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We analyze the amplitude behavior of reverse-time migration and show that modifying the initial-value problem into a boundary-value problem for the source wavefield, plus implementing an appropriate imaging condition, yields a true-amplitude version of RTM. We also discuss different ways to suppress the migration artifacts. Finally, we introduce a "harmonic-source" phase-encoding method to allow a relatively efficient delayed-shot or plane-wave RTM. Taken together, these yield a powerful true-amplitude migration method that uses the complete two-way acoustic wave equation to image complex structures.