A sequential Bayesian approach for inverting elastic seismic data in the frequency-ray parameter domain

Summary Accurately estimating low frequency trends in seismic attributes is very important for seismic imaging and full waveform inversion. In this study, we develop a sequential Bayesian model to invert elastic seismic data in the frequency-ray parameter domain for recovering the low frequency components of geophysical parameters. We first transform time-offset seismic data to the delay time and ray parameter domain through discrete Radom transformation and then to the frequency-ray parameter domain by temporal Fourier transformation. The frequency-p seismic data are divided into several frequency subgroups. We invert them sequentially starting from low to higher frequency subgroups using the results of previous inversion as priors for subsequent inversions. For each frequency subgroup, we can further divide the data into different ray parameter subgroups. We apply the method to a synthetic case that was developed based on real borehole logs. We invert the seismic data generated using frequencies from 3 to 15 Hz for acoustic and shear impedance and density. While simultaneously inverting seismic data at all the frequencies has trouble reaching a stationary distribution, the sequential approach is very effective for finding solutions. Comparison with the true model shows that the developed method can recover the low frequency (0-3 Hz) acoustic and shear impedance in the frequency band below that in the used seismic data (3-15 Hz).