A robust source-independent misfit function for time domain waveform inversion based on normalized convolved wavefield

It is usually necessary to provide a source wavelet before the waveform inversion, and accuracy of the wavelet determines whether the synthetic data matches the observed record. In addition to directly estimating a wavelet, another method is to construct a source-independent objective function. The source difference disappears in the convolved wavefield waveform inversion through the convolution of one data set and the reference trace selected from the other data set, because two different wavelets are already present in the two convolution terms. However, the convolution wavefield inversion is also seriously affected by the incorrect amplitude information of the seismic waves. The attenuation of seismic waves in underground media is quite common in practice. In contrast, the method based on the global normalized wavefield is less sensitive to the amplitude loss because it compares the phase information of the two data sets. The approach we present in this paper is a combination of two methods, that is to construct the normalized wavefield on the basis of the convolution wavefield. In this way, we alleviate the problem of the traditional convolution wavefield inversion caused by amplitude mismatch, and further extend the applicability of this method. The new normalized convolution wavefield inversion combines the advantages of the two methods, which are independence on the source wavelet and being insensitive to amplitude loss, we give a multi-scale and multi-stage inversion strategy for the new objective function, which can improve the implementation of the multi-scale strategy and effectively deal with missing low frequencies.