Method of Simulating Sonar Returns

In order to accurately simulate the returns from the sonar units, their locations in 3D space were determined using information from as-built drawings of the bridge piers for vertical location and a conservative estimate from photographs for horizontal location. The resulting coordinates were stored, one associated with the northern pier, the other with the southern pier, and treated as the origin for each respective projected ray.

Figure 1. Cyan dots represent the spatial location of each sonar unit, each is placed 6 feet below MLLW. North is to the left of the image.



Ray lines were defined by projecting a series of points along each ray vector, which was defined by systematically stepping through changes in latitude (tilt) and longitude (rotation). In this simulation the steps are 1degree in each direction; this model uses stepping in longitude first to generate the ray lines, but this is arbitrary as all of the rays are generated regardless of order. Each ray line represents the centerline of the sonar¡¯s projection cone. In order to find where each ray line intersects the bathymetry, the rays were discretized during their generation into 2000 points, each defined by an x-y-z coordinate group. Each of these coordinate groups was compared to the interpolated bathymetry data, and the last ray point that occurred above the bathymetry was stored as the intersection point of the centerline with the bathymetry (now referred to as centerpoints). This result was seen in Figure 3 and Figure 4 on the previous page.

The small errors incurred from using the discrete ray points could potentiall be minimized by interpolating between each ray point to store the precise location of coincidence between the bathymetry data and ray line; however given that the data is interpolated and that the rays do not exceed 400 feet in length in the area of study, the method listed is considered a good approximation.

Next, the projection cone associated with each centerline was generated by cycling through pairs of small changes in latitude and longitude around each centerpoint. Instead of storing every elevation of the bathymetry that fell inside each projection cone, an approximation of 16 points is used; 8 of these points form an octagon inscribed in the cone limits, and the other 8 points form a smaller octagon inscribed in a cone half the size.

Figure 2. This set of octagons approximates the field of vision of one sonar beam.



The coincidences of these 16 points with the bathymetry are found in the same manner as the centerpoints. The 16 cone approximation points will be called nodes.

Figure 3. A sample of selected octagonal patches shown over the bathymetry. Black are projected from the southern pier, white from the north.



The average z-coordinate of the centerpoint and its associated nodes was stored and linked to the centerpoint coordinates to simulate the returns from the sonar for each beam. Then these values were gridded and the surface was filled between them to generate the final simulated bathymetry seen in Figure 5 and Figure 6 on the previous page.

Additionally, the distance between each centerpoint and its generating sonar location, as well as the approximated minor axis of the projection cone were stored and linked to their respective centerpoints for calculations regarding relative resolution estimates of the simulated bathymetry.


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