Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent wavelet-based L1-regularization term to cure the ill-posedness of the airborne (time-domain) electromagnetic induction inverse problem. The regularization term is flexible, as it can recover blocky, smooth and tunable in-between inversion models, based on a suitable wavelet basis function. For each orientation, a different wavelet basis function can be used, introducing an additional relative regularization parameter. We propose a calibration method to determine (an educated initial guess for) this relative regularization parameter, which reduces the need to optimize for this parameter, and, consequently, the overall computation time is under control. We apply our novel scheme to a time-domain airborne electromagnetic data set in Belgian saltwater intrusion context, but the scheme could equally apply to any other 2D or 3D geophysical inverse problem.
New regional stratigraphic insights from a 3D geological model of the Nasia sub-basin, Ghana, developed for hydrogeological purposes and based on reprocessed B-field data originally collected for mineral exploration
Global Structure-Constrained 4D prestack inversion
Chengdu University of Technology（成都理工大学）；State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation（油气藏地质及开发工程国家重点实验室）；Key Laboratory of Earth Exploration & Information Techniques of Ministry of Education（教育部地球探测与信息技术重点实验室）
Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity
Princeton University（普林斯顿大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）；GéoAzur Université de Nice（尼斯大学地理与地球物理实验室）；Program in Applied and Computational Mathematics Princeton University（普林斯顿大学应用与计算数学项目）
A new practical and effective source-independent full-waveform inversion with a velocity-distribution supported deep image prior: Applications to two real datasets
Jilin University（吉林大学）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿业大学）
Reliability-calibrated deep residual full-waveform inversion using geometry-invariant physics encoding: synthetic validation and zero-shot Marmousi-2 testing
Institute of Geophysics, Polish Academy of Sciences（波兰科学院地球物理研究所）；University of Allahabad（阿拉哈巴德大学）；CSIR–National Geophysical Research Institute（印度科学工业研究理事会国家地球物理研究所）
