In this paper, one-way wave equations with true amplitude are established by the decomposition of the wave field operator for wave equation in 3-D heterogeneous media. Moreover, the Split Step Fourier (SSF) and Fourier Finite Difference (FFD) migration operators with true amplitude are derived mathematically and specific steps are given.

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In the study of rock physics, Biot-Gassmann theory is one of the most classic and practical instruments which is used to calculate the effect of fluid saturation on seismic properties and to predict the relation between the elastic velocities and the physical properties of rocks. But Biot-Gassmann theory does not illuminate the relation between the moduli of the dry frame and that of the matrix, there are several models which illustrate the relation. We have applied Krief, Nur and Pride models to Biot-Gassmann theory and checked their accuracy and applicability.

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