Waveform inversion by one-way wavefield extrapolation

Jeff Shragge

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ABSTRACT

Forward modeling in frequency-domain waveform inversion is often implemented using finite difference (FD) methods. However, the cost of FD modeling remains too expensive for typical 3D seismic data volumes. One-way wavefield extrapolation is an alternative forward-modeling strategy considerably cheaper to implement. This approach, though, comes with caveats that typically include lower accuracy at steep propagation angles in laterally varying media, a difficulty for incorporating source radiation patterns, and an inability to propagate turning or multiply reflected waves. Each of these factors can play a role in determining the success or failure of a waveform inversion analysis. This study examines the potential for using one-way Riemannian wavefield extrapolation (RWE) operators in the forward modeling component of frequency-domain waveform inversion. RWE modeling is carried out on computational meshes designed to conform to the general direction of turning-wave propagation, which enables the calculation of the direct arrivals, wide-angle reflections and refractions important for a successful waveform inversion. The waveform inversion procedure otherwise closely resembles conventional frequency-domain approaches. Forward modeling test results indicate that RWE waveforms match fairly well with those generated by FD modeling at wider offsets. Preliminary tests of a RWE waveform inversion scheme demonstrate its ability to invert FD-generated synthetic data for moderate (10$\%$) 1D velocity perturbations.