vector, 0s the elevation angle to surface (rad), 0b the elevation angle to bottom (rad) and c the sound speed (ms-1).

Hodgkiss (1984) provided sample results from REVMOD for the case of a bottom-mounted transducer with a steerable, axially symmetric beam pattern (Figure 9.4). Wind-driven surface waves and a surface current both contributed to spectral broadening and Doppler shifting of the transmit spectrum upon backscattering from the sea surface. The volume-backscattering

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