Quasi-linear inversion of the acoustic wavefield

In the QL approximation, we assume that the scattered acoustic field inside the inhomogeneous domain D is linearly proportional to the incident field p through some reflectivity coefficient A  

At the same time, according to (14.38), p can be calculated as an integral involving A and the incident field  

Following the basic principles of electromagnetic QL inversion, we can introduce a material property parameter m, equal to 

Substituting expression (15.152) into (15.151), we arrive at a linear equation for the material property parameter m  

The reflectivity coefficient A can be determined from the following linear equation inside the inhomogeneous domain D, as long as we know m  

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