


 Interferometric imaging condition for waveequation migration  

Next: Appendix C
Up: Appendix B
Previous: Appendix B
Acoustic waves characterized by pressure
propagate according to the second order acoustic waveequation
for constant density

(21) 
where
is a wavelet of characteristic wavelength
.
Given the parameters (size of inhomogeneities),
(wavelength size), (propagation distance) and (noise
strength), we can define several propagation regimes.
The weak fluctuations regime characterized by waves with
wavelength of size comparable to that of typical inhomogeneities
propagating over a medium with small fluctuations to a distance of
many wavelengths. This regime is characterized by negligible back
scattering, and the randomness impacts the propagating waves through
forward multipathing. The relevant length parameters are related by

(22) 
and the noise strength is assumed small

(23) 
The diffusion approximation regime characterized by waves with
wavelength much larger than that of typical inhomogeneities propagate
over a medium with strong fluctuations to a distance of many
wavelengths. This regime is characterized by traveling waves that are
statistically stable but diffuse with time. Back propagation of such
waves in a medium without random fluctuations results in loss of
resolution. The relevant length parameters are related by

(24) 
and the noise strength is not assumed small

(25) 



 Interferometric imaging condition for waveequation migration  

Next: Appendix C
Up: Appendix B
Previous: Appendix B
20130829