Full waveform inversion with fractional anisotropic total p-variation regularization

Full waveform inversion is a precise method for parameter inversion, harnessing the complete wavefield information of seismic waves. It holds the potential to intricately characterize the detailed features of the model with high accuracy. However, due to inaccurate initial models, the absence of low-frequency data, and incomplete observational data, full waveform inversion (FWI) exhibits pronounced nonlinear characteristics. When the strata are buried deep, the inversion capability of this method is constrained. To enhance the accuracy and precision of FWI, this paper introduces a novel approach to address the aforementioned challenges—namely, a fractional-order anisotropic total p-variation regularization for full waveform inversion (FATpV-FWI). This method incorporates fractional-order total variation (TV) regularization to construct the inversion objective function, building upon TV regularization, and subsequently employs the alternating direction multiplier method for solving. This approach mitigates the step effect stemming from total variation in seismic inversion, thereby facilitating the reconstruction of sharp interfaces of geophysical parameters while smoothing background variations. Simultaneously, replacing integer-order differences with fractional-order differences bolsters the correlation among seismic data and diminishes the scattering effect caused by integer-order differences in seismic inversion. The outcomes of model tests validate the efficacy of this method, highlighting its ability to enhance the overall accuracy of the inversion process.