Multi-source multi-scale source-independent full waveform inversion

Abstract Multi-scale full waveform inversion (FWI) in the time domain requires an accurate source signature estimation, which is difficult to obtain from the field data. As an alternative, we present a source-independent inversion algorithm that modifies Wiener filter calculations. A low-pass Wiener filter can be computed by using information from a reference trace rather than the true source wavelet. A Wiener filter was designed to handle observed and modeled wave fields separately, with a misfit function consisting of the filtered wave field. The source wavelets for the observed and modeled wave fields are both eliminated in the misfit function, thus offsetting any adverse effects from a directly observed or adjoint source wavelet. As the filtered data can be expressed as a convolution of the reflection coefficient and the target source wavelet, it is straightforward to use a low to high frequency selection strategy. Although this new method uses the same forward-modeling and inversion schemes as conventional FWI, it differs in how it calculates the misfit function and corresponding adjoint source. In order to achieve more faithful inversion results and promote computational efficiency, multi-scale source-independent inversion and multi-source inversion strategies were also adopted. In particular, we realized that a weighted average of the zero-offset traces in the super gather constitutes a better choice for reference traces. Aside from this, the noise resistance capability of the proposed method was tested and synthetic data evaluations of both the source-independent and multi-source inversion strategies were undertaken to assess the efficiency of the proposed method.