A Source-Independent TV-Regularized Full Waveform Inversion Method for Peripheral Imaging Around a Borehole

Borehole reflection imaging (BRI) is an advanced technique designed to provide in-depth insights into the geological and geophysical properties of the subsurface surrounding a borehole. A notable challenge associated with BRI is the absence of a dependable velocity model. Traditional BRI methods employ velocity models that vary with depth, resulting in less reliable images and reduced confidence in the final results. In response to this limitation, we turn to full waveform inversion (FWI), a method known for its ability to generate high-resolution velocity models. Nonetheless, several challenges persist in the effective application of FWI to BRI. These include the low signal-to-noise ratio (SNR) in data reflected from distant regions and concerns related to the accuracy of source functions. To address these challenges, we introduce a source-independent and total-variation regularized FWI (SITV-FWI) approach to build the velocity model around the borehole. By leveraging the variable projection method, SITV-FWI can perform inversion without requiring precise information about the source wavelet. Additionally, the application of total-variation (TV) regularization plays a pivotal role in mitigating artifacts introduced by noisy data and inaccuracies in source functions. Numerical experiments clearly demonstrate the resilience of SITV-FWI when faced with inaccuracies in the source wavelet and noisy data, establishing it as a valuable and trustworthy tool for subsurface imaging and characterization.