Introduction 



The contour map of oceanic depths, or bathymetrlc chart, has pro- 

 vided a fundamental tool for Inferring deep-sea processes, both sedl- 

 mentologlcal and tectonic. The Identification of the major features of 

 the sea floor led to more elaborate geophysical studies and such unify- 

 ing theories as sea-floor spreading. The efforts of numerous Institu- 

 tion, world-wide have produced comprehensive contour charts of global 

 bathymetry, which have formed the basis of further geophysical survey 

 efforts. 



The method of contouring has the mathematical equivalent of fitting 

 a continuous surface to discrete three-dimensional data. In the case of 

 ba thyme trie contours, the discrete data are usually In the form of vari- 

 ably spaced and randomly oriented ship tracks along which are discrete 

 soundings at some Interval. Modem soundings are normally estimated 

 from surface ships using acoustic sounders In which the two-way travel 

 time of a pulse of sound Is Interpreted as a depth at a discrete point. 

 Geometric spreading of the sound with depth causes a large area of the 

 sea floor to be Insonlfled (often called the "footprint"), and the meas- 

 ure of the first significant return of sound to the ship Is Interpreted 

 as a sample of the shallowest depth from this large Insonlfled area. 

 The uncertainties In the precise location of the measured depth, the 

 sound velocity structure of the water column and the positioning of the 

 ship at sea, combine to Introduce a noise component Into the output sig- 

 nal. The random noise of measurement. In addition to the uncertainty of 

 Interpolation between often widely spaced samples and ship tracks. 



