II- 1 



II. SUMMARY 



A. BASIC PRINCIPLES 



There are a few basic notions of wave propagation (such as incident 

 and scattered wave, single and multiple scattering) which pervade this report. 

 We wish to outline these ideas briefly before summarizing the separate chapters 

 on strong and weak inhomogeneities. 



Throughout the report we are concerned with fields of pressure (p) or 

 of velocity potential (cp) caused by the insonification of an inhomogeneous medium. 

 The mental picture with which we approach the analysis is invariably the following: 



1 . Instead of insonifying the inhomogeneous medium, we insonify a 

 corresponding homogeneous medium by placing in it a source of acoustic energy. 

 The resulting field is generally referred to as the incident or exciting field 



(Pine '^inc)- 



2 . The insonification of an inhomogeneous medium by a corresponding 

 source will cause a different total field (p, cp). The difference between the two 

 fields is called the scattered field: 



p = p +p ,cp = cp +cp 

 mc sc inc sc 



The next step in the analysis is usually to consider a single isolated 

 inhomogeneity in a perfect medium subjected to the exciting field <Pinc" "'^^ 

 scattered field resulting from the inhomogeneity can generally be thought of as 

 caused by the surface or the volume (or both) of the scatterer acting as a sec- 

 ondary source. In other words, the local values of the total field (p or cp) at the 

 surface or throughout the scatterer cause the scatterer to emit its scattered wave. 



The scattered wave is therefore a functional of the total field: 



= l{cp} 



In most of the cases which concern us, the functional L is linear in the sense 

 that a linear combination of two fields corresponds to the same linear combina- 

 tion of the two Individually scattered fields. The precise description of the 



Arthur ia.littleJnt. 



