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Joint Migration Inversion (JMI) offers an attractive feature. It is an operator-based model-independent approach to the inverse problem, in contrast with the model-dependent conventional approach of Full Waveform Inversion, which not only uses the physical model parameters, velocity and density in the acoustic situation, but also forces the data to obey a certain model, e.g. isotropic or anisotropic. The operators sought by the proposed JMI method are reflection and augmented transmission operators (the sum of slowness and transmission operators), yet the reference/background operators are only the simpler Green’s primary-only operators. This formulation is sufficient to explain not only the primaries but also the multiples. Then, the operator-based inverse problem can be solved in a non-linear sense, where phantom sources are obtained only as an intermediary step to obtain those operators. A numerical example shows that the method is capable of distinguishing between the relatively easily-obtained vertical heterogeneity, embedded in the reflection operator, and the more difficulty-obtained lateral heterogeneity, embedded in the augmented transmission operator. This feature, among others, are expected to have a major influence on the inversion process, including its convergence properties.