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Figure 9.7 Example from the REVMOD reverberation model showing the surface-scattering function for a downwind case. (Hodgkiss, 1984; IEEE J. Oceanic Eng., 10, 285-9; copyright by IEEE.)

were 102 and 86 ms, respectively. See Ziomek (1985: chapters 3 and 4) for a discussion of complex apertures and directivity functions.

The Doppler of the surface component of the scattering function reflects a complex interaction with this moving boundary (specifically, a negative Doppler ridge), as shown in Figure 9.7. This ridge corresponds to the Doppler-shifting effects of the surface wave and current velocity vectors.

9.5 Bistatic reverberation 9.5.1 Computational considerations

Most traditional active sonars are configured in what is termed a monostatic geometry, meaning that the source and receiver are at the same position.

Figure 9.8 Geometry for bistatic reverberation showing relative positions of the source (s), target (t) and receiver (r) in either the vertical or the horizontal plane.

In some sonar systems, however, the source and receiver are separated in range or depth, or both, in what is termed a bistatic configuration. Bista-tic geometries are characterized by a triangle of source, target and receiver positions, and by their respective velocities (Cox, 1989). Such geometries are commonly employed in sonobuoy applications (Bartberger, 1985) and also in active surveillance applications (Franchi et al., 1984). Geometries involving multiple sources and receivers are termed multistatic.

A bistatic sonar must detect the target signal against the background noise level that is the intensity sum of the ambient noise, the surface, bottom and volume reverberation, and the energy propagating directly from the source to the receiver over a set of one-way paths referred to as direct arrivals (Figure 9.8). These direct arrivals represent a significant difference between bistatic and monostatic sonars. Since the direct (one-way) paths are very intense, they must be carefully considered in predicting the performance of bistatic sonars (Bartberger, 1985). Each different propagation path may require separate predictions of transmission loss. Bistatic reverberation models are commonly confronted with substantial bookkeeping requirements associated with sorting the various reverberation and noise contributions. In the monostatic situation, reverberation is due to backscatter. In bistatics, forward and out-of-plane scattering are important (Cox, 1989).

The bistatic problem is further complicated by the presence of certain bathymetric features, particularly seamounts, which can introduce a discrimination problem between acoustic returns from these geologic features and from potential targets of interest. Eller and Haines (1987) described seamount statistics as well as the characteristics of acoustic reverberation from seamounts. A real-time bathymetric reflection and scattering prediction system was developed to support at-sea acoustical surveys (Haines et al., 1988). The system utilized gridded databases to generate 3D environmental scenarios in conjunction with the ASTRAL propagation model and the ANDES noise model. As configured, the system operated on a HP-9020 desktop computer and provided color graphic displays of predicted ocean bottom reverberation as well as echoes from seamounts.

A computer model called ocean refraction and bathymetric scattering (ORBS) was developed to calculate the directional distribution of bottom-scattered acoustic energy received at an array (Baer et al., 1985; Wright et al., 1988). ORBS incorporated the refractive effects of a varying sound speed structure in the ocean volume as well as the effects of out-of-plane scattering caused by rough bathymetry. A seamount could be considered where it made sense to consider only a single encounter with the sea floor. The numerical techniques used included the split-step solution to the parabolic equation away from the boundary, propagation of the coherence function near the boundary, and a modified Kirchhoff formulation to incorporate scattering. Smith et al. (1996) used field measurements and model results to correlate reverberation events with bathymetric features.

9.5.2 The bistatic acoustic model - a specific example

The bistatic acoustic model (BAM) predicts the performance of a sonar system consisting of a sound source and a receiver separated in both range and depth (Bartberger, 1991a; Vendetti et al., 1993a). BAM computes the echo-to-background ratios for targets located at a set of bipolar grid locations in a horizontal plane containing a specific target. The bipolar grid points are defined by the intersections of circles of constant range about the source and receiver. There are three separate versions of BAM corresponding to three different sonar system configurations: vertical line array, horizontal line array or volumetric array. BAM consists of four computer programs:

1 BISON computes the ray arrival structure, the surface, bottom and volume reverberation time histories, and the vertical distribution of ambient noise.

2 BISTAT computes the echo-to-background ratios on a bipolar grid within a specified circle about the receiver.

3 CTEST generates the time series of the direct arrivals, the surface, bottom and volume reverberation, and the combined interference of all of these components.

4 PLOSS calculates the source-to-target transmission loss and the target-to-receiver transmission loss as a function of range.

A sample output product from BAM is illustrated in Figure 9.9, which shows computed echo-to-background levels. These levels are numerically coded to facilitate printer output. The digital pattern in Figure 9.9 indicates the potential for target detection under the hypothetical problem geometry and acoustic conditions:

• source depth = 300 m (four-element omni source array);

• receiver depth = 500 m (six-element omni receiver array);

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