Source Wavelet Estimation in Full Waveform Inversion

In full-waveform inversion (FWI), a small disturbance in the source wavelet may lead to large discrepancies in the inverted model, which becomes larger as the depth increases due to error accumulation. Hence, accurate source wavelet estimation becomes crucial in a successful inversion. On the other hand, an inaccurate model would jeopardize a wavelet estimation based on both simulated and observed data without proper constraints, which may in turn lead to wrong model updates and finally hazard the inversion.

To resolve this inversion dilemma, we propose a shallow-response based variable projection type of strategy to estimate the source wavelet alongside model parameters during FWI. Our approach embeds wavelet estimation naturally into FWI iteration as a standard variable reduction step, and restricts the computation to parts of the data that mainly consist of responses to shallow parts of a model. As the model becomes more and more accurate, one could always use more and more data, which might increase the robustness of wavelet estimation. To demonstrate the feasibility and robustness of our approach, we present inversion experiments with both synthetic and real data-sets, which suggest that shallow responses suffice to yield robust wavelet estimation that facilitates FWI.