Frequency-domain full waveform inversion with plane-wave data

We derived an efficient frequency-domain full waveform inversion (FWI) method using plane-wave encoded shot records. The forward modeling involved application of position dependent linear time shifts at all source locations. This was followed by propagation of wavefields into the medium from all shotpoints simultaneously. The gradient of the cost function needed in the FWI was calculated first by transforming the densely sampled seismic data into the frequency-ray parameter domain and then backpropagating the residual wavefield using an adjoint-state approach. We used a Gauss-Newton framework for model updating. The approximate Hessian matrix was formed with a plane-wave encoding strategy, which required a summation over source and receiver ray parameters of the Green’s functions. Plane-wave encoding considerably reduces the computational burden and crosstalk artifacts are effectively suppressed by stacking over different ray parameters. It also has the advantage of directional illumination of the selected targets. Numerical examples show the accuracy and efficiency of our method.