FIELD THEORETICAL MODEL OF ACOUSTIC PROPAGATION WITH ROUGH BOUNDARIES

A NOVEL APPROACH IS TAKEN IN THIS PROPOSAL FOR THE RIGOROUS TREATMENT OF THE PROBLEM OF ACOUSTIC WAVE PROPAGATION THROUGH SHALLOW WATER BOUNDED BY ICE AND BOTTOM WITH ROUGH SURFACES. THIS TREATMENT INCLUDES A FIELD-THEORETIC CONSIDERATION OF WAVE PROPAGATION AND A STATISTICAL-PHYSICS MODEL OF ROUGH ICE AND BOTTOM SURFACES. THE FIELD-THEORETIC MODEL SHALL ACCOUNT FOR ALL MODES OF WAVE PROPAGATION IN LAYERED MEDIA AND TREAT THE INTERACTION WITH ROUGH SURFACES BY EXPANDING THE EXACT SOLUTION INTO PERTURBATION SERIES IN POWERS OF A SMALL PARAMETER, THE RELATIVE ENERGY LOSS PER WAVELENGTH. IT ACCOUNTSFOR WAVE INTERACTIONS WITH FLUCTUATIONS OF BOTH GEOMETRICAL SHAPE AND RIGIDITY, WHICH ARE KNOWN TO CAUSE SIGNIFICANT ENERGY LOSSES. A MODEL BASED ON THE THEORY OF PHASE TRANISTIONS BETWEEN LIQUID, NONRIGID, AND RIGID PHASES IS USED TO DESCRIBE THE ROUGH ICE AND BOTTOM SURFACES. THIS MODEL WILL PREDICT THE RIGIDITY FLUCTUATIONS IN ICE ON THE BOTTOM AND ALSO RELATE THE GEOMETRICAL DISTRIBUTION OF ICE AND BOTTOM ROUGHNESS TO THE AVERAGE LOCAL ENERGY DISTRIBUTIONS ON DIFFERENT SCALES. THE MODEL RESULTS ARE COMPARED WITH EXISTING DATA.