Enhanced Inversion for Distributed Acoustic Sensing: A Robust Approach with HOLp-OGS Regularization

Conversion from distributed acoustic sensing (DAS) measurements to geophone-equivalent data is important for integrating DAS into conventional seismic workflows. This is because most established seismic-processing algorithms are designed for particle-velocity or acceleration data, whereas DAS measures strain or strain rate. Recovering geophone-equivalent particle velocity from DAS strain-rate measurements requires inversion of a gauge-length-dependent spatial-difference operator, which can amplify measurement noise, particularly in field data with low signal-to-noise ratios (SNRs). Existing single-regularization methods often trade noise attenuation against waveform fidelity and the preservation of weak coherent events. To address these limitations, we propose an inverse reconstruction framework combining high-order L_p (HOLp) and overlapping group sparsity (OGS) regularizations. HOLp promotes a compact representation of second-order differences and suppresses incoherent fluctuations, whereas OGS exploits local coherence to reduce isolated artifacts and preserve weak continuous events. The resulting objective function is solved using the alternating direction method of multipliers, with iteratively reweighted L₁ minimization for the HOLp subproblem and a majorization-minimization strategy for the OGS subproblem. Numerical and field experiments confirm that the method restores amplitude and waveform fidelity under low SNR conditions, demonstrating robust and reliable DAS-to-geophone conversion.