Analyzing uncertainty of 3D inversion using airborne geophysical data conditioned on petrophysical measurements

Airborne geophysics has proven to be an efficient and effective tool for understanding the dynamics of various Earth systems and imaging subsurface structures and compositions. Inversion, among other techniques, has been successfully used to interpret airborne geophysical data in a wide range of applications. However, assessing the uncertainty of inversion results has been challenging so far, especially for regional scale 3D inversion. We developed an empirical method to quantify the uncertainty of 3D inversion in the deterministic framework using mixed Lp norm regularization where different p norm values (0<=p<=2) can be imposed on the different components of the regularization term. We focused on two user-specified parameters, among others, whose values determine the types of features in the recovered models. We randomly sampled these two tuning parameters multiple times, correspondingly carried out multiple 3D inversions, and obtained a suite of recovered models that all fit the observed data well but span a wide spectrum of model features. Based on the prior petrophysical information from rock sample measurements, we developed an acceptance-rejection strategy to determine which models to use for subsequent uncertainty assessment. These accepted models then allow us to analyze uncertainty through simple statistical calculations such as standard deviations and means. Compared with existing methods, our method is computationally more efficient and allows for exploration of a larger model space within a reasonable amount of time. We applied our method to a set of airborne gravity gradient data over the Decorah area located in the northeast of Iowa. The field example shows that the uncertainty of recovered 3D density models can be empirically quantified, which provides additional information and constraints for geologic interpretations. We also estimated the uncertainty of the volume and mass of an anomalous body, interpreted to be metagabbro intrusion, in the context of natural resource evaluation. Our numerical results indicate that (1) the mass of the anomalous body can be reliably estimated with less uncertainty, and (2) the uncertainty of the volume estimate is reduced by about 60% when prior density measurements are used.