The Impact of Acoustic Imaging Geometry on the Fidelity of Seabed Bathymetric Models
Attributes derived from digital bathymetric models (DBM) are a powerful means of analyzing seabed characteristics. Those models however are inherently constrained by the method of seabed sampling. Most bathymetric models are derived by collating a number of discrete corridors of multibeam sonar data. Within each corridor the data are collected over a wide range of distances, azimuths and elevation angles and thus the quality varies significantly. That variability therefore becomes imprinted
... comes imprinted into the DBM. Subsequent users of the DBM, unfamiliar with the original acquisition geometry, may potentially misinterpret such variability as attributes of the seabed. This paper examines the impact on accuracy and resolution of the resultant derived model as a function of the imaging geometry. This can be broken down into the range, angle, azimuth, density and overlap attributes. These attributes in turn are impacted by the sonar configuration including beam widths, beam spacing, bottom detection algorithms, stabilization strategies, platform speed and stability. Superimposed over the imaging geometry are residual effects due to imperfect integration of ancillary sensors. As the platform (normally a surface vessel), is moving with characteristic motions resulting from the ocean wave spectrum, periodic residuals in the seafloor can become imprinted that may again be misinterpreted as geomorphological information. 2 of 20 provided for those system artefacts that are developed close to the limit of the achievable resolution. This is because, as noted by several researches [5, 12] , the seafloor geomorphic features of interest are often at, or close to, the limit of achievable resolution and are thus prone to potential distortion. Each aspect discussed is illustrated by specific example data so that the reader may recognize the net result in a derived terrain model. Specific formulas to attempt to calculate solution density are omitted as they are strongly dependent on sonar configurations and motion history which are continuously variable and rarely stored with derived gridded products. Multibeam Imaging Geometry A multibeam echosounder is an acoustic scanner that delivers sequential topographic profiles aligned approximately orthogonal to the platform (a surface or submerged vehicle) trajectory. It does this by taking advantage of the Mills Cross array geometry to ensonify a corridor and then receiving the backscattered energy through a number of discrete beamformed channels at a variety of elevation angles [13, 14] . As the vehicle advances, successive profile solutions build up a swath corridor. Different sonar models utilize different beam dimensions, spacings and density. As these sonar systems operate predominantly from underway platforms, they vary in their approach to stabilization in order to compensate for motions primarily within the ocean wave spectrum. It is those resultant data that are the underlying input to digital bathymetric models (DBM). Two primary, but quite separate, factors concerning the input data will become apparent in this discussion: The solution density, and the achievable resolution based on the footprint within which a single solution in derived. Were those swaths of data made up of evenly spaced solutions, each of which represented the depth from an identically sized footprint, the data might be expected to be equivalent. In reality, however, as the vehicle does not follow a straight line path and rotates on three axes (roll, pitch and yaw), the solution density is uneven. Furthermore, the ensonified area, defined by the product of the transmission and receiver patterns (and/or pulse duration and processing), is not of uniform size and the incidence angle of acoustic energy is highly variable. As a result, both the solution density and the solution resolution vary strongly with both elevation and across a single swath. These factors will impact the resolved terrain roughness thereby affecting any classification scheme based on surface characteristics. The closest analogous instrument used for terrestrial surveying is an airborne laser scanner (ALS). To contrast a multibeam sonar to an ALS, the geometric differences need to be appreciated (Figure 1) . The laser scanner sector elevation angle is typically only varying from vertical to~20-25 • incidence angle. For a typical ALS, the projected laser beam divergence is on the order of~1 millradian (0.0573 • )  . At a flying height of~550 m this has a footprint then of 0.55 m at nadir growing to only 0.64 m at the edge of the swath. As the flying height is normally much larger than the variation in elevation of the feature of interest (e.g., examining rock ridges of ±20 m scale), the beam footprint only varies by ±3-4% as a result of within swath surface elevation fluctuations. For larger scale terrain fluctuations that occur over longer wavelengths, the aircraft is free to adjust its vertical trajectory to maintain a similar altitude. In contrast, a good multibeam has a beam width of typically 1 • (qualifications on this will be discussed later), but projected over an angular sector of up to ±65 • . For a continental shelf depth of 50 m, this results in footprints ranging from 0.87 m at nadir to 2.1 m (along) or 4.9 m (across-track) at the edge of the swath. Additionally, for the case of within swath topography that varies within the same range (±20 m), those dimensions fluctuate by up to 40%. The preceding simplified geometric scaling calculations demonstrate that variations in the effective resolution are going to be much more pronounced across a multibeam swath than an ALS swath. Even with the reduced changes, the variation in the ALS footprint is known to have an impact in the effective data quality  . Such effects are thus magnified for the multibeam geometry which, in turn, will impact the achievable terrain discrimination using geomorphometric techniques.