September 2021: Xiaolong Wei

Geophysical data sets have been widely used to recover subsurface models which serve as important, sometimes the only, bases for subsequent geological interpretations. Geophysical inversions are typically performed to reconstruct such subsurface models. Deterministic inversions have been successfully applied in many applications at various scales. Despite the widespread use of deterministic inversions, quantifying the uncertainties of the resulting subsurface models remains underexplored. The goal of our work is to develop an empirical and efficient method, in the deterministic framework, to quantify the uncertainties of both the physical property models and the associated quasi-geology models derived from geophysical data.

We implemented mixed Lp norm inversion strategy where various norm values can be imposed on different components of the regularization term. We randomly sampled two user-specified parameters multiple times and generated a large sequence of physical property models that all fit the geophysical data but span a wide spectrum of possible model characteristics. The variability of these diverse model features reflects the underlying uncertainties. We further used prior petrophysical information to determine which models to accept and which to reject. To empirically quantify the uncertainty of physical property models, we then performed statistical analysis of the physical property values in the accepted models. To quantify the uncertainty of quasi-geology models, we performed geology differentiation for all accepted models obtained from joint inversions and generated multiple 3D quasi-geology models. These equally valid quasi-geology models allow us to construct 3D probabilistic quasi-geology models via simple statistical calculations.

We applied our method to field data collected over the Decorah area located in Northeast Iowa. Using the mixed Lp norm inversion strategy and prior petrophysical measurements from a drillhole, we successfully quantified the uncertainty of the 3D density models as well as the mass and volume of a metagabbro intrusion. We also built 3D probabilistic geology differentiation models that show the uncertainty of the differentiated geological units. Our work is built upon established deterministic inversion theory and open source framework SimPEG. We, therefore, believe that our method can be readily applied to many other areas where drillhole physical property measurements exist.