Summary

The adjoint state method has been widely used in geophysics for various applications, such as reverse time migration, full waveform inversion and migration velocity analysis (MVA) using the one-way wave equation. It allows rapid calculation of the gradient of an objective function without explicitly calculating the Jacobian matrix. MVA using the adjoint state method needs to access the source and receiver wavefield at each depth level during the back-propagation for the gradient calculation. Unfortunately, the volume of storage required for these wavefields in shot-record MVA (SMVA) would be enormous, and disk I/O would make it painfully slow. We therefore propose modifications to standard one-way waveequation propagation in order to allow their recalculation from the bottom up, thereby only requiring the final level of the wavefield to be stored. These comprise a random phase shift method for the evanescent waves and using random/reflecting boundary condition during wave propagation. This reduces or eliminates the need for disk I/O such that 3-D SMVA is possible on an industrial scale.

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