Source-Independent Acoustic Logging Stratigraphic Imaging: Full Waveform Inversion Based on Time-Domain Waveform Convolution

Abstract In acoustic logging, the complexity of the instrument structure and extreme underground conditions result in inevitable slight discrepancies between the observed source produced by the transducer and the ideal synthetic source, posing a significant challenge to the practical application of full waveform inversion (FWI). In this study, we imparted source independence to FWI by utilizing a time-domain waveform convolution. Specifically, the observed waveforms were convolved with the reference signal of the synthetic waveform, and the synthetic waveforms were convolved with the reference signal of the observed waveform. The two convolved datasets can be treated as being obtained by an identical source wavelet, thereby eliminating the necessity for precisely observed source information in FWI. Near-offset traces are preferentially selected as reference signals because they preserve more complete information, thereby enhancing the resolution of the inversion. Numerical examples demonstrate that when the setting errors of the source parameters are only 3%, FWI is ineffective for recovering subsurface stratigraphic information. In contrast, source-independent FWI transforms the synthetic source from a constraint condition into a useful inversion tool that can be strategically utilized to optimize inversion models and improve both the robustness and resolution of imaging results. Additionally, the use of the hybrid-norm misfit function improves the robustness of the inversion by testing the observed data in the presence of uniform white noise.