Localized quasi-linear inversion

The quasi-linear inversion, introduced above, cannot be used for interpretation of multi-transmitter data, because both the reflectivity tensor A and the material property tensor in depend on the illuminating background electromagnetic field. However, in many geophysical applications, for example, in airborne EM and in well-logging, the data are collected with moving transmitters. In this case one can build an effective inversion scheme based on the localized quasi-linear approximation, introduced in Chapter 9, which is source independent. 

Localized quasi-linear inversion increases the accuracy and efficiency of wave-field data interpretation because it is based on a much more accurate forward modeling solution than the Born approximation, used in the original Bleistein method. An example of successful application of the localized QL approximation in radar-diffraction tomography can be found in (Zhou and Liu, 2000). 

Zhdanov, M. S., and E. Tartaras, 2002, Inversion of multi-transmitter 3-D electromagnetic data based on the localized quasi-linear approximation Geophys. J. Int., 148, No 3. 

By full analogy with the electromagnetic case, one can consider different ways of introducing the reflectivity coefficient A. In particular, two of these solutions play an important role in inversion theory. One is the so-called quasi-analytical (QA) solution, and the other is the localized quasi-linear (LQL) approximation. In this section I will introduce the QA approximation for the acoustic wavefield. 

CPR = conjugate peak refinement GDIIS = geometry direct inversion in the iterative subspace GE = gradient extremal LST = linear synchronous transit LTP = line then plane LUP = locally updated planes NR = Newton-Raph-son P-RFO = partitioned rational function optimization QA = quadratic approximation QST = quadratic synchronous transit SPW = self-penalty walk STQN = synchronous transit-guided quasi-Newton TRIM = trust radius image minimization TS = transition structure. 

---