5. DELINEATION OF STATISTICALLY HOMOGENEOUS PROVINCES 45 



A. General Philosophy .45 



B. Generation of Amplitude Spectra 48 



C. Physical Interpretation of the Amplitude Spectrum. . .50 



D. The Phase Spectrum 56 



E. Creation of the Model and Interpretation 63 



6. ANISOTROPY OF SURFACES 79 



A. Theoretical Model 79 



B. Comparison of Theoretical Functional Forms with 

 Multibeam Sonar Data 87 



C. Estimation of Two-Dimensional Spectra from 

 Randomly Oriented Ship Track 103 



7. PREDICTION OF HIGH FREQUENCY ROUGHNESS 107 



A. Source of Error in Spectral Estimates 107 



B. Propagation of Error to High Frequency Estimates. .. Ill 



C. Comparison of Surface-Ship Sonar Results to 

 Deep-Towed Sonar Results and Results from 



Bottom Photography 112 



vii 



