In full waveform inversion or wave-equation traveltime tomography, the functional gradient is calculated by the integration of an incident wavefield and an adjoint wavefield. However, the incident and adjoint wavefield must be accessed simultaneously to calculate the gradient, which requires additional wavefield storage or re-computation. In this paper, we propose a method to recover the macro-velocity model using the monochromatic traveltime sensitivity kernel (MTSK) with the random boundary condition. Due to the significantly reduced memory occupancy and computational cost, the application of traveltime inversion using a monochromatic gradient would be very promising for large-scale 3-D problems. Numerical examples of 3-D field data demonstrate that the inverted near-surface velocity model is much better than the inversion result using ray tomography.

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