Random‐Objective Waveform Inversion of 3D‐9C Shallow‐Seismic Field Data

Robustness and uncertainty estimation are two challenging topics in full‐waveform inversion (FWI). To overcome these challenges, we present the methodology of random‐objective waveform inversion (ROWI), which adopts a multi‐objective framework and a preconditioned stochastic gradient descent optimization algorithm. The use of one shot per iteration avoids using redundant data and reduces the computational cost. The Pareto solutions represent a group of most likely solutions and their differences quantifies the model uncertainty associated with the trade‐off between conflicting objective functions. Due to the high dimensionality in the data and model spaces, it is prohibitively expensive to check the Pareto optimality of all solutions explicitly. Thus, we decompose the original multi‐objective function into shot‐related subproblems and use the Pareto solutions of the subproblems for trade‐off analysis. We apply ROWI to a field multi‐component shallow‐seismic data set acquired in Rheinstetten, Germany. The 3D near‐surface model is successfully reconstructed by ROWI and the main target, a refilled trench, is delineated. We compare the results estimated by ROWI and a conventional least squares FWI to prove the high efficiency of ROWI. We run six ROWI tests on the field data with different solution paths to prove the robustness of ROWI against the random solution path. The validity of the reconstructed model is verified by multiple 2D ground‐penetrating radar profiles. We estimate 246 Pareto solutions of multi‐objective subproblems for trade‐off analysis. Another four ROWI tests starting from different poor initial models are performed, whose results prove the relatively high robustness of ROWI against the initial model.